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Like this: sage: R.<x> = PolynomialRing(GF(2)) sage: f = x^3 - 1 sage: g = x - 1 sage: f // g x^2 + x + 1 sage: t

sage: R.<x> = PolynomialRing(GF(2)) sage: f = x^3 - 1 sage: g = x - 1 sage: f // g x^2 + x + 1

sage: R.<x> = PolynomialRing(GF(2)) sage: f = x^3 - 1 sage: g = x - 1 sage: f // g x^2 + x + 1 sage: type(f // g)

You can do it like this: sage: R.<x> = PolynomialRing(ZZ) sage: n = 3 sage: f = x^3 + 1 sage: all(n.divides(c) fo

You can do hdul[int(0)] to work around Sage's Integer wrapper for literal integers.

Indeed SageMathCell has a time limit for computations. That print statement is not executed because J1.dimension() is a

Yes, this is just a factorization: sage: var('μ,ν') sage: (μ^8+4*μ^6*ν^2+6*μ^4*ν^4+4*μ^2*ν^6+ν^8).factor() (μ^2 + ν^2)^

Go this way instead: sage: P = K.ideal(p) sage: R = P.residue_field() sage: R.cardinality() 13 sage: [z.lift() for z in

In fact the colors are correct but the labels are wrong. I've submitted a pull request to fix it here: Fix element la

In fact the colors are correct but the labels are wrong. I've submitted a pull request to fix it here: Fix element lab

I suppose you mean https://github.com/0xf0f/codenode Running sage -pip install 0xf0f-codenode works without issue on my

Sage displays all vector spaces with the basis given in rows of a matrix; see the documentation of basis_matrix. The ba

What you expected should be read sideways, and then it's just a different basis of the same column space: sage: A = mat

The explanation is that solve_diophantine simply calls sympy's diophantine, which ignores all assumptions. So you will

De rien! That is a valid use case for old SageMath versions of course. There are instructions for conversion of .sws to

De rien! That's is a valid use case for old SageMath versions of course. There are instructions for conversion of .sws t

De rien! That's is a valid use case for old SageMath versions of course. There are instructions for conversion of .sws t

Any particular reason you're using a version of Sage that's over four years old? Try sage -pip install astropy to instal

Any particular reason you're using a version of Sage that's over four years old? Try sage -pip install astropy to instal

It's A.one() like it is for most objects with a unit, but that doesn't seem to solve the problem.

With that definition DiGraph([(2, 3), (3, 0), (1, 0)]) would be stable (contrary to your example), is that right?

What is the precise definition of stable in this case? To me DiGraph([(1, 3), (3, 2), (2, 0)]) does not look stable unde

How is the initial element in QQbar constructed? Since you have hundreds of thousands of them, you might add at least on

How is the initial element in QQbar constructed? Since you have hundreds of thousands of them, you might add at least on

Which version of SageMath are you using? I remember investigating this over a year ago and the issue #33010 should be fi

Which version of SageMath are you using? I remember investigating this over a year ago and it should be fixed by #33010

What is the end goal here? This sounds like an XY problem. You might use an ExpressionTreeWalker to solve this problem Y

I think the syntax is inspired by Magma.

Instead of symbolic variables you can use the generators of a polynomial ring: sage: R.<x,y,z> = PolynomialRing(G

sage: mymatrix.apply_map(lambda z: z.expr()) [f(t, r, th, ph) + g(t, r, th, ph) g(t, r, th, ph)

You're welcome! Indeed it wouldn't make a difference in performance, it would just be cleaner than using the pexpect int

You can use Singular's notion of a ring with parameters, but Sage's PolynomialRing interface to Singular doesn't underst

Cross-posted to MathOverflow: Gröbner implicitization with relationships between the variables.

The solutions can all be expressed in terms of radicals: R.<x,y,z> = QQ[] I = R.ideal([x^2+y^2+z^2-2, x^3+y^3+z^3

The solutions can all be expressed in terms of radicals.

Do you want to do this just for linear functions? In that case I would just determine the intersection points and draw t

You should specify not only an ordering of variables but a monomial ordering or term ordering. An algorithm for the elim

Here is a different approach, not necessarily optimal but working: R.<c1, c2, x, y, cos_beta, sin_beta, r> = Poly

Here is a different approach, not necessarily optimal but working: R.<c1, c2, x, y, cos_beta, sin_beta, r> = Poly

Please add minimal working code to define your finite matrix group.