# Tagged Questions

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### Plot Cayley graphs for generic element groups

I'm a beginner in Abstract Algebra, currently trying to solve all exercises in "A Book of Abstract Algebra" by Pinter. I was wondering if there is a way to draw Cayley graphs for generic element ...
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### In SAGE, what function factors a polynomial whose coefficients are parameters?

In SAGE the function "factor" will factorize elementary polynomials with coefficients in $\Bbb Q$. For example: x,y = var('x,y') poly = x^3-y^2*x factor(poly) SAGE: x*(x-y)*(x+y) ...
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### hasse diagram of a subset of a poset in sage

E = {1,2,3} P = SetPartitions(E) This gives the set of all partitions of E,. I have a subset Q of P and I want to construct the directed graph whose vertex set is this set Q and we draw an arrow ...
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### Multivariate Polynomials Sage

Sorry if I'm in the wrong Stackexchange (but sage is a math program...) I'm computing something on multivariate polynomials: I have a primary variable $x$ and several other variables $a, b, c, \dots$....
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### SAGE: Is it possible to extract the irreducible factor of a polynomial for the purpose of constructing a Number Field?

I'm in the middle of making a program that tests a certain fact for many number fields. At this current step I get say a hundred polynomials, which are reducible. I want to factor them (over Q), take ...
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### Genus of the graph $K_{4,2,2,2}$.

What is the genus of the complete $4-$partite graph $K_{4,2,2,2}$? What i know: Since $K_{4,4,2}$ is a subgraph of $K_{4,2,2,2}$, and genus of $K_{4,4,2}$ is 2, $K_{4,2,2,2}$ has genus greater than ...
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I asked a question the other day: Multidimensional Hensel lifting which @Hurkyl kindly and very elegantly answered. A follow-on from this is that I have tried to implement exactly the "algorithm" ...
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### $\mathbb{Q}$ isn't a number field for SAGE

This is more a question about the weird behavior of SAGE: ...
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### Using sage to test for squares in residue fields

Let $K$ be a number field, $x \in \mathcal{O}_K$, and $\mathfrak{p}$ a prime of $K$. I want to find out using sage whether or not the reduction of $x$ modulo $\mathfrak{p}$ is a square in the ...
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### Software for computing generators of the invariant rings of the symmetric groups

(Please skip to the last paragraph if you are interested in just the question) I wish to compute the generators of the ring of invariants for a symmetric group acting on a polynomial ring using a ...
Let us define an associative algebra over $\mathbb{C}$ with generators $x, y, z$ and the following relations: $x^2=x, y^2=y, z^2=z, 2yxy=y, 3zyz=z, xz=zx$. I am interested in finding center of this ...