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If you want to XOR you can just use integers directly with the ^^ operator in SageMath (or ^ in Python). Integers can be

Your first (original) attempt can be fixed by making k and K symbolic, and using substitution: import scipy.stats n=20

Here are the roots with multiplicities, using a different solution method: sage: R.<a,b,c,d,e,f,g,x> = QQ[] sage:

Here are the roots with multiplicities, using a different solution method: sage: R.<a,b,c,d,e,f,g,x> = QQ[] sage:

Yes it's possible like this: sage: var('a,b,c,d,e,f,g,h,i,j,k,l,x,y,p,q,r,s,t,u,v,A,B,C,D,E,F,G,H,T,K,L,M,N') sage: sol

A basis of the quotient ring $K[x_1,\ldots,x_n]/I$ as a $K$-vector space is also called a normal basis of the ideal $I$.

Note Serving notebooks from local directory: /home/vickram, which could explain "no directories present". You could star

Why do you need to define a polynomial from a string? Sounds like it could be an XY problem.

Symbolic matrix: sage: matrix(SR, 3, 2, lambda i,j: var('x_{}_{}'.format(i,j))) [x_0_0 x_0_1] [x_1_0 x_1_1] [x_2_0 x_2_

The result of Df(x1,x2) is a vector with symbolic entries, and testing equality with the tuple (0, 0) returns False, hen

That inconsistent behavior in the univariate case looks undesirable to me, but changing it would break compatibility wit

You can map z in L0 to one of z.minpoly().change_ring(L).roots(multiplicities=False) in L. Unfortunately defining a homo

That p does not belong to that I, so no valid choice of c exists in that case. Did you make a typing mistake somewhere i

That p does not belong to that I, so no valid choice of c exists. Did you make a typing mistake somewhere in your input?

There is a subdivide_edges method but it doesn't seem to give control over the names of the new vertices. If I understo

There is a subdivide_edges method but it doesn't seem to give control over the names of the new vertices. If I understo

The definition of mu looks suspicious, as alph is simply overwritten with each iteration of the loop.

You will need something like a custom Jupyter Widget to achieve this. Such a widget would be usable more generally than

If you enter PermutationGroupElement? at a SageMath prompt you will see the required format of the input, and that your

Where do you get 0x7f7467c66450 from? It is too large to correspond to an element of the field F.

Where do you get 0x7f7467c66450 from?

An efficient way is to use directg from nauty, which is accessible in SageMath through digraphs.nauty_directg. The optio

I've updated the answer to address the second part of the question.

An efficient way is to use directg from nauty, which is accessible in SageMath through digraphs.nauty_directg. The optio

An efficient way is to use directg from nauty, which is accessible in SageMath through digraphs.nauty_directg. The optio

The break in the code should be continue instead.

The method from section 5 of Computing power integral bases in algebraic number fields yields that the powers of (c + 1)

Are you sure you want e.polynomial(R)? (Check the parent/ring of the element you get; it is probably not what you want.)

You can use MakeCallable = vector: sage: R=PolynomialRing(QQ,5,"x") sage: R.inject_variables() Defining x0, x1, x2, x3,

You can't really, unless you make a custom type, or call a custom printing function. I offer SageMath's Set as an altern

To circumvent this problem the frozenset (which can't be modified after creation) was invented: sage: a.add(frozenset(b

To circumvent this problem the frozenset (which can't be modified after creation) was invented: sage: a.add(frozenset(b

You are operating on the wrong types. The extended euclidean algorithm takes polynomials as input and returns polynomial

You are operating on the wrong types. The extended euclidean algorithm takes polynomials as input and returns polynomial

You are operating on the wrong types. The extended euclidean algorithm takes polynomials as input. Elements of a finite

You can define the symmetric group on your set instead: sage: P = SymmetricGroup(var('x,y,z')); P Symmetric group of or

For a symbolic approach you can use a substitution with a wildcard: sage: var('p,a') sage: f = (a*p+1)^2 sage: w0 = SR.

Your bash script should say e.g. sage HPC2.sage instead of trying to use two lines like that. Whoever offers access to t