# Questions tagged [symbolic-computation]

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### 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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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?...
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 ...
5k views

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### 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'...
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 ...
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 ...