TP08.tst
2.29 KB
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"Warning: some commands like subs might change arguments order",
(t)->
begin
'nop';
cos(t)/sin(t)^3,sin(t)/sin(t)^3;
end,
(x,y,z)->x^3-3*x*y*z-z^3,
"Done",
"Done",
4,
(t^2+1)/t,
t,
proc(P,Q)
a:=expand(P[1]*Q[2]-P[2]*Q[1]);
b:=expand(P[3]*Q[2]-P[2]*Q[3]);
c:=expand(P[1]*Q[3]-P[3]*Q[1]);
if [a,b,c]=[0,0,0] then true;
fi ;
end;,
proc(a,b,c,P,Q)
local d,C,QQ,M,sol,R;
C:=(-y^2)*z+x^3+a*x^2*z+b*x*z^2+c*z^3;
if egal(P,Q) then
QQ:=[subs(x=(P[1]),y=(P[2]),z=(P[3]),diff(C,y)),subs(x=(P[1]),y=(P[2]),z=(P[3]),-(diff(C,x))),0];
M:=normal(P+t*QQ);
d:=subs(x=(M[1]),y=(M[2]),z=(M[3]),C);
sol:=quo(d,t^2,t);
if egal(QQ,[0,1,0]) then R:=[0,1,0]; else R:=normal((-coeff(sol,t,1))*P+coeff(sol,t,0)*QQ);
fi else
M:=expand(P+t*Q);
d:=subs(x=(M[1]),y=(M[2]),z=(M[3]),C);
sol:=quo(d,t,t);
R:=expand((-coeff(sol,t,1))*P+coeff(sol,t,0)*Q)
fi ;
end;,
[0,0,1],
[1,1,1],
[0,1,0],
0,
0,
[-1,-1,1],
[0,0,1],
[0,0,1],
[0,1,0],
[0,1,0],
proc(a,b,c,P,Q)
local R;
R:=pointresiduel(a,b,c,P,Q);
R[2]:=-(R[2]);
R;
end;,
[0,-1,0],
[0,0,1],
[0,-1,0],
[-1,1,1],
proc(a,b,c,P,n)
local Y,m,X;
Y:=[0,1,0];
X:=P;
m:=n;
while m>0 do if odd(m) then
Y:=plus(a,b,c,X,Y);
X:=plus(a,b,c,X,X);
m:=(m-1)/2 else
X:=plus(a,b,c,X,X);
m:=m/2
fi ;
od;;
Y;
end;,
[0,-1,0],[64,-64,64],[0,-512,0],[0,0,-512],[64,-64,64],[0,9223372036854775808,0],
"Done",
[37247908142/10128208321,7601802384416381/1019292757217119],
[-427565988743127340745490673457692672,-867064742032008311629520873313009664,-116260955875848891425809428000014336],
[0,0],
proc(P,N)
local Q,a,b,c,g;
Q:=[0,1,0];
a:=expand(P[1]*Q[2]-P[2]*Q[1]);
b:=expand(P[3]*Q[2]-P[2]*Q[3]);
c:=expand(P[1]*Q[3]-P[3]*Q[1]);
g:=igcd(a,b,c,N);
if (g<>1) and (g<>N) then g; else 1;
fi ;
end;,
proc(a,b,c,P,n,N)
local Y,m,X;
Y:=[0,1,0];
X:=P;
m:=n;
while (m>0) and ((egalomega(Y,N)) = 1) do
if odd(m) then
Y:=plus(a,b,c,X,Y);
X:=plus(a,b,c,X,X);
m:=(m-1)/2 else
X:=plus(a,b,c,X,X);
m:=m/2
fi ;
Y:=mods(Y,N);
X:=mods(X,N);
od;;
egalomega(Y,N);
end;,
232792560,
[2,1,1],
800620099,
1,
"Done",
9449868410449,
3099044504245996706400,
"Done"