# Questions tagged [symbolic-computation]

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### Prove the existence of a certain number of real solutions to a real coefficient nonlinear algebraic system

The factorization of a real element $3\times 4$ matrix $P=(p_{i,j})$, was finally converted into the problem of solving a $9\times 9$ nonlinear polynomial system as below. All $p_{i,j}$'s are ...
97 views

### Is the smallest root of this quartic always the closest point on the Hyperbola? [closed]

Let $a>b>0$. Suppose we want to minimize $$f(x)=(x-a)^2+(1/x-b)^2,$$ over $x>0$. Equating $f'(x)=0$ leads to the quartic equation $$g(x)=x^4-ax^3+bx-1=0. \tag{1}$$ Question: Is the ...
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1 vote
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### 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 ...
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### 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 ...
387 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 ...
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### 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 ...
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764 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 ...
• 45k
1 vote
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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 ...
1k 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
257 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 "...
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### 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 ...
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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'...
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1 vote
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### 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 ...
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### 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 ...
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 ...
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