**14**

votes

**6**answers

2k views

### “Oldest” bug in computer algebra system?

The goal of this question is to find an error in a computation by a computer algebra system where the 'correct' answer (complete with correct reasoning to justify the answer) can be found in the ...

**6**

votes

**3**answers

2k views

### Rational exponential expressions

Consider the following extension of polynomials. The rational exponential expressions (REXes) are given by:
The leaves 1 and $x$ for $x$ drawn from a class of variables; and
Closed under the binary ...

**75**

votes

**33**answers

18k views

### Computer Algebra Errors

In the course of doing mathematics, I make extensive use of computer-based calculations. There's one CAS that I use mostly, even though I occasionally come across out-and-out wrong answers.
After ...

**6**

votes

**1**answer

649 views

### Choosing a fast computer algebra system that works in characteristic p?

Hi all,
I want to compute in $\mathbb{F}_q (x)((y))$ i.e. a Laurent series ring over the rational functions over $\mathbb{F}_q$. The computations are fairly basic, but they involve raising to the qth ...

**3**

votes

**1**answer

402 views

### Decomposition of modules using computer packages

I am interested in computing direct sum decomposition of modules over some quotients of polynomial rings over a field (do not care much about the field at this point). Does any one know a package ...

**0**

votes

**1**answer

514 views

### Does MAGMA have a function to decide if two indefinite, integral quadratic forms are isometric?

Let's say we have two $n$-dimensional lattices $(V,b)$ and $(W,b_1)$ equipped with integral bilinear forms $b$ and $b_1$ respectively. Is there an implemented function in MAGMA that decides whether ...

**10**

votes

**2**answers

363 views

### Counting points on varieties of low codimension

The graduate students here at MIT have been thinking about questions like the following: Over $\mathbb{F}\_q$, how many symmetric matrices are there with nonzero determinant and $0$'s on the diagonal? ...

**0**

votes

**2**answers

110 views

### Properties of adjacent submatrixes [closed]

Hi!
I've encountered a matrix problem when designing an algorithm, which I cannot seem to figure out. I have a (square) matrix with the following properties:
j<k → aij<aik, aji<aki
...

**23**

votes

**4**answers

2k views

### Can Gröbner bases be used to compute solutions to large, real-world problems?

In particular, suppose I have an affine algebraic variety over $\mathbb{R}^n$ described by generators of a radical ideal $I$ and I want to find (perhaps not all of the) points in the variety. Several ...

**2**

votes

**4**answers

2k views

### Symmetrical Presentation of 4-Dimensional Rotation Matrix

This question is not urgent; just a matter of curiosity...
It is relatively easy to generate an arbitrary 3D or even 4D rotation matrix using conjugation (i.e. YXY−1) of orthogonal rotations. I ...

**7**

votes

**5**answers

4k views

### Finding minimal or canonical expressions for Boolean truth tables

This is not an urgent question, but something I've been curious about for quite some time.
Consider a Boolean function in n inputs: the truth table for this function has 2n rows.
There are uses of ...

**10**

votes

**9**answers

2k views

### Is there a non self-referencing non-computable function?

I've seen in college that some functions are not computable.
The proof for that was the case of Halt(x,y) function.
The thing is, the proof used a very artificial (IMHO) case
which is evaluating ...

**2**

votes

**4**answers

397 views

### CAS for finding closed form solutions to PDEs and SDEs?

Are there any specialized Computer Algebra Systems (or packages for these) for finding closed form solutions to
a) partial differential equations,
b) stochastic differential equations?
If yes, what ...

**9**

votes

**3**answers

1k views

### Is there a stable algorithm for polynomial division (in several variables)?

Suppose you have a homogeneous ideal $I$ inside the algebra $\mathbb{C}[x_1,...,x_d]$ of complex polynomials in $d$-variables. Can one find a basis for $I$, say $\{f_1,...,f_k\}$, such that every $h ...

**5**

votes

**4**answers

443 views

### Sections of a divisor on elliptic curve

I'm interested in producing explicit bases for the sections of a line bundle on an embedded genus 1 curve. Let me restrict to the first case that I don't know how to do, so that I can be as concrete ...

**9**

votes

**8**answers

3k views

### Which computer algebra system should I be using to solve large systems of sparse linear equations over a number field?

This is related to Noah's recent question about solving quadratics in a number field, but about an even earlier and easier step.
Suppose I have a huge system of linear equations, say ~10^6 equations ...

**97**

votes

**69**answers

15k views

### Most helpful math resources on the web

What are really helpful math resources out there on the web?
Please don't only post a link but a short description of what it does and why it is helpful.
Please only one resource per answer and let ...

**5**

votes

**4**answers

399 views

### Software for rigorous optimization of real polynomials

I am looking for software that can find a global minimum of a polynomial function in R^n over a polyhedral domain (given by some linear inequalities say). The number of variables n is not more than a ...

**5**

votes

**3**answers

628 views

### Is there a software package that does Schubert Calculus computations?

Is there a good software package for doing computations in the cohomology ring of Grassmannians? Things like, I can write down a polynomial in, in fact, special Schubert classes, but it's one where ...

**9**

votes

**5**answers

591 views

### is there a good computer package for working with bicomplexes?

I'm interested in working with bicomplexes of modules over polynomial rings, specifically tensoring them together, and the operation of taking cohomology in one direction, and then the other. Is ...

**7**

votes

**1**answer

544 views

### Is there a good computer package for working with complexes over non-commutative rings?

I'm interested in doing computations with certain non-commutative rings, most of which involve taking derived tensor products. Does anyone know of a computer algebra package which will find ...