2023-06-08 18:29:51 +0200 received badge ● Famous Question (source) 2022-10-30 13:18:47 +0200 received badge ● Notable Question (source) 2022-06-24 21:25:30 +0200 received badge ● Notable Question (source) 2022-02-06 15:48:08 +0200 received badge ● Popular Question (source) 2021-04-13 10:52:00 +0200 received badge ● Popular Question (source) 2021-02-04 10:30:42 +0200 commented question Sage crash when computing variety for an ideal with many variables @rburing I understand that the Groebner basis is a set of polynomials then equated to 0 the solutions to these equations are the variety that I want. But Sage's variety function doesn't allow to choose which algorithm to use to calculate the Groebner basis. I can compute the Groebner basis with either I.groebner_basis(algorithm='singular:std') or I.groebner_basis() so this doesn't seem to be the issue. 2021-02-03 20:48:28 +0200 received badge ● Nice Question (source) 2021-02-03 19:40:03 +0200 commented question Sage crash when computing variety for an ideal with many variables @rburing Thank you for your comment, the code in my questions fails as expected now. If I understand right, the last three lines should be changes as you suggested. 2021-02-03 18:59:18 +0200 commented question Sage crash when computing variety for an ideal with many variables How do I that? 2021-02-02 13:04:30 +0200 asked a question Sage crash when computing variety for an ideal with many variables I try to run a code (on a Jupyter notebook) which computes the variety of an ideal for some polynomial in many variables (64 for in this case. Notice I solve for a and not for x,y,z). My code crashes with the following message: RuntimeError: error in Singular function call 'groebner': int overflow in hilb 1 error occurred in or before standard.lib::stdhilb line 299:  intvec hi = hilb( Id(1),1,W ); expected intvec-expression. type 'help intvec;' leaving standard.lib::stdhilb leaving standard.lib::groebner  This is the code: K = PolynomialRing(GF(2),2^6,'a') R = K["x, y, z"] x, y, z = R.gens()[0], R.gens()[1], R.gens()[2] a = K.gens() pbc = lambda p :(( p%(x^4+1))%(y^4+1))%(z^4+1) e_L = Matrix([[R((1 + x + y + z)^(2^4)/(1 + x + y + z))], [0]]) X,Y,Z = [Matrix(g.powers(4)) for g in [x,y,z]] XY=X.tensor_product(Y) XYZ = XY.tensor_product(Z) poly = (Matrix(a)*XYZ.transpose())[0,0] RHS_eq = Matrix([[pbc((1 + x*y + x*z + y*z) * poly)], [pbc((1 + x + y + z) * poly)]]) IJK = list(Words(alphabet=range(4), length=3)) for i,j,k in IJK: P = pbc(e_L + (x^i*y^j*z^k)*e_L) lhs = RHS_eq + P Eq = Matrix([[R(lhs[0,0])], [R(lhs[1,0])]]) I = K.ideal(Eq[0,0].coefficients() + Eq[1,0].coefficients() + [q^4+q for q in K.gens()]) sols = I.variety(GF(2^6,'w')) sols_arr = np.asarray([list(sol.values()) for sol in sols]) print(sols_arr)  2021-01-28 09:20:12 +0200 commented answer Solve for coefficients of polynomials @tmonteil I changed the names as you suggested, I got another error (my question was updeated) 2021-01-27 18:34:30 +0200 received badge ● Editor (source) 2021-01-27 18:13:17 +0200 received badge ● Student (source) 2021-01-27 17:53:43 +0200 asked a question Solve for coefficients of polynomials I want to solve for the coefficients $\alpha(n, m, k)$ an equation that looks like this: $$0 = (1 + x + y + z) \sum_{n, m, k \in \{0, 1, \dots, N\}} \alpha(n, m, k) x^n y^m z^k$$ where $\alpha(n, m, k) \in \{0, 1\}$ and $x^n y^m z^k$ are polynomials over $\mathbb{F}_2$ that satisfy $x^L = y^L = z^L = 1$ for some integer $L$. Is there a way to do this in Sage? Notice there are three generators $x,y,$ but the number of coefficents $\alpha$ is $2^{3L}$. I tried to follow this answer and wrote this code that failed- R = PolynomialRing(GF(2),3,"xyz") x,y,z = R.gens() S. = R.quotient((x^2 + 1,y^2+1,z^2+1)) K = PolynomialRing(GF(2),2,'q') # Coefficients q = K.gens() Pol = (q[1]*a+q[0])*(a*b)-5*b*a # Equation to solve I = K.ideal(Pol.coefficients()) I.variety()  And I get the following error: TypeError Traceback (most recent call last) in 5 q = K.gens() 6 ----> 7 Pol = (q[Integer(1)]*a+q[Integer(0)])*(a*b)-Integer(5)*b*a # Equation to solve 8 9 K.ideal(Pol.coefficients()) /opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/structure/element.pyx in sage.structure.element.Element.__mul__ (build/cythonized/sage/structure/element.c:12199)() 1513 return (left)._mul_(right) 1514 if BOTH_ARE_ELEMENT(cl): -> 1515 return coercion_model.bin_op(left, right, mul) 1516 1517 cdef long value /opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/structure/coerce.pyx in sage.structure.coerce.CoercionModel.bin_op (build/cythonized/sage/structure/coerce.c:11304)() 1246 # We should really include the underlying error. 1247 # This causes so much headache. -> 1248 raise bin_op_exception(op, x, y) 1249 1250 cpdef canonical_coercion(self, x, y): TypeError: unsupported operand parent(s) for *: 'Multivariate Polynomial Ring in q0, q1 over Finite Field of size 2' and 'Quotient of Multivariate Polynomial Ring in x, y, z over Finite Field of size 2 by the ideal (x^2 + 1, y^2 + 1, z^2 + 1)'