rpn.cc
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// -*- mode:C++ ; compile-command: "g++-3.4 -I.. -g -c rpn.cc -DIN_GIAC -DHAVE_CONFIG_H" -*-
#include "giacPCH.h"
/*
* Copyright (C) 2001,14 B. Parisse, Institut Fourier, 38402 St Martin d'Heres
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
using namespace std;
#include "rpn.h"
#include "symbolic.h"
#include "unary.h"
#include <algorithm>
#include "prog.h"
#include "usual.h"
#include "identificateur.h"
#include <stdio.h>
#ifdef HAVE_UNISTD_H
#include <unistd.h>
#if !defined NSPIRE && !defined NUMWORKS
#include <dirent.h>
#ifndef __MINGW_H
#include <pwd.h>
#endif // MINGW
#endif // NSPIRE
#endif // UNISTD
#include "input_lexer.h"
#include "plot.h"
#include "tex.h"
#include "ti89.h"
#include "maple.h"
#include "misc.h"
#include "permu.h"
#include "intg.h"
#include "derive.h"
#include "sym2poly.h"
#include "input_parser.h"
#include "solve.h"
#include "subst.h"
#include "csturm.h"
#include "giacintl.h"
#ifdef GIAC_HAS_STO_38
#include "aspen.h"
//THPObj *EditMat(int);
#endif
#ifndef NO_NAMESPACE_GIAC
namespace giac {
#endif // ndef NO_NAMESPACE_GIAC
string enmajuscule(const string & s){
string res;
string::const_iterator it=s.begin(),itend=s.end();
for (;it!=itend;++it){
if ((*it>='a') && (*it<='z'))
res += char(*it-32);
else
res += char(*it);
}
return res;
}
string printasconstant(const gen & feuille,const char * sommetstr,GIAC_CONTEXT){
return sommetstr;
}
#ifdef RTOS_THREADX
gen return_undef(const gen &,GIAC_CONTEXT){
return undef;
}
static const char _rpn_s []="rpn";
static define_unary_function_eval2 (__rpn,&return_undef,_rpn_s,&printasconstant);
define_unary_function_ptr5( at_rpn ,alias_at_rpn ,(unary_function_eval*)&__rpn,0,true);
static const char _alg_s []="alg";
static define_unary_function_eval2 (__alg,&return_undef,_alg_s,&printasconstant);
define_unary_function_ptr5( at_alg ,alias_at_alg ,(unary_function_eval *)&__alg,0,true);
static const char _ROLL_s []="ROLL";
static define_unary_function_eval (__ROLL,&return_undef,_ROLL_s);
define_unary_function_ptr( at_ROLL ,alias_at_ROLL ,&__ROLL);
static const char _ROLLD_s []="ROLLD";
static define_unary_function_eval (__ROLLD,&return_undef,_ROLLD_s);
define_unary_function_ptr( at_ROLLD ,alias_at_ROLLD ,&__ROLLD);
static const char _SWAP_s []="SWAP";
static define_unary_function_eval (__SWAP,&return_undef,_SWAP_s);
define_unary_function_ptr5( at_SWAP ,alias_at_SWAP ,&__SWAP,0,T_RPN_OP);
static const char _DUP_s []="DUP";
static define_unary_function_eval (__DUP,&return_undef,_DUP_s);
define_unary_function_ptr5( at_DUP ,alias_at_DUP ,&__DUP,0,T_RPN_OP);
static const char _OVER_s []="OVER";
static define_unary_function_eval (__OVER,&return_undef,_OVER_s);
define_unary_function_ptr5( at_OVER ,alias_at_OVER ,&__OVER,0,T_RPN_OP);
static const char _PICK_s []="PICK";
static define_unary_function_eval (__PICK,&return_undef,_PICK_s);
define_unary_function_ptr5( at_PICK ,alias_at_PICK ,&__PICK,0,T_RPN_OP);
static const char _DROP_s []="DROP";
static define_unary_function_eval (__DROP,&return_undef,_DROP_s);
define_unary_function_ptr5( at_DROP ,alias_at_DROP ,&__DROP,0,T_RPN_OP);
static const char _NOP_s []="NOP";
static define_unary_function_eval2_index (136,__NOP,&return_undef,_NOP_s,&printasconstant);
define_unary_function_ptr5( at_NOP ,alias_at_NOP ,&__NOP,0,T_RPN_OP);
static const char _IFTE_s []="IFTE";
static define_unary_function_eval2_index (126,__IFTE,&return_undef,_IFTE_s,&printasconstant);
define_unary_function_ptr5( at_IFTE ,alias_at_IFTE ,&__IFTE,0,T_RPN_OP);
static const char _RPN_LOCAL_s []="RPN_LOCAL";
static define_unary_function_eval2_index (130,__RPN_LOCAL,&return_undef,_RPN_LOCAL_s,&printasconstant);
define_unary_function_ptr5( at_RPN_LOCAL ,alias_at_RPN_LOCAL ,&__RPN_LOCAL,0,T_RPN_OP);
static const char _RPN_FOR_s []="RPN_FOR";
static define_unary_function_eval2_index (132,__RPN_FOR,&return_undef,_RPN_FOR_s,&printasconstant);
define_unary_function_ptr5( at_RPN_FOR ,alias_at_RPN_FOR ,&__RPN_FOR,0,T_RPN_OP);
static const char _RPN_WHILE_s []="RPN_WHILE";
static define_unary_function_eval2_index (134,__RPN_WHILE,&return_undef,_RPN_WHILE_s,&printasconstant);
define_unary_function_ptr5( at_RPN_WHILE ,alias_at_RPN_WHILE ,&__RPN_WHILE,0,T_RPN_OP);
static const char _RPN_CASE_s []="RPN_CASE";
static define_unary_function_eval2_index (128,__RPN_CASE,&return_undef,_RPN_CASE_s,&printasconstant);
define_unary_function_ptr5( at_RPN_CASE ,alias_at_RPN_CASE ,&__RPN_CASE,0,T_RPN_OP);
static const char _RPN_UNTIL_s []="RPN_UNTIL";
static define_unary_function_eval2 (__RPN_UNTIL,&return_undef,_RPN_UNTIL_s,&printasconstant);
define_unary_function_ptr( at_RPN_UNTIL ,alias_at_RPN_UNTIL ,&__RPN_UNTIL);
static const char _rpn_prog_s []="rpn_prog";
static define_unary_function_eval2_index (83,__rpn_prog,&return_undef,_rpn_prog_s,&printasconstant);
define_unary_function_ptr5( at_rpn_prog ,alias_at_rpn_prog,&__rpn_prog,_QUOTE_ARGUMENTS,0);
#else // RTOS_THREADX
static gen symb_rpn(const gen & args){
return symbolic(at_rpn,args);
}
gen _rpn(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
rpn_mode(contextptr)=true;
return symb_rpn(args);
}
static const char _rpn_s []="rpn";
static define_unary_function_eval2 (__rpn,&_rpn,_rpn_s,&printasconstant);
define_unary_function_ptr5( at_rpn ,alias_at_rpn ,(unary_function_eval*)&__rpn,0,true);
static gen symb_alg(const gen & args){
return symbolic(at_alg,args);
}
gen _alg(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
rpn_mode(contextptr)=false;
return symb_alg(args);
}
static const char _alg_s []="alg";
static define_unary_function_eval2 (__alg,&_alg,_alg_s,&printasconstant);
define_unary_function_ptr5( at_alg ,alias_at_alg ,(unary_function_eval *)&__alg,0,true);
void roll(int i,vecteur & v){
if (i<2)
return;
iterateur it=v.begin(),itend=v.end();
if (itend-it<i)
return;
it=itend-i;
gen save=*it;
for (;;){
++it;
if (it==itend)
break;
*(it-1)=*it;
}
*(it-1)=save;
}
void ROLL(int i,GIAC_CONTEXT){
roll(i,history_in(contextptr));
roll(i,history_out(contextptr));
}
gen _ROLL(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args._VECTptr->empty())
return args;
gen e=args._VECTptr->back();
args._VECTptr->pop_back();
if (e.type==_INT_)
roll(e.val,*args._VECTptr);
if (e.type==_DOUBLE_)
roll(int(e._DOUBLE_val),*args._VECTptr);
return args;
}
static const char _ROLL_s []="ROLL";
static define_unary_function_eval (__ROLL,&_ROLL,_ROLL_s);
define_unary_function_ptr( at_ROLL ,alias_at_ROLL ,&__ROLL);
void rolld(int i,vecteur & v){
if (i<2)
return;
iterateur it=v.begin(),itend=v.end();
if (itend-it<i)
return;
it=itend-i;
--itend;
gen save=*itend;
for (;it!=itend;){
--itend;
*(itend+1)=*itend;
}
*it=save;
}
void ROLLD(int i,GIAC_CONTEXT){
rolld(i,history_in(contextptr));
rolld(i,history_out(contextptr));
}
gen _ROLLD(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args._VECTptr->empty())
return args;
gen e=args._VECTptr->back();
args._VECTptr->pop_back();
if (e.type==_INT_)
rolld(e.val,*args._VECTptr);
if (e.type==_DOUBLE_)
rolld(int(e._DOUBLE_val),*args._VECTptr);
return args;
}
static const char _ROLLD_s []="ROLLD";
static define_unary_function_eval (__ROLLD,&_ROLLD,_ROLLD_s);
define_unary_function_ptr( at_ROLLD ,alias_at_ROLLD ,&__ROLLD);
void stack_swap(vecteur & v){
iterateur it=v.begin(),itend=v.end();
int s=int(itend-it);
if (s<2)
return;
--itend;
gen tmp=*itend;
*itend=*(itend-1);
*(itend-1)=tmp;
}
void SWAP(GIAC_CONTEXT){
stack_swap(history_in(contextptr));
stack_swap(history_out(contextptr));
}
gen _SWAP(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
stack_swap(*args._VECTptr);
return args;
}
static const char _SWAP_s []="SWAP";
static define_unary_function_eval (__SWAP,&_SWAP,_SWAP_s);
define_unary_function_ptr5( at_SWAP ,alias_at_SWAP ,&__SWAP,0,T_RPN_OP);
void dup(vecteur & v){
if (!v.empty())
v.push_back(v.back());
}
gen _DUP(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
dup(*args._VECTptr);
return args;
}
static const char _DUP_s []="DUP";
static define_unary_function_eval (__DUP,&_DUP,_DUP_s);
define_unary_function_ptr5( at_DUP ,alias_at_DUP ,&__DUP,0,T_RPN_OP);
void over(vecteur & v){
int s=int(v.size());
if (s>=2)
v.push_back(v[s-2]);
}
gen _OVER(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
over(*args._VECTptr);
return args;
}
static const char _OVER_s []="OVER";
static define_unary_function_eval (__OVER,&_OVER,_OVER_s);
define_unary_function_ptr5( at_OVER ,alias_at_OVER ,&__OVER,0,T_RPN_OP);
void pick(int i,vecteur & v){
int s=int(v.size());
if ((i>=1) && (s>=i))
v.push_back(v[s-i]);
}
gen _PICK(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args._VECTptr->empty())
return args;
gen e=args._VECTptr->back();
args._VECTptr->pop_back();
if (e.type==_INT_)
pick(e.val,*args._VECTptr);
if (e.type==_DOUBLE_)
pick(int(e._DOUBLE_val),*args._VECTptr);
return args;
}
static const char _PICK_s []="PICK";
static define_unary_function_eval (__PICK,&_PICK,_PICK_s);
define_unary_function_ptr5( at_PICK ,alias_at_PICK ,&__PICK,0,T_RPN_OP);
void drop(vecteur & v){
if (v.empty())
return;
v.pop_back();
}
gen _DROP(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
drop(*args._VECTptr);
return args;
}
static const char _DROP_s []="DROP";
static define_unary_function_eval (__DROP,&_DROP,_DROP_s);
define_unary_function_ptr5( at_DROP ,alias_at_DROP ,&__DROP,0,T_RPN_OP);
static string printasNOP(const gen & feuille,const char * sommetstr,GIAC_CONTEXT){
return sommetstr;
}
gen symb_NOP(const gen & args){
return vecteur(1,symbolic(at_NOP,args));
}
gen _NOP(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
return args;
}
static const char _NOP_s []="NOP";
static define_unary_function_eval2_index (136,__NOP,&_NOP,_NOP_s,&printasNOP);
define_unary_function_ptr5( at_NOP ,alias_at_NOP ,&__NOP,0,T_RPN_OP);
static string printasIFTE(const gen & feuille,const char * sommetstr,GIAC_CONTEXT){
const_iterateur it=feuille._VECTptr->begin();
string res("IF " + printinner_VECT(*it->_VECTptr,_RPN_FUNC__VECT,contextptr));
res += " THEN ";
++it;
res += printinner_VECT(*it->_VECTptr,_RPN_FUNC__VECT,contextptr) + " ELSE ";
++it;
return res + printinner_VECT(*it->_VECTptr,_RPN_FUNC__VECT,contextptr)+ " END";
}
gen symb_IFTE(const gen & args){
return symbolic(at_IFTE,args);
}
gen _IFTE(const gen & args,const context * contextptr){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args.type!=_VECT || args._VECTptr->size()<3)
return gensizeerr(contextptr);
gen no=args._VECTptr->back();
args._VECTptr->pop_back();
gen yes=args._VECTptr->back();
args._VECTptr->pop_back();
gen e=args._VECTptr->back();
args._VECTptr->pop_back();
if (e.type==_VECT){
rpn_eval(e,*args._VECTptr,contextptr);
if (args._VECTptr->empty())
return args;
e=args._VECTptr->back();
args._VECTptr->pop_back();
}
if (is_zero(e))
return rpn_eval(no,*args._VECTptr,contextptr);
else
return rpn_eval(yes,*args._VECTptr,contextptr);
}
static const char _IFTE_s []="IFTE";
static define_unary_function_eval2_index (126,__IFTE,&_IFTE,_IFTE_s,&printasIFTE);
define_unary_function_ptr5( at_IFTE ,alias_at_IFTE ,&__IFTE,0,T_RPN_OP);
static string printasRPN_LOCAL(const gen & feuille,const char * sommetstr,GIAC_CONTEXT){
string s("-> ");
s += printinner_VECT(*feuille._VECTptr->front()._VECTptr,_RPN_FUNC__VECT,contextptr);
gen e= feuille._VECTptr->back();
if ( (e.type==_VECT) && (e.subtype==_RPN_FUNC__VECT))
return s + " " +e.print(contextptr);
else {
if ( (e.type==_SYMB) && (e._SYMBptr->sommet==at_quote))
return s + " '"+e._SYMBptr->feuille.print(contextptr)+"'";
else
return s + " '"+e.print(contextptr)+"'";
}
}
gen symb_RPN_LOCAL(const gen & a,const gen & b){
return symbolic(at_RPN_LOCAL,makesequence(a,b));
}
gen _RPN_LOCAL(const gen & args,const context * contextptr) {
if ( args.type==_STRNG && args.subtype==-1) return args;
// stack level 2=symbolic names, level 1=program
if (args.type!=_VECT)
return symbolic(at_RPN_LOCAL,args);
int s=int(args._VECTptr->size());
if (s<3)
return gentoofewargs("RPN_LOCAL must have at least 3 args");
gen prog=args._VECTptr->back();
args._VECTptr->pop_back();
vecteur names=*(args._VECTptr->back()._VECTptr); // must be a vector
args._VECTptr->pop_back();
// get values from stack
int nvars=int(names.size());
if (s-2<nvars)
return gentoofewargs("RPN_LOCAL");
vecteur values(names);
for (int j=nvars-1;j>=0;--j){
values[j]=args._VECTptr->back();
args._VECTptr->pop_back();
}
// Initialization
context * newcontextptr = (context *) contextptr;
int protect=giac::bind(values,names,newcontextptr);
vecteur res;
if ((prog.type==_SYMB) && (prog._SYMBptr->sommet==at_quote)){
args._VECTptr->push_back(prog._SYMBptr->feuille.eval(eval_level(contextptr),newcontextptr));
res=*args._VECTptr;
}
else
res=rpn_eval(prog,*args._VECTptr,newcontextptr);
leave(protect,names,newcontextptr);
return gen(res,_RPN_STACK__VECT);
}
static const char _RPN_LOCAL_s []="RPN_LOCAL";
static define_unary_function_eval2_index (130,__RPN_LOCAL,&_RPN_LOCAL,_RPN_LOCAL_s,&printasRPN_LOCAL);
define_unary_function_ptr5( at_RPN_LOCAL ,alias_at_RPN_LOCAL ,&__RPN_LOCAL,0,T_RPN_OP);
static string printasRPN_FOR(const gen & feuille,const char * sommetstr,GIAC_CONTEXT){
if ( (feuille.type!=_VECT) && (feuille._VECTptr->size()!=2))
return "Invalid_RPN_FOR";
string s;
gen controle=feuille._VECTptr->front();
gen prog=feuille._VECTptr->back();
bool is_start= (controle[0].print(contextptr)==" j");
if (is_start)
s="START ";
else
s="FOR "+controle[0].print(contextptr)+" ";
s += printinner_VECT(*prog._VECTptr,_RPN_FUNC__VECT,contextptr);
if (is_one(controle[1]))
s+=" NEXT";
else
s+= " "+controle[1].print(contextptr)+" STEP";
return s;
}
gen symb_RPN_FOR(const gen & a,const gen & b){
return symbolic(at_RPN_FOR,makesequence(a,b));
}
gen _RPN_FOR(const gen & args,const context * contextptr) {
if ( args.type==_STRNG && args.subtype==-1) return args;
// stack level 4=init
// stack level 3=end
// stack level 2=[init_var,step]
// level 1=program to execute,
if (args.type!=_VECT)
return symbolic(at_RPN_FOR,args);
int s=int(args._VECTptr->size());
if (s<4)
return gentoofewargs("RPN_FOR must have at least 4 args");
gen prog=args._VECTptr->back();
args._VECTptr->pop_back();
vecteur controle=*(args._VECTptr->back()._VECTptr); // it must be a vector
args._VECTptr->pop_back();
gen fin=args._VECTptr->back();
args._VECTptr->pop_back();
gen debut=args._VECTptr->back();
args._VECTptr->pop_back();
// Initialization
vecteur names(1,controle[0]);
gen test=inferieur_egal(controle[0],fin,contextptr);
context * newcontextptr = (context *) contextptr;
int protect=giac::bind(vecteur(1,debut),names,newcontextptr);
vecteur res;
for (;!is_zero(test.eval(eval_level(newcontextptr),newcontextptr).evalf(eval_level(contextptr),newcontextptr));sto(eval(controle[0]+controle[1],eval_level(newcontextptr),newcontextptr),controle[0],newcontextptr)){
res=rpn_eval(prog,*args._VECTptr,newcontextptr);
}
leave(protect,names,newcontextptr);
return gen(res,_RPN_STACK__VECT);
}
static const char _RPN_FOR_s []="RPN_FOR";
static define_unary_function_eval2_index (132,__RPN_FOR,&_RPN_FOR,_RPN_FOR_s,&printasRPN_FOR);
define_unary_function_ptr5( at_RPN_FOR ,alias_at_RPN_FOR ,&__RPN_FOR,0,T_RPN_OP);
static string printasRPN_WHILE(const gen & feuille,const char * sommetstr,GIAC_CONTEXT){
if ( (feuille.type!=_VECT) && (feuille._VECTptr->size()!=2))
return "Invalid_RPN_WHILE";
return "WHILE "+ printinner_VECT(*feuille._VECTptr->front()._VECTptr,_RPN_FUNC__VECT,contextptr) + " REPEAT "+printinner_VECT(*feuille._VECTptr->back()._VECTptr,_RPN_FUNC__VECT,contextptr)+ " END ";
}
gen symb_RPN_WHILE(const gen & a,const gen & b){
return symbolic(at_RPN_WHILE,makesequence(a,b));
}
gen _RPN_WHILE(const gen & args,const context * contextptr) {
if ( args.type==_STRNG && args.subtype==-1) return args;
// stack level 2=condition
// level 1=program to execute
if (args.type!=_VECT)
return symbolic(at_RPN_WHILE,args);
int s=int(args._VECTptr->size());
if (s<2)
return gentoofewargs("RPN_WHILE must have at least 2 args");
gen prog=args._VECTptr->back();
args._VECTptr->pop_back();
gen controle=args._VECTptr->back();
args._VECTptr->pop_back();
vecteur res;
for (;;){
res=rpn_eval(controle,*args._VECTptr,contextptr);
if (args._VECTptr->empty())
return gentoofewargs("WHILE");
gen tmp=args._VECTptr->back();
args._VECTptr->pop_back();
if (is_zero(tmp.eval(1,contextptr).evalf(1,contextptr)))
break;
res=rpn_eval(prog,*args._VECTptr,contextptr);
}
return gen(res,_RPN_STACK__VECT);
}
static const char _RPN_WHILE_s []="RPN_WHILE";
static define_unary_function_eval2_index (134,__RPN_WHILE,&_RPN_WHILE,_RPN_WHILE_s,&printasRPN_WHILE);
define_unary_function_ptr5( at_RPN_WHILE ,alias_at_RPN_WHILE ,&__RPN_WHILE,0,T_RPN_OP);
static string printasRPN_CASE(const gen & feuille,const char * sommetstr,GIAC_CONTEXT){
if (feuille.type!=_VECT)
return "Invalid_RPN_CASE";
vecteur v=*feuille._VECTptr;
if ((v.size()!=1) ||(v.front().type!=_VECT))
return "Invalid_RPN_CASE";
string res("CASE ");
const_iterateur it=v.front()._VECTptr->begin(),itend=v.front()._VECTptr->end();
for (;it!=itend;){
res += printinner_VECT(*it->_VECTptr,_RPN_FUNC__VECT,contextptr);
++it;
if (it==itend)
break;
res += " THEN " + printinner_VECT(*it->_VECTptr,_RPN_FUNC__VECT,contextptr) + " END ";
++it;
}
return res+" END ";
}
gen symb_RPN_CASE(const gen & a){
return symbolic(at_RPN_CASE,vecteur(1,a));
}
gen _RPN_CASE(const gen & args,const context * contextptr) {
if ( args.type==_STRNG && args.subtype==-1) return args;
// level 1=[case1, prg1, case2,prg2,..., [default]]
if (args.type!=_VECT)
return symbolic(at_RPN_CASE,args);
int s=int(args._VECTptr->size());
if (s<1)
return gentoofewargs("RPN_CASE must have at least 1 arg");
vecteur controle=*args._VECTptr->back()._VECTptr;
args._VECTptr->pop_back();
const_iterateur it=controle.begin(),itend=controle.end();
vecteur res;
for (;it!=itend;){
res=rpn_eval(*it,*args._VECTptr,contextptr);
if (args._VECTptr->empty())
return gentoofewargs("CASE");
++it;
if (it==itend) // default of the case struct
break;
gen test=args._VECTptr->back();
args._VECTptr->pop_back();
if (!(is_zero(test.eval(1,contextptr).evalf(1,contextptr)))){
res=rpn_eval(*it,*args._VECTptr,contextptr);
break;
}
++it;
}
return gen(*args._VECTptr,_RPN_STACK__VECT);
}
static const char _RPN_CASE_s []="RPN_CASE";
static define_unary_function_eval2_index (128,__RPN_CASE,&_RPN_CASE,_RPN_CASE_s,&printasRPN_CASE);
define_unary_function_ptr5( at_RPN_CASE ,alias_at_RPN_CASE ,&__RPN_CASE,0,T_RPN_OP);
static string printasRPN_UNTIL(const gen & feuille,const char * sommetstr,GIAC_CONTEXT){
if ( (feuille.type!=_VECT) && (feuille._VECTptr->size()!=2))
return "Invalid_RPN_UNTIL";
return "DO "+ printinner_VECT(*feuille._VECTptr->front()._VECTptr,_RPN_FUNC__VECT,contextptr) + " UNTIL "+printinner_VECT(*feuille._VECTptr->back()._VECTptr,_RPN_FUNC__VECT,contextptr)+ " END ";
}
gen symb_RPN_UNTIL(const gen & a,const gen & b){
return symbolic(at_RPN_UNTIL,makesequence(a,b));
}
gen _RPN_UNTIL(const gen & args,const context * contextptr) {
if ( args.type==_STRNG && args.subtype==-1) return args;
// stack level 2=program
// level 1=condition
if (args.type!=_VECT)
return symbolic(at_RPN_UNTIL,args);
int s=int(args._VECTptr->size());
if (s<2)
return gentoofewargs("RPN_UNTIL must have at least 2 args");
gen controle=args._VECTptr->back();
args._VECTptr->pop_back();
gen prog=args._VECTptr->back();
args._VECTptr->pop_back();
vecteur res;
for (;;){
res=rpn_eval(prog,*args._VECTptr,contextptr);
res=rpn_eval(controle,*args._VECTptr,contextptr);
if (args._VECTptr->empty())
return gentoofewargs("UNTIL");
gen tmp=args._VECTptr->back();
args._VECTptr->pop_back();
if (!is_zero(tmp.eval(eval_level(contextptr),contextptr).evalf(eval_level(contextptr),contextptr)))
break;
}
return gen(res,_RPN_STACK__VECT);
}
static const char _RPN_UNTIL_s []="RPN_UNTIL";
static define_unary_function_eval2 (__RPN_UNTIL,&_RPN_UNTIL,_RPN_UNTIL_s,&printasRPN_UNTIL);
define_unary_function_ptr( at_RPN_UNTIL ,alias_at_RPN_UNTIL ,&__RPN_UNTIL);
// RPN evaluation loop (_VECTEVAL), no return stack currently
vecteur rpn_eval(const vecteur & prog,vecteur & pile,const context * contextptr){
const_iterateur it=prog.begin(),itend=prog.end();
for (;it!=itend;++it){
if (it->type==_FUNC){
// test nargs with subtype
int nargs=it->subtype;
if (nargs>signed(pile.size()))
return vecteur(1,gentoofewargs(it->print(contextptr)+": stack "+gen(pile).print(contextptr)));
if (nargs==1){
pile.back()=(*it->_FUNCptr)(pile.back(),contextptr);
}
else {
if (nargs){
vecteur v(nargs);
for (int k=nargs-1;k>=0;--k){
v[k]=pile.back();
pile.pop_back();
}
pile.push_back((*it->_FUNCptr)(v,contextptr));
}
else {
gen res;
if (*it->_FUNCptr==at_eval){ // eval stack level 1
if (pile.empty())
return vecteur(1,gentoofewargs("EVAL"));
res=pile.back();
pile.pop_back();
if ( (res.type==_SYMB) && (res._SYMBptr->sommet==at_rpn_prog))
res=res._SYMBptr->feuille;
res=rpn_eval(res,pile,contextptr);
}
else
res=(*it->_FUNCptr)(pile,contextptr);
if ( (res.type==_VECT) && (res.subtype==_RPN_STACK__VECT) )
pile= *res._VECTptr;
else
pile= vecteur(1,res);
}
}
}
else {
// test for special symbolic (control struct)
const unary_function_ptr control_op[]={*at_RPN_LOCAL,*at_RPN_FOR,*at_IFTE,*at_RPN_CASE,*at_RPN_WHILE,*at_RPN_UNTIL,0};
if ( (it->type==_SYMB) && equalposcomp(control_op,it->_SYMBptr->sommet)){
// push args of it to the stack and call sommet on the stack
if (it->_SYMBptr->feuille.type!=_VECT) // should not happen!
pile.push_back(it->_SYMBptr->feuille);
else
pile=mergevecteur(pile,*it->_SYMBptr->feuille._VECTptr);
gen res=it->_SYMBptr->sommet(pile,contextptr);
if ( (res.type==_VECT) && (res.subtype==_RPN_STACK__VECT) )
pile= *res._VECTptr;
else
pile= vecteur(1,res);
}
else {
if ( (it->type!=_VECT)
// || (it->subtype==_RPN_FUNC__VECT)
){
gen res=it->eval(1,contextptr);
if ( (res.type==_VECT) && (res.subtype==_RPN_STACK__VECT))
pile=*res._VECTptr;
else
pile.push_back(res);
}
else
pile.push_back(*it);
}
}
}
return pile;
}
vecteur rpn_eval(const gen & prog,vecteur & pile,const context * contextptr){
if (prog.type!=_VECT)
return rpn_eval(vecteur(1,prog),pile,contextptr);
else
return rpn_eval(*prog._VECTptr,pile,contextptr);
}
static string printasrpn_prog(const gen & feuille,const char * sommetstr,GIAC_CONTEXT){
if (feuille.type!=_VECT)
return "<< "+feuille.print(contextptr)+" >>";
return "<< "+printinner_VECT(*feuille._VECTptr,_RPN_FUNC__VECT,contextptr)+" >>";
}
gen symb_rpn_prog(const gen & args){
return symbolic(at_rpn_prog,args);
}
gen _rpn_prog(const gen & args,const context * contextptr){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (!rpn_mode(contextptr) || (args.type!=_VECT))
return symbolic(at_rpn_prog,args);
vecteur pile(history_out(contextptr));
*logptr(contextptr) << pile << " " << args << endl;
return gen(rpn_eval(*args._VECTptr,pile,contextptr),_RPN_STACK__VECT);
}
static const char _rpn_prog_s []="rpn_prog";
static define_unary_function_eval2_index (83,__rpn_prog,&_rpn_prog,_rpn_prog_s,&printasrpn_prog);
define_unary_function_ptr5( at_rpn_prog ,alias_at_rpn_prog,&__rpn_prog,_QUOTE_ARGUMENTS,0);
#endif // RTOS_THREADX
gen _RCL(const gen & args,const context * contextptr) {
if ( args.type==_STRNG && args.subtype==-1) return args;
// stack level 2=condition
// level 1=program to execute
if (args.type!=_IDNT)
return symbolic(at_RCL,args);
return args._IDNTptr->eval(1,args,contextptr);
}
static const char _RCL_s []="RCL";
static define_unary_function_eval (__RCL,&_RCL,_RCL_s);
define_unary_function_ptr5( at_RCL ,alias_at_RCL ,&__RCL,0,T_RPN_OP);
#if defined(__APPLE__) // || defined(__FreeBSD__)
static int int_one (struct dirent *unused){
return 1;
}
#else
static int int_one (const struct dirent *unused){
return 1;
}
#endif
gen _VARS(const gen & args,const context * contextptr) {
if ( args.type==_STRNG && args.subtype==-1) return args;
bool val=is_one(args);
bool valsto=is_minus_one(args);
vecteur res;
if (contextptr){
if (contextptr->globalcontextptr && contextptr->globalcontextptr->tabptr){
sym_tab::const_iterator it=contextptr->globalcontextptr->tabptr->begin(),itend=contextptr->globalcontextptr->tabptr->end();
vecteur * keywordsptr=keywords_vecteur_ptr();
for (;it!=itend;++it){
gen g=identificateur(it->first);
if (!equalposcomp(*keywordsptr,g)){
if (val)
g=symbolic(at_equal,makesequence(g,it->second));
if (valsto)
g=symb_sto(it->second,g);
res.push_back(g);
}
}
}
return res;
}
if (!variables_are_files(contextptr)){
lock_syms_mutex();
sym_string_tab::const_iterator it=syms().begin(),itend=syms().end();
for (;it!=itend;++it){
gen id=it->second;
if (id.type==_IDNT && id._IDNTptr->value){
res.push_back(id);
}
}
unlock_syms_mutex();
if (is_one(args) && current_folder_name.type==_IDNT && current_folder_name._IDNTptr->value){ // add variables of the current folder
gen & tmp=*current_folder_name._IDNTptr->value;
if (tmp.type==_VECT){
vecteur v=*current_folder_name._IDNTptr->value->_VECTptr;
iterateur it=v.begin(),itend=v.end();
for (;it!=itend;++it){
if (it->type!=_VECT || it->_VECTptr->size()!=2)
continue;
vecteur & w=*it->_VECTptr;
res.push_back(w[0]);
}
}
}
return res;
}
#ifndef VARIABLE_ARE_FILES
return undef;
#else
struct dirent **eps;
int n;
n = scandir ("./", &eps, int_one, alphasort);
if (n >= 0){
string s;
int cnt;
for (cnt = 0; cnt < n; ++cnt){
s=string(eps[cnt]->d_name);
unsigned k=0;
for (;k<s.size();++k){
if (!isalphan(s[k]))
break;
}
if ( (k==s.size()-4) && (s[k]=='.') && (s.substr(k+1,3)=="cas") )
res.push_back(identificateur(s.substr(0,k)));
}
if ( rpn_mode(contextptr) && (args.type==_VECT) && (args.subtype==_RPN_STACK__VECT) ){
args._VECTptr->push_back(res);
return args;
}
return res;
}
else
settypeerr ("Couldn't open the directory");
return 0;
#endif
}
static const char _VARS_s []="VARS";
static define_unary_function_eval (__VARS,&_VARS,_VARS_s);
define_unary_function_ptr( at_VARS ,alias_at_VARS ,&__VARS);
gen purgenoassume(const gen & args,const context * contextptr){
if (args.type==_VECT){
vecteur & v=*args._VECTptr;
vecteur res;
for (unsigned i=0;i<v.size();++i)
res.push_back(purgenoassume(v[i],contextptr));
return res;
}
if (args.type!=_IDNT)
return gensizeerr("Invalid purgenoassume "+args.print(contextptr));
if (!contextptr)
return _purge(args,0);
const char * ch=args._IDNTptr->id_name;
if (strlen(ch)==1){
if (ch[0]=='O' && (series_flags(contextptr) & (1<<6)) )
series_flags(contextptr) ^= (1<<6);
if (ch[0]==series_variable_name(contextptr)){
if (series_flags(contextptr) & (1<<5))
series_flags(contextptr) ^= (1<<5);
if (series_flags(contextptr) & (1<<6))
series_flags(contextptr) ^= (1<<6);
}
}
// purge a global variable
sym_tab::iterator it=contextptr->tabptr->find(ch),itend=contextptr->tabptr->end();
if (it==itend)
return string2gen("No such variable "+args.print(contextptr),false);
gen res=it->second;
if (it->second.type==_POINTER_ && it->second.subtype==_THREAD_POINTER)
return gentypeerr(args.print(contextptr)+" is locked by thread "+it->second.print(contextptr));
if (contextptr->previous)
it->second=identificateur(it->first);
else
contextptr->tabptr->erase(it);
if (res.is_symb_of_sommet(at_rootof))
_purge(res,contextptr);
return res;
}
gen _purge(const gen & args,const context * contextptr) {
if ( args.type==_STRNG && args.subtype==-1) return args;
if (rpn_mode(contextptr) && (args.type==_VECT)){
if (!args._VECTptr->size())
return gentoofewargs("purge");
gen apurger=args._VECTptr->back();
_purge(apurger,contextptr);
args._VECTptr->pop_back();
return gen(*args._VECTptr,_RPN_STACK__VECT);
}
if (args.type==_VECT)
return apply(args,contextptr,giac::_purge);
if (args.is_symb_of_sommet(at_at)){
gen & f = args._SYMBptr->feuille;
if (f.type==_VECT && f._VECTptr->size()==2){
gen m = eval(f._VECTptr->front(),eval_level(contextptr),contextptr);
gen indice=eval(f._VECTptr->back(),eval_level(contextptr),contextptr);
if (m.type==_MAP){
gen_map::iterator it=m._MAPptr->find(indice),itend=m._MAPptr->end();
if (it==itend)
return gensizeerr(gettext("Bad index")+indice.print(contextptr));
m._MAPptr->erase(it);
return 1;
}
}
}
if (contextptr && args.is_symb_of_sommet(at_rootof)){
gen a=eval(args,1,contextptr);
if (!a.is_symb_of_sommet(at_rootof))
return gensizeerr(gettext("Bad rootof"));
if (!contextptr->globalcontextptr->rootofs)
contextptr->globalcontextptr->rootofs=new vecteur;
gen Pmin=a._SYMBptr->feuille;
if (Pmin.type!=_VECT || Pmin._VECTptr->size()!=2 || Pmin._VECTptr->front()!=makevecteur(1,0))
return gensizeerr(gettext("Bad rootof"));
Pmin=Pmin._VECTptr->back();
vecteur & r =*contextptr->globalcontextptr->rootofs;
for (unsigned i=0;i<r.size();++i){
gen ri=r[i];
if (ri.type==_VECT && ri._VECTptr->size()==2 && Pmin==ri._VECTptr->front()){
gen a=ri._VECTptr->back();
r.erase(r.begin()+i);
return _purge(a,contextptr);
}
}
return 0;
}
if (args.type!=_IDNT)
return symbolic(at_purge,args);
// REMOVED! args.eval(eval_level(contextptr),contextptr);
if (contextptr){
if (contextptr->globalcontextptr!=contextptr){
// purge a local variable = set it to assume(DOM_SYMBOLIC)
gen a2(_SYMB);
a2.subtype=1;
return sto(gen(makevecteur(a2),_ASSUME__VECT),args,contextptr);
}
return purgenoassume(args,contextptr);
}
if (current_folder_name.type==_IDNT && current_folder_name._IDNTptr->value && current_folder_name._IDNTptr->value->type==_VECT){
vecteur v=*current_folder_name._IDNTptr->value->_VECTptr;
iterateur it=v.begin(),itend=v.end();
gen val;
for (;it!=itend;++it){
if (it->type!=_VECT || it->_VECTptr->size()!=2)
continue;
vecteur & w=*it->_VECTptr;
if (w[0]==args){
val=w[1];
break;
}
}
if (it!=itend){
v.erase(it);
gen res=gen(v,_FOLDER__VECT);
*current_folder_name._IDNTptr->value=res;
#ifdef HAVE_SIGNAL_H_OLD
if (!child_id && signal_store)
_signal(symb_quote(symbolic(at_sto,makesequence(res,current_folder_name))),contextptr);
#endif
return val;
}
}
if (args._IDNTptr->value){
#if !defined RTOS_THREADX && !defined BESTA_OS && !defined FREERTOS
if (variables_are_files(contextptr))
unlink((args._IDNTptr->name()+string(cas_suffixe)).c_str());
#endif
gen res=*args._IDNTptr->value;
if (res.type==_VECT && res.subtype==_FOLDER__VECT){
if (res._VECTptr->size()!=1)
return gensizeerr(gettext("Non-empty folder"));
}
delete args._IDNTptr->value;
args._IDNTptr->value=0;
#ifdef HAVE_SIGNAL_H_OLD
if (!child_id && signal_store)
_signal(symb_quote(symb_purge(args)),contextptr);
#endif
return res;
}
else
return string2gen(args.print(contextptr)+" not assigned",false);
}
static const char _purge_s []="purge";
static define_unary_function_eval_quoted (__purge,&_purge,_purge_s);
define_unary_function_ptr5( at_purge ,alias_at_purge,&__purge,_QUOTE_ARGUMENTS,0);
static string printasdivision(const gen & feuille,const char * s,GIAC_CONTEXT){
if (feuille.type!=_VECT || feuille._VECTptr->size()!=2)
return printsommetasoperator(feuille,s,contextptr);
gen n=feuille._VECTptr->front();
bool need=need_parenthesis(n);
string res;
if (need) res+='(';
res += n.print(contextptr);
if (need) res += ')';
res += '/';
gen f=feuille._VECTptr->back();
if ( (f.type==_SYMB && ( f._SYMBptr->sommet==at_plus || f._SYMBptr->sommet==at_prod || f._SYMBptr->sommet==at_division || f._SYMBptr->sommet==at_inv || need_parenthesis(f._SYMBptr->sommet) )) || (f.type==_CPLX) || (f.type==_MOD)){
res += '(';
res += f.print(contextptr);
res += ')';
}
else
res += f.print(contextptr);
return res;
}
static string texprintasdivision(const gen & feuille,const char * s,GIAC_CONTEXT){
if (feuille.type!=_VECT || feuille._VECTptr->size()!=2)
return "invalid /";
return "\\frac{"+gen2tex(feuille._VECTptr->front(),contextptr)+"}{"+gen2tex(feuille._VECTptr->back(),contextptr)+"}";
}
static gen symb_division(const gen & args){
return symbolic(at_division,args);
}
gen _division(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if ( (args.type!=_VECT) || (args._VECTptr->size()!=2) )
return symb_division(args);
gen a=args._VECTptr->front(),b=args._VECTptr->back();
if (a.is_approx()){
gen b1;
if (has_evalf(b,b1,1,contextptr) && b.type!=b1.type){
#ifdef HAVE_LIBMPFR
if (a.type==_REAL){
gen b2=accurate_evalf(b,mpfr_get_prec(a._REALptr->inf));
if (b2.is_approx())
return (*a._REALptr)/b2;
}
#endif
return rdiv(a,b1,contextptr);
}
}
if (b.is_approx()){
gen a1;
if (has_evalf(a,a1,1,contextptr) && a.type!=a1.type){
#ifdef HAVE_LIBMPFR
if (b.type==_REAL){
gen a2=accurate_evalf(a,mpfr_get_prec(b._REALptr->inf));
if (a2.is_approx())
return a2/b;
}
#endif
return rdiv(a1,b,contextptr);
}
}
return rdiv(a,b,contextptr);
}
static const char _division_s []="/";
static define_unary_function_eval4_index (10,__division,&_division,_division_s,&printasdivision,&texprintasdivision);
define_unary_function_ptr( at_division ,alias_at_division ,&__division);
static gen symb_binary_minus(const gen & args){
return symbolic(at_binary_minus,args);
}
gen _binary_minus(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if ( (args.type!=_VECT) || (args._VECTptr->size()!=2) )
return symb_binary_minus(args);
return args._VECTptr->front()-args._VECTptr->back();
}
static const char _binary_minus_s[]="-";
static define_unary_function_eval4_index (6,__binary_minus,&_binary_minus,_binary_minus_s,&printsommetasoperator,&texprintsommetasoperator);
define_unary_function_ptr( at_binary_minus ,alias_at_binary_minus ,&__binary_minus);
vecteur tab2vecteur(gen tab[]){
vecteur res;
for (;!is_zero(*tab);++tab)
res.push_back(*tab);
return res;
}
// hp38 compatibility
// model
gen _hp38(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if ( (args.type!=_VECT) || (args._VECTptr->size()!=2) )
return gensizeerr(contextptr);
return undef;
}
static const char _hp38_s[]="hp38";
static define_unary_function_eval (__hp38,&_hp38,_hp38_s);
define_unary_function_ptr5( at_hp38 ,alias_at_hp38,&__hp38,0,true);
// real/complex
gen _ABS(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args.type!=_VECT)
return abs(args,contextptr);
if (args.subtype)
return apply(args,giac::_abs,contextptr);
vecteur v;
aplatir(*args._VECTptr,v);
return _l2norm(v,contextptr);
}
static const char _ABS_s[]="ABS";
static define_unary_function_eval (__ABS,&_ABS,_ABS_s);
define_unary_function_ptr5( at_ABS ,alias_at_ABS,&__ABS,0,T_UNARY_OP_38);
gen _ARG38(const gen & g,GIAC_CONTEXT){
// if (angle_radian(contextptr)==0) return arg(evalf2bcd(g,1,contextptr),contextptr);
return arg(g,contextptr);
}
static const char _ARG38_s[]="ARG";
static define_unary_function_eval (__ARG38,&_ARG38,_ARG38_s);
define_unary_function_ptr5( at_ARG38 ,alias_at_ARG38,&__ARG38,0,T_UNARY_OP_38);
static const char _CONJ_s[]="CONJ";
static define_unary_function_eval (__CONJ,(const gen_op_context)giac::conj,_CONJ_s);
define_unary_function_ptr5( at_CONJ ,alias_at_CONJ,&__CONJ,0,T_UNARY_OP_38);
static const char _RE_s[]="RE";
static define_unary_function_eval (__RE,(const gen_op_context)giac::re,_RE_s);
define_unary_function_ptr5( at_RE ,alias_at_RE,&__RE,0,T_UNARY_OP_38);
static const char _IM_s[]="IM";
static define_unary_function_eval (___IM,(const gen_op_context)giac::im,_IM_s);
define_unary_function_ptr5( at_IM ,alias_at_IM,&___IM,0,T_UNARY_OP_38);
static const char _FLOOR_s[]="FLOOR";
static define_unary_function_eval (__FLOOR,(const gen_op_context)giac::_floor,_FLOOR_s);
define_unary_function_ptr5( at_FLOOR ,alias_at_FLOOR,&__FLOOR,0,T_UNARY_OP_38);
static const char _CEILING_s[]="CEILING";
static define_unary_function_eval (__CEILING,(const gen_op_context)giac::_ceil,_CEILING_s);
define_unary_function_ptr5( at_CEILING ,alias_at_CEILING,&__CEILING,0,T_UNARY_OP_38);
gen FP(const gen & g,GIAC_CONTEXT){
if (is_undef(g))
return g;
if (is_equal(g))
return apply_to_equal(g,FP,contextptr);
return g-_INT(g,contextptr);
}
static const char _FRAC_s[]="FP";
static define_unary_function_eval (__FRAC,&giac::FP,_FRAC_s);
define_unary_function_ptr5( at_FRAC ,alias_at_FRAC,&__FRAC,0,T_UNARY_OP_38);
static const char _MAX_s[]="MAX";
static define_unary_function_eval (__MAX,&giac::_max,_MAX_s);
define_unary_function_ptr5( at_MAX ,alias_at_MAX,&__MAX,0,T_UNARY_OP_38);
static const char _MIN_s[]="MIN";
static define_unary_function_eval (__MIN,&giac::_min,_MIN_s);
define_unary_function_ptr5( at_MIN ,alias_at_MIN,&__MIN,0,T_UNARY_OP_38);
gen _MODULO(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args.type==_VECT && args._VECTptr->size()==2){
gen a=args._VECTptr->front(),b=args._VECTptr->back();
if (is_zero(b))
return a;
if (is_integer(a)&&is_integer(b))
return _irem(args,contextptr);
if (a.type==_FLOAT_){
if (b.type==_FLOAT_)
return fmod(a._FLOAT_val,b._FLOAT_val);
if (b.type==_INT_)
return fmod(a._FLOAT_val,giac_float(b.val));
}
return a-b*_floor(a/b,contextptr);
}
return gentypeerr(contextptr);
}
static const char _MOD_s[]="MOD";
static define_unary_function_eval4 (__MOD,&giac::_MODULO,_MOD_s,&printsommetasoperator,&texprintsommetasoperator);
define_unary_function_ptr5( at_MOD ,alias_at_MOD,&__MOD,0,T_DIV);
static const char _ROUND_s[]="ROUND";
static define_unary_function_eval (__ROUND,&giac::_round,_ROUND_s);
define_unary_function_ptr5( at_ROUND ,alias_at_ROUND,&__ROUND,0,T_UNARY_OP_38);
gen _INTERSECT(const gen & g,GIAC_CONTEXT){
return _intersect(g,contextptr);
}
static const char _INTERSECT_s[]="INTERSECT";
static define_unary_function_eval (__INTERSECT,&giac::_INTERSECT,_INTERSECT_s);
define_unary_function_ptr5( at_INTERSECT ,alias_at_INTERSECT,&__INTERSECT,0,T_UNARY_OP_38);
gen _UNION(const gen & g,GIAC_CONTEXT){
return _union(g,contextptr);
}
static const char _UNION_s[]="UNION";
static define_unary_function_eval (__UNION,&giac::_UNION,_UNION_s);
define_unary_function_ptr5( at_UNION ,alias_at_UNION,&__UNION,0,T_UNARY_OP_38);
gen _MINUS(const gen & g,GIAC_CONTEXT){
return _minus(g,contextptr);
}
static const char _MINUS_s[]="MINUS";
static define_unary_function_eval (__MINUS,&giac::_MINUS,_MINUS_s);
define_unary_function_ptr5( at_MINUS ,alias_at_MINUS,&__MINUS,0,T_UNARY_OP_38);
gen _trunc(const gen & args,GIAC_CONTEXT);
static const char _TRUNCATE_s[]="TRUNCATE";
static define_unary_function_eval (__TRUNCATE,&giac::_trunc,_TRUNCATE_s);
define_unary_function_ptr5( at_TRUNCATE ,alias_at_TRUNCATE,&__TRUNCATE,0,T_UNARY_OP_38);
static const char _QUOTE_s[]="QUOTE";
static define_unary_function_eval_quoted (__QUOTE,&giac::quote,_QUOTE_s);
define_unary_function_ptr5( at_QUOTE ,alias_at_QUOTE,&__QUOTE,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
// Note that 0 is necessary otherwise conflict on freeBSD
static const char _SIGN_s[]="SIGN";
static define_unary_function_eval (__SIGN0,&giac::sign,_SIGN_s);
define_unary_function_ptr5( at_SIGN ,alias_at_SIGN,&__SIGN0,0,T_UNARY_OP_38);
// proba
static const char _COMB_s[]="COMB";
static define_unary_function_eval (__COMB,&giac::_comb,_COMB_s);
define_unary_function_ptr5( at_COMB ,alias_at_COMB,&__COMB,0,T_UNARY_OP_38);
static const char _PERM_s[]="PERM";
static define_unary_function_eval (__PERM,&giac::_perm,_PERM_s);
define_unary_function_ptr5( at_PERM ,alias_at_PERM,&__PERM,0,T_UNARY_OP_38);
string printasRANDOM(const gen & feuille,const char * s,GIAC_CONTEXT){
if (feuille.type==_VECT && feuille._VECTptr->empty())
return s;
return "("+(s+(" "+feuille.print())+")");
}
gen _RANDOM(const gen & g0,GIAC_CONTEXT){
gen g(g0);
if ( g.type==_STRNG && g.subtype==-1) return g;
is_integral(g);
if (g.type==_CPLX)
return _rand(gen(makevecteur(*g._CPLXptr,*(g._CPLXptr+1)),_SEQ__VECT),contextptr);
if (g.type!=_VECT || g.subtype!=_SEQ__VECT || !g._VECTptr->empty())
return _rand(g,contextptr);
return double(giac_rand(contextptr))/rand_max2;
}
static const char _RANDOM_s[]="RANDOM";
static define_unary_function_eval2 (__RANDOM,&giac::_RANDOM,_RANDOM_s,&printasRANDOM);
define_unary_function_ptr5( at_RANDOM ,alias_at_RANDOM,&__RANDOM,0,T_RETURN);
static const char _RANDSEED_s[]="RANDSEED";
static define_unary_function_eval (__RANDSEED,&giac::_srand,_RANDSEED_s);
define_unary_function_ptr5( at_RANDSEED ,alias_at_RANDSEED,&__RANDSEED,0,T_RETURN);
gen _MAXREAL(const gen & g,GIAC_CONTEXT){
if ( g.type==_STRNG && g.subtype==-1) return g;
#if 0 // def BCD
return_bcd_maxreal;
#else
return 1.79769313486e+308;
#endif
}
static const char _MAXREAL_s[]="MAXREAL";
static define_unary_function_eval (__MAXREAL,&giac::_MAXREAL,_MAXREAL_s);
define_unary_function_ptr5( at_MAXREAL ,alias_at_MAXREAL,&__MAXREAL,0,T_NUMBER);
gen _MINREAL(const gen & g,GIAC_CONTEXT){
if ( g.type==_STRNG && g.subtype==-1) return g;
#if 0 // def BCD
return_bcd_minreal;
// return_bcd_minreal;
#else
return 2.22507385851e-308; // smallest non-denormalized double
// return 1.26480805335e-321;
#endif
}
static const char _MINREAL_s[]="MINREAL";
static define_unary_function_eval (__MINREAL,&giac::_MINREAL,_MINREAL_s);
define_unary_function_ptr5( at_MINREAL ,alias_at_MINREAL,&__MINREAL,0,T_NUMBER);
// transcendent
static const char _EXP_s[]="EXP";
static define_unary_function_eval (__EXP,&giac::exp,_EXP_s);
define_unary_function_ptr5( at_EXP ,alias_at_EXP,&__EXP,0,T_UNARY_OP_38);
#if 0
define_partial_derivative_onearg_genop( D_at_expm1,"D_at_expm1",&giac::exp);
#endif
gen _EXPM1(const gen & g,GIAC_CONTEXT){
if ( g.type==_STRNG && g.subtype==-1) return g;
return exp(g,contextptr)-1;
}
static const char _EXPM1_s[]="EXPM1";
static define_unary_function_eval (__EXPM1,&giac::_EXPM1,_EXPM1_s);
define_unary_function_ptr5( at_EXPM1 ,alias_at_EXPM1,&__EXPM1,0,T_UNARY_OP_38);
#if 0
static gen d_lnp1(const gen & args,GIAC_CONTEXT){
return inv(args+1,contextptr);
}
define_partial_derivative_onearg_genop( D_at_lnp1,"D_at_lnp1",&d_lnp1);
#endif
gen _LNP1(const gen & g,GIAC_CONTEXT){
if ( g.type==_STRNG && g.subtype==-1) return g;
return ln(g+1,contextptr);
}
static const char _LNP1_s[]="LNP1";
static define_unary_function_eval (__LNP1,&giac::_LNP1,_LNP1_s);
define_unary_function_ptr5( at_LNP1 ,alias_at_LNP1,&__LNP1,0,T_UNARY_OP_38);
static const char _LN_s[]="LN";
static define_unary_function_eval (__LN,&giac::ln,_LN_s);
define_unary_function_ptr5( at_LN ,alias_at_LN,&__LN,0,T_UNARY_OP_38);
gen _LOG(const gen & g,GIAC_CONTEXT){
if (g.type==_VECT && g.subtype==_SEQ__VECT && g._VECTptr->size()==2)
return _logb(g,contextptr);
return giac::log10(g,contextptr);
}
static const char _LOG_s[]="LOG";
static define_unary_function_eval (__LOG,&_LOG,_LOG_s);
define_unary_function_ptr5( at_LOG ,alias_at_LOG,&__LOG,0,T_UNARY_OP_38);
static const char _ALOG_s[]="ALOG";
static define_unary_function_eval (__ALOG,&giac::alog10,_ALOG_s);
define_unary_function_ptr5( at_ALOG ,alias_at_ALOG,&__ALOG,0,T_UNARY_OP_38);
static const char _SIN_s[]="SIN";
static define_unary_function_eval (__SIN,&giac::sin,_SIN_s);
define_unary_function_ptr5( at_SIN ,alias_at_SIN,&__SIN,0,T_UNARY_OP_38);
static const char _COS_s[]="COS";
static define_unary_function_eval (__COS,&giac::cos,_COS_s);
define_unary_function_ptr5( at_COS ,alias_at_COS,&__COS,0,T_UNARY_OP_38);
static const char _TAN_s[]="TAN";
static define_unary_function_eval (__TAN,&giac::tan,_TAN_s);
define_unary_function_ptr5( at_TAN ,alias_at_TAN,&__TAN,0,T_UNARY_OP_38);
static const char _ASIN_s[]="ASIN";
static define_unary_function_eval (__ASIN,&giac::asin,_ASIN_s);
define_unary_function_ptr5( at_ASIN ,alias_at_ASIN,&__ASIN,0,T_UNARY_OP_38);
static const char _ACOS_s[]="ACOS";
static define_unary_function_eval (__ACOS,&giac::acos,_ACOS_s);
define_unary_function_ptr5( at_ACOS ,alias_at_ACOS,&__ACOS,0,T_UNARY_OP_38);
static const char _ATAN_s[]="ATAN";
static define_unary_function_eval (__ATAN,&giac::atan,_ATAN_s);
define_unary_function_ptr5( at_ATAN ,alias_at_ATAN,&__ATAN,0,T_UNARY_OP_38);
static const char _SINH_s[]="SINH";
static define_unary_function_eval (__SINH,&giac::sinh,_SINH_s);
define_unary_function_ptr5( at_SINH ,alias_at_SINH,&__SINH,0,T_UNARY_OP_38);
static const char _COSH_s[]="COSH";
static define_unary_function_eval (__COSH,&giac::cosh,_COSH_s);
define_unary_function_ptr5( at_COSH ,alias_at_COSH,&__COSH,0,T_UNARY_OP_38);
static const char _TANH_s[]="TANH";
static define_unary_function_eval (__TANH,&giac::tanh,_TANH_s);
define_unary_function_ptr5( at_TANH ,alias_at_TANH,&__TANH,0,T_UNARY_OP_38);
static const char _ASINH_s[]="ASINH";
static define_unary_function_eval (__ASINH,&giac::asinh,_ASINH_s);
define_unary_function_ptr5( at_ASINH ,alias_at_ASINH,&__ASINH,0,T_UNARY_OP_38);
static const char _ACOSH_s[]="ACOSH";
static define_unary_function_eval (__ACOSH,&giac::acosh,_ACOSH_s);
define_unary_function_ptr5( at_ACOSH ,alias_at_ACOSH,&__ACOSH,0,T_UNARY_OP_38);
static const char _ATANH_s[]="ATANH";
static define_unary_function_eval (__ATANH,&giac::atanh,_ATANH_s);
define_unary_function_ptr5( at_ATANH ,alias_at_ATANH,&__ATANH,0,T_UNARY_OP_38);
bool is_Ans(const gen & g){
if (g.type==_FUNC && *g._FUNCptr==at_Ans)
return true;
if (g.type==_SYMB && g._SYMBptr->sommet==at_Ans)
return true;
return false;
}
/* matrices */
gen _ADDROW(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
vecteur v(gen2vecteur(args));
if (!v.empty() && is_Ans(v[0]))
v[0]=eval(v[0],1,contextptr);
if (!v.empty() && v[0].type==_IDNT){
gen v0=v[0];
gen g=eval(args,eval_level(contextptr),contextptr);
if (ckmatrix(g[0])){
gen tmp=_ADDROW(g,contextptr);
return is_undef(tmp)?tmp:sto(tmp,v0,contextptr);
}
}
if (v.size()!=3)
return gentypeerr(contextptr);
v[1]=eval(v[1],1,contextptr);
v[2]=eval(v[2],1,contextptr);
v[2]=_floor(v[2],contextptr);
if (!ckmatrix(v[0]) || v[1].type!=_VECT || v[2].type!=_INT_)
return gentypeerr(contextptr);
vecteur & w = *v[0]._VECTptr;
if (w.front()._VECTptr->size()!=v[1]._VECTptr->size())
return gendimerr(contextptr);
int s=int(w.size());
int shift = xcas_mode(contextptr)!=0 || abs_calc_mode(contextptr)==38;
int l2=v[2].val-shift;
if (l2<0 || l2>s)
return gendimerr(contextptr);
matrice res(w.begin(),w.begin()+l2);
res.push_back(v[1]);
for (int i=l2;i<s;++i)
res.push_back(w[i]);
return res;
}
static const char _ADDROW_s[]="ADDROW";
static define_unary_function_eval_quoted (__ADDROW,&giac::_ADDROW,_ADDROW_s);
define_unary_function_ptr5( at_ADDROW ,alias_at_ADDROW,&__ADDROW,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
gen _ADDCOL(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
vecteur v(gen2vecteur(args));
if (!v.empty() && is_Ans(v[0]))
v[0]=eval(v[0],1,contextptr);
if (!v.empty() && v[0].type==_IDNT){
gen v0=v[0];
gen g=eval(args,eval_level(contextptr),contextptr);
if (ckmatrix(g[0])){
gen tmp=_ADDCOL(g,contextptr);
return is_undef(tmp)?tmp:sto(tmp,v0,contextptr);
}
}
if (v.size()!=3 || !ckmatrix(v[0]))
return gensizeerr(contextptr);
matrice m;
mtran(*v[0]._VECTptr,m);
gen res=_ADDROW(makesequence(m,v[1],v[2]),contextptr);
if (res.type==_VECT){
mtran(*res._VECTptr,m);
res=m;
}
return res;
}
static const char _ADDCOL_s[]="ADDCOL";
static define_unary_function_eval_quoted (__ADDCOL,&giac::_ADDCOL,_ADDCOL_s);
define_unary_function_ptr5( at_ADDCOL ,alias_at_ADDCOL,&__ADDCOL,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
gen _SCALE(const gen & g,GIAC_CONTEXT){
if ( g.type==_STRNG && g.subtype==-1) return g;
if (g.type!=_VECT || g._VECTptr->size()!=3)
return gensizeerr(contextptr);
vecteur v =*g._VECTptr;
v[1]=eval(v[1],1,contextptr);
v[2]=eval(v[2],1,contextptr);
swapgen(v[0],v[1]);
return _mRow(gen(v,_SEQ__VECT),contextptr);
}
static const char _SCALE_s[]="SCALE";
static define_unary_function_eval_quoted (__SCALE,&giac::_SCALE,_SCALE_s);
define_unary_function_ptr5( at_SCALE ,alias_at_SCALE,&__SCALE,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
static const char _scale_s[]="scale";
static define_unary_function_eval_quoted (__scale,&giac::_SCALE,_scale_s);
define_unary_function_ptr5( at_scale ,alias_at_scale,&__scale,_QUOTE_ARGUMENTS,T_UNARY_OP);
gen _SCALEADD(const gen & g,GIAC_CONTEXT){
if ( g.type==_STRNG && g.subtype==-1) return g;
if (g.type!=_VECT || g._VECTptr->size()!=4)
return gensizeerr(contextptr);
vecteur v =*g._VECTptr;
v[1]=eval(v[1],1,contextptr);
v[2]=eval(v[2],1,contextptr);
v[3]=eval(v[3],1,contextptr);
swapgen(v[0],v[1]);
return _mRowAdd(gen(v,_SEQ__VECT),contextptr);
}
static const char _SCALEADD_s[]="SCALEADD";
static define_unary_function_eval_quoted (__SCALEADD,&giac::_SCALEADD,_SCALEADD_s);
define_unary_function_ptr5( at_SCALEADD ,alias_at_SCALEADD,&__SCALEADD,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
static const char _scaleadd_s[]="scaleadd";
static define_unary_function_eval_quoted (__scaleadd,&giac::_SCALEADD,_scaleadd_s);
define_unary_function_ptr5( at_scaleadd ,alias_at_scaleadd,&__scaleadd,_QUOTE_ARGUMENTS,T_UNARY_OP);
gen _SWAPCOL(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
vecteur v(gen2vecteur(args));
if (!v.empty() && is_Ans(v[0]))
v[0]=eval(v[0],1,contextptr);
if (!v.empty() && v[0].type==_IDNT){
gen v0=v[0];
gen g=eval(args,eval_level(contextptr),contextptr);
if (ckmatrix(g[0]))
return sto(_SWAPCOL(g,contextptr),v0,contextptr);
}
if (v.size()!=3 || !ckmatrix(v[0]))
return gensizeerr(contextptr);
v[1]=eval(v[1],1,contextptr);
v[2]=eval(v[2],1,contextptr);
matrice m;
mtran(*v[0]._VECTptr,m);
gen res=_rowSwap(makesequence(m,v[1],v[2]),contextptr);
if (res.type==_VECT){
mtran(*res._VECTptr,m);
res=m;
}
return res;
}
static const char _SWAPCOL_s[]="SWAPCOL";
static define_unary_function_eval_quoted (__SWAPCOL,&giac::_SWAPCOL,_SWAPCOL_s);
define_unary_function_ptr5( at_SWAPCOL ,alias_at_SWAPCOL,&__SWAPCOL,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
static const char _colswap_s[]="colswap";
static define_unary_function_eval (__colswap,&_SWAPCOL,_colswap_s);
define_unary_function_ptr5( at_colswap ,alias_at_colswap,&__colswap,0,true);
static const char _swapcol_s[]="swapcol";
static define_unary_function_eval (__swapcol,&_SWAPCOL,_swapcol_s);
define_unary_function_ptr5( at_swapcol ,alias_at_swapcol,&__swapcol,0,true);
static const char _colSwap_s[]="colSwap";
static define_unary_function_eval (__colSwap,&_SWAPCOL,_colSwap_s);
define_unary_function_ptr5( at_colSwap ,alias_at_colSwap,&__colSwap,0,true);
static const char _DELCOL_s[]="DELCOL";
static define_unary_function_eval_quoted (__DELCOL,&giac::_delcols,_DELCOL_s);
define_unary_function_ptr5( at_DELCOL ,alias_at_DELCOL,&__DELCOL,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
static const char _DELROW_s[]="DELROW";
static define_unary_function_eval_quoted (__DELROW,&giac::_delrows,_DELROW_s);
define_unary_function_ptr5( at_DELROW ,alias_at_DELROW,&__DELROW,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
static const char _SWAPROW_s[]="SWAPROW";
static define_unary_function_eval_quoted (__SWAPROW,&giac::_rowSwap,_SWAPROW_s);
define_unary_function_ptr5( at_SWAPROW ,alias_at_SWAPROW,&__SWAPROW,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
gen _SUB(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
vecteur v(gen2vecteur(args));
gen v0=v[0];
v=*eval(v,eval_level(contextptr),contextptr)._VECTptr;
if (v0.type!=_IDNT){
if (v.size()<3)
return gendimerr(contextptr);
if (ckmatrix(v[0]))
return _subMat(gen(makevecteur(v[0],v[1],v[2]),_SEQ__VECT),contextptr);
int shift = xcas_mode(contextptr)!=0 || abs_calc_mode(contextptr)==38;
if (v[0].type==_VECT && v[1].type==_INT_ && v[2].type==_INT_){
vecteur & w =*v[0]._VECTptr;
int v2=v[1].val-shift, v3=v[2].val-shift;
if (v2<=v3 && v2>=0 && v3<int(w.size()))
return gen(vecteur(w.begin()+v2,w.begin()+v3+1),v[1].subtype);
}
}
if (v.size()==3)
v.insert(v.begin(),v0);
if (v.size()<4)
return gendimerr(contextptr);
v[2]=_floor(v[2],contextptr);
v[3]=_floor(v[3],contextptr);
if (ckmatrix(v[1]))
return sto(_subMat(gen(makevecteur(v[1],v[2],v[3]),_SEQ__VECT),contextptr),v0,contextptr);
int shift = xcas_mode(contextptr)!=0 || abs_calc_mode(contextptr)==38;
if (v[1].type==_VECT && v[2].type==_INT_ && v[3].type==_INT_){
vecteur & w =*v[1]._VECTptr;
int v2=v[2].val-shift, v3=v[3].val-shift;
if (v2<=v3 && v2>=0 && v3<int(w.size()))
return sto(gen(vecteur(w.begin()+v2,w.begin()+v3+1),v[1].subtype),v0,contextptr);
}
return undef;
}
static const char _SUB_s[]="SUB";
static define_unary_function_eval_quoted (__SUB,&giac::_SUB,_SUB_s);
define_unary_function_ptr5( at_SUB ,alias_at_SUB,&__SUB,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
gen _RANDMAT(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
vecteur v(gen2vecteur(args));
int s=int(v.size());
if (s==1){
v[0]=_floor(v[0],contextptr);
if (v[0].type!=_INT_)
return gentypeerr(contextptr);
return vranm(v[0].val,0,contextptr);
}
if (s<2)
return gensizeerr(contextptr);
gen name=v[0];
if (name.type!=_IDNT && !name.is_symb_of_sommet(at_double_deux_points))
return _ranm(eval(args,eval_level(contextptr),contextptr),contextptr);
v=*eval(v,eval_level(contextptr),contextptr)._VECTptr;
v[1]=_floor(v[1],contextptr);
if (v[1].type!=_INT_)
return gentypeerr(contextptr);
if (s==2)
return sto(vranm(v[1].val,0,contextptr),name,contextptr);
v[2]=_floor(v[2],contextptr);
if (v[2].type!=_INT_)
return gentypeerr(contextptr);
return sto(mranm(v[1].val,v[2].val,0,contextptr),name,contextptr);
}
static const char _RANDMAT_s[]="RANDMAT";
static define_unary_function_eval_quoted (__RANDMAT,&giac::_RANDMAT,_RANDMAT_s);
define_unary_function_ptr5( at_RANDMAT ,alias_at_RANDMAT,&__RANDMAT,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
gen _REDIM(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
vecteur v(gen2vecteur(args));
int s=int(v.size());
if (s==3)
return _REDIM(gen(makevecteur(v[0],makevecteur(v[1],v[2])),_SEQ__VECT),contextptr);
gen name=v[0];
if (s!=2)
return gensizeerr(contextptr);
bool unnamed= name.type!=_IDNT && !name.is_symb_of_sommet(at_double_deux_points);
v=*eval(v,eval_level(contextptr),contextptr)._VECTptr;
if (v[0].type!=_VECT)
return gentypeerr(contextptr);
vecteur w=*v[0]._VECTptr,argv;
argv=gen2vecteur(v[1]);
for (unsigned i=0;i<argv.size();++i){
if (!is_integral(argv[i]))
return gentypeerr(contextptr);
}
if (ckmatrix(v[0])){
if (argv.size()==2){
w.clear();
int newl=argv[0].val,newc=argv[1].val;
if (newl<=0 || newc<=0 || newl*newc>LIST_SIZE_LIMIT)
return gendimerr(contextptr);
// create w
vecteur & v0=*v[0]._VECTptr;
newl=giacmin(newl,int(v0.size()));
int nc=giacmin(newc,int(v0.front()._VECTptr->size())),j;
for (int i=0;i<newl;++i){
vecteur & cur = *v0[i]._VECTptr;
for (j=0;j<nc;++j){
w.push_back(cur[j]);
}
for (;j<newc;++j)
w.push_back(0);
}
}
else
aplatir(*v[0]._VECTptr,w);
}
argv.push_back(w);
if (unnamed)
return _matrix(gen(argv,_SEQ__VECT),contextptr);
return sto(_matrix(gen(argv,_SEQ__VECT),contextptr),name,contextptr);
}
static const char _REDIM_s[]="REDIM";
static define_unary_function_eval_quoted (__REDIM,&giac::_REDIM,_REDIM_s);
define_unary_function_ptr5( at_REDIM ,alias_at_REDIM,&__REDIM,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
static const char _redim_s[]="redim";
static define_unary_function_eval_quoted (__redim,&giac::_REDIM,_redim_s);
define_unary_function_ptr5( at_redim ,alias_at_redim,&__redim,_QUOTE_ARGUMENTS,T_UNARY_OP);
gen _REPLACE(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
vecteur v(gen2vecteur(args));
int s=int(v.size());
gen name=v[0];
if (s!=3)
return gensizeerr(contextptr);
bool unnamed= name.type!=_IDNT && !name.is_symb_of_sommet(at_double_deux_points);
v=*eval(v,eval_level(contextptr),contextptr)._VECTptr;
if (v[0].type!=_VECT || v[2].type!=_VECT)
return gentypeerr(contextptr);
v[1]=_floor(v[1],contextptr);
int pos,l,c=0,shift=abs_calc_mode(contextptr)==38; // && v[1].subtype==_LIST__VECT;
vecteur w0=*v[0]._VECTptr,w2=*v[2]._VECTptr,argv;
if (ckmatrix(v[0])){
mdims(w0,l,c);
if (ckmatrix(v[2]) && v[1].type==_VECT){
vecteur & v1=*v[1]._VECTptr;
if (v1.size()!=2 || v1.front().type!=_INT_ || v1.back().type!=_INT_)
return gentypeerr(contextptr);
int ls,cs,pos1=v1.front().val-shift,pos2=v1.back().val-shift;
if (pos1<0 || pos1>=l || pos2<0 || pos2>=c)
return gendimerr(contextptr);
mdims(w2,ls,cs);
std_matrix<gen> target,source;
matrice2std_matrix_gen(w2,source);
matrice2std_matrix_gen(w0,target);
for (int i=0;i<ls;++i){
if (i+pos1>=l)
break;
vecteur & ws =source[i];
vecteur & wt =target[i+pos1];
for (int j=0;j<cs;++j){
if (j+pos2>=c)
break;
wt[j+pos2]=ws[j];
}
}
std_matrix_gen2matrice(target,w0);
if (unnamed)
return gen(w0,_MATRIX__VECT);
return sto(gen(w0,_MATRIX__VECT),name,contextptr);
}
aplatir(*v[0]._VECTptr,w0);
}
else
l=int(w0.size());
if (v[1].type==_VECT){
vecteur & v1=*v[1]._VECTptr;
if (v1.size()!=2 || v1.front().type!=_INT_ || v1.back().type!=_INT_)
return gentypeerr(contextptr);
pos=(v1.front().val-shift)*c+(v1.back().val-shift);
}
else {
if (v[1].type!=_INT_)
return gentypeerr(contextptr);
pos=v[1].val;
if (abs_calc_mode(contextptr)==38)
--pos;
}
if (ckmatrix(v[2]))
aplatir(*v[2]._VECTptr,w2);
int w0s=int(w0.size()),w2s=int(w2.size()),i=giacmax(pos,0),j=0;
for (;i<w0s && j<w2s;++j,++i){
w0[i]=w2[j];
}
if (!c){
if (unnamed)
return gen(w0,v[0].subtype);
return sto(gen(w0,v[0].subtype),name,contextptr);
}
if (unnamed)
return _matrix(gen(makevecteur(l,c,w0),_SEQ__VECT),contextptr);
return sto(_matrix(gen(makevecteur(l,c,w0),_SEQ__VECT),contextptr),name,contextptr);
}
static const char _REPLACE_s[]="REPLACE";
static define_unary_function_eval_quoted (__REPLACE,&giac::_REPLACE,_REPLACE_s);
define_unary_function_ptr5( at_REPLACE ,alias_at_REPLACE,&__REPLACE,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
static const char _replace_s[]="replace";
static define_unary_function_eval_quoted (__replace,&giac::_REPLACE,_replace_s);
define_unary_function_ptr5( at_replace ,alias_at_replace,&__replace,_QUOTE_ARGUMENTS,T_UNARY_OP);
static const char _COLNORM_s[]="COLNORM";
static define_unary_function_eval (__COLNORM,&giac::_colNorm,_COLNORM_s);
define_unary_function_ptr5( at_COLNORM ,alias_at_COLNORM,&__COLNORM,0,T_UNARY_OP_38);
static const char _ROWNORM_s[]="ROWNORM";
static define_unary_function_eval (__ROWNORM,&giac::_rowNorm,_ROWNORM_s);
define_unary_function_ptr5( at_ROWNORM ,alias_at_ROWNORM,&__ROWNORM,0,T_UNARY_OP_38);
static const char _CROSS_s[]="CROSS";
static define_unary_function_eval (__CROSS,&giac::_cross,_CROSS_s);
define_unary_function_ptr5( at_CROSS ,alias_at_CROSS,&__CROSS,0,T_UNARY_OP_38);
static const char _DET_s[]="DET";
static define_unary_function_eval (__DET,&giac::_det,_DET_s);
define_unary_function_ptr5( at_DET ,alias_at_DET,&__DET,0,T_UNARY_OP_38);
static const char _DOT_s[]="DOT";
static define_unary_function_eval (__DOT,&giac::_dotprod,_DOT_s);
define_unary_function_ptr5( at_DOT ,alias_at_DOT,&__DOT,0,T_UNARY_OP_38);
gen _EIGENVAL(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (!is_squarematrix(args))
return gendimerr(contextptr);
bool b=complex_mode(contextptr);
complex_mode(true,contextptr);
gen res=_egvl(evalf(args,1,contextptr),contextptr);
res=_diag(res,contextptr);
complex_mode(b,contextptr);
return res;
}
static const char _EIGENVAL_s[]="EIGENVAL";
static define_unary_function_eval (__EIGENVAL,&giac::_EIGENVAL,_EIGENVAL_s);
define_unary_function_ptr5( at_EIGENVAL ,alias_at_EIGENVAL,&__EIGENVAL,0,T_UNARY_OP_38);
gen _EIGENVV(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (!is_squarematrix(args))
return gendimerr(contextptr);
bool b=complex_mode(contextptr);
complex_mode(true,contextptr);
gen res=_jordan(evalf(args,1,contextptr),contextptr);
complex_mode(b,contextptr);
if (res.type==_VECT)
res.subtype=_LIST__VECT;
return res;
}
static const char _EIGENVV_s[]="EIGENVV";
static define_unary_function_eval (__EIGENVV,&giac::_EIGENVV,_EIGENVV_s);
define_unary_function_ptr5( at_EIGENVV ,alias_at_EIGENVV,&__EIGENVV,0,T_UNARY_OP_38);
static const char _IDENMAT_s[]="IDENMAT";
static define_unary_function_eval (__IDENMAT,&giac::_idn,_IDENMAT_s);
define_unary_function_ptr5( at_IDENMAT ,alias_at_IDENMAT,&__IDENMAT,0,T_UNARY_OP_38);
static const char _INVERSE_s[]="INVERSE";
static define_unary_function_eval (__INVERSE,&giac::inv,_INVERSE_s);
define_unary_function_ptr5( at_INVERSE ,alias_at_INVERSE,&__INVERSE,0,T_UNARY_OP_38);
gen _TRACE(const gen & g,GIAC_CONTEXT){
if (!is_squarematrix(g))
return gensizeerr(contextptr);
return mtrace(*g._VECTptr);
}
static const char _TRACE_s[]="TRACE";
static define_unary_function_eval (__TRACE,&giac::_TRACE,_TRACE_s);
define_unary_function_ptr5( at_TRACE ,alias_at_TRACE,&__TRACE,0,T_UNARY_OP_38);
static const char _TRN_s[]="TRN";
static define_unary_function_eval (__TRN,&giac::_trn,_TRN_s);
define_unary_function_ptr5( at_TRN ,alias_at_TRN,&__TRN,0,T_UNARY_OP_38);
static const char _RANK_s[]="RANK";
static define_unary_function_eval (__RANK,&giac::_rank,_RANK_s);
define_unary_function_ptr5( at_RANK ,alias_at_RANK,&__RANK,0,T_UNARY_OP_38);
gen _SIZE(const gen& args,GIAC_CONTEXT){
if (ckmatrix(args))
return _dim(args,contextptr);
else
return _size(args,contextptr);
}
static const char _SIZE_s[]="SIZE";
static define_unary_function_eval (__SIZE,&giac::_SIZE,_SIZE_s);
define_unary_function_ptr5( at_SIZE ,alias_at_SIZE,&__SIZE,0,T_UNARY_OP_38);
static const char _SORT_s[]="SORT";
static define_unary_function_eval (__SORT,&giac::_sort,_SORT_s);
define_unary_function_ptr5( at_SORT ,alias_at_SORT,&__SORT,0,T_UNARY_OP_38);
static const char _DELTALIST_s[]="ΔLIST";
static define_unary_function_eval (__DELTALIST,&giac::_deltalist,_DELTALIST_s);
define_unary_function_ptr5( at_DELTALIST ,alias_at_DELTALIST,&__DELTALIST,0,T_UNARY_OP_38);
static const char _CONCAT_s[]="CONCAT";
static define_unary_function_eval (__CCONCAT,&giac::_concat,_CONCAT_s);
define_unary_function_ptr5( at_CONCAT ,alias_at_CONCAT,&__CCONCAT,0,T_UNARY_OP_38);
gen _PILIST(const gen & args,GIAC_CONTEXT){
if (args.type==_VECT)
return _product(change_subtype(args,0),contextptr);
return _product(args,contextptr);
}
static const char _PILIST_s[]="ΠLIST";
static define_unary_function_eval (__PILIST,&giac::_PILIST,_PILIST_s);
define_unary_function_ptr5( at_PILIST ,alias_at_PILIST,&__PILIST,0,T_UNARY_OP_38);
gen _SIGMALIST(const gen & args,GIAC_CONTEXT){
if (args.type==_VECT)
return _sum(change_subtype(args,0),contextptr);
return _sum(args,contextptr);
}
static const char _SIGMALIST_s[]="ΣLIST";
static define_unary_function_eval (__SIGMALIST,&giac::_SIGMALIST,_SIGMALIST_s);
define_unary_function_ptr5( at_SIGMALIST ,alias_at_SIGMALIST,&__SIGMALIST,0,T_UNARY_OP_38);
static const char _REVERSE_s[]="REVERSE";
static define_unary_function_eval (__REVERSE,&giac::_revlist,_REVERSE_s);
define_unary_function_ptr5( at_REVERSE ,alias_at_REVERSE,&__REVERSE,0,T_UNARY_OP_38);
gen _POS(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if ( (args.type!=_VECT) || (args._VECTptr->size()!=2) || (args._VECTptr->front().type!=_VECT) )
return gensizeerr(contextptr);
return equalposcomp(*args._VECTptr->front()._VECTptr,evalf2bcd(args._VECTptr->back(),1,contextptr));
}
static const char _POS_s[]="POS";
static define_unary_function_eval (__POS,&giac::_POS,_POS_s);
define_unary_function_ptr5( at_POS ,alias_at_POS,&__POS,0,T_UNARY_OP_38);
gen _MAKELIST(const gen & args,GIAC_CONTEXT){
if (args.type!=_VECT || (args._VECTptr->size()!=4 && args._VECTptr->size()!=5))
return gensizeerr(contextptr);
vecteur & v = *args._VECTptr;
if (v.size()==5 && is_positive(-v[4]*(v[3]-v[2]),contextptr))
return gensizeerr(gettext("Invalid step value"));
gen res=giac::_seq(args,contextptr);
if (res.type==_VECT)
res.subtype=_LIST__VECT;
return res;
}
static const char _MAKELIST_s[]="MAKELIST";
static define_unary_function_eval (__MAKELIST,&giac::_MAKELIST,_MAKELIST_s);
define_unary_function_ptr5( at_MAKELIST ,alias_at_MAKELIST,&__MAKELIST,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
gen _INT(const gen & g,GIAC_CONTEXT){
if ( g.type==_STRNG && g.subtype==-1) return g;
if (g.type==_VECT)
return apply(g,_INT,contextptr);
if (g.type==_CPLX)
return _INT(*g._CPLXptr,contextptr)+cst_i*_INT(*(g._CPLXptr+1),contextptr);
if (is_positive(g,contextptr))
return _floor(g,contextptr);
else {
if (is_positive(-g,contextptr))
return _ceil(g,contextptr);
gen sg=sign(g,contextptr);
return sg*_floor(g*sg,contextptr);//symbolic(at_when,makesequence(symbolic(at_superieur_egal,makesequence(g,0)),symbolic(at_floor,g),symbolic(at_ceil,g)));
}
}
static const char _INT_s[]="IP";
static define_unary_function_eval (__INT,&giac::_INT,_INT_s);
define_unary_function_ptr5( at_INT ,alias_at_INT,&__INT,0,T_UNARY_OP_38);
static int taylorxn=0;
static void hp38_eval(vecteur & v,gen & x,gen& newx,GIAC_CONTEXT){
x=v[1];
if (is_equal(x))
x=x._SYMBptr->feuille[0];
identificateur idx("taylorx"+print_INT_(taylorxn));
++taylorxn;
newx=idx;
gen tmp=subst(v[0],x,newx,false,contextptr);
gen tmp1=eval(tmp,eval_level(contextptr),contextptr);
if (!is_undef(tmp1))
tmp=tmp1;
tmp1=subst(tmp,x,newx,false,contextptr);
if (!is_undef(tmp1))
tmp=tmp1;
v[0]=tmp;
v[1]=newx;
int s=int(v.size());
for (int i=2;i<s;++i)
v[i]=eval(v[i],eval_level(contextptr),contextptr);
}
gen _HPDIFF(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
gen tmp;
if (args.type==_VECT && args.subtype==_SEQ__VECT && args._VECTptr->size()>=2){
gen value=(*args._VECTptr)[1],var=value;
if (is_equal(value)){
var=value._SYMBptr->feuille[0];
value=value._SYMBptr->feuille[1];
}
if (var.type!=_IDNT && abs_calc_mode(contextptr)==38)
return gensizeerr(gettext("∂(expression,variable=value)"));
int ndiff=1;
if (args._VECTptr->size()>=3 && (*args._VECTptr)[2].type==_INT_ ){
ndiff=(*args._VECTptr)[2].val;
if (ndiff<0)
return gensizeerr(gettext("Order of derivation must be positive"));
}
if (args._VECTptr->size()>=4 && abs_calc_mode(contextptr)!=38)
value=(*args._VECTptr)[3];
static int count=0;
gen newx("hpdiffx"+print_INT_(count),contextptr);
++count;
gen arg0=eval(subst(args._VECTptr->front(),var,newx,false,contextptr),eval_level(contextptr),contextptr);
arg0=subst(arg0,var,newx,false,contextptr);
if (ndiff==0){
value=eval(value,1,contextptr);
tmp=gen(makevecteur(arg0,newx,value),_SEQ__VECT);
return _limit(tmp,contextptr);
}
else {
if (ndiff==1)
tmp=gen(makesequence(arg0,newx));
else
tmp=gen(makevecteur(arg0,newx,ndiff),_SEQ__VECT);
tmp=_derive(tmp,contextptr);
// return _limit(makesequence(tmp,newx,value),contextptr);
tmp=subst(tmp,newx,value,false,contextptr);
tmp=eval(tmp,1,contextptr);
return tmp;
}
}
else {
gen a(args);
if (guess_program(a,contextptr))
return _derive(a,contextptr);
return _HPDIFF(gen(makevecteur(args,vx_var),_SEQ__VECT),contextptr);
}
}
static const char _HPDIFF_s[]="∂";
static define_unary_function_eval_quoted (__HPDIFF,&giac::_HPDIFF,_HPDIFF_s);
define_unary_function_ptr5( at_HPDIFF ,alias_at_HPDIFF,&__HPDIFF,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
gen _HPINT(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args.type==_VECT && args.subtype==_SEQ__VECT){
vecteur v = *args._VECTptr;
if (v.size()==3){
if (is_equal(v.front())){
gen var=v.front()._SYMBptr->feuille[0];
gen lower=v.front()._SYMBptr->feuille[1];
v=makevecteur(v[2],var,lower,v[1]);
}
if (is_equal(v[1])){
gen var=v[1]._SYMBptr->feuille[0];
gen lower=v[1]._SYMBptr->feuille[1];
v=makevecteur(v.front(),var,lower,v[2]);
}
if (v.size()==3)
return _integrate(args,contextptr);
}
if (v.size()>=4){
if (v[1].type!=_IDNT){
return gensizeerr(gettext("∫(expression,var,lower,upper)"));
// swapgen(v[0],v[2]);
// swapgen(v[1],v[3]);
}
gen x,newx;
hp38_eval(v,x,newx,contextptr);
gen tmp=_integrate(gen(v,_SEQ__VECT),contextptr);
if (eval(x,1,contextptr)!=x)
return tmp;
else
return subst(tmp,newx,x,false,contextptr);
// if we subst then the value of x may alter tmp even with subst
}
}
#ifndef CAS38_DISABLED
return _integrate(args,contextptr);
#else
return gensizeerr(contextptr);
#endif
}
static const char _HPINT_s[]="∫";
static define_unary_function_eval_quoted (__HPINT,&giac::_HPINT,_HPINT_s);
define_unary_function_ptr5( at_HPINT ,alias_at_HPINT,&__HPINT,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
gen _HPSUM(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args.type==_VECT && args.subtype==_SEQ__VECT && args._VECTptr->size()<=3){
if (args._VECTptr->size()!=3)
return gensizeerr(contextptr);
const vecteur & v = *args._VECTptr;
if (is_equal(v[0])){
gen var=v[0]._SYMBptr->feuille[0];
if (var.type!=_IDNT)
return gensizeerr(contextptr);
gen inf=v[0]._SYMBptr->feuille[1];
gen sup=v[1];
gen expr=v[2];
return _sum(gen(makevecteur(expr,var,inf,sup),_SEQ__VECT),contextptr);
}
if (is_equal(v[1])){
gen var=v[1]._SYMBptr->feuille[0];
if (var.type!=_IDNT)
return gensizeerr(contextptr);
gen inf=v[1]._SYMBptr->feuille[1];
gen sup=v[2];
gen expr=v[0];
return _sum(gen(makevecteur(expr,var,inf,sup),_SEQ__VECT),contextptr);
}
}
return _sum(args,contextptr);
}
static const char _HPSUM_s[]="Σ"; // "∑";
// static const char _HPSUM_s[]="∑"; // "Σ";
static define_unary_function_eval_quoted (__HPSUM,&giac::_HPSUM,_HPSUM_s);
define_unary_function_ptr5( at_HPSUM ,alias_at_HPSUM,&__HPSUM,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
gen _TAYLOR(const gen & args,GIAC_CONTEXT){
#ifdef CAS38_DISABLED
return gensizeerr(contextptr);
#endif
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args.type!=_VECT)
return gentypeerr(contextptr);
vecteur v = *args._VECTptr;
if (v.size()<2)
v.push_back(x__IDNT_e);
gen x,newx;
hp38_eval(v,x,newx,contextptr);
gen res=subst(_taylor(gen(v,_SEQ__VECT),contextptr),newx,x,false,contextptr);
v=lop(res,at_order_size);
res=subst(res,v,vecteur(v.size()),false,contextptr);
return res;
}
static const char _TAYLOR_s[]="TAYLOR";
static define_unary_function_eval_quoted (__TAYLOR,&_TAYLOR,_TAYLOR_s);
define_unary_function_ptr5( at_TAYLOR ,alias_at_TAYLOR,&__TAYLOR,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
gen _POLYCOEFF(const gen &args0,GIAC_CONTEXT){
gen args=eval(args0,1,contextptr);
if (args.type==_VECT && args.subtype!=_SEQ__VECT)
return _pcoeff(args,contextptr);
return _symb2poly(args0,contextptr);
}
static const char _POLYCOEF_s[]="POLYCOEF";
static define_unary_function_eval (__POLYCOEF,&giac::_POLYCOEFF,_POLYCOEF_s);
define_unary_function_ptr5( at_POLYCOEF ,alias_at_POLYCOEF,&__POLYCOEF,_QUOTE_ARGUMENTS,T_UNARY_OP);
gen _horner(const gen & args,GIAC_CONTEXT);
gen _POLYEVAL(const gen & args,GIAC_CONTEXT){
if (args.type!=_VECT)
return gentypeerr(contextptr);
if (args.subtype!=_SEQ__VECT)
return _POLYFORM(_horner(gen(makevecteur(args,vx_var),_SEQ__VECT),contextptr),contextptr);
return _horner(args,contextptr);
}
static const char _POLYEVAL_s[]="POLYEVAL";
static define_unary_function_eval (__POLYEVAL,&giac::_POLYEVAL,_POLYEVAL_s);
define_unary_function_ptr5( at_POLYEVAL ,alias_at_POLYEVAL,&__POLYEVAL,0,T_UNARY_OP_38);
gen evalfunc(const gen & args,GIAC_CONTEXT){
#ifdef GIAC_HAS_STO_38
vecteur v(lidnt(args));
vecteur lf,lfval;
for (unsigned i=0;i<v.size();++i){
if (v[i].type!=_IDNT)
continue;
const char * ch=v[i]._IDNTptr->id_name;
if (strlen(ch)==2 && (ch[0]=='F' || ch[0]=='X' || ch[0]=='Y' || ch[0]=='R')){
lf.push_back(v[i]);
lfval.push_back(eval(v[i],1,contextptr));
}
}
if (lf.empty())
return args;
return subst(args,lf,lfval,false,contextptr);
#else
return args;
#endif
}
static string printasPOLYFORM(const gen &feuille,const char * sommetstr,GIAC_CONTEXT){
if (feuille.type==_VECT && feuille._VECTptr->size()==2 && feuille._VECTptr->back().type==_FUNC){
const char * s=feuille._VECTptr->back()._FUNCptr->ptr()->s;
return feuille._VECTptr->front().print(contextptr)+"\xe2\x96\xba"+((strcmp(s,"eval")==0)?"\xe2\x96\xba":s);
}
return string(sommetstr)+('('+feuille.print(contextptr)+')');
}
gen _POLYFORM(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
gen tmp;
if (args.type==_VECT && !args._VECTptr->empty()){
const vecteur & v = *args._VECTptr;
tmp=v[0];
tmp=eval(tmp,1,context0);
tmp=evalfunc(tmp,contextptr);
int vs=int(v.size());
#ifdef CAS38_DISABLED
if (vs==2 && v.back()==at_prod && is_integral(tmp))
return _ifactor(tmp,context0);
#else
if (vs==2){
if (v.back()==at_eval) return tmp;
if (v.back()==at_prod){
if (is_integral(tmp))
return _ifactor(tmp,context0);
return _factor(tmp,context0);
}
if (v.back()==at_plus)
return _partfrac(tmp,context0);
if (v.back().type==_FUNC)
return _convert(gen(makevecteur(tmp,v.back()),_SEQ__VECT),context0);
}
#endif
if (v.back().type==_FUNC) // additional check for STO> +/-/etc. if CAS38_DISABLED is set
return gensizeerr(contextptr);
if (vs>1)
return _reorder(makesequence(tmp,vecteur(v.begin()+1,v.end())),context0);
}
tmp=eval(args,1,context0);
tmp=evalfunc(tmp,contextptr);
return _recursive_normal(tmp,context0); // return symb_quote(_partfrac(args,contextptr)); // return symb_quote(recursive_normal(args,1,contextptr)); // symb_quote(simplify(eval(args,1,context0),context0));
}
static const char _POLYFORM_s[]="POLYFORM";
static define_unary_function_eval2_quoted (__POLYFORM,&giac::_POLYFORM,_POLYFORM_s,&printasPOLYFORM);
define_unary_function_ptr5( at_POLYFORM ,alias_at_POLYFORM,&__POLYFORM,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
gen _POLYROOT(const gen & args0,GIAC_CONTEXT){
gen args=eval(args0,1,contextptr);
if (args.type==_VECT && args.subtype!=_SEQ__VECT)
;
else
args=args0;
gen res;
if (complex_mode(contextptr))
res=_proot(args,contextptr);
else {
#if 0 // set to 1 : POLYROOT returns only real roots without multiplicities, SLOW on aspen
vecteur vas_res;
if (vas(symb2poly_num(args,contextptr),0,0,1e-14,vas_res,false,contextptr))
res=vas_res;
else
res=_proot(args,contextptr);
#else
res=_proot(args,contextptr);
#endif
}
#ifdef GIAC_HAS_STO_38
if (res.type==_VECT)
res.subtype=_LIST__VECT;
#endif
return res;
}
static const char _POLYROOT_s[]="POLYROOT";
static define_unary_function_eval (__POLYROOT,&giac::_POLYROOT,_POLYROOT_s);
define_unary_function_ptr5( at_POLYROOT ,alias_at_POLYROOT,&__POLYROOT,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
gen _ISOLATE(const gen & args0,GIAC_CONTEXT){
#ifdef CAS38_DISABLED
return gensizeerr(contextptr);
#endif
return symb_quote(_solve(args0,contextptr));
}
static const char _ISOLATE_s[]="ISOLATE";
static define_unary_function_eval_quoted (__ISOLATE,&giac::_ISOLATE,_ISOLATE_s);
define_unary_function_ptr5( at_ISOLATE ,alias_at_ISOLATE,&__ISOLATE,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
static const char _QUAD_s[]="QUAD";
static define_unary_function_eval_quoted (__QUAD,&giac::_ISOLATE,_QUAD_s);
define_unary_function_ptr5( at_QUAD ,alias_at_QUAD,&__QUAD,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
gen _IS_LINEAR(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args.type==_VECT && args._VECTptr->size()==2){
vecteur & v = *args._VECTptr;
gen a,b;
if (v[1].type==_IDNT && is_linear_wrt(v[0],v[1],a,b,contextptr))
return makevecteur(eval(a,eval_level(contextptr),contextptr),eval(b, eval_level(contextptr),contextptr));
else
return 0;
}
return gentypeerr(contextptr);
// return 0;
}
static const char _IS_LINEAR_s[]="LINEAR?";
static define_unary_function_eval_quoted (__IS_LINEAR,&giac::_IS_LINEAR,_IS_LINEAR_s);
define_unary_function_ptr5( at_IS_LINEAR ,alias_at_IS_LINEAR,&__IS_LINEAR,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
static const char _FNROOT_s[]="FNROOT";
static define_unary_function_eval (__FNROOT,&giac::_fsolve,_FNROOT_s);
define_unary_function_ptr5( at_FNROOT ,alias_at_FNROOT,&__FNROOT,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
gen _SVD(const gen & args0,GIAC_CONTEXT){
if ( args0.type==_STRNG && args0.subtype==-1) return args0;
if (!ckmatrix(args0))
return gentypeerr(contextptr);
if (!has_num_coeff(args0))
*logptr(contextptr) << gettext("SVD is implemented for numeric matrices, running evalf first") << endl;
gen args=evalf(args0,1,contextptr);
gen res= _svd(gen(makevecteur(args,-1),_SEQ__VECT),contextptr);
if (res.type==_VECT) res.subtype=_LIST__VECT;
return res;
}
static const char _SVD_s[]="SVD";
static define_unary_function_eval (__SVD,&giac::_SVD,_SVD_s); // FIXME
define_unary_function_ptr5( at_SVD ,alias_at_SVD,&__SVD,0,T_UNARY_OP_38);
gen _SVL(const gen & args0,GIAC_CONTEXT){
if ( args0.type==_STRNG && args0.subtype==-1) return args0;
if (!ckmatrix(args0))
return gentypeerr(contextptr);
gen args=evalf(args0,1,contextptr);
return _svd(gen(makevecteur(args,-2),_SEQ__VECT),contextptr);
}
static const char _SVL_s[]="SVL";
static define_unary_function_eval (__SVL,&giac::_SVL,_SVL_s);
define_unary_function_ptr5( at_SVL ,alias_at_SVL,&__SVL,0,T_UNARY_OP_38);
static const char _svl_s[]="svl";
static define_unary_function_eval (__svl,&giac::_SVL,_svl_s);
define_unary_function_ptr5( at_svl ,alias_at_svl,&__svl,0,T_UNARY_OP);
gen _SPECRAD(const gen & args0,GIAC_CONTEXT){
if ( args0.type==_STRNG && args0.subtype==-1) return args0;
gen args=evalf(args0,1,contextptr);
if (!is_squarematrix(args))
return gentypeerr(contextptr);
vecteur v=megvl(*args._VECTptr,contextptr);
if (is_undef(v)) return v;
gen res,tmp;
int s=int(v.size());
for (int i=0;i<s;++i){
tmp=abs(v[i],contextptr);
if (ck_is_strictly_greater(tmp,res,contextptr))
res=tmp;
}
return res;
}
static const char _SPECRAD_s[]="SPECRAD";
static define_unary_function_eval (__SPECRAD,&giac::_SPECRAD,_SPECRAD_s); // FIXME
define_unary_function_ptr5( at_SPECRAD ,alias_at_SPECRAD,&__SPECRAD,0,T_UNARY_OP_38);
gen _SPECNORM(const gen & args0,GIAC_CONTEXT){
if ( args0.type==_STRNG && args0.subtype==-1) return args0;
gen args=evalf(args0,1,contextptr);
if (!ckmatrix(args)){
if (args.type==_VECT)
return _l2norm(args,contextptr);
return gentypeerr(contextptr);
}
return _max(_SVL(*args._VECTptr,contextptr),contextptr);
}
static const char _SPECNORM_s[]="SPECNORM";
static define_unary_function_eval (__SPECNORM,&giac::_SPECNORM,_SPECNORM_s); // FIXME
define_unary_function_ptr5( at_SPECNORM ,alias_at_SPECNORM,&__SPECNORM,0,T_UNARY_OP_38);
gen _COND(const gen & args0,GIAC_CONTEXT){
if ( args0.type==_STRNG && args0.subtype==-1) return args0;
// COND(matrix,2) L2norm condition number
// otherwise COLNORM(args0)*COLNORM(inv(args0))
if (args0.type==_VECT && args0._VECTptr->size()==2){
if (args0._VECTptr->back()==1)
return _COND(args0._VECTptr->front(),contextptr);
if (args0._VECTptr->back()==2){
gen args=args0._VECTptr->front();
if (!ckmatrix(args))
return gentypeerr(contextptr);
double save_eps=epsilon(contextptr);
epsilon(0.0,contextptr); // otherwise small singular values are cancelled and condition is infinity
gen g=_SVL(args,contextptr);
epsilon(save_eps,contextptr);
if (is_undef(g)) return g;
if (g.type!=_VECT)
return undef;
vecteur & v =*g._VECTptr;
int s=int(v.size());
gen mina(plus_inf),maxa(0);
for (int i=0;i<s;++i){
gen tmp=abs(v[i],contextptr);
if (ck_is_strictly_greater(mina,tmp,contextptr))
mina=tmp;
if (ck_is_strictly_greater(tmp,maxa,contextptr))
maxa=tmp;
}
return maxa/mina;
}
if (is_inf(args0._VECTptr->back())){
gen args=evalf(args0._VECTptr->front(),1,contextptr);
if (!is_squarematrix(args))
return gensizeerr(contextptr);
gen invargs=inv(args,contextptr);
if (is_undef(invargs))
return undef;
return _rowNorm(args,contextptr)*_rowNorm(invargs,contextptr);
}
}
gen args=evalf(args0,1,contextptr);
if (!is_squarematrix(args))
return gensizeerr(contextptr);
gen invargs=inv(args,contextptr);
if (is_undef(invargs))
return undef;
return _colNorm(args,contextptr)*_colNorm(invargs,contextptr);
// return _colNorm(args,contextptr)*_rowNorm(args,contextptr)/abs(_det(args,contextptr),contextptr);
}
static const char _COND_s[]="COND";
static define_unary_function_eval (__COND,&giac::_COND,_COND_s); // FIXME
define_unary_function_ptr5( at_COND ,alias_at_COND,&__COND,0,T_UNARY_OP_38);
static const char _cond_s[]="cond";
static define_unary_function_eval (__cond,&giac::_COND,_cond_s); // FIXME
define_unary_function_ptr5( at_cond ,alias_at_cond,&__cond,0,T_UNARY_OP);
gen _SCHUR(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
gen res;
if (ckmatrix(args)){
if (!is_squarematrix(args))
return gendimerr(contextptr);
#ifdef HAVE_LIBMPFR
res= _hessenberg(gen(makevecteur(args,epsilon(contextptr)),_SEQ__VECT),contextptr);
#else
res= _hessenberg(gen(makevecteur(args,1e-12),_SEQ__VECT),contextptr);
#endif
}
else
res= _hessenberg(args,contextptr);
if (res.type==_VECT) res.subtype=_LIST__VECT;
return res;
}
static const char _SCHUR_s[]="SCHUR";
static define_unary_function_eval (__SCHUR,&giac::_SCHUR,_SCHUR_s); // FIXME
define_unary_function_ptr5( at_SCHUR ,alias_at_SCHUR,&__SCHUR,0,T_UNARY_OP_38);
static const char _schur_s[]="schur";
static define_unary_function_eval (__schur,&giac::_SCHUR,_schur_s); // FIXME
define_unary_function_ptr5( at_schur ,alias_at_schur,&__schur,0,T_UNARY_OP);
gen _LQ(const gen & args0,GIAC_CONTEXT){
if ( args0.type==_STRNG && args0.subtype==-1) return args0;
gen args=evalf(args0,1,contextptr);
if (!ckmatrix(args))
return gentypeerr(contextptr);
gen res=qr(makevecteur(_trn(args,contextptr),-1),contextptr);
if (is_undef(res) || res.type!=_VECT || res._VECTptr->size()<3)
return gensizeerr(contextptr);
vecteur v(*res._VECTptr);
v[0]=_trn(v[0],contextptr);
v[1]=_trn(v[1],contextptr);
swapgen(v[0],v[1]);
// v[2]=midn(v[0]._VECTptr->size());
return gen(v,_LIST__VECT);
}
static const char _LQ_s[]="LQ";
static define_unary_function_eval (__LQ,&giac::_LQ,_LQ_s);
define_unary_function_ptr5( at_LQ ,alias_at_LQ,&__LQ,0,T_UNARY_OP_38);
static const char _RREF_s[]="RREF";
static define_unary_function_eval (__RREF,&giac::_rref,_RREF_s); // FIXME
define_unary_function_ptr5( at_RREF ,alias_at_RREF,&__RREF,0,T_UNARY_OP_38);
gen _XPON(const gen & g0,GIAC_CONTEXT){
if (g0.type==_STRNG && g0.subtype==-1) return g0;
if (is_equal(g0))
return apply_to_equal(g0,_XPON,contextptr);
if (g0.type==_VECT)
return apply(g0,_XPON,contextptr);
#if 0 // def BCD
gen g=evalf2bcd(g0,1,contextptr);
#else
gen g=evalf_double(g0,1,contextptr);
#endif
if (is_exactly_zero(g))
return undef;
gen gf=_floor(log10(abs(g,contextptr),contextptr),contextptr);
if (gf.type!=_INT_ && gf.type!=_FLOAT_)
return gensizeerr(contextptr);
return gf;
}
static const char _XPON_s[]="XPON";
static define_unary_function_eval (__XPON,&giac::_XPON,_XPON_s); // FIXME
define_unary_function_ptr5( at_XPON ,alias_at_XPON,&__XPON,0,T_UNARY_OP_38);
gen mantissa(const gen & g0,bool includesign,GIAC_CONTEXT){
#if 0 // def BCD
gen g=evalf2bcd(g0,1,contextptr);
#else
gen g=evalf_double(g0,1,contextptr);
#endif
if (is_exactly_zero(g))
return g;
gen gabs=abs(g,contextptr);
gen gf=_floor(log10(gabs,contextptr),contextptr);
if (abs_calc_mode(contextptr)!=38 && gf.type!=_INT_)
return gensizeerr(contextptr);
// FIXME number of digits
return (includesign?sign(g,contextptr):1)*evalf(gabs*alog10(-gf,contextptr),1,contextptr);
}
gen _MANT(const gen & g0,GIAC_CONTEXT){
if (g0.type==_STRNG && g0.subtype==-1) return g0;
if (is_equal(g0))
return apply_to_equal(g0,_MANT,contextptr);
if (g0.type==_VECT)
return apply(g0,_MANT,contextptr);
return mantissa(g0,true,contextptr);
}
static const char _MANT_s[]="MANT";
static define_unary_function_eval (__MANT,&giac::_MANT,_MANT_s);
define_unary_function_ptr5( at_MANT ,alias_at_MANT,&__MANT,0,T_UNARY_OP_38);
gen _mantissa(const gen & g0,GIAC_CONTEXT){
if (g0.type==_STRNG && g0.subtype==-1) return g0;
if (is_equal(g0))
return apply_to_equal(g0,_mantissa,contextptr);
if (g0.type==_VECT)
return apply(g0,_mantissa,contextptr);
return mantissa(g0,false,contextptr);
}
static const char _mantissa_s[]="mantissa";
static define_unary_function_eval (__mantissa,&giac::_mantissa,_mantissa_s);
define_unary_function_ptr5( at_mantissa ,alias_at_mantissa,&__mantissa,0,T_UNARY_OP);
gen _HMSX(const gen & g0,GIAC_CONTEXT){
if ( g0.type==_STRNG && g0.subtype==-1) return g0;
if (g0.type==_VECT)
return apply(g0,_HMSX,contextptr);
gen g(evalf(g0,1,contextptr));
if (g.type==_DOUBLE_)
g = g+1e-12;
if (g.type==_FLOAT_)
g = g+plus_one/20000;
if (g.type!=_DOUBLE_ && g.type!=_FLOAT_)
return gentypeerr(contextptr);
gen h=_floor(g,contextptr);
gen m=_floor(100*(g-h),contextptr);
gen s=_floor(100*(100*(g-h)-m),contextptr);
return h+m/giac_float(60.)+s/giac_float(3600.);
}
static const char _HMSX_s[]="HMSX";
static define_unary_function_eval (__HMSX,&giac::_HMSX,_HMSX_s);
define_unary_function_ptr5( at_HMSX ,alias_at_HMSX,&__HMSX,0,T_UNARY_OP_38);
gen _XHMS(const gen & g0,GIAC_CONTEXT){
if ( g0.type==_STRNG && g0.subtype==-1) return g0;
if (g0.type==_VECT)
return apply(g0,_XHMS,contextptr);
gen g(evalf(g0,1,contextptr));
if (g.type==_DOUBLE_)
g = g+1e-12;
if (g.type==_FLOAT_)
g=g+plus_one/7200;
if (g.type!=_DOUBLE_ && g.type!=_FLOAT_)
return gentypeerr(contextptr);
gen h=_floor(g,contextptr);
gen m=_floor(60*(g-h),contextptr);
gen s=_floor(60*(60*(g-h)-m),contextptr);
return h+m/giac_float(100.)+s/giac_float(10000.);
}
static const char _XHMS_s[]="XHMS";
static define_unary_function_eval (__XHMS,&giac::_XHMS,_XHMS_s);
define_unary_function_ptr5( at_XHMS ,alias_at_XHMS,&__XHMS,0,T_UNARY_OP_38);
gen _DEGXRAD(const gen & g,GIAC_CONTEXT){
if ( g.type==_STRNG && g.subtype==-1) return g;
if (g.type==_VECT)
return apply(g,_DEGXRAD,contextptr);
return deg2rad_d*g;
}
static const char _DEGXRAD_s[]="DEGXRAD";
static define_unary_function_eval (__DEGXRAD,&giac::_DEGXRAD,_DEGXRAD_s);
define_unary_function_ptr5( at_DEGXRAD ,alias_at_DEGXRAD,&__DEGXRAD,0,T_UNARY_OP_38);
gen _RADXDEG(const gen & g,GIAC_CONTEXT){
if ( g.type==_STRNG && g.subtype==-1) return g;
if (g.type==_VECT)
return apply(g,_RADXDEG,contextptr);
return rad2deg_d*g;
}
static const char _RADXDEG_s[]="RADXDEG";
static define_unary_function_eval (__RADXDEG,&giac::_RADXDEG,_RADXDEG_s);
define_unary_function_ptr5( at_RADXDEG ,alias_at_RADXDEG,&__RADXDEG,0,T_UNARY_OP_38);
gen _PERCENT(const gen & g,GIAC_CONTEXT){
if ( g.type==_STRNG && g.subtype==-1) return g;
if (g.type!=_VECT || g._VECTptr->size()!=2)
return gentypeerr(contextptr);
return g._VECTptr->front()*g._VECTptr->back()/giac_float(100.);
}
static const char _PERCENT_s[]="%"; // FIXE
static define_unary_function_eval (__PERCENT,&giac::_PERCENT,_PERCENT_s);
define_unary_function_ptr5( at_PERCENT ,alias_at_PERCENT,&__PERCENT,0,T_UNARY_OP_38);
gen _PERCENTCHANGE(const gen & g,GIAC_CONTEXT){
if ( g.type==_STRNG && g.subtype==-1) return g;
if (g.type!=_VECT || g._VECTptr->size()!=2)
return gentypeerr(contextptr);
return giac_float(100.)*(g._VECTptr->back()-g._VECTptr->front())/g._VECTptr->front();
}
static const char _PERCENTCHANGE_s[]="%CHANGE";
static define_unary_function_eval (__PERCENTCHANGE,&giac::_PERCENTCHANGE,_PERCENTCHANGE_s);
define_unary_function_ptr5( at_PERCENTCHANGE ,alias_at_PERCENTCHANGE,&__PERCENTCHANGE,0,T_UNARY_OP_38);
gen _PERCENTTOTAL(const gen & g,GIAC_CONTEXT){
if ( g.type==_STRNG && g.subtype==-1) return g;
if (g.type!=_VECT || g._VECTptr->size()!=2)
return gentypeerr(contextptr);
return giac_float(100.)*g._VECTptr->back()/g._VECTptr->front();
}
static const char _PERCENTTOTAL_s[]="%TOTAL";
static define_unary_function_eval (__PERCENTTOTAL,&giac::_PERCENTTOTAL,_PERCENTTOTAL_s);
define_unary_function_ptr5( at_PERCENTTOTAL ,alias_at_PERCENTTOTAL,&__PERCENTTOTAL,0,T_UNARY_OP_38);
gen _DISP(const gen & g,GIAC_CONTEXT){
if (g.type!=_VECT || g._VECTptr->size()!=2)
return gensizeerr(contextptr);
gen a=g._VECTptr->front();
if (a.type!=_INT_ || a.val <0 || a.val>10)
setdimerr(contextptr);
gen b=g._VECTptr->back();
return _legende(gen(makevecteur(makevecteur(0,a*gen(12)),b),_SEQ__VECT),contextptr);
}
static const char _DISP_s []="DISP";
static define_unary_function_eval_quoted (__DISP,&giac::_DISP,_DISP_s);
define_unary_function_ptr5( at_DISP ,alias_at_DISP,&__DISP,0,T_UNARY_OP_38);
static const char _WAIT_s []="WAIT";
static define_unary_function_eval (__WAIT,&giac::_Pause,_WAIT_s);
define_unary_function_ptr5( at_WAIT ,alias_at_WAIT,&__WAIT,0,T_UNARY_OP_38);
#if 0 // def GIAC_HAS_STO_38
gen aspen_input(const vecteur & v,GIAC_CONTEXT);
gen aspen_msgbox(const vecteur & v,GIAC_CONTEXT);
#endif
// INPUT(A) or INPUT(A,"title") or INPUT(A,"title","label") or INPUT(A,"title","label","help")
// or INPUT(A,"title","label","help",default_value)
gen _INPUT(const gen & args,GIAC_CONTEXT){
vecteur v=gen2vecteur(args);
int s=int(v.size());
if (s==1){
v.push_back(string2gen("Input"));
++s;
}
if (s==2){
v.push_back(string2gen(v[0].print(contextptr),false));
++s;
}
if (s==3){
v.push_back(string2gen("Enter value for "+v[0].print(contextptr),false));
++s;
}
// check types
if (v[0].is_symb_of_sommet(at_double_deux_points) && v[0]._SYMBptr->feuille.type==_VECT && v[0]._SYMBptr->feuille._VECTptr->size()==2)
v[0]=v[0]._SYMBptr->feuille._VECTptr->back();
for (int i=1; i<=3; i++) { if (v[i].type!=_STRNG) v[i]= eval(v[i], 1, contextptr); if (v[i].type!=_STRNG) v[i]= string2gen(v[i].print(contextptr)); }
if (v[0].type!=_IDNT || s>5)
return gentypeerr(contextptr);
// set default value in v[0]
if (s==5){
gen tmpsto=sto(v[4],v[0],contextptr);
if (is_undef(tmpsto)) return tmpsto;
v.pop_back();
s=4;
}
#if 0 // def GIAC_HAS_STO_38
return aspen_input(v,contextptr);
#else
// now make a dialog
v[1]=symbolic(at_Title,v[1]);
v[2]=symbolic(at_Request,makesequence(v[2],v[0]));
v[3]=symbolic(at_Text,v[3]);
v.erase(v.begin());
return _Dialog(gen(v,_SEQ__VECT),contextptr);
#endif
}
static const char _INPUT_s []="INPUT";
static define_unary_function_eval_quoted (__INPUT,giac::_INPUT,_INPUT_s);
define_unary_function_ptr5( at_INPUT ,alias_at_INPUT,&__INPUT,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
#if 0 // def GIAC_HAS_STO_38
// MSGBOX(txt) or MSGBOX(txt, true/false) to have OK/Cancel or just OK menus
gen _MSGBOX(const gen & args,GIAC_CONTEXT){
vecteur v=gen2vecteur(args);
int s=int(v.size());
if (s==1) { v.push_back(gen(0)); ++s; }
return aspen_msgbox(v,contextptr);
}
#else
gen _MSGBOX(const gen & args,GIAC_CONTEXT){
return _output(args,contextptr);
}
#endif
static const char _MSGBOX_s []="MSGBOX";
static define_unary_function_eval (__MSGBOX,giac::_MSGBOX,_MSGBOX_s);
define_unary_function_ptr5( at_MSGBOX ,alias_at_MSGBOX,&__MSGBOX,0,T_UNARY_OP_38);
static const char _GETKEY_s[]="GETKEY";
#if 0 // def GIAC_HAS_STO_38
static define_unary_function_eval(__GETKEY,&at_GETKEYAspen,_GETKEY_s);
// unary_function_eval __GETKEY(0,&at_GETKEYAspen,_GETKEY_s);
#else
unary_function_eval __GETKEY(0,&_getKey,_GETKEY_s);
#endif
define_unary_function_ptr5( at_GETKEY ,alias_at_GETKEY,&__GETKEY,0,T_UNARY_OP_38);
gen _ITERATE(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args.type!=_VECT || args._VECTptr->size()!=4)
return gentypeerr(contextptr);
vecteur v = plotpreprocess(args,contextptr);
gen v0=v[0];
gen v1=v[1];
// v[2]=eval(v[2],eval_level(contextptr),contextptr);
// v[3]=eval(v[3],eval_level(contextptr),contextptr);
if (v[3].type!=_INT_)
return gentypeerr(contextptr);
int n=v[3].val;
bool all=n<0;
if (all){
n=-n;
if (n>LIST_SIZE_LIMIT)
return gendimerr(contextptr);
}
gen value=v[2];
vecteur res;
if (all)
res=vecteur(n+1,value);
for (int i=0;!ctrl_c && !interrupted && i<n;++i){
#ifdef TIMEOUT
control_c();
#endif
value=evalf(subst(v0,v1,value,false,contextptr),eval_level(contextptr),contextptr);
if (is_undef(value))
return value;
if (all)
res[i+1]=value;
}
return all?res:value;
}
static const char _ITERATE_s[]="ITERATE";
static define_unary_function_eval_quoted (__ITERATE,&_ITERATE,_ITERATE_s);
define_unary_function_ptr5( at_ITERATE ,alias_at_ITERATE,&__ITERATE,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
#ifndef GIAC_HAS_STO_38
gen _RECURSE(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args.type!=_VECT || args._VECTptr->size()<2)
return gentypeerr(contextptr);
vecteur v = *args._VECTptr;
gen v0=v[0];
gen v1=v[1];
int s=int(v.size());
for (int i=2;i<s;++i)
v[i]=eval(v[i],eval_level(contextptr),contextptr);
if (v[0].type!=_IDNT)
return _rsolve(gen(v,args.subtype),contextptr);
// HP38 syntax, define recurrent sequence
// idnt, expression, first term, second term
// e.g. RECURSE(U,U(N-1)*N,1,2) STO> U1(N)
return gentypeerr(contextptr);
return undef;
}
static const char _RECURSE_s[]="RECURSE";
static define_unary_function_eval_quoted (__RECURSE,&_RECURSE,_RECURSE_s);
define_unary_function_ptr5( at_RECURSE ,alias_at_RECURSE,&__RECURSE,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
#endif
gen _MAKEMAT(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args.type!=_VECT || args._VECTptr->size()!=3)
return gentypeerr(contextptr);
vecteur v = *args._VECTptr;
gen v0=v[0];
gen v1=eval(v[1],eval_level(contextptr),contextptr);
gen v2=eval(v[2],eval_level(contextptr),contextptr);
is_integral(v1);
is_integral(v2);
if (v1.type!=_INT_ || v2.type!=_INT_ || v1.val<1 || v2.val<1)
return gensizeerr(contextptr);
int l=giacmax(v1.val,1),c=giacmax(v2.val,1);
if (longlong(l)*c>LIST_SIZE_LIMIT)
return gendimerr(contextptr);
identificateur idI("I"),idJ("J");
vecteur IJ=makevecteur(idI,idJ);
vecteur IJval(2),res;
for (int i=1;i<=l;++i){
vecteur ligne(c);
IJval[0]=i;
for (int j=1;j<=c;++j){
IJval[1]=j;
ligne[j-1]=eval(subst(v0,IJ,IJval,false,contextptr),eval_level(contextptr),contextptr);
}
res.push_back(ligne);
}
return res;
}
static const char _MAKEMAT_s[]="MAKEMAT";
static define_unary_function_eval_quoted (__MAKEMAT,&_MAKEMAT,_MAKEMAT_s);
define_unary_function_ptr5( at_MAKEMAT ,alias_at_MAKEMAT,&__MAKEMAT,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
// For over-determined system, find the solution such that || A*X-B || (L2) is min
// for under-determined system, find a solution X of A*X=B such that ||X|| is min
gen _LSQ(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args.type!=_VECT || args._VECTptr->size()<2)
return gentypeerr(contextptr);
vecteur v = *args._VECTptr;
gen v0=v[0]; // evalf(v[0],1,contextptr)
gen v1=v[1];
int vs=int(v.size());
if (vs==3){
v.push_back(vecteur(0));
++vs;
}
if (vs==4){
gen v2=v[2],v3=v[3];
if (v0.type==_VECT && v1.type==_VECT && !v0._VECTptr->empty() && v0._VECTptr->size()==v1._VECTptr->size() && v2.type==_VECT && v3.type==_VECT){
// v0=list of values of x or of [x,y,...], v1= observed value at x,
// v2=v[vs-2]=list of expressions f_i(x) or f_i(x,y) or [f_i(vars)],[vars]
// v3=v.back()=list of constraints = list of
// [X_k,n_k (number of derivatives), Y_k=value of n_k-th diff at X_k]
// or [[X_k,Y_k,...],[n_k],value]
// minimize sum_j=1..N (y_j-sum_i=1..M(a_i*f_i(x_j),i))^2
// under sum_i=1..M a_i*diff(f_i,n_k)(X_k) = 0 for k=1..K
vecteur expr(*v2._VECTptr),constraints(*v3._VECTptr);
if (!constraints.empty() && constraints.front().type!=_VECT)
constraints=vecteur(1,constraints);
if (!constraints.empty() && (!ckmatrix(constraints) || constraints.front()._VECTptr->size()!=3))
return gensizeerr(contextptr);
vecteur & x=*v0._VECTptr;
vecteur & y=*v1._VECTptr;
unsigned M=unsigned(expr.size()), K=unsigned(constraints.size()),N=unsigned(v0._VECTptr->size());
vecteur vars(1,x__IDNT_e);
int dim=2;
if (x.front().type==_VECT){
if (!ckmatrix(x))
return gensizeerr(contextptr);
dim=int(x.front()._VECTptr->size())+1;
if (dim<2)
return gendimerr(contextptr);
}
if (dim==3)
vars.push_back(y__IDNT_e);
if (expr.front().type==_VECT){
if (M!=2 || expr.back().type!=_VECT)
return gensizeerr(contextptr);
vars=*expr.back()._VECTptr;
if (int(vars.size())!=dim-1)
return gendimerr(contextptr);
expr=*expr.front()._VECTptr;
M=unsigned(expr.size());
}
else {
if (dim>3)
return gendimerr(contextptr);
}
// F_{i,j}=f_i(x_j)
matrice F; // M rows, N cols
for (unsigned i=0;i<M;++i){
gen fi=expr[i];
vecteur ligne;
for (unsigned j=0;j<N;++j){
ligne.push_back(subst(fi,vars,gen2vecteur(x[j]),false,contextptr));
}
F.push_back(ligne);
}
// dF_{i,k}=diff(f_i,n_k)(X_k)
matrice dF; // M rows, K cols
for (unsigned i=0;i<M;++i){
gen fi=expr[i];
vecteur ligne;
for (unsigned k=0;k<K;++k){
gen nk=constraints[k][1];
gen tmp=derive(fi,vars,gen2vecteur(nk),contextptr);
ligne.push_back(subst(tmp,vars,gen2vecteur(constraints[k][0]),false,contextptr));
}
dF.push_back(ligne);
}
matrice mat; // M+K rows, M+K+1 cols
// first M equations of linear system: for l=1..M
// sum_i=1..M a_i*sum_j=1..N f_l(x_j)*f_i(x_j) + sum_k=1..K lagrange_k*diff(f_l,n_k)(X_k) = sum_j=1..N f_l(x_j)*y_j
for (unsigned l=0;l<M;++l){
vecteur ligne;
for (unsigned i=0;i<M;++i){
gen tmp=0;
for (unsigned j=0;j<N;++j)
tmp += F[l][j]*F[i][j];
ligne.push_back(tmp);
}
for (unsigned k=0;k<K;++k){
ligne.push_back(dF[l][k]);
}
gen tmp=0;
for (unsigned j=0;j<N;++j){
tmp += F[l][j]*y[j];
}
ligne.push_back(tmp);
mat.push_back(ligne);
}
// last K equations
// sum_i=1..M a_i*diff(f_i,n_k)(X_k)=Y_k
// giving a (M+K,M+K) matrix -> linsolve, first M coordinates
// -> sum_i=1..M a_i f_i(x)
for (unsigned k=0;k<K;++k){
vecteur ligne(M+K+1);
ligne[M+K]=constraints[k][2];
for (unsigned i=0;i<M;++i){
ligne[i]=dF[i][k];
}
mat.push_back(ligne);
}
// now solve linear system
vecteur res=mker(mat,contextptr);
if (res.size()!=1 || res.front().type!=_VECT || res.front()._VECTptr->size()!=M+K+1)
return gensizeerr("Singular linear system");
vecteur Res=*res.front()._VECTptr;
res=vecteur(Res.begin(),Res.begin()+M);
return gen(res);
}
else
return gensizeerr(contextptr);
}
if (!ckmatrix(v0) || v1.type!=_VECT)
return gentypeerr(contextptr);
int neq=int(v0._VECTptr->size()); // neq equations
v0=_trn(v0,contextptr);
matrice A=*v0._VECTptr,B;
if (ckmatrix(v1))
B=gen2vecteur(_trn(v1,contextptr));
else
B=vecteur(1,v1);
if (int(B[0]._VECTptr->size())!=neq)
return gendimerr(contextptr);
int as=int(A.size()),bs=int(B.size());
// bs system to solve, each with neq equations and as variables
if (as>neq){ // under-determined system, find the smallest solution
if (has_num_coeff(A)){
// QR factorization of A=trn(system matrix)
// R_1=neq first rows of R
// Q_1=neq first cols of Q
// solve R_1^* c = B[i] then output Q_1*c
gen qrdec=qr(A,contextptr);
if (qrdec.type==_VECT && qrdec._VECTptr->size()==2){
gen q=qrdec._VECTptr->front(),r=qrdec._VECTptr->back();
if (ckmatrix(q) && ckmatrix(r)){
if (!is_zero(r[neq-1])){
vecteur R(r._VECTptr->begin(),r._VECTptr->begin()+neq);
r=mtran(R);
R=*r._VECTptr;
vecteur qt=mtran(*q._VECTptr);
matrice res;
qt=vecteur(qt.begin(),qt.begin()+neq);
qt=mtran(qt);
for (int i=0;i<bs;++i){
gen Bi=B[i];
vecteur v,w;
linsolve_l(R,*Bi._VECTptr,v);
multmatvecteur(qt,v,w);
res.push_back(w);
}
return mtran(res);
}
}
}
}
// not optimal since we solve the system for each Bi
A.push_back(0);
matrice res;
for (int i=0;i<bs;++i){
gen Bi=B[i];
A[as]=Bi;
matrice At=gen2vecteur(_trn(A,contextptr));
vecteur B=mker(At,contextptr);
if (is_undef(B) || B.empty())
return undef;
// The last element of B must have a non-zero last component
vecteur Bend=*B.back()._VECTptr;
gen last=-Bend.back();
if (is_zero(last))
return vecteur(0);
vecteur R=divvecteur(Bend,last);
R.pop_back();
B.pop_back();
int Bs=int(B.size());
for (int j=0;j<Bs;j++)
B[j]._VECTptr->pop_back();
// The solution is R+Vect(B[0],..,B[Bs-1])
// the smallest solution is the orthogonal projection of 0 on R+Vect(B)
// i.e. R + projection of -R on Vect(B)
matrice r,Bg=gramschmidt(B,r,false,contextptr);
gen Rtmp(R);
for (int j=0;j<Bs;++j){
Rtmp -= dotvecteur(Bg[j],R)/dotvecteur(Bg[j],Bg[j])*Bg[j];
}
res.push_back(Rtmp);
}
res=gen2vecteur(_trn(res,contextptr));
return res;
}
matrice res;
if (has_num_coeff(v)){
// <Ax-b|Ax-b> minimal, i.e. A* Ax=A* b or
// A=QR, if A has m rows and n cols and m>=n, then Q is m*m and R is m*n
// first n cols of Q are Q1, first n rows of R are R1
// solve R1*x=Q1^t*b
gen qrdec=qr(v[0],contextptr);
if (qrdec.type==_VECT && qrdec._VECTptr->size()==2){
gen q=qrdec._VECTptr->front(),r=qrdec._VECTptr->back();
if (ckmatrix(q) && ckmatrix(r)){
if (!is_zero(r[int(A.size())-1])){
gen qt=_trn(q,contextptr);
vecteur R(r._VECTptr->begin(),r._VECTptr->begin()+A.size());
for (int i=0;i<bs;++i){
gen Bi=B[i];
vecteur v;
linsolve_u(R,multmatvecteur(*qt._VECTptr,*Bi._VECTptr),v);
res.push_back(v);
}
return mtran(res);
}
// A* Ax=A* b => R* Rx=R* Qb
gen rstar=_trn(r,contextptr);
gen rr=rstar*r;
gen rq=rstar*q*B;
return _linsolve(makesequence(rr,rq),contextptr);
}
}
}
// orthogonal projection of each vector of B on image of A
if (A.size()>20)
*logptr(contextptr) << "LSQ: exact data, running Gramschmidt instead of qr, this is much slower for large matrices" << endl;
matrice r,Ag=gramschmidt(A,r,false,contextptr);
for (int i=0;i<bs;++i){
gen Bi=B[i];
vecteur tmp(as);
for (int j=0;j<as;++j){
tmp[j] = scalar_product(Ag[j],Bi,contextptr)/scalar_product(Ag[j],Ag[j],contextptr);
}
res.push_back(tmp);
}
res=gen2vecteur(_trn(res,contextptr));
return mmult(*inv(r,contextptr)._VECTptr,res);
}
static const char _LSQ_s[]="LSQ";
static define_unary_function_eval (__LSQ,&_LSQ,_LSQ_s);
define_unary_function_ptr5( at_LSQ ,alias_at_LSQ,&__LSQ,0,T_UNARY_OP_38);
static const char _lsq_s []="lsq";
static define_unary_function_eval (__lsq,&_LSQ,_lsq_s);
define_unary_function_ptr5( at_lsq ,alias_at_lsq,&__lsq,0,true);
static string printasNTHROOT(const gen & feuille,const char * sommetstr,GIAC_CONTEXT){
if (feuille.type==_VECT && feuille._VECTptr->size()==2 && abs_calc_mode(contextptr)!=38)
return "surd("+feuille[1].print(contextptr)+","+feuille[0].print(contextptr)+")";
// return '('+(printsommetasoperator(feuille," NTHROOT ",contextptr))+')';
return printsommetasoperator(feuille," NTHROOT ",contextptr);
}
static string texprintasNTHROOT(const gen & g,const char * s,GIAC_CONTEXT){
return texprintsommetasoperator(g,"\\mbox{ NTHROOT }",contextptr);
}
gen _NTHROOT(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args.type!=_VECT || args._VECTptr->size()!=2)
return gensizeerr(contextptr);
return _surd(gen(makevecteur(args._VECTptr->back(),args._VECTptr->front()),_SEQ__VECT),contextptr);
}
static const char _NTHROOT_s[]="NTHROOT";
static define_unary_function_eval4 (__NTHROOT,&_NTHROOT,_NTHROOT_s,&printasNTHROOT,&texprintasNTHROOT);
define_unary_function_ptr5( at_NTHROOT ,alias_at_NTHROOT,&__NTHROOT,0,T_POW);
#ifndef GIAC_HAS_STO_38
gen * rpn_ans(){
return 0;
}
#endif
gen _Ans(const gen & args,GIAC_CONTEXT){
if (rpn_ans())
return *rpn_ans();
return _ans(0,contextptr);
}
static const char _Ans_s[]="Ans";
static string printasAns(const gen & feuille,const char * sommetstr,GIAC_CONTEXT){
return _Ans_s;
}
static define_unary_function_eval2 (__Ans,&_Ans,_Ans_s,&printasAns);
define_unary_function_ptr5( at_Ans ,alias_at_Ans,&__Ans,0,T_LITERAL);
gen _EXPORT_(const gen & args,GIAC_CONTEXT){
// eval sto only
vecteur v =gen2vecteur(args);
int nsto=0,s=int(v.size());
for (int i=0;i<s;++i){
if (v[i].is_symb_of_sommet(at_sto)){
++nsto;
eval(v[i],1,contextptr);
}
}
return nsto;
}
static const char _EXPORT__s[]="EXPORT";
static define_unary_function_eval (__EXPORT_,&_EXPORT_,_EXPORT__s);
define_unary_function_ptr5( at_EXPORT ,alias_at_EXPORT_,&__EXPORT_,_QUOTE_ARGUMENTS,T_RETURN);
gen _VIEWS(const gen & args,GIAC_CONTEXT){
return _EXPORT_(args,contextptr);
}
static const char _VIEWS_s[]="VIEWS";
static define_unary_function_eval (__VIEWS,&_VIEWS,_VIEWS_s);
define_unary_function_ptr5( at_VIEWS ,alias_at_VIEWS,&__VIEWS,_QUOTE_ARGUMENTS,T_RETURN);
#ifdef USE_GMP_REPLACEMENTS
unsigned long long mpz_get_ull(mpz_t n){
return 0; // FIXME!!!!
}
#else
unsigned long long mpz_get_ull(mpz_t n){
unsigned int lo, hi;
mpz_t tmp;
mpz_init( tmp );
mpz_mod_2exp( tmp, n, 64 ); /* tmp = (lower 64 bits of n) */
lo = mpz_get_ui( tmp ); /* lo = tmp & 0xffffffff */
mpz_div_2exp( tmp, tmp, 32 ); /* tmp >>= 32 */
hi = mpz_get_ui( tmp ); /* hi = tmp & 0xffffffff */
mpz_clear( tmp );
return (((unsigned long long)hi) << 32) + lo;
}
#endif
gen _pointer(const gen & args,GIAC_CONTEXT){
if (args.type!=_VECT || args._VECTptr->size()!=2)
return gensizeerr(contextptr);
if (args._VECTptr->back().type!=_INT_)
return gentypeerr(contextptr);
if (args._VECTptr->front().type==_INT_)
return gen((void *)(unsigned long)args._VECTptr->front().val, args._VECTptr->back().val);
if (args._VECTptr->front().type==_ZINT){
unsigned long u=mpz_get_ull(*args._ZINTptr);
return gen((void *)u,args._VECTptr->back().val);
}
return gentypeerr(contextptr);
}
static const char _pointer_s[]="pointer";
static define_unary_function_eval (__pointer,&_pointer,_pointer_s);
define_unary_function_ptr5( at_pointer ,alias_at_pointer,&__pointer,0,T_UNARY_OP);
int is_known_name_home_38(const char * idname){
int s=int(strlen(idname));
if (s==1 && idname[0]>='A' && idname[0]<='Z')
return 3;
if (s==2 && !strcmp(idname,"θ"))
return 3;
if (s==2 && (idname[0]=='Z' || idname[0]=='L' || idname[0]=='M') && idname[1]>='0' && idname[1]<='9')
return 3;
return is_known_name_38?is_known_name_38(0,idname):0;
}
// 1 and 2 app or program variable, 3 home variable
int is_known_name_home_38(const char * name_space,const char * idname){
if (name_space)
return is_known_name_38?is_known_name_38(name_space,idname):0;
return is_known_name_home_38(idname);
}
static gen qualifysubst(const gen & g,const vecteur & vin,const vecteur & vout,GIAC_CONTEXT){
if (vin.empty()) return g;
if (g.type!=_VECT){
if (g.is_symb_of_sommet(at_sto)){
gen & f = g._SYMBptr->feuille;
if (f.type==_VECT && f._VECTptr->size()==2){
return symbolic(at_sto,gen(makevecteur(subst(f._VECTptr->front(),vin,vout,true,contextptr),f._VECTptr->back()),_SEQ__VECT));
}
}
return subst(g,vin,vout,true,contextptr);
}
const_iterateur it=g._VECTptr->begin(),itend=g._VECTptr->end();
vecteur res;
res.reserve(itend-it);
for (;it!=itend;++it)
res.push_back(qualifysubst(*it,vin,vout,contextptr));
return gen(res,g.subtype);
}
void qualify(gen & g,const vecteur & v,const gen & prog,GIAC_CONTEXT){
if (v.empty()) return;
vecteur w(v);
unsigned s=unsigned(v.size());
for (unsigned i=0;i<s;++i){
w[i]=symbolic(at_double_deux_points,gen(makevecteur(prog,w[i]),_SEQ__VECT));
}
g=subst(g,v,w,true,contextptr);
//g=qualifysubst(g,v,w,contextptr);
}
#if 0
// 0: ok, -1: invalid views, -2: invalid VIEWS/EXPORT declaration in a program
static int parse_program_decl(vecteur & assignation_by_equal,vecteur & undeclared_global_vars,vecteur & declared_global_vars,vecteur & declared_functions,vecteur & exported_function_names,vecteur & exported_variable_names,vecteur & unknown_exported,vecteur & unexported,vecteur & unexported_declared_global_vars,vecteur & views,vecteur & errors,const gen & prog,gen & parsed,GIAC_CONTEXT){
check_local_assign(parsed,vecteur(0),assignation_by_equal,undeclared_global_vars,declared_global_vars,declared_functions,true,contextptr);
vecteur vprog=lop(parsed,at_program);
if (!lop(vprog,at_VIEWS).empty() || !lop(vprog,at_EXPORT).empty())
return -2;
// views
vecteur vviews=lop(parsed,at_VIEWS);
iterateur vt=vviews.begin(),vtend=vviews.end();
for (;vt!=vtend;++vt){
gen & f = vt->_SYMBptr->feuille;
if (f.type==_VECT){
vecteur v=*f._VECTptr;
if (v.size()==2){
if (v.front().type==_STRNG)
reverse(v.begin(),v.end());
if (v.front().is_symb_of_sommet(at_sto))
v.front()=v.front()._SYMBptr->feuille[1];
views=mergevecteur(views,v);
}
else return -1;
}
}
// exported/unexported: declaration like export f,"help for f";
vecteur exported=lop(parsed,at_EXPORT),exported_names;
if (exported.empty()){
unexported=declared_functions;
}
else {
iterateur it=exported.begin(),itend=exported.end();
for (;it!=itend;++it){
gen & f = it->_SYMBptr->feuille;
if (f.type==_VECT){
vecteur v=*f._VECTptr;
if (!v.empty()){
if (v.front().type==_STRNG)
reverse(v.begin(),v.end());
if (v.front().is_symb_of_sommet(at_sto))
v.front()=v.front()._SYMBptr->feuille[1];
exported_names=mergevecteur(exported_names,v);
}
}
else {
exported_names.push_back(f.is_symb_of_sommet(at_sto)?f._SYMBptr->feuille[1]:f);
}
}
// check if exported functions are defined or exported variables declared
// check also that we do not redefine regular home variables
itend=exported_names.end();
// first replace function definition by function name
for (it=exported_names.begin();it!=itend;++it){
if (it->is_symb_of_sommet(at_sto)){
*it=it->_SYMBptr->feuille;
if (it->type==_VECT && it->_VECTptr->size()==2)
*it=it->_VECTptr->back();
}
}
for (it=exported_names.begin();it!=itend;++it){
if (it->type!=_STRNG){
if (equalposcomp(declared_functions,*it) && !equalposcomp(declared_global_vars,*it) && !equalposcomp(undeclared_global_vars,*it))
unknown_exported.push_back(*it);
if (it->type==_IDNT && is_known_name_home_38(it->_IDNTptr->id_name))
errors.push_back(*it);
}
}
it=declared_functions.begin(),itend=declared_functions.end();
for (;it!=itend;++it){
if (!equalposcomp(exported_names,*it))
unexported.push_back(*it);
}
}
// remove exported functions/views and variables from undeclared global vars
// check other: either home variables or put in errors
vecteur tmp;
tmp=undeclared_global_vars;
undeclared_global_vars.clear();
const_iterateur jt=tmp.begin(),jtend=tmp.end();
for (;jt!=jtend;++jt){
if (jt->type!=_IDNT)
continue;
if (!equalposcomp(declared_functions,*jt) && !equalposcomp(exported_names,*jt)){
if (is_known_name_home_38(0,jt->_IDNTptr->id_name))
undeclared_global_vars.push_back(*jt);
else
errors.push_back(*jt);
}
}
// keep only home and app variables in declared global vars
tmp=declared_global_vars;
declared_global_vars.clear();
jt=tmp.begin(); jtend=tmp.end();
for (;jt!=jtend;++jt){
if (jt->type==_IDNT && !equalposcomp(exported_names,*jt)){
if (is_known_name_home_38(0,jt->_IDNTptr->id_name))
declared_global_vars.push_back(*jt);
else
unexported_declared_global_vars.push_back(*jt);
}
}
// split exported_names into function/variables
exported_function_names.clear();
exported_variable_names.clear();
if (!exported_names.empty()){
vecteur sto_var=lop(parsed,at_sto);
int s=int(exported_names.size());
int is_var=-1;
for (int i=0;i<s;++i){
gen & var=exported_names[i];
if (var.type==_IDNT){
const_iterateur it=sto_var.begin(),itend=sto_var.end();
for (;it!=itend;++it){
if (it->type!=_SYMB) continue;
gen & f =it->_SYMBptr->feuille;
if (f.type==_VECT && f._VECTptr->size()==2 && f._VECTptr->back()==var){
if (f._VECTptr->front().is_symb_of_sommet(at_program))
is_var=0;
else
is_var=1;
break;
}
}
if (it==itend)
is_var=1;
}
if (is_var>=0){
if (is_var)
exported_variable_names.push_back(var);
else
exported_function_names.push_back(var);
}
}
}
// qualify unexported functions and declared unexported variables
qualify(parsed,unexported,prog,contextptr);
qualify(parsed,unexported_declared_global_vars,prog,contextptr);
qualify(parsed,exported_variable_names,prog,contextptr);
#if !defined RTOS_THREADX && !defined NSPIRE
ofstream of("c:\\log"); of << "=" << assignation_by_equal << endl << "undecl vars:" << undeclared_global_vars << endl << "decl vars:" << declared_global_vars << endl << "decl func.:" << declared_functions << endl << "exported func:" << exported_function_names << endl << "exported vars:"<<exported_variable_names << endl << "unknown exported:"<<unknown_exported << endl << "unexported:" << unexported << endl << "unexported declared global vars:"<<unexported_declared_global_vars << endl << "views:" << views << endl << "errors:" << errors << endl << "prog:"<<prog << endl << "parsed:" << parsed; of.close();
#endif
return int(errors.size());
}
// 0: ok, -1: invalid view, >0: #errors
int parse_program(const wchar_t * source,const wchar_t * progname,vecteur & assignation_by_equal,vecteur & undeclared_global_vars,vecteur & declared_global_vars,vecteur & exported_function_names,vecteur & exported_variable_names,vecteur & unknown_exported,vecteur & unexported,vecteur & unexported_declared_global_vars,vecteur & views,vecteur & errors,gen & parsed,GIAC_CONTEXT){
unsigned utfs = giacmax(utf8length(source),utf8length(progname));
char * utf8source = new char[utfs+1];
unicode2utf8(source,utf8source,wstrlen(source));
string s(utf8source);
unicode2utf8(progname,utf8source,wstrlen(progname));
string utf8progname(utf8source);
gen prog=identificateur(utf8progname);
delete [] utf8source;
int c=calc_mode(contextptr);
calc_mode(contextptr)=-38;
parsed=gen(s,contextptr);
calc_mode(contextptr)=c;
vecteur declared_functions;
int err=parse_program_decl(assignation_by_equal,undeclared_global_vars,declared_global_vars,declared_functions,exported_function_names,exported_variable_names,unknown_exported,unexported,unexported_declared_global_vars,views,errors,prog,parsed,contextptr);
return err;
}
gen _testfunc(const gen & g0,GIAC_CONTEXT){
if (g0.type==_STRNG){
int c=calc_mode(contextptr);
calc_mode(contextptr)=-38;
gen parsed(*g0._STRNGptr,contextptr);
calc_mode(contextptr)=c;
gen prog("abc",contextptr);
vecteur assignation_by_equal,undeclared_global_vars,declared_global_vars,declared_functions,exported_function_names,exported_variable_names,unknown_exported,unexported,unexported_declared_global_vars,views,errors;
parse_program_decl(assignation_by_equal,undeclared_global_vars,declared_global_vars,declared_functions,exported_function_names,exported_variable_names,unknown_exported,unexported,unexported_declared_global_vars,views,errors,prog,parsed,contextptr);
// eval
gen res=eval(parsed,1,contextptr);
vecteur resv=makevecteur(assignation_by_equal,undeclared_global_vars,declared_global_vars,exported_function_names,exported_variable_names,unknown_exported,unexported,unexported_declared_global_vars,errors);
resv.push_back(res);
return resv;
}
return undef;
}
static const char _testfunc_s[]="testfunc";
static define_unary_function_eval(__testfunc,&_testfunc,_testfunc_s);
define_unary_function_ptr5( at_testfunc ,alias_at_testfunc,&__testfunc,0,true);
#else
gen _testfunc(const gen & g0,GIAC_CONTEXT){
return g0;
}
static const char _testfunc_s[]="testfunc";
static define_unary_function_eval(__testfunc,&_testfunc,_testfunc_s);
define_unary_function_ptr5( at_testfunc ,alias_at_testfunc,&__testfunc,0,true);
#endif // old code not used anymore
#ifdef DOUBLEVAL
const identificateur nsymbolic__IDNT("nsymbolic");
const gen nsymbolic(nsymbolic__IDNT);
const identificateur u0_nm1__IDNT("u0_nm1");
const gen u0_nm1(u0_nm1__IDNT);
const identificateur v0_nm2__IDNT("v0_nm2");
const gen v0_nm2(v0_nm2__IDNT);
const identificateur U0__IDNT("U0");
const gen U0_idnt(U0__IDNT);
const identificateur u1_nm1__IDNT("u1_nm1");
const gen u1_nm1(u1_nm1__IDNT);
const identificateur v1_nm2__IDNT("v1_nm2");
const gen v1_nm2(v1_nm2__IDNT);
const identificateur U1__IDNT("U1");
const gen U1_idnt(U1__IDNT);
const identificateur u2_nm1__IDNT("u2_nm1");
const gen u2_nm1(u2_nm1__IDNT);
const identificateur v2_nm2__IDNT("v2_nm2");
const gen v2_nm2(v2_nm2__IDNT);
const identificateur U2__IDNT("U2");
const gen U2_idnt(U2__IDNT);
const identificateur u3_nm1__IDNT("u3_nm1");
const gen u3_nm1(u3_nm1__IDNT);
const identificateur v3_nm2__IDNT("v3_nm2");
const gen v3_nm2(v3_nm2__IDNT);
const identificateur U3__IDNT("U3");
const gen U3_idnt(U3__IDNT);
const identificateur u4_nm1__IDNT("u4_nm1");
const gen u4_nm1(u4_nm1__IDNT);
const identificateur v4_nm2__IDNT("v4_nm2");
const gen v4_nm2(v4_nm2__IDNT);
const identificateur U4__IDNT("U4");
const gen U4_idnt(U4__IDNT);
const identificateur u5_nm1__IDNT("u5_nm1");
const gen u5_nm1(u5_nm1__IDNT);
const identificateur v5_nm2__IDNT("v5_nm2");
const gen v5_nm2(v5_nm2__IDNT);
const identificateur U5__IDNT("U5");
const gen U5_idnt(U5__IDNT);
const identificateur u6_nm1__IDNT("u6_nm1");
const gen u6_nm1(u6_nm1__IDNT);
const identificateur v6_nm2__IDNT("v6_nm2");
const gen v6_nm2(v6_nm2__IDNT);
const identificateur U6__IDNT("U6");
const gen U6_idnt(U6__IDNT);
const identificateur u7_nm1__IDNT("u7_nm1");
const gen u7_nm1(u7_nm1__IDNT);
const identificateur v7_nm2__IDNT("v7_nm2");
const gen v7_nm2(v7_nm2__IDNT);
const identificateur U7__IDNT("U7");
const gen U7_idnt(U7__IDNT);
const identificateur u8_nm1__IDNT("u8_nm1");
const gen u8_nm1(u8_nm1__IDNT);
const identificateur v8_nm2__IDNT("v8_nm2");
const gen v8_nm2(v8_nm2__IDNT);
const identificateur U8__IDNT("U8");
const gen U8_idnt(U8__IDNT);
const identificateur u9_nm1__IDNT("u9_nm1");
const gen u9_nm1(u9_nm1__IDNT);
const identificateur v9_nm2__IDNT("v9_nm2");
const gen v9_nm2(v9_nm2__IDNT);
const identificateur U9__IDNT("U9");
const gen U9_idnt(U9__IDNT);
#else // GIAC_HAS_STO_38
const alias_ref_identificateur ref_nsymbolic={-1,0,0,"nsymbolic",0,0};
const define_alias_gen(alias_nsymbolic,_IDNT,0,&ref_nsymbolic);
const gen & nsymbolic = * (gen *) & alias_nsymbolic;
const alias_ref_identificateur ref_u0_nm1={-1,0,0,"u0_nm1",0,0};
const define_alias_gen(alias_u0_nm1,_IDNT,0,&ref_u0_nm1);
const gen & u0_nm1 = * (gen *) & alias_u0_nm1;
const alias_ref_identificateur ref_v0_nm2={-1,0,0,"v0_nm2",0,0};
const define_alias_gen(alias_v0_nm2,_IDNT,0,&ref_v0_nm2);
const gen & v0_nm2 = * (gen *) & alias_v0_nm2;
const alias_ref_identificateur ref_U0_idnt={-1,0,0,"U0",0,0};
const define_alias_gen(alias_U0_idnt,_IDNT,0,&ref_U0_idnt);
const gen & U0_idnt = * (gen *) & alias_U0_idnt;
const alias_ref_identificateur ref_u1_nm1={-1,0,0,"u1_nm1",0,0};
const define_alias_gen(alias_u1_nm1,_IDNT,0,&ref_u1_nm1);
const gen & u1_nm1 = * (gen *) & alias_u1_nm1;
const alias_ref_identificateur ref_v1_nm2={-1,0,0,"v1_nm2",0,0};
const define_alias_gen(alias_v1_nm2,_IDNT,0,&ref_v1_nm2);
const gen & v1_nm2 = * (gen *) & alias_v1_nm2;
const alias_ref_identificateur ref_U1_idnt={-1,0,0,"U1",0,0};
const define_alias_gen(alias_U1_idnt,_IDNT,0,&ref_U1_idnt);
const gen & U1_idnt = * (gen *) & alias_U1_idnt;
const alias_ref_identificateur ref_u2_nm1={-1,0,0,"u2_nm1",0,0};
const define_alias_gen(alias_u2_nm1,_IDNT,0,&ref_u2_nm1);
const gen & u2_nm1 = * (gen *) & alias_u2_nm1;
const alias_ref_identificateur ref_v2_nm2={-1,0,0,"v2_nm2",0,0};
const define_alias_gen(alias_v2_nm2,_IDNT,0,&ref_v2_nm2);
const gen & v2_nm2 = * (gen *) & alias_v2_nm2;
const alias_ref_identificateur ref_U2_idnt={-1,0,0,"U2",0,0};
const define_alias_gen(alias_U2_idnt,_IDNT,0,&ref_U2_idnt);
const gen & U2_idnt = * (gen *) & alias_U2_idnt;
const alias_ref_identificateur ref_u3_nm1={-1,0,0,"u3_nm1",0,0};
const define_alias_gen(alias_u3_nm1,_IDNT,0,&ref_u3_nm1);
const gen & u3_nm1 = * (gen *) & alias_u3_nm1;
const alias_ref_identificateur ref_v3_nm2={-1,0,0,"v3_nm2",0,0};
const define_alias_gen(alias_v3_nm2,_IDNT,0,&ref_v3_nm2);
const gen & v3_nm2 = * (gen *) & alias_v3_nm2;
const alias_ref_identificateur ref_U3_idnt={-1,0,0,"U3",0,0};
const define_alias_gen(alias_U3_idnt,_IDNT,0,&ref_U3_idnt);
const gen & U3_idnt = * (gen *) & alias_U3_idnt;
const alias_ref_identificateur ref_u4_nm1={-1,0,0,"u4_nm1",0,0};
const define_alias_gen(alias_u4_nm1,_IDNT,0,&ref_u4_nm1);
const gen & u4_nm1 = * (gen *) & alias_u4_nm1;
const alias_ref_identificateur ref_v4_nm2={-1,0,0,"v4_nm2",0,0};
const define_alias_gen(alias_v4_nm2,_IDNT,0,&ref_v4_nm2);
const gen & v4_nm2 = * (gen *) & alias_v4_nm2;
const alias_ref_identificateur ref_U4_idnt={-1,0,0,"U4",0,0};
const define_alias_gen(alias_U4_idnt,_IDNT,0,&ref_U4_idnt);
const gen & U4_idnt = * (gen *) & alias_U4_idnt;
const alias_ref_identificateur ref_u5_nm1={-1,0,0,"u5_nm1",0,0};
const define_alias_gen(alias_u5_nm1,_IDNT,0,&ref_u5_nm1);
const gen & u5_nm1 = * (gen *) & alias_u5_nm1;
const alias_ref_identificateur ref_v5_nm2={-1,0,0,"v5_nm2",0,0};
const define_alias_gen(alias_v5_nm2,_IDNT,0,&ref_v5_nm2);
const gen & v5_nm2 = * (gen *) & alias_v5_nm2;
const alias_ref_identificateur ref_U5_idnt={-1,0,0,"U5",0,0};
const define_alias_gen(alias_U5_idnt,_IDNT,0,&ref_U5_idnt);
const gen & U5_idnt = * (gen *) & alias_U5_idnt;
const alias_ref_identificateur ref_u6_nm1={-1,0,0,"u6_nm1",0,0};
const define_alias_gen(alias_u6_nm1,_IDNT,0,&ref_u6_nm1);
const gen & u6_nm1 = * (gen *) & alias_u6_nm1;
const alias_ref_identificateur ref_v6_nm2={-1,0,0,"v6_nm2",0,0};
const define_alias_gen(alias_v6_nm2,_IDNT,0,&ref_v6_nm2);
const gen & v6_nm2 = * (gen *) & alias_v6_nm2;
const alias_ref_identificateur ref_U6_idnt={-1,0,0,"U6",0,0};
const define_alias_gen(alias_U6_idnt,_IDNT,0,&ref_U6_idnt);
const gen & U6_idnt = * (gen *) & alias_U6_idnt;
const alias_ref_identificateur ref_u7_nm1={-1,0,0,"u7_nm1",0,0};
const define_alias_gen(alias_u7_nm1,_IDNT,0,&ref_u7_nm1);
const gen & u7_nm1 = * (gen *) & alias_u7_nm1;
const alias_ref_identificateur ref_v7_nm2={-1,0,0,"v7_nm2",0,0};
const define_alias_gen(alias_v7_nm2,_IDNT,0,&ref_v7_nm2);
const gen & v7_nm2 = * (gen *) & alias_v7_nm2;
const alias_ref_identificateur ref_U7_idnt={-1,0,0,"U7",0,0};
const define_alias_gen(alias_U7_idnt,_IDNT,0,&ref_U7_idnt);
const gen & U7_idnt = * (gen *) & alias_U7_idnt;
const alias_ref_identificateur ref_u8_nm1={-1,0,0,"u8_nm1",0,0};
const define_alias_gen(alias_u8_nm1,_IDNT,0,&ref_u8_nm1);
const gen & u8_nm1 = * (gen *) & alias_u8_nm1;
const alias_ref_identificateur ref_v8_nm2={-1,0,0,"v8_nm2",0,0};
const define_alias_gen(alias_v8_nm2,_IDNT,0,&ref_v8_nm2);
const gen & v8_nm2 = * (gen *) & alias_v8_nm2;
const alias_ref_identificateur ref_U8_idnt={-1,0,0,"U8",0,0};
const define_alias_gen(alias_U8_idnt,_IDNT,0,&ref_U8_idnt);
const gen & U8_idnt = * (gen *) & alias_U8_idnt;
const alias_ref_identificateur ref_u9_nm1={-1,0,0,"u9_nm1",0,0};
const define_alias_gen(alias_u9_nm1,_IDNT,0,&ref_u9_nm1);
const gen & u9_nm1 = * (gen *) & alias_u9_nm1;
const alias_ref_identificateur ref_v9_nm2={-1,0,0,"v9_nm2",0,0};
const define_alias_gen(alias_v9_nm2,_IDNT,0,&ref_v9_nm2);
const gen & v9_nm2 = * (gen *) & alias_v9_nm2;
const alias_ref_identificateur ref_U9_idnt={-1,0,0,"U9",0,0};
const define_alias_gen(alias_U9_idnt,_IDNT,0,&ref_U9_idnt);
const gen & U9_idnt = * (gen *) & alias_U9_idnt;
#endif
int has_Un(const gen & g){
vecteur l(lvar(g));
for (unsigned i=0;i<l.size();++i){
if (l[i].type==_IDNT){
const char * s=l[i]._IDNTptr->id_name;
if (strlen(s)==2 && s[0]=='U' && s[1]>='0' && s[1]<='9')
return s[1]-'0';
}
}
return -1;
}
static void seqapp_lop_of(const gen & g,vecteur & res){
vecteur vof(lop(g,at_of));
const_iterateur it=vof.begin(),itend=vof.end();
for (;it!=itend;++it){
gen & f=it->_SYMBptr->feuille;
if (f.type!=_VECT || f._VECTptr->size()!=2 || f._VECTptr->front().type!=_IDNT)
continue;
if (f._VECTptr->back().type==_SYMB)
seqapp_lop_of(f._VECTptr->back(),res);
res.push_back(*it);
}
}
int is_n_minus_one_or_two(const gen & arg){
if (arg.type!=_SYMB)
return 0;
if (arg._SYMBptr->feuille.type==_VECT && arg._SYMBptr->feuille._VECTptr->size()==2){
gen a1=arg._SYMBptr->feuille._VECTptr->front();
gen a2=arg._SYMBptr->feuille._VECTptr->back();
if (a1.type==_IDNT && !strcmp(a1._IDNTptr->id_name,"N")){
if (arg._SYMBptr->sommet==at_plus){
if (a2==-1) return 1;
if (a2==-2) return 2;
}
if (arg._SYMBptr->sommet==at_binary_minus){
if (a2==1) return 1;
if (a2==2) return 2;
}
}
}
return 0;
}
// Prepares app sequence for computing a recurrence relation
// Valid if 1 sequence is checked and does not depend on other sequences
// Given expr_un, the expression of UK(N) in terms of UK(N-1) and UK(N-2)
// write the recurrence relation as UK(N)=subst(expr,vars,[N,UK(N-1),UK(N-2)])
// Return 0 or -10-val if expr_un is invalid or depends on Uval,
// 1 if it does not depend on UK(N-2)
// 3 if not recurrent
// 2 otherwise
int seqapp_prepare(const gen & expr_un,gen & expr,vecteur & vars,GIAC_CONTEXT,int seqno){
if (has_Un(expr_un)!=-1)
return 0;
vecteur vof; seqapp_lop_of(expr_un,vof); // (lop(expr_un,at_of));
// check functions with names in U0-U9
int s=int(vof.size()),retval=1;
gen uk(vx_var);
bool notrecurrent=true;
for (int i=0;i<s;++i){
gen & f=vof[i]._SYMBptr->feuille;
if (f.type!=_VECT || f._VECTptr->size()!=2 || f._VECTptr->front().type!=_IDNT)
continue;
gen & id=f._VECTptr->front();
const char * idname=id._IDNTptr->id_name;
if (strlen(idname)!=2 || idname[0]!='U' || idname[1]<'0' || idname[1]>'9')
continue;
notrecurrent=false;
uk=id;
if (seqno==-1){
seqno=idname[1]-'0';
}
else {
if (seqno!=idname[1]-'0')
return -10-(idname[1]-'0');
}
gen & arg=f._VECTptr->back();
#if 1
int test=is_n_minus_one_or_two(arg);
if (!test)
return 0;
if (test==2)
retval=2;
#else
if (arg!=n__IDNT_e-1 && arg!=n__IDNT_e-2)
return 0;
if (arg==n__IDNT_e-2)
retval=2;
#endif
}
identificateur uk_nm1_("uk_nm1"),uk_nm2_("uk_nm2");
gen uk_nm1(uk_nm1_),uk_nm2(uk_nm2_);
vecteur vars0(makevecteur(n__IDNT_e,symb_of(uk,n__IDNT_e-1),symb_of(uk,n__IDNT_e-2)));
vars=makevecteur(nsymbolic,uk_nm1,uk_nm2);
expr=subst(expr_un,vars0,vars,true,contextptr);
/* additional checking disabled
vecteur lv(makevecteur(uk_nm1,uk_nm2));
lidnt(expr,lv);
s=lv.size();
for (int i=2;i<s;++i){
gen & g =lv[i];
if (g.type!=_IDNT)
return 0;
if (strlen(g._IDNTptr->id_name)>1)
return 0;
if (g._IDNTptr->id_name[0]<'A' || g._IDNTptr->id_name[0]>'Z')
return 0;
}
*/
return notrecurrent?3:retval;
}
// Compute UK(N) for K=k to m, where UK(k) and UK(k+1) are given
// If the recurrence relation does not depend on UK(N-2), set UK(k+1) to undef
vecteur seqapp_compute(const gen & expr0,const vecteur & vars,const gen & UK_k,const gen &UK_kp1,int k,int m,GIAC_CONTEXT){
gen f1f9(lidnt_function38(expr0));
gen f1f9value=eval(f1f9,1,contextptr);
gen expr(expr0);
if (f1f9.type==_VECT && !f1f9._VECTptr->empty())
expr=subst(expr0,f1f9,f1f9value,true,contextptr);
gen UK_nm2(UK_k),UK_nm1(UK_kp1),tmp;
if (is_undef(UK_k))// also compute UK_n
UK_nm2=subst(expr,vars,makevecteur(k,UK_k,undef),false,contextptr);
if (is_undef(UK_kp1))// compute UK_np1
UK_nm1=subst(expr,vars,makevecteur(k+1,UK_k,undef),false,contextptr);
UK_nm1=evalf(UK_nm1,1,contextptr);
if (UK_nm1.type>_REAL && UK_nm1.type!=_FLOAT_)
UK_nm1=undef;
UK_nm2=evalf(UK_nm2,1,contextptr);
if (UK_nm2.type>_REAL && UK_nm2.type!=_FLOAT_)
UK_nm2=undef;
vecteur res(makevecteur(UK_nm2,UK_nm1));
for (int n=k+2;n<=m;++n){
tmp=subst(expr,vars,makevecteur(n,UK_nm1,UK_nm2),false,contextptr);
tmp=evalf(tmp,1,contextptr);
if (tmp.type>_REAL && tmp.type!=_FLOAT_)
res.push_back(undef);
else
res.push_back(tmp);
UK_nm2=UK_nm1;
UK_nm1=tmp;
}
return res;
}
// Prepares app sequence for computing all recurrences relations
// expr_un should contain the expression for U0(N) to UK(N) for K<=9
// undef may be used if the sequence is not checked
// Rewrite the recurrence relation as [U0(N),...,UK(N)]=subst(expr,vars,[N,U0(N-1),U0(N-2),...])
// Return 0 if expr_un is invalid, -10-val if Uval should be checked
// Return 1 if it does not depend on UK(N-2), 3 if not recurrent, 2 otherwise
int seqapp_prepare(const vecteur & expr_un,vecteur & expr,vecteur & vars,GIAC_CONTEXT){
int dim=int(expr_un.size());
if (has_Un(expr_un)!=-1)
return 0;
vecteur vof; seqapp_lop_of(expr_un,vof); // (lop(expr_un,at_of));
vector<int> defined_seqs;
for (unsigned i=0;i<expr_un.size();++i){
if (!is_undef(expr_un[i]))
defined_seqs.push_back(i); // allowed sequences numbers (starts with U0, not U1)
}
// check functions with names in U0-U9
int s=int(vof.size()),retval=3;
gen uk;
for (int i=0;i<s;++i){
gen & f=vof[i]._SYMBptr->feuille;
if (f.type!=_VECT || f._VECTptr->size()!=2 || f._VECTptr->front().type!=_IDNT)
continue;
gen & id=f._VECTptr->front();
const char * idname=id._IDNTptr->id_name;
if (strlen(idname)!=2 || idname[0]!='U' || idname[1]<'0' || idname[1]>'9')
continue;
int val=idname[1]-'0';
if (!equalposcomp(defined_seqs,val))
return -val-10;
gen & arg=f._VECTptr->back();
#if 1
int test=is_n_minus_one_or_two(arg);
if (!test)
return 0;
if (test==2)
retval=2;
else {
if (retval!=2)
retval=1;
}
#else
if (arg!=n__IDNT_e-1 && arg!=n__IDNT_e-2)
return 0;
if (arg==n__IDNT_e-2)
retval=2;
else {
if (retval!=2)
retval=1;
}
#endif
}
vecteur vars0(1,n__IDNT_e); vars=vecteur(1,nsymbolic);
vecteur tab_uk(30);
tab_uk[0]=u0_nm1; // (identificateur("u0_nm1"));
tab_uk[1]=v0_nm2; // (identificateur("v0_nm2"));
tab_uk[2]=U0_idnt; // (identificateur("U0"));
tab_uk[3]=u1_nm1; // (identificateur("u1_nm1"));
tab_uk[4]=v1_nm2; // (identificateur("v1_nm2"));
tab_uk[5]=U1_idnt; // (identificateur("U1"));
tab_uk[6]=u2_nm1; // (identificateur("u2_nm1"));
tab_uk[7]=v2_nm2; // (identificateur("v2_nm2"));
tab_uk[8]=U2_idnt; // (identificateur("U2"));
tab_uk[9]=u3_nm1; // (identificateur("u3_nm1"));
tab_uk[10]=v3_nm2; // (identificateur("v3_nm2"));
tab_uk[11]=U3_idnt; // (identificateur("U3"));
tab_uk[12]=u4_nm1; // (identificateur("u4_nm1"));
tab_uk[13]=v4_nm2; // (identificateur("v4_nm2"));
tab_uk[14]=U4_idnt; // (identificateur("U4"));
tab_uk[15]=u5_nm1; // (identificateur("u5_nm1"));
tab_uk[16]=v5_nm2; // (identificateur("v5_nm2"));
tab_uk[17]=U5_idnt; // (identificateur("U5"));
tab_uk[18]=u6_nm1; // (identificateur("u6_nm1"));
tab_uk[19]=v6_nm2; // (identificateur("v6_nm2"));
tab_uk[20]=U6_idnt; // (identificateur("U6"));
tab_uk[21]=u7_nm1; // (identificateur("u7_nm1"));
tab_uk[22]=v7_nm2; // (identificateur("v7_nm2"));
tab_uk[23]=U7_idnt; // (identificateur("U7"));
tab_uk[24]=u8_nm1; // (identificateur("u8_nm1"));
tab_uk[25]=v8_nm2; // (identificateur("v8_nm2"));
tab_uk[26]=U8_idnt; // (identificateur("U8"));
tab_uk[27]=u9_nm1; // (identificateur("u9_nm1"));
tab_uk[28]=v9_nm2; // (identificateur("v9_nm2"));
tab_uk[29]=U9_idnt; // (identificateur("U9"));
gen n_minus_1=n__IDNT_e-1;
for (int i=0;i<dim;++i){
gen uk=tab_uk[3*i+2];
vars0.push_back(new_ref_symbolic(symbolic(at_of,makenewvecteur(uk,n_minus_1))));
vars.push_back(tab_uk[3*i]);
}
gen n_minus_2=n__IDNT_e-2;
for (int i=0;i<dim;++i){
gen uk=tab_uk[3*i+2];
vars0.push_back(new_ref_symbolic(symbolic(at_of,makenewvecteur(uk,n_minus_2))));
vars.push_back(tab_uk[3*i+1]);
}
expr=subst(expr_un,vars0,vars,true,contextptr);
/* additional checking disabled
vecteur lv(vars);
lidnt(expr,lv);
s=lv.size();
for (int i=vars.size();i<s;++i){
gen & g =lv[i];
if (is_undef(g)) continue;
if (g.type!=_IDNT)
return 0;
if (strlen(g._IDNTptr->id_name)>1)
return 0;
if (g._IDNTptr->id_name[0]<'A' || g._IDNTptr->id_name[0]>'Z')
return 0;
}
*/
return retval;
}
// Compute UK(N) for K=k to m, where UK(k) and UK(k+1) are given
// If the recurrence relation does not depend on UK(N-2), set UK_kp1 to vecteur(0)
vecteur seqapp_compute(const vecteur & expr0,const vecteur & vars,const vecteur & UK_k,const vecteur &UK_kp1,int k,int m,GIAC_CONTEXT){
gen f1f9(lidnt_function38(expr0));
gen f1f9value=eval(f1f9,1,contextptr);
vecteur expr(expr0);
if (f1f9.type==_VECT && !f1f9._VECTptr->empty()){
iterateur it=expr.begin(),itend=expr.end();
for (;it!=itend;++it){
*it = subst(*it,f1f9,f1f9value,true,contextptr);
}
}
int dim=int(expr.size());
vecteur UK_nm2(UK_k),UK_nm1(UK_kp1),tmp(dim);
vecteur vals(2*dim+1);
if (UK_k.empty()){// compute UK_n
vals[0]=k;
for (int i=0;i<dim;++i){
vals[i+1]=undef;
}
for (int i=0;i<dim;++i)
vals[dim+i+1]=undef;
UK_nm2=gen2vecteur(subst(expr,vars,vals,false,contextptr));
}
if (dim!=int(UK_nm2.size()))
return vecteur(dim,gendimerr(contextptr));
if (UK_kp1.empty()){// compute UK_np1
vals[0]=k+1;
for (int i=0;i<dim;++i){
vals[i+1]=UK_nm2[i];
}
for (int i=0;i<dim;++i)
vals[dim+i+1]=undef;
UK_nm1=subst(expr,vars,vals,false,contextptr);
}
gen tmpU=evalf(UK_nm2,1,contextptr);
if (tmpU.type!=_VECT)
return vecteur(dim,gendimerr(contextptr));
UK_nm2=*tmpU._VECTptr;
tmpU=evalf(UK_nm1,1,contextptr);
if (tmpU.type!=_VECT)
return vecteur(dim,gendimerr(contextptr));
UK_nm1=*tmpU._VECTptr;
vecteur res(makevecteur(UK_nm2,UK_nm1));
res.reserve(m-k+1);
for (int n=k+2;n<=m;++n){
vals[0]=n;
for (int i=0;i<dim;++i){
vals[i+1]=UK_nm1[i];
}
for (int i=0;i<dim;++i){
vals[dim+i+1]=UK_nm2[i];
}
vecteur::const_iterator it=expr.begin(),itend=expr.end();
for (int i=0;it!=itend;++it,++i)
tmp[i]=is_undef(*it)?*it:evalf(sortsubst(*it,vars,vals,false,contextptr),1,contextptr);
res.push_back(tmp);
UK_nm2=UK_nm1;
UK_nm1=tmp;
}
return res;
}
gen _tests(const gen & g0,GIAC_CONTEXT){
// return eval_before_diff(g0,vx_var,contextptr);
if (g0.type==_VECT){
vecteur expr,vars;
if (g0.subtype==_SEQ__VECT && g0._VECTptr->front().type==_VECT && g0._VECTptr->size()==3){
int i=seqapp_prepare(*g0._VECTptr->front()._VECTptr,expr,vars,contextptr);
if (i<0)
return gensizeerr(contextptr);
gen g01=(*g0._VECTptr)[1];
gen g02=(*g0._VECTptr)[2];
vecteur v2;
if (i==2 && g02.type==_VECT)
v2=*g02._VECTptr;
if (g01.type==_VECT)
return seqapp_compute(expr,vars,*g01._VECTptr,v2,0,20,contextptr);
}
int i=seqapp_prepare(*g0._VECTptr,expr,vars,contextptr);
if (i<0)
return gensizeerr(contextptr);
return seqapp_compute(expr,vars,vecteur(expr.size(),1.0),i==1?vecteur(0):vecteur(expr.size(),2.0),0,20,contextptr);
}
gen expr; vecteur vars;
int i=seqapp_prepare(g0,expr,vars,contextptr);
if (!i)
return undef;
return seqapp_compute(expr,vars,1.0,i==1?undef:2.0,0,20,contextptr);
}
static const char _tests_s[]="tests";
static define_unary_function_eval(__tests,&_tests,_tests_s);
define_unary_function_ptr5( at_tests ,alias_at_tests,&__tests,0,T_UNARY_OP);
gen _CHOOSE(const gen & args,GIAC_CONTEXT){
if ( args.type==_STRNG && args.subtype==-1) return args;
if (args.type!=_VECT || args._VECTptr->size()<3)
return gentypeerr(contextptr);
vecteur v = *args._VECTptr;
if (v[0].is_symb_of_sommet(at_double_deux_points) && v[0]._SYMBptr->feuille.type==_VECT && v[0]._SYMBptr->feuille._VECTptr->size()==2)
v[0]=v[0]._SYMBptr->feuille._VECTptr->back();
for (int i=1; i<=1; i++) { if (v[i].type!=_STRNG) v[i]= eval(v[i], 1, contextptr); if (v[i].type!=_STRNG) v[i]= string2gen(v[i].print(contextptr)); }
if (v.front().type!=_IDNT || v[1].type!=_STRNG)
return gentypeerr(contextptr);
#ifdef NSPIRE
return undef;
#else
#ifndef GIAC_HAS_STO_38
vecteur res(3);
res[2]=v[0];
res[0]=v[1];
vecteur tmp;
for (unsigned i=2;i<v.size();i++)
tmp.push_back(eval(v[i],1,contextptr));
res[1]=tmp;
return __inputform.op(symbolic(at_choosebox,gen(res,_SEQ__VECT)),contextptr);
#endif
#endif
return undef;
}
static const char _CHOOSE_s []="CHOOSE";
static define_unary_function_eval_quoted (__CHOOSE,&giac::_CHOOSE,_CHOOSE_s);
define_unary_function_ptr5( at_CHOOSE ,alias_at_CHOOSE,&__CHOOSE,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
#if 0 // def GIAC_HAS_STO_38
// encoding is up to 8 nibbles with various values...
// 1 optional graphic name
// 2 graphic name
// 3 coordinate pair
// 4 optional coordinate pair
// 5 color
// 6 optional color
// 7 integer
// 8 boolean
// 9 graphic name, return the adresses'adress and does not allow G0!!!
// a: angle
// b: optional integer
// c: w/h based on 0/0
// 0x631 means : optional graphic name, coordinate pair, optional color
#define CyrilleFnc(n) static const char _##n##_s []= #n; static define_unary_function_eval_quoted (__##n,&giac::_##n,_##n##_s); define_unary_function_ptr5( at_##n ,alias_at_##n,&__##n,0,T_UNARY_OP_38);
gen _FREEZE(const gen & args,GIAC_CONTEXT)
{
dofreeze();
return 1;
}
CyrilleFnc(FREEZE);
gen _GETPIX(const gen & args,GIAC_CONTEXT)
{
void *g=0; int xy[2];
if (!GraphicVerifInputs(args, &g, xy, 0x31, NULL, contextptr)) return gensizeerr(contextptr);
return gen(dogetpix(g, xy[0], xy[1]));
}
CyrilleFnc(GETPIX);
gen _LINE(const gen & args,GIAC_CONTEXT)
{
void *g=0; int xy[4], c= 0;
if (!GraphicVerifInputs(args, &g, xy, 0x6331, &c, contextptr)) return gensizeerr(contextptr);
doline(g, xy[0], xy[1], xy[2], xy[3], c);
return 1;
}
CyrilleFnc(LINE);
gen _RECT(const gen & args,GIAC_CONTEXT)
{
void *g=0; int xy[4]= {0, 0, 0x0fffffff,0x0fffffff}, c[2]= { 3, -1};
if (!GraphicVerifInputs(args, &g, xy, 0x66441, c, contextptr)) return gensizeerr(contextptr);
if (c[1]==-1) c[1]= c[0];
dorect(g, xy[0], xy[1], xy[2]-xy[0]+1, xy[3]-xy[1]+1, c[0], c[1]);
return 1;
}
CyrilleFnc(RECT);
gen _INVERT(const gen & args,GIAC_CONTEXT)
{
void *g=0; int xy[4]= {0, 0, 0x0fffffff, 0x0fffffff };
if (!GraphicVerifInputs(args, &g, xy, 0x441, NULL, contextptr)) return gensizeerr(contextptr);
doinvert(g, xy[0], xy[1], xy[2]-xy[0]+1, xy[3]-xy[1]+1);
return 1;
}
CyrilleFnc(INVERT);
gen _BLIT(const gen & args,GIAC_CONTEXT)
{
void *g[2]={0,0}; int xy[8]= { 0, 0, 0xfffffff, 0xfffffff, 0, 0, 0xfffffff, 0xfffffff }, c= -1;
if (!GraphicVerifInputs(args, g, xy, 0x6442431, NULL, contextptr)) return gensizeerr(contextptr);
xy[3]+= -xy[1]+1; if (xy[3]<0) xy[3]= -2-xy[3];
xy[7]+= -xy[5]+1; if (xy[7]<0) xy[7]= -2-xy[7];
doblit(g[0], xy[0], xy[1], xy[2]-xy[0]+1, xy[3], g[1], xy[4], xy[5], xy[6]-xy[4]+1, xy[7], c);
return 1;
}
CyrilleFnc(BLIT);
gen _TEXTOUT(const gen &args, GIAC_CONTEXT)
{
if (args.type!=_VECT) return gensizeerr(contextptr);
int s= args._VECTptr->size();
if (s<3) return gensizeerr(contextptr);
gen t= *args._VECTptr->begin();
gen v(*args._VECTptr); v._VECTptr->erase(v._VECTptr->begin());
void *g=0; int xy[2]={0, 0}, c[4]= {0, 0, 1023, -1};
//TEXTOUT("text", [G?], x, y, [font, [color, [width, [color]]]])
if (!GraphicVerifInputs(v, &g, xy, 0x6b6b31, c, contextptr)) return gensizeerr(contextptr);
return gen(dotextout(&t, g, xy, c, contextptr));
}
CyrilleFnc(TEXTOUT);
gen _PIXON(const gen & args,GIAC_CONTEXT){
void *g=0; int xy[2], c= 0;
if (!GraphicVerifInputs(args, &g, xy, 0x631, &c, contextptr)) return gensizeerr(contextptr);
dopixon(g, xy[0], xy[1], c);
return 1;
}
gen _PIXOFF(const gen & args,GIAC_CONTEXT){
void *g=0; int xy[2];
if (!GraphicVerifInputs(args, &g, xy, 0x31, NULL, contextptr)) return gensizeerr(contextptr);
dopixon(g, xy[0], xy[1], 3);
return 1;
}
gen _DIMGROB(const gen &args,GIAC_CONTEXT)
{
void *g=0; int xy[2], c= 3;
if (!GraphicVerifInputs(args, &g, xy, 0x6c9, &c, contextptr)) return gensizeerr(contextptr);
dodimgrob((void**)g, xy[0], xy[1], c, gen());
return 1;
}
CyrilleFnc(DIMGROB);
gen _SUBGROB(const gen &args,GIAC_CONTEXT)
{
void *g[2]={0,0}; int xy[4]= {0, 0, 0xfffffff, 0xfffffff};
if (!GraphicVerifInputs(args, g, xy, 0x9441, NULL, contextptr)) return gensizeerr(contextptr);
dosubgrob(g, xy);
return 1;
}
CyrilleFnc(SUBGROB);
gen _ARC(const gen & args,GIAC_CONTEXT)
{
///< draws a circle, or an arc between a1 and a2. full circle is 4096...
// if OldColor is !=-1 and indiate the background color of the screen BEFORE the arc is drawn, the arc is filled...
//int Arc(int x, int y, int r, int color, int a1=0, int a2=4096, int OldColor=-1);
// ARC(x, y, r, [c, [a1, a2]])
void *g=0; int xy[2], c[4]= { 0, 0, 0, 4096};
if (!GraphicVerifInputs(args, &g, xy, 0xaab731, c, contextptr)) return gensizeerr(contextptr);
doarc(g, true, xy, c);
return 1;
}
gen _GETPIX_P(const gen & args,GIAC_CONTEXT)
{
void *g=0; int xy[2];
if (!GraphicVerifInputs2(args, &g, xy, 0x31, NULL, true, contextptr)) return gensizeerr(contextptr);
return gen(dogetpix(g, xy[0], xy[1]));
}
CyrilleFnc(GETPIX_P);
gen _LINE_P(const gen & args,GIAC_CONTEXT)
{
void *g=0; int xy[4], c= 0;
if (!GraphicVerifInputs2(args, &g, xy, 0x6331, &c, true, contextptr)) return gensizeerr(contextptr);
doline(g, xy[0], xy[1], xy[2], xy[3], c);
return 1;
}
CyrilleFnc(LINE_P);
gen _RECT_P(const gen & args,GIAC_CONTEXT)
{
void *g=0; int xy[4]= {0, 0, 0x0fffffff,0x0fffffff}, c[2]= { 3, -1};
if (!GraphicVerifInputs2(args, &g, xy, 0x66441, c, true, contextptr)) return gensizeerr(contextptr);
if (c[1]==-1) c[1]= c[0];
if (xy[0]>xy[2]) swap(xy[0], xy[2]);
if (xy[1]>xy[3]) swap(xy[1], xy[3]);
dorect(g, xy[0], xy[1], xy[2]-xy[0]+1, xy[3]-xy[1]+1, c[0], c[1]);
return 1;
}
CyrilleFnc(RECT_P);
gen _INVERT_P(const gen & args,GIAC_CONTEXT)
{
void *g=0; int xy[4]= {0, 0, 0x0fffffff, 0x0fffffff };
if (!GraphicVerifInputs2(args, &g, xy, 0x441, NULL, true, contextptr)) return gensizeerr(contextptr);
doinvert(g, xy[0], xy[1], xy[2]-xy[0]+1, xy[3]-xy[1]+1);
return 1;
}
CyrilleFnc(INVERT_P);
gen _BLIT_P(const gen & args,GIAC_CONTEXT)
{
void *g[2]={0,0}; int xy[8]= { 0, 0, 0xfffffff, 0xfffffff, 0, 0, 0xfffffff, 0xfffffff }, c= -1;
if (!GraphicVerifInputs2(args, g, xy, 0x6442431, NULL, true, contextptr)) return gensizeerr(contextptr);
xy[3]+= -xy[1]+1; if (xy[3]<0) xy[3]= -2-xy[3];
xy[7]+= -xy[5]+1; if (xy[7]<0) xy[7]= -2-xy[7];
doblit(g[0], xy[0], xy[1], xy[2]-xy[0]+1, xy[3], g[1], xy[4], xy[5], xy[6]-xy[4]+1, xy[7], c);
return 1;
}
CyrilleFnc(BLIT_P);
gen _TEXTOUT_P(const gen &args, GIAC_CONTEXT)
{
if (args.type!=_VECT) return gensizeerr(contextptr);
int s= args._VECTptr->size();
if (s<3) return gensizeerr(contextptr);
gen t= *args._VECTptr->begin();
gen v(*args._VECTptr); v._VECTptr->erase(v._VECTptr->begin());
void *g=0; int xy[2]={0, 0}, c[4]= {0, 0, 1023, -1};
//TEXTOUT("text", [G?], x, y, [font, [color, [width, [color]]]])
if (!GraphicVerifInputs2(v, &g, xy, 0x6b6b31, c, true, contextptr)) return gensizeerr(contextptr);
return gen(dotextout(&t, g, xy, c, contextptr));
}
CyrilleFnc(TEXTOUT_P);
gen _PIXON_P(const gen & args,GIAC_CONTEXT)
{
void *g=0; int xy[2], c= 0;
if (!GraphicVerifInputs2(args, &g, xy, 0x631, &c, true, contextptr)) return gensizeerr(contextptr);
dopixon(g, xy[0], xy[1], c);
return 1;
}
CyrilleFnc(PIXON_P);
gen _PIXOFF_P(const gen & args,GIAC_CONTEXT)
{
void *g=0; int xy[2];
if (!GraphicVerifInputs2(args, &g, xy, 0x31, NULL, true, contextptr)) return gensizeerr(contextptr);
dopixon(g, xy[0], xy[1], 3);
return 1;
}
CyrilleFnc(PIXOFF_P);
gen _DIMGROB_P(const gen &args,GIAC_CONTEXT)
{
void *g=0; int xy[2], c= 3;
if (!GraphicVerifInputs2(args, &g, xy, 0x6c9, &c, false, contextptr)) return gensizeerr(contextptr);
dodimgrob((void**)g, xy[0], xy[1], c, args._VECTptr->end()[-1]);
return 1;
}
CyrilleFnc(DIMGROB_P);
gen _SUBGROB_P(const gen &args,GIAC_CONTEXT)
{
void *g[2]={0,0}; int xy[4]= {0, 0, 0xfffffff, 0xfffffff};
if (!GraphicVerifInputs2(args, g, xy, 0x9441, NULL, true, contextptr)) return gensizeerr(contextptr);
dosubgrob(g, xy);
return 1;
}
CyrilleFnc(SUBGROB_P);
gen _ARC_P(const gen & args,GIAC_CONTEXT)
{
///< draws a circle, or an arc between a1 and a2. full circle is 4096...
// if OldColor is !=-1 and indiate the background color of the screen BEFORE the arc is drawn, the arc is filled...
//int Arc(int x, int y, int r, int color, int a1=0, int a2=4096, int OldColor=-1);
// ARC(x, y, r, [c, [a1, a2]])
void *g=0; int xy[2], c[4]= { 0, 0, 0, 4096};
if (!GraphicVerifInputs2(args, &g, xy, 0xaab731, c, true, contextptr)) return gensizeerr(contextptr);
doarc(g, false, xy, c);
return 1;
}
CyrilleFnc(ARC_P);
gen _GROBW_P(const gen & args, GIAC_CONTEXT)
{
void *g=0; if (!GraphicVerifInputs(args, &g, NULL, 1, NULL, contextptr)) return gensizeerr(contextptr);
return gen(dogrobw(g));
}
CyrilleFnc(GROBW_P);
gen _GROBH_P(const gen & args, GIAC_CONTEXT)
{
void *g=0; if (!GraphicVerifInputs(args, &g, NULL, 1, NULL, contextptr)) return gensizeerr(contextptr);
return gen(dogrobh(g, false));
}
CyrilleFnc(GROBH_P);
gen _GROBW(const gen & args, GIAC_CONTEXT)
{
void *g=0; if (!GraphicVerifInputs(args, &g, NULL, 1, NULL, contextptr)) return gensizeerr(contextptr);
int w= dogrobw(g);
return w*getxrangeperpixel();
}
CyrilleFnc(GROBW);
gen _GROBH(const gen & args, GIAC_CONTEXT)
{
void *g=0; if (!GraphicVerifInputs(args, &g, NULL, 1, NULL, contextptr)) return gensizeerr(contextptr);
int h= dogrobh(g, true);
return h*getyrangeperpixel();
}
CyrilleFnc(GROBH);
CyrilleFnc(ISKEYDOWN);
#else
gen _ARC(const gen & args,GIAC_CONTEXT){
if (args.type!=_VECT || args._VECTptr->size()!=5)
return gensizeerr(contextptr);
vecteur & v =*args._VECTptr;
return _cercle(gen(makevecteur(v[0]+cst_i*v[1],v[2],v[3],v[4]),_SEQ__VECT),contextptr);
}
gen _PIXON(const gen & args,GIAC_CONTEXT){
if (args.type!=_VECT || args._VECTptr->size()!=2)
return gensizeerr(contextptr);
vecteur & v =*args._VECTptr;
return symb_pnt(v.front()+cst_i*v.back(),int(FL_BLACK),contextptr);
}
gen _PIXOFF(const gen & args,GIAC_CONTEXT){
if (args.type!=_VECT || args._VECTptr->size()!=2)
return gensizeerr(contextptr);
vecteur & v =*args._VECTptr;
return symb_pnt(v.front()+cst_i*v.back(),int(FL_WHITE),contextptr);
}
gen _LINE(const gen & args,GIAC_CONTEXT){
if (args.type!=_VECT || args._VECTptr->size()!=4)
return _droite(args,contextptr);
vecteur & v =*args._VECTptr;
return _droite(gen(makevecteur(v[0]+cst_i*v[1],v[2]+cst_i*v[3]),_SEQ__VECT),contextptr);
}
static const char _LINE_s []="LINE";
static define_unary_function_eval (__LINE,&giac::_LINE,_LINE_s);
define_unary_function_ptr5( at_LINE ,alias_at_LINE,&__LINE,0,T_UNARY_OP_38);
gen _RECT(const gen & args,GIAC_CONTEXT){
if (args.type!=_VECT || args._VECTptr->size()!=4)
return _droite(args,contextptr);
vecteur & v =*args._VECTptr;
gen a=v[0],b=v[1],c=v[2],d=v[3];
if (is_greater(a,c,contextptr))
swapgen(a,c);
if (is_greater(b,d,contextptr))
swapgen(b,d);
gen e=a+b*cst_i,f=c+b*cst_i,g=a+d*cst_i,h=c+d*cst_i;
gen res=pnt_attrib(gen(makevecteur(e,f,h,g,e),_GROUP__VECT),vecteur(1,int(FL_BLACK)),contextptr);
return res;
}
static const char _RECT_s []="RECT";
static define_unary_function_eval (__RECT,&giac::_RECT,_RECT_s);
define_unary_function_ptr5( at_RECT ,alias_at_RECT,&__RECT,0,T_UNARY_OP_38);
#endif
static const char _PIXON_s []="PIXON";
static define_unary_function_eval (__PIXON,&giac::_PIXON,_PIXON_s);
define_unary_function_ptr5( at_PIXON ,alias_at_PIXON,&__PIXON,0,T_UNARY_OP_38);
static const char _PIXOFF_s []="PIXOFF";
static define_unary_function_eval (__PIXOFF,&giac::_PIXOFF,_PIXOFF_s);
define_unary_function_ptr5( at_PIXOFF ,alias_at_PIXOFF,&__PIXOFF,0,T_UNARY_OP_38);
static const char _ARC_s []="ARC";
static define_unary_function_eval (__ARC,&giac::_ARC,_ARC_s);
define_unary_function_ptr5( at_ARC ,alias_at_ARC,&__ARC,0,T_UNARY_OP_38);
static const char _PRINT_s []="PRINT";
static define_unary_function_eval_quoted (__PRINT,&giac::_print,_PRINT_s);
define_unary_function_ptr5( at_PRINT ,alias_at_PRINT,&__PRINT,0,T_UNARY_OP_38);
static const char _SEC_s []="SEC";
static define_unary_function_eval (__SEC,&giac::_sec,_SEC_s);
define_unary_function_ptr5( at_SEC ,alias_at_SEC,&__SEC,0,T_UNARY_OP_38);
static const char _CSC_s []="CSC";
static define_unary_function_eval (__CSC,&giac::_csc,_CSC_s);
define_unary_function_ptr5( at_CSC ,alias_at_CSC,&__CSC,0,T_UNARY_OP_38);
static const char _COT_s []="COT";
static define_unary_function_eval (__COT,&giac::_cot,_COT_s);
define_unary_function_ptr5( at_COT ,alias_at_COT,&__COT,0,T_UNARY_OP_38);
static const char _ASEC_s []="ASEC";
static define_unary_function_eval (__ASEC,&giac::_asec,_ASEC_s);
define_unary_function_ptr5( at_ASEC ,alias_at_ASEC,&__ASEC,0,T_UNARY_OP_38);
static const char _ACSC_s []="ACSC";
static define_unary_function_eval (__ACSC,&giac::_acsc,_ACSC_s);
define_unary_function_ptr5( at_ACSC ,alias_at_ACSC,&__ACSC,0,T_UNARY_OP_38);
static const char _ACOT_s []="ACOT";
static define_unary_function_eval (__ACOT,&giac::_acot,_ACOT_s);
define_unary_function_ptr5( at_ACOT ,alias_at_ACOT,&__ACOT,0,T_UNARY_OP_38);
gen _Celsius2Fahrenheit(const gen & g,GIAC_CONTEXT){
if (g.type==_VECT)
return apply(g,_Celsius2Fahrenheit,contextptr);
return (g*gen(9))/5+32;
}
static const char _Celsius2Fahrenheit_s []="Celsius2Fahrenheit";
static define_unary_function_eval (__Celsius2Fahrenheit,&giac::_Celsius2Fahrenheit,_Celsius2Fahrenheit_s);
define_unary_function_ptr5( at_Celsius2Fahrenheit ,alias_at_Celsius2Fahrenheit,&__Celsius2Fahrenheit,0,T_UNARY_OP);
gen _Fahrenheit2Celsius(const gen & g,GIAC_CONTEXT){
if (g.type==_VECT)
return apply(g,_Fahrenheit2Celsius,contextptr);
return (g-32)*gen(5)/9;
}
static const char _Fahrenheit2Celsius_s []="Fahrenheit2Celsius";
static define_unary_function_eval (__Fahrenheit2Celsius,&giac::_Fahrenheit2Celsius,_Fahrenheit2Celsius_s);
define_unary_function_ptr5( at_Fahrenheit2Celsius ,alias_at_Fahrenheit2Celsius,&__Fahrenheit2Celsius,0,T_UNARY_OP);
// put here function names that are in lowercase in giac and should be printed uppercase
// on HP
static const char * const display_in_maj[] ={
"ABS",
"ACOS",
"ACOSH",
"ACOT",
"ACSC",
// "ADDCOL",
// "ADDROW",
// "ALOG",
"AND",
// "ARC",
"ARG",
"ASEC",
"ASIN",
"ASINH",
"ATAN",
"ATANH",
"BINOMIAL",
"BINOMIAL_CDF",
"BINOMIAL_ICDF",
"BITAND",
// "BITNOT",
"BITOR",
"BITXOR",
//"BREAK",
"CEILING",
"CFACTOR",
"CHAR",
"CHISQUARE",
"CHISQUARE_CDF",
"CHISQUARE_ICDF",
//"CHOOSE",
"COLNORM",
"COMB",
"CONCAT",
// "COND",
"CONJ",
"COS",
"COSH",
"COT",
"CROSS",
"CSC",
"CSOLVE",
// "DEGXRAD",
// "DELCOL",
// "DELROW",
"DET",
"DIM",
//"DISP",
"DOT",
// "EIGENVAL",
// "EIGENVV",
"EXP",
// "EXPM1",
// "EXPORT",
"EXPR",
"FLOOR",
"FISHER",
"FISHER_CDF",
"FISHER_ICDF",
"FLOOR",
//"FNROOT",
"FP",
// "FREEZE",
// "GETKEY",
// "GF",
//"HMSX",
//"IDENMAT",
"IM",
// "INPUT",
"IP",
"INVERSE",
// "ISOLATE",
"ISPRIME",
// "ITERATE",
"LINE",
// "LINEAR?",
"LN",
// "LNP1",
"LOG",
// "LQ",
// "LSQ",
"LU",
//"MAKELIST",
"MAKEMAT",
// "MANT",
"MAX",
// "MAXREAL",
"MID",
"MIN",
// "MINREAL",
"MKSA",
// "MOD", // removed as cas has MOD and mod (operator and function)
// "MSGBOX",
"NEG",
"NORMALD",
"NORMALD_CDF",
"NORMALD_ICDF",
"NOT",
// "NTHROOT",
"OR",
"PERM",
"PI",
"PIECEWISE",
// "PIXOFF",
// "PIXON",
"POISSON",
"POISSON_CDF",
"POISSON_ICDF",
// "POLYCOEF",
// "POLYEVAL",
// "POLYFORM",
// "POLYROOT",
// "POS",
"PRINT",
"QR",
// "QUAD",
"QUOTE",
// "RADXDEG",
//"RANDMAT",
"RANDNORM",
// "RANDOM",
"RANDSEED",
"RANK",
"RE",
// "RECURSE",
// "REDIM",
// "REPLACE",
"RETURN",
//"REVERSE",
"RIGHT",
"ROTATE",
"ROUND",
"ROWNORM",
"RREF",
// "SCALE",
// "SCALEADD",
// "SCHUR",
"SEC",
"SIGN",
"SIN",
"SINH",
"SIZE",
"SORT",
// "SPECNORM",
// "SPECRAD",
"STRING",
"STUDENT",
"STUDENT_CDF",
"STUDENT_ICDF",
//"SUB",
// "SVD",
// "SVL",
// "SWAPCOL",
// "SWAPROW",
"TAN",
"TANH",
"TAYLOR",
"TCOLLECT",
"TEXPAND",
//"TRACE",
"TRN",
//"TRUNCATE",
//"UTPC",
//"UTPF",
//"UTPN",
//"UTPT",
// "VIEWS",
//"WAIT",
// "XHMS",
"XOR",
// "XPON",
};
static const int display_in_maj_size=sizeof(display_in_maj)/sizeof(const char *);
// check if a lowercase commandname should be uppercased
static char maj_converted[16];
char * hp38_display_in_maj(const char * s){
int l=int(strlen(s));
if (l>15)
return 0;
maj_converted[l]=0;
for (int i=0;i<l;++i){
maj_converted[i]=toupper(s[i]);
}
int beg=0,end=display_in_maj_size,cur,test;
// string index is always >= begin and < end
for (;;){
cur=(beg+end)/2;
test=strcmp(maj_converted,display_in_maj[cur]);
if (!test)
return maj_converted;
if (cur==beg){
return 0;
}
if (test>0)
beg=cur;
else
end=cur;
}
return 0;
}
gen _polar_complex(const gen & g,GIAC_CONTEXT){
if (g.type==_STRNG && g.subtype==-1) return g;
if (g.type!=_VECT || g._VECTptr->size()!=2)
return gensizeerr(contextptr);
gen res= g._VECTptr->front();
gen angle=g._VECTptr->back();
if (angle.is_symb_of_sommet(at_unit)){
gen f=angle._SYMBptr->feuille;
gen f0=f[0],f1=f[1];
if (f1==(gen("_deg",contextptr)._SYMBptr->feuille)[1])
return res*exp(cst_i*f0*cst_pi/gen(180),contextptr);
if (f1==(gen("_grad",contextptr)._SYMBptr->feuille)[1])
return res*exp(cst_i*f0*cst_pi/gen(200),contextptr);
if (f1==(gen("_rad",contextptr)._SYMBptr->feuille)[1])
return res*exp(cst_i*f0,contextptr);
}
#ifdef GIAC_HAS_STO_38
angle=evalf(angle,1,contextptr);
res= evalf(res,1,contextptr);
if (angle.type==_FLOAT_ && res.type==_FLOAT_)
{
HP_Real a, r, s, c;
fExpand(gen2HP(angle), &a); fExpand(gen2HP(res), &r);
fisin(&a, &s, angle_radian(contextptr)?AMRad:(angle_degree(contextptr)?AMDeg:AMGrad)); ficos(&a, &c, angle_radian(contextptr)?AMRad:(angle_degree(contextptr)?AMDeg:AMGrad)); //grad
fimul_L(&s, &r, &s); fimul_L(&c, &r, &c);
HP_gen C= fUnExpand(&c), S= fUnExpand(&s);
gen gC, gS; gC= HP2gen(C); gS= HP2gen(S);
res= gC+gS*cst_i;
} else {
if(!angle_radian(contextptr))
{
//grad
if(angle_degree(contextptr))
angle = angle * m_pi(contextptr) / 180;
else
angle = angle * m_pi(contextptr) / 200;
}
res=res*exp(cst_i*angle,contextptr);
}
#else
res=res*(cos(angle,contextptr)+cst_i*sin(angle,contextptr));
#endif
if (res.type==_CPLX){
int * ptr = complex_display_ptr(res);
if (ptr)
*ptr=1;
return res;
}
else
return calc_mode(contextptr)==1?symbolic(at_ggb_ang,g):symbolic(at_polar_complex,g);
}
#ifdef BCD
static const char _polar_complex_s[]="\xe2\x88\xa1";
#else
static const char _polar_complex_s[]="∡"; // " polar_complex ";
#endif
static define_unary_function_eval4 (__polar_complex,&giac::_polar_complex,_polar_complex_s,&printsommetasoperator,&texprintsommetasoperator);
define_unary_function_ptr5( at_polar_complex ,alias_at_polar_complex,&__polar_complex,0,T_MOD);
static const char _ggb_ang_s []="ggb_ang"; // prefixed version of polar complex
static define_unary_function_eval (__ggb_ang,&_polar_complex,_ggb_ang_s);
define_unary_function_ptr5( at_ggb_ang ,alias_at_ggb_ang,&__ggb_ang,0,true);
#ifdef GIAC_HAS_STO_38
gen aspen_HDigits(int i);
gen aspen_HFormat(int i);
gen aspen_HAngle(int i);
gen aspen_HComplex(int i);
gen aspen_HLanguage(int i);
#endif
gen _HDigits(const gen & g0,GIAC_CONTEXT){
gen g=g0;
if (g.type==_VECT && g._VECTptr->empty()){
g=-1;
}
else {
if (g.type==_FLOAT_)
g=get_int(g0._FLOAT_val);
if (g.type==_DOUBLE_)
g=_floor(g,contextptr);
if (g.type!=_INT_)
return gentypeerr(contextptr);
if (g.val<0 || g.val>12)
return gensizeerr(contextptr);
}
#ifdef GIAC_HAS_STO_38
return aspen_HDigits(g.val);
#else
return _Digits(g,contextptr);
#endif
}
static const char _HDigits_s []="HDigits";
static define_unary_function_eval2 (__HDigits,&_HDigits,_HDigits_s,&printasDigits);
define_unary_function_ptr( at_HDigits ,alias_at_HDigits ,&__HDigits);
gen _HFormat(const gen & g0,GIAC_CONTEXT){
gen g=g0;
if (g.type==_VECT && g._VECTptr->empty()){
g=-1;
}
else {
if (g.type==_FLOAT_)
g=get_int(g0._FLOAT_val);
if (g.type==_DOUBLE_)
g=_floor(g,contextptr);
if (g.type!=_INT_)
return gentypeerr(contextptr);
if (g.val<0 || g.val>4)
return gensizeerr(contextptr);
}
#ifdef GIAC_HAS_STO_38
return aspen_HFormat(g.val);
#else
return _scientific_format(g,contextptr);
#endif
}
static const char _HFormat_s []="HFormat";
static define_unary_function_eval2 (__HFormat,&_HFormat,_HFormat_s,&printasDigits);
define_unary_function_ptr( at_HFormat ,alias_at_HFormat ,&__HFormat);
gen _HAngle(const gen & g0,GIAC_CONTEXT){
gen g=g0;
if (g.type==_VECT && g._VECTptr->empty()){
g=-1;
}
else {
if (g.type==_FLOAT_)
g=get_int(g0._FLOAT_val);
if (g.type==_DOUBLE_)
g=_floor(g,contextptr);
if (g.type!=_INT_)
return gentypeerr(contextptr);
if (g.val<1 || g.val>2)
return gensizeerr(contextptr);
}
#ifdef GIAC_HAS_STO_38
return aspen_HAngle(g.val);
#else
return _angle_radian(g-1,contextptr);
#endif
}
static const char _HAngle_s []="HAngle";
static define_unary_function_eval2 (__HAngle,&_HAngle,_HAngle_s,&printasDigits);
define_unary_function_ptr( at_HAngle ,alias_at_HAngle ,&__HAngle);
gen _HComplex(const gen & g0,GIAC_CONTEXT){
gen g=g0;
if (g.type==_VECT && g._VECTptr->empty()){
g=-1;
}
else {
if (g.type==_FLOAT_)
g=get_int(g0._FLOAT_val);
if (g.type==_DOUBLE_)
g=_floor(g,contextptr);
if (g.type!=_INT_)
return gentypeerr(contextptr);
if (g.val<0 || g.val>1)
return gensizeerr(contextptr);
}
#ifdef GIAC_HAS_STO_38
return aspen_HComplex(g.val);
#else
return _complex_mode(g,contextptr);
#endif
}
static const char _HComplex_s []="HComplex";
static define_unary_function_eval2 (__HComplex,&_HComplex,_HComplex_s,&printasDigits);
define_unary_function_ptr( at_HComplex ,alias_at_HComplex ,&__HComplex);
gen _HLanguage(const gen & g0,GIAC_CONTEXT){
gen g=g0;
if (g.type==_VECT && g._VECTptr->empty()){
g=-1;
}
else {
if (g.type==_FLOAT_)
g=get_int(g0._FLOAT_val);
if (g.type==_DOUBLE_)
g=_floor(g,contextptr);
if (g.type!=_INT_)
return gentypeerr(contextptr);
if (g.val<0 || g.val>2)
return gensizeerr(contextptr);
}
#ifdef GIAC_HAS_STO_38
return aspen_HLanguage(g.val);
#else
if (g==-1)
return language(contextptr);
language(g.val,contextptr);
return g.val;
#endif
}
static const char _HLanguage_s []="HLanguage";
static define_unary_function_eval2 (__HLanguage,&_HLanguage,_HLanguage_s,&printasDigits);
define_unary_function_ptr( at_HLanguage ,alias_at_HLanguage ,&__HLanguage);
gen _EDITMAT(const gen & args,GIAC_CONTEXT){
if (args.type==_STRNG && args.subtype==-1) return args;
#ifdef GIAC_HAS_STO_38
if (args.type!=_IDNT)
return gensizeerr(contextptr);
const char * id = args._IDNTptr->id_name;
if (id[0]!='M' || id[1]<'0' || id[1]>'9')
return gensizeerr(contextptr);
int i=id[1]-'0';
// EditMat(i?i-1:9);
#endif
return eval(args,1,contextptr);
}
static const char _EDITMAT_s []="EDITMAT";
static define_unary_function_eval_quoted (__EDITMAT,&giac::_EDITMAT,_EDITMAT_s);
define_unary_function_ptr5( at_EDITMAT ,alias_at_EDITMAT,&__EDITMAT,_QUOTE_ARGUMENTS,T_UNARY_OP_38);
#ifndef NO_NAMESPACE_GIAC
} // namespace giac
#endif // ndef NO_NAMESPACE_GIAC