Error, invalid input: PolynomialIdeals:-Quotient expects its 1st argument, J, to be of type Or(PolynomialIdeals:-PolynomialIdeal, radalgfun, list(radalgfun), set(radalgfun)), but received Vector(3, {(1) = 0, (2) = y^2-x-y, (3) = 0})

restart;

with(Groebner):

IsNullZero := proc(tau)

if assigned(tau) then

return tau

else

return 0

end if

end proc;

DoExist := proc(tau, n)

if rtable_num_elems(tau) >= n then

return tau[n];

else

return 0;

end if;

end proc;

LeadingTermVector := proc(a,b)

result := a;

for i from 1 to rtable_num_elems(a) do

result[i] = `*`(LeadingTerm(a[i], b));

od;

return result;

end proc;

LCMVector := proc(a,b)

result := a;

for i from 1 to rtable_num_elems(a) do

result[i] = lcm(a[i], b[i]);

od;

return result;

end proc;

SPolynomialVector := proc(a, b, c)

result := a;

for i from 1 to rtable_num_elems(a) do

result[i] = SPolynomial(a[i], b[i], c);

od;

return result;

end proc;

DivideVector := proc(a, b)

result8 := a;

for i from 1 to rtable_num_elems(a) do

if a[i] = 0 then

result8[i] = 0;

else

result8[i] = a[i]/b[i];

end if;

od;

return result8;

end proc;

BasisVector := proc(a, b, n)

result6 := 0;

for i from 1 to n do

result6[i] := 0;

od;

for i from 1 to n do

result6[i] := Basis(convert(a(i, 1 .. -1),list), b);

od;

return result6;

end proc;

NormalFormVector := proc(a, b, c, d, n)

for i from 1 to n do

NormalForm(a[i], b[i], c, d);

od;

end proc;

g1 := Vector([0, y, x]);

g2 := Vector([0, y^2-x-y, 0]);

g3 := Vector([x, x+y, 0]);

g4 := Vector([y, -y, 0]);

g5 := Vector([0, x*y+x/2+y/2, 0]);

g6 := Vector([0, x^2-x/4-y/4, 0]);

X1 := `*`(LeadingTermVector(g1, tdeg(x, y)));

X2 := `*`(LeadingTermVector(g2, tdeg(x, y)));

X3 := `*`(LeadingTermVector(g3, tdeg(x, y)));

X4 := `*`(LeadingTermVector(g4, tdeg(x, y)));

X5 := `*`(LeadingTermVector(g5, tdeg(x, y)));

X6 := `*`(LeadingTermVector(g6, tdeg(x, y)));

#X1 := `*`(LeadingTerm(g1, tdeg(x, y)));

#X2 := `*`(LeadingTerm(g2, tdeg(x, y)));

#X3 := `*`(LeadingTerm(g3, tdeg(x, y)));

#X4 := `*`(LeadingTerm(g4, tdeg(x, y)));

#X5 := `*`(LeadingTerm(g5, tdeg(x, y)));

#X6 := `*`(LeadingTerm(g6, tdeg(x, y)));

X12 := LCMVector(X1,X2);

X13 := LCMVector(X1,X3);

X14 := LCMVector(X1,X4);

X15 := LCMVector(X1,X5);

X16 := LCMVector(X1,X6);

X23 := LCMVector(X2,X3);

X24 := LCMVector(X2,X4);

X25 := LCMVector(X2,X5);

X26 := LCMVector(X2,X6);

X34 := LCMVector(X3,X4);

X35 := LCMVector(X3,X5);

X36 := LCMVector(X3,X6);

X45 := LCMVector(X4,X5);

X46 := LCMVector(X4,X6);

X56 := LCMVector(X5,X6);

with(PolynomialIdeals):

Quotient(X25,X2);