# Questions tagged [symbolic-computation]

The symbolic-computation tag has no usage guidance.

26
questions

**3**

votes

**1**answer

147 views

### Symbolic powers of a prime ideal of height one

Can someone please give me an example of a Noetherian normal local domain of dimension two such that there exists a prime ideal $P$ of height one having the property $P^{(n)}$ is not a principal ideal ...

**0**

votes

**0**answers

160 views

### Advice on how to deal with an elementary "long-to-prove" statement

I am not entirely sure if this question totally fits here. If it doesn't, I apologise in advance.
In a paper I've been working on, we have a very elegant result which, when forgetting about the ...

**2**

votes

**0**answers

134 views

### How to decide if an algebraic number is a root of a given polynomial?

Let $p$ be a polynomial with rational coefficients and $\alpha = \sqrt[n]{q}e^{i2k\pi/m}$ for some natural numbers $n,m,k$ and a rational number $q > 0$. Is there an effective algorithm for ...

**4**

votes

**0**answers

183 views

### Effective bounds for a Bertini-type result

Suppose $X$ is a projective subvariety of $\mathbb{P}^n$ of codimension $r$ over $\mathbb{C}$, defined set-theoretically by $r$ homogeneous polynomials $P_1,\dots,P_r$ of degree at most $d$. By ...

**7**

votes

**2**answers

158 views

### Books/Lecture notes which contrast Risch algorithm with basic standard procedure of finding an antiderivative

I vaguely remember a book/some lecture notes which introduce integration algorithms such as Risch algorithm by first giving a list of quasi-algorithmic way of evaluating symbolic integrals. (For ...

**2**

votes

**1**answer

102 views

### Existence of solutions of polynomials systems (and their "rough" shape) over $\mathbb{R}$ & friends with positive-dimensional ideals

This is a follow-up (but self-contained) question to my previous one. There I asked about state-of-the-art methods to solve multivariate polynomials systems over non-algebraically closed fields in ...

**1**

vote

**0**answers

360 views

### Differences between GAP and MAGMA [closed]

GAP and MAGMA are computer algebra systems. What are the objective differences between the two?
Which capabilities are not shared?
How do they compare on facilities for working with character tables?...

**2**

votes

**1**answer

63 views

### CAS implementing free algebras with involution

Is there any software that easily allows to make symbolic computations with involutions and homomorphisms? I need to define a product in an associative algebra with an (abstract) involution and ...

**22**

votes

**3**answers

5k views

### Minimal polynomial of cos(π/n)

I know that $\cos(\pi/n)$ is a root of the Chebyshev polynomial $(T_n + 1)$, in fact it is the largest root of that polynomial, but often that polynomial factors. For example, if $n = 2 k$ then $\cos(\...

**5**

votes

**1**answer

228 views

### speeding up Gosper and WZ algorithms

In our ongoing work to speed up symbolic summation and other similar algorithms in Sagemath, we notice that naive implementations of Gosper and Wilf-Zeilberger (a.k.a. WZ) algorithms are usually quite ...

**7**

votes

**2**answers

2k views

### Fast Symbolic Linear Algebra CAS?

I am a regular user of Mathematica, Julia, and MATLAB but I am looking for something different. The problem I am trying to solve in Mathematica only requires (dense) linear algebra to specify but is ...

**6**

votes

**1**answer

353 views

### Finite field analogue of Chebotaryov theorem on roots of unity?

Chebotarev's theorem on roots of unity says that all the minors of a prime-length DFT matrix over the complex numbers are nonzero. I was wondering if there was an analogue for finite fields.
More ...

**3**

votes

**0**answers

105 views

### Algorithmic quantifier elimination over p-adic fields

It is known that the first-order theory of p-adic fields is decidable, and that the p-adics admit elimination of quantifiers. What is the state of the art in algorithmic aspects of quantifier ...

**6**

votes

**2**answers

691 views

### How to compute the normals to Costa's minimal surface?

I am trying to draw Costa's minimal surface in high resolution using the PovRay raytracer. For this I need to compute points on the surface as well as the normals. It is relatively easy to compute the ...

**1**

vote

**0**answers

183 views

### 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 ...

**2**

votes

**1**answer

998 views

### Finding zeros of a multi-variable nonlinear trigonometric function

I am trying to calculate analytic solution (or locus) of zeros of a very large multi-variable function which is consisted of thousands of nonlinear trigonometric terms. All the variables are real ...

**5**

votes

**1**answer

500 views

### The existential theory of the reals

Some definitions of the existential theory of the reals (ETR) allow a real closed field and some definitions allow only rational numbers as coefficients of polynomials. Which one is correct? Will the ...

**2**

votes

**0**answers

96 views

### Tools for "bound guessing"

I have a somewhat complicated symbolic expression of the form $\frac{J-a+\frac{q}{a}}{J(J-a)+q}$, where $J,a$ and $q$ are themselves affine functions of four other variables $d,r,c,s$, and I want to ...

**2**

votes

**1**answer

354 views

### Computer algebra system (CAS) with good re-presenting or transformation support

Such heavy-weight transformations as expanding or factoring are provided by most of CAS-es, but what about light-weight, but a useful transformations, like "reorder some terms to make expression more ...

**5**

votes

**0**answers

255 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 "...

**2**

votes

**2**answers

2k 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 ...

**4**

votes

**1**answer

745 views

### Symbolic computations with differential operators (universal envelopings i.e. non-commutative variables) ?

Please give suggestions about soft to make symbolic computations with NON-commutative variables.
Typical examples I am interesting - Capelli identities
http://en.wikipedia.org/wiki/Capelli'...

**1**

vote

**0**answers

1k views

### symbolic diagonalization of a matrix

Hi,
I am looking for algorithms that can perform a diagonalization, in a symbolic way,
of a given matrix. I need to find a similarity transformation, if it exists. Desired features of the algorithms ...

**3**

votes

**2**answers

516 views

### What are some resources discussing mathematical notation?

I'm looking for resources discussing mathematical notation, the theory, the philosophy, the distinct advantages of various notations. Stuff about notation for computer algebra systems is interesting ...

**2**

votes

**2**answers

2k views

### The easiest symbolic integration method to try implementing.

Hello! I wonder how hard is it to implement more or less general symbolic integration algorithm (number of lines in a certain language)? Maybe someone here did this or knows some good blog posts ...

**6**

votes

**0**answers

1k views

### Why is mechanical differentiation so hard to get right?

This question is related to this question on differentiation/integration which asks why differentiation is mechanical but integration is an art. The answers given all make a huge assumption: that one ...