maple_mode(1);
w := [ [ 1, 1, 1, 12, 9, 22, 8, 32, 7, 42, 6, 52, 5, 62, 4, 72, 3, 82, 2, 92, 1 ],
[ 2, 2, 1, 13, 9, 23, 8, 33, 7, 43, 6, 53, 5, 63, 4, 73, 3, 83, 2, 93, 1 ],
[ 3, 3, 1, 14, 9, 24, 8, 34, 7, 44, 6, 54, 5, 64, 4, 74, 3, 84, 2, 94, 1 ],
[ 4, 4, 1, 15, 9, 25, 8, 35, 7, 45, 6, 55, 5, 65, 4, 75, 3, 85, 2, 95, 1 ],
[ 5, 5, 1, 16, 9, 26, 8, 36, 7, 46, 6, 56, 5, 66, 4, 76, 3, 86, 2, 96, 1 ],
[ 6, 6, 1, 17, 9, 27, 8, 37, 7, 47, 6, 57, 5, 67, 4, 77, 3, 87, 2, 97, 1 ],
[ 7, 7, 1, 18, 9, 28, 8, 38, 7, 48, 6, 58, 5, 68, 4, 78, 3, 88, 2, 98, 1 ],
[ 8, 8, 1, 19, 9, 29, 8, 39, 7, 49, 6, 59, 5, 69, 4, 79, 3, 89, 2, 99, 1 ],
[ 9, 9, 1, 20, 9, 30, 8, 40, 7, 50, 6, 60, 5, 70, 4, 80, 3, 90, 2, 100, 1 ],
[10, 10, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ],
[11, 2, 10, 11, 1, 22, 8, 32, 7, 42, 6, 52, 5, 62, 4, 72, 3, 82, 2, 92, 1 ],
[12, 3, 10, 12, 1, 23, 8, 33, 7, 43, 6, 53, 5, 63, 4, 73, 3, 83, 2, 93, 1 ],
[13, 4, 10, 13, 1, 24, 8, 34, 7, 44, 6, 54, 5, 64, 4, 74, 3, 84, 2, 94, 1 ],
[14, 5, 10, 14, 1, 25, 8, 35, 7, 45, 6, 55, 5, 65, 4, 75, 3, 85, 2, 95, 1 ],
[15, 6, 10, 15, 1, 26, 8, 36, 7, 46, 6, 56, 5, 66, 4, 76, 3, 86, 2, 96, 1 ],
[16, 7, 10, 16, 1, 27, 8, 37, 7, 47, 6, 57, 5, 67, 4, 77, 3, 87, 2, 97, 1 ],
[17, 8, 10, 17, 1, 28, 8, 38, 7, 48, 6, 58, 5, 68, 4, 78, 3, 88, 2, 98, 1 ],
[18, 9, 10, 18, 1, 29, 8, 39, 7, 49, 6, 59, 5, 69, 4, 79, 3, 89, 2, 99, 1 ],
[19, 10, 10, 19, 1, 30, 8, 40, 7, 50, 6, 60, 5, 70, 4, 80, 3, 90, 2, 100, 1 ],
[20, 20, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ],
[21, 2, 10, 12, 9, 21, 1, 32, 7, 42, 6, 52, 5, 62, 4, 72, 3, 82, 2, 92, 1 ],
[22, 3, 10, 13, 9, 22, 1, 33, 7, 43, 6, 53, 5, 63, 4, 73, 3, 83, 2, 93, 1 ],
[23, 4, 10, 14, 9, 23, 1, 34, 7, 44, 6, 54, 5, 64, 4, 74, 3, 84, 2, 94, 1 ],
[24, 5, 10, 15, 9, 24, 1, 35, 7, 45, 6, 55, 5, 65, 4, 75, 3, 85, 2, 95, 1 ],
[25, 6, 10, 16, 9, 25, 1, 36, 7, 46, 6, 56, 5, 66, 4, 76, 3, 86, 2, 96, 1 ],
[26, 7, 10, 17, 9, 26, 1, 37, 7, 47, 6, 57, 5, 67, 4, 77, 3, 87, 2, 97, 1 ],
[27, 8, 10, 18, 9, 27, 1, 38, 7, 48, 6, 58, 5, 68, 4, 78, 3, 88, 2, 98, 1 ],
[28, 9, 10, 19, 9, 28, 1, 39, 7, 49, 6, 59, 5, 69, 4, 79, 3, 89, 2, 99, 1 ],
[29, 10, 10, 20, 9, 29, 1, 40, 7, 50, 6, 60, 5, 70, 4, 80, 3, 90, 2, 100, 1 ],
[30, 30, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ],
[31, 2, 10, 12, 9, 22, 8, 31, 1, 42, 6, 52, 5, 62, 4, 72, 3, 82, 2, 92, 1 ],
[32, 3, 10, 13, 9, 23, 8, 32, 1, 43, 6, 53, 5, 63, 4, 73, 3, 83, 2, 93, 1 ],
[33, 4, 10, 14, 9, 24, 8, 33, 1, 44, 6, 54, 5, 64, 4, 74, 3, 84, 2, 94, 1 ],
[34, 5, 10, 15, 9, 25, 8, 34, 1, 45, 6, 55, 5, 65, 4, 75, 3, 85, 2, 95, 1 ],
[35, 6, 10, 16, 9, 26, 8, 35, 1, 46, 6, 56, 5, 66, 4, 76, 3, 86, 2, 96, 1 ],
[36, 7, 10, 17, 9, 27, 8, 36, 1, 47, 6, 57, 5, 67, 4, 77, 3, 87, 2, 97, 1 ],
[37, 8, 10, 18, 9, 28, 8, 37, 1, 48, 6, 58, 5, 68, 4, 78, 3, 88, 2, 98, 1 ],
[38, 9, 10, 19, 9, 29, 8, 38, 1, 49, 6, 59, 5, 69, 4, 79, 3, 89, 2, 99, 1 ],
[39, 10, 10, 20, 9, 30, 8, 39, 1, 50, 6, 60, 5, 70, 4, 80, 3, 90, 2, 100, 1 ],
[40, 40, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ],
[41, 2, 10, 12, 9, 22, 8, 32, 7, 41, 1, 52, 5, 62, 4, 72, 3, 82, 2, 92, 1 ],
[42, 3, 10, 13, 9, 23, 8, 33, 7, 42, 1, 53, 5, 63, 4, 73, 3, 83, 2, 93, 1 ],
[43, 4, 10, 14, 9, 24, 8, 34, 7, 43, 1, 54, 5, 64, 4, 74, 3, 84, 2, 94, 1 ],
[44, 5, 10, 15, 9, 25, 8, 35, 7, 44, 1, 55, 5, 65, 4, 75, 3, 85, 2, 95, 1 ],
[45, 6, 10, 16, 9, 26, 8, 36, 7, 45, 1, 56, 5, 66, 4, 76, 3, 86, 2, 96, 1 ],
[46, 7, 10, 17, 9, 27, 8, 37, 7, 46, 1, 57, 5, 67, 4, 77, 3, 87, 2, 97, 1 ],
[47, 8, 10, 18, 9, 28, 8, 38, 7, 47, 1, 58, 5, 68, 4, 78, 3, 88, 2, 98, 1 ],
[48, 9, 10, 19, 9, 29, 8, 39, 7, 48, 1, 59, 5, 69, 4, 79, 3, 89, 2, 99, 1 ],
[49, 10, 10, 20, 9, 30, 8, 40, 7, 49, 1, 60, 5, 70, 4, 80, 3, 90, 2, 100, 1 ],
[50, 50, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ],
[51, 2, 10, 12, 9, 22, 8, 32, 7, 42, 6, 51, 1, 62, 4, 72, 3, 82, 2, 92, 1 ],
[52, 3, 10, 13, 9, 23, 8, 33, 7, 43, 6, 52, 1, 63, 4, 73, 3, 83, 2, 93, 1 ],
[53, 4, 10, 14, 9, 24, 8, 34, 7, 44, 6, 53, 1, 64, 4, 74, 3, 84, 2, 94, 1 ],
[54, 5, 10, 15, 9, 25, 8, 35, 7, 45, 6, 54, 1, 65, 4, 75, 3, 85, 2, 95, 1 ],
[55, 6, 10, 16, 9, 26, 8, 36, 7, 46, 6, 55, 1, 66, 4, 76, 3, 86, 2, 96, 1 ],
[56, 7, 10, 17, 9, 27, 8, 37, 7, 47, 6, 56, 1, 67, 4, 77, 3, 87, 2, 97, 1 ],
[57, 8, 10, 18, 9, 28, 8, 38, 7, 48, 6, 57, 1, 68, 4, 78, 3, 88, 2, 98, 1 ],
[58, 9, 10, 19, 9, 29, 8, 39, 7, 49, 6, 58, 1, 69, 4, 79, 3, 89, 2, 99, 1 ],
[59, 10, 10, 20, 9, 30, 8, 40, 7, 50, 6, 59, 1, 70, 4, 80, 3, 90, 2, 100, 1 ],
[60, 60, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ],
[61, 2, 10, 12, 9, 22, 8, 32, 7, 42, 6, 52, 5, 61, 1, 72, 3, 82, 2, 92, 1 ],
[62, 3, 10, 13, 9, 23, 8, 33, 7, 43, 6, 53, 5, 62, 1, 73, 3, 83, 2, 93, 1 ],
[63, 4, 10, 14, 9, 24, 8, 34, 7, 44, 6, 54, 5, 63, 1, 74, 3, 84, 2, 94, 1 ],
[64, 5, 10, 15, 9, 25, 8, 35, 7, 45, 6, 55, 5, 64, 1, 75, 3, 85, 2, 95, 1 ],
[65, 6, 10, 16, 9, 26, 8, 36, 7, 46, 6, 56, 5, 65, 1, 76, 3, 86, 2, 96, 1 ],
[66, 7, 10, 17, 9, 27, 8, 37, 7, 47, 6, 57, 5, 66, 1, 77, 3, 87, 2, 97, 1 ],
[67, 8, 10, 18, 9, 28, 8, 38, 7, 48, 6, 58, 5, 67, 1, 78, 3, 88, 2, 98, 1 ],
[68, 9, 10, 19, 9, 29, 8, 39, 7, 49, 6, 59, 5, 68, 1, 79, 3, 89, 2, 99, 1 ],
[69, 10, 10, 20, 9, 30, 8, 40, 7, 50, 6, 60, 5, 69, 1, 80, 3, 90, 2, 100, 1 ],
[70, 70, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ],
[71, 2, 10, 12, 9, 22, 8, 32, 7, 42, 6, 52, 5, 62, 4, 71, 1, 82, 2, 92, 1 ],
[72, 3, 10, 13, 9, 23, 8, 33, 7, 43, 6, 53, 5, 63, 4, 72, 1, 83, 2, 93, 1 ],
[73, 4, 10, 14, 9, 24, 8, 34, 7, 44, 6, 54, 5, 64, 4, 73, 1, 84, 2, 94, 1 ],
[74, 5, 10, 15, 9, 25, 8, 35, 7, 45, 6, 55, 5, 65, 4, 74, 1, 85, 2, 95, 1 ],
[75, 6, 10, 16, 9, 26, 8, 36, 7, 46, 6, 56, 5, 66, 4, 75, 1, 86, 2, 96, 1 ],
[76, 7, 10, 17, 9, 27, 8, 37, 7, 47, 6, 57, 5, 67, 4, 76, 1, 87, 2, 97, 1 ],
[77, 8, 10, 18, 9, 28, 8, 38, 7, 48, 6, 58, 5, 68, 4, 77, 1, 88, 2, 98, 1 ],
[78, 9, 10, 19, 9, 29, 8, 39, 7, 49, 6, 59, 5, 69, 4, 78, 1, 89, 2, 99, 1 ],
[79, 10, 10, 20, 9, 30, 8, 40, 7, 50, 6, 60, 5, 70, 4, 79, 1, 90, 2, 100, 1 ],
[80, 80, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ],
[81, 2, 10, 12, 9, 22, 8, 32, 7, 42, 6, 52, 5, 62, 4, 72, 3, 81, 1, 92, 1 ],
[82, 3, 10, 13, 9, 23, 8, 33, 7, 43, 6, 53, 5, 63, 4, 73, 3, 82, 1, 93, 1 ],
[83, 4, 10, 14, 9, 24, 8, 34, 7, 44, 6, 54, 5, 64, 4, 74, 3, 83, 1, 94, 1 ],
[84, 5, 10, 15, 9, 25, 8, 35, 7, 45, 6, 55, 5, 65, 4, 75, 3, 84, 1, 95, 1 ],
[85, 6, 10, 16, 9, 26, 8, 36, 7, 46, 6, 56, 5, 66, 4, 76, 3, 85, 1, 96, 1 ],
[86, 7, 10, 17, 9, 27, 8, 37, 7, 47, 6, 57, 5, 67, 4, 77, 3, 86, 1, 97, 1 ],
[87, 8, 10, 18, 9, 28, 8, 38, 7, 48, 6, 58, 5, 68, 4, 78, 3, 87, 1, 98, 1 ],
[88, 9, 10, 19, 9, 29, 8, 39, 7, 49, 6, 59, 5, 69, 4, 79, 3, 88, 1, 99, 1 ],
[89, 10, 10, 20, 9, 30, 8, 40, 7, 50, 6, 60, 5, 70, 4, 80, 3, 89, 1, 100, 1 ],
[90, 90, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ],
[91, 2, 10, 12, 9, 22, 8, 32, 7, 42, 6, 52, 5, 62, 4, 72, 3, 82, 2, 91, 1 ],
[92, 3, 10, 13, 9, 23, 8, 33, 7, 43, 6, 53, 5, 63, 4, 73, 3, 83, 2, 92, 1 ],
[93, 4, 10, 14, 9, 24, 8, 34, 7, 44, 6, 54, 5, 64, 4, 74, 3, 84, 2, 93, 1 ],
[94, 5, 10, 15, 9, 25, 8, 35, 7, 45, 6, 55, 5, 65, 4, 75, 3, 85, 2, 94, 1 ],
[95, 6, 10, 16, 9, 26, 8, 36, 7, 46, 6, 56, 5, 66, 4, 76, 3, 86, 2, 95, 1 ],
[96, 7, 10, 17, 9, 27, 8, 37, 7, 47, 6, 57, 5, 67, 4, 77, 3, 87, 2, 96, 1 ],
[97, 8, 10, 18, 9, 28, 8, 38, 7, 48, 6, 58, 5, 68, 4, 78, 3, 88, 2, 97, 1 ],
[98, 9, 10, 19, 9, 29, 8, 39, 7, 49, 6, 59, 5, 69, 4, 79, 3, 89, 2, 98, 1 ],
[99, 10, 10, 20, 9, 30, 8, 40, 7, 50, 6, 60, 5, 70, 4, 80, 3, 90, 2, 99, 1 ],
[100, 100, 1, 101, 1, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0, 1,0 ],
[101, 1, 10, 11, 9, 21, 8, 31, 7, 41, 6, 51, 5, 61, 4, 71, 3, 81, 2, 91, 1 ] ] ;
m := makemat(0,101, 101):
l := [0$101]:
fill :=
proc() local k, j, l;
begin
for k from 1 to 101 do
// l:=m[k];
for j from 1 to 10 do
m[k, w[k, 2*j]] =< w[k, 2*j+1]; // l[w[k, 2*j]]:= w[k, 2*j+1];
end_for
// m[k]:=l;
end_for
"done";
end_proc;
fill();
det(m);
pcar(m);
// hermiteForm(m):
maple_mode(0);
det(m % 181);
pcar_hessenberg(m % 181);
maple_mode(1);
m2 := m:
fill2 :=
proc() local a, k, j;
begin
for k from 1 to 101 do
a := m2[k, 1];
l := m2[k];
for j from 1 to 100 do
l[j]:= m2[k, j+1]; // m2[k, j] := m2[k, j+1]
end_for;
m2[k]:=l;
m2[k, 101] := a
end_for
"done";
end_proc;
fill3 :=
proc() local k, j;
begin
for k from 1 to 101 do
l := m2[k];
for j from 1 to 101 do
if m[k, j] <> 0 then
l[j]:= m[k, j]; // m2[k, j] := m[k, j]
end_if
end_for
m2[k]:=l;
end_for
"done";
end_proc;
fill2();
fill3();
write("m2",m2);
det(m2);
pcar(m2);
maple_mode(0);
det(m2 %181);
pcar_hessenberg(m2 %181);
maple_mode(1);