# Questions tagged [computer-algebra]

Using computer-aid approach 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 or ag.algebraic-geometry.

**0**

votes

**1**answer

62 views

### Quantifier elimination and where is this quantified convex program in the polynomial hierarchy?

I have a quantified convex program of the form that I need to solve
$$\exists(x_{1,1},\dots,x_{1,n})\in\mathbb R^n\quad\forall(x_{2,1},\dots,x_{2,n})\in\mathbb R^n$$
$$\vdots$$
$$\exists(x_{2t-1,1},\...

**3**

votes

**1**answer

129 views

### Branching to Levi subgroups in SAGE and the circle action

In the SAGE computer package, there useful exist tools for branching representations of a simple Lie group to a Levi subgroup:
http://doc.sagemath.org/html/en/reference/combinat/sage/combinat/...

**-1**

votes

**1**answer

67 views

### Perform a univariate integral, involving a Gauss hypergeometric function

This is a follow-up question to the one posed in Compute the two-fold partial integral, where the three-fold full integral is known . (I hope that doing so is viewed as a legitimate step. If not so, I ...

**2**

votes

**4**answers

487 views

### Compute the two-fold partial integral, where the three-fold full integral is known

I have the following trivariate ($\rho_{11}, \rho_{22}, \mu$) function
\begin{equation}
4 \mu ^{3 \beta +1} \rho_{11}^{3 \beta +1} \left(-\rho_{11}-\rho_{22}+1\right){}^{3 \beta +1}
\rho_{22}^{3 \...

**1**

vote

**2**answers

178 views

### Computing Groebner basis for a complicated systems of polynomials

I am trying to solve complicated systems of polynomial equations. The first step is to determine maximal sets of independent variables for the solution manifold (ideal) or the number of isolated ...

**5**

votes

**2**answers

142 views

### Obtaining quiver and relations for finite p-groups

Given a finite field $K$ with $p$ elements and a finite $p$-group $G$, is there a way to obtain the quiver and relations of $KG$ with GAP (and its package QPA)?
Since $KG$ is local, the quiver should ...

**4**

votes

**0**answers

94 views

### Recovering the bimodule from the trivial extension

Given a ring $S$ with a non-zero $S$-bimodule $M$, the trivial extension of $(S,M)$ is defined as the ring $R:=T_M(S)$ with $R= S \oplus M$ with multiplication $(s,m)(s',m')=(s s', sm' +m s')$.
We ...

**0**

votes

**0**answers

53 views

### Quadrics over the univariate function field with discriminant of minimal degree

Consider a non-degenerate quadric $Q(x,y,z) \subset \mathrm{P}^2$ over the univariate function field $\mathbb{F}_p(t)$, where $\mathbb{F}_p$ is a prime finite field, $p > 2$. For simplicity assume ...

**1**

vote

**0**answers

123 views

### Computing the class-preserving automorphism group of finite $p$-groups

Let $G$ be a finite non-abelian $p$-group, where $p$ is a prime. An automorphism $\alpha$ of $G$ is called a class-preserving if for each $x\in G$, there exists an element $g_x\in G$ such that $\alpha(...

**3**

votes

**1**answer

84 views

### Computing double coset operators in a computer algebra system

I want to do double coset operators computations on modular forms of half integer weight and with character such as the trace operators that map modular forms of congruence subgroups $\Gamma_0(N)$ to ...

**2**

votes

**0**answers

48 views

### Obtaining the reduced incidence algebra in QPA

Given a finite poset $P$ (we can assume it is connected), the reduced incidence algebra of $P$ is the subalgebra of the incidence algebra of $P$ consisting of functions constant on isomorphic ...

**2**

votes

**0**answers

48 views

### Efficient algorithm to prove that a polynomial ideal contains 1

I have the following problem:
Suppose to have an ideal $I\triangleleft k[x_1,...,x_n]$ defined by generators. There exists an efficient algorithm (perhaps more efficient than calculating the Groebner ...

**0**

votes

**0**answers

106 views

### lcalc and the Analytic Rank of $y^2 = x^3 + 432764797 x^2 + 332896 x$

I'm looking at elliptic curves associated with $a/(b+c) + b/(a+c) + c/(a+b) = N$. For the case $N=10400$, Michael Rubinstein's lcalc gives the analytic rank of the associated elliptic curve $y^2 = x^3 ...

**5**

votes

**1**answer

224 views

### Calculating the Ext-algebra with a computer

Given a finite dimensional quiver algebra $A$ over an arbitrary field and a module $M$ of finite injective dimension or finite projective dimension.
Let $B$ be the Ext algebra of $M$, that is $B:=\...

**4**

votes

**0**answers

96 views

### Compute the closure of graph of function from complement of hypersurface in $\mathbb{A}^n$

I'm hoping someone can give me some tips to help speed up computation on the following problem:
Suppose I have a map $G=(g_1/f,\dots,g_m/f):\mathbb{A}^n\setminus{V(f)}\to \mathbb{A}^m$. I'm ...