# Tagged Questions

Using computers to solve algebraic problems. Questions with this tag should typically include at least one other tag indicating what sort of algebraic problem is involved, such as ac.commutative-algebra or rt.representation-theory.

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### efficient arithmetic with (short) Conway games?

We consider "games" in the sense of ONAG. Conway's definition of a game $G$ as a pair $G = \{L \mid R \}$ of sets of games, together with the definitions of inequality and the arithmetic operations (...
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### Finding relations between invariant polynomials

Suppose I have an action of a linear reductive group ($GL(2,\mathbb{C})^2$ in this case) on a complex vector space (of dimension $16$) and I want to compute explicitly the ring of invariants of this ...
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### Finding particular reduced words for Weyl group elements

I am studying cluster algebra structures on the coordinate rings of partial flag varieties, as defined in the paper Partial flag varieties and preprojective algebras by Geiss, Leclerc and Schröer. One ...
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### Finding a generator of an ideal in an algebraic function field

I have an algebraic function field $\mathbb{Q}(x,y)$, where $y$ satisfies $$(y^2-1)^2 = x^2(1+x^2),$$ and I need to find a rational function that has a first order root at $x=0,y=1$ a first order ...
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### The Representation of $\mathrm{Sp}_{2n}$ of Dimension $2^n$ in characteristic 2

Let $G:=\mathrm{Sp}_{2n}$ be the simple algebraic group of simply connected type with root-system $C_n$. Is there a way, to explicitly construct the highest weight representation $\mathrm{L}(\lambda)$,...
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### Testing functional equivalence

We are looking for the most efficient (most recent, or best) techniques to check if two algebraic expressions (elementary, Calculus-type functions) are equivalent (or if an expression is equivalent to ...
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### Main open computational problems in quantifier elimination?

A language is said to have quantifier elimination if every first-order-logic sentence in the language can be shown to be equivalent to a quantifier-free sentence, i.e., a sentence without any $\forall$...
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### Using the Affine Maxima Package

The Maxima computer algebra system has a package called Affine for doing the calculations implicit in Bergman's diamond lemma for rings. It can be viewed as a kind of noncommutative analogue of ...
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### On finding A-polynomials

I have two questions to obtain the explicit forms of A-polynomials. Takata used the mathematica pacage qMultisum.m to obtain the recursion relation of the colored Jones polynomials for twist knots. ...
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### Non-Uniform Root of Polynomial in Open Cube

I'm looking to find a root $(x_1,\dots,x_n)$ of a polynomial $p \in {\mathbb R}[x_1,\dots,x_n]$ such that $0 \leq x_i < 1$ for all $i$. Further, I know in advance that setting $x_1 = \cdots = x_n$ ...
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### Reasonable implementation of finding Gröbner bases over non-field coefficient rings

Gröbner bases are usually considered in the ring of polynomials over a field. However, there are useful definitions and algorithms for Gröbner bases over other coefficient rings; see, for instance, ...
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### What is the largest computed summatory liouville interval ?

I am interested to know the largest computed summatory liouville interval, an implementation of which is detailed in Section 4.1 of [1]. The wikipedia page [2] for the function charts summatory ...
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I would like to be able to find maximum values of degree-3 homogeneous polynomials, when the variables are non-negative real numbers that sum to 1. For example, For example, the maximum value of $xy^... 0answers 255 views ### Computer Algebra solution for simplicial resolutions for André-Quillen cohomology Hello, I would like to experiment with André-Quillen (co)homology. Especially for singular rings. A key problem is that the construction of a simplicial resolution of a ring seems to require a rather ... 7answers 2k views ### Computer package for representation theory of the symmetric group Is there a computer algebra package in which I can compute the following for representations of a specific symmetric group (e.g.$S_7$): (1)$V \otimes W$(2)$S_\lambda V$, where$S_\lambda$is a ... 3answers 453 views ### the Richardson theorem and the base identities problem In the fields related to school mathematics there is some acitivity on proving (or disproving) deducibility/decidability for some classes of school identities. In particular, 1) In logic they ... 1answer 183 views ### Changing the Type of a Module in MAGMA I am currently working with irreducible$k[G]$-modules in MAGMA for finite fields$k$and finite groups$G$. To construct these modules, I am using the commands IrreducibleModules(G,k) This results in ... 2answers 338 views ### Working with group cosets in MAGMA When working with group cosets in MAGMA is there a way of treating the cosets as subsets of the overlying group. Specifically I have a group$G$and subgroups$H$and$K$. I wish ... 4answers 1k views ### Program for computing group cohomology Is there any computer program with which I can compute the group cohomology H^n(G,V) for a group G acting linearly on a vector space? I mainly care about infinite groups. 3answers 394 views ### Checking for invertibility of large matrices in MAGMA If you have a number of large matrices, and you wish to determine whether each matrix has determinant zero or not, what is the most efficient way to do this in MAGMA (it appears that calculating the ... 3answers 673 views ### Is there a way of canonically labelling permutation groups? When working with large numbers of graphs, a canonical labelling routine is essential as, after the initial cost of canonically labelling each graph, it permits isomorphism checks to be replaced with ... 0answers 236 views ### What became of PoSSo and FRISCO I know PoSSo and FRISCO were pretty big projects involving many European universities. Interestingly, I couldn't find much information about these projects (the the top of the PoSSo homepage says "... 2answers 326 views ### Monomial orderings in noncommutative setting An ordering of monomials in the free associative algebra$k\langle x_1,\ldots,x_n\rangle$is called a monomial ordering (EDIT: it seems that an equally common term used in this context is "term ... 1answer 396 views ### Basis of a Finite Dimensional Algebra with a Finitely Generated Relation Set By Computer Let$A$be a noncommutative finitely generated algebra with a finitely generated set of relations. Moreover, assume that$A$is finite dimensional as a vector space. What I want to know is, can ... 2answers 1k views ### Solving a system of equations/inequalities that have trigonometric functions on the left-hand side Is there any known (symbolic) method that solves a system of equations/inequalities that have trigonometric functions on the left-hand side of the system? Ex) Find$x,y,\theta \in \mathbb{R}$that ... 2answers 1k views ### Computing the fixed field of an automorphism of a function field Let say we have a function field$k(x,y)$defined by$f(x,y)$over$k$, with$\sigma \in Aut(k(x,y)/k)$and. Suppose, I'm not that out of luck, so that either of$\prod \sigma^i(x)$or$\sum \sigma^i(...
Group $A_5$ has presentation $〈 a, b | a^2 = b^3 = (ab)^5 = 1 〉$. Items equal to 1 are relators, so a presentation of $A_5$ as a set of relators could be $(a^2, b^3, (ab)^5)$ $Q_{16}$ is SmallGroup(...