Articles of symbolic computation

Is there a symbolic math package for octave?

I am using Octave (3.6) on Ubuntu 10.0.4 LTS. I want to do some research involving symbolic math. I was thinking of downloading sage (I just found about it today) – but thought I’d better ask in here – at least, I’m already familiar with Octave.

Simplifying polynomials

Suppose I have a (multivariate) polynomial with coefficients in $\mathbb Z$ or $\mathbb Q$, given in fully expanded form. How can I simplify this to reduce the number of elementary operations (addition, subtraction, multiplication) used in its representation (and therefore evaluation once you substitute values for the indeterminates)? I’m not interested in the case where […]

Algorithms for symbolic definite integration?

What are the algorithms for symbolic definite integration? Apart from computing the antiderivative first. What are the basic ideas behind such algorithms? As far as I got it, the main idea behind symbolic indefinite integration is that we actually know what kind of terms should be in the answer. And it is easy to believe […]

Computer algebra system to simplify huge rational functions (of order 100 Mbytes)

I have a huge rational function of three variables (which is of order ~100Mbytes if dumped to a text file) which I believe to be identically zero. Unfortunately, neither Mathematica nor Maple succeeded in simplifying the expression to zero. I substituted a random set of three integers to the rational function and indeed it evaluated […]

Resultant of Two Univariate Polynomials

I am trying to implement an algorithm for computing Res(f(x),g(x),x) where f(x) and g(x) uni variate polynomials with integer coefficients. Could any one list the various algorithms for computing Res(f(x),g(x),x) along with a brief comparison (e.g. time complexity analysis)? I know that the resultant is the determinant of the Sylvester matrix. But is this the […]

Series expansion for iterated function

I would like to find the MacLaurin expansion of an iterated function. Finding the first few terms is not hard, but it doesn’t take long before Mathematica runs out of memory using the straightforward program. Is there some good way to find terms with reasonable time and space? My problem allows some flexibility with the […]

What is the best way to factor arbitrary polynomials?

I am currently working on a Computer Algebra System and was wondering for suggestions on methods of finding roots/factors of polynomials. I am currently using the Numerical Durand-Kerner method but was wondering if there are any good non-numerical methods (primarily for simplifying fractions etc). Ideally this should work for equations in multiple variables.

How much does symbolic integration mean to mathematics?

(Before reading, I apologize for my poor English ability.) I have enjoyed calculating some symbolic integrals as a hobby, and this has been one of the main source of my interest towards the vast world of mathematics. For instance, the integral below $$ \int_0^{\frac{\pi}{2}} \arctan (1 – \sin^2 x \; \cos^2 x) \,\mathrm dx = […]

symbolic computation program/software

What is your recommended symbolic computation program/software for free and commercial respectively? What are its strength and weakness? For example, efficiency, comprehensiveness, etc Thanks!

Algorithms for Symbolic Manipulation

If you take a look at WolframAlpha, or other computer algebraic system, you will find that it is able to do symbolic manipulation like real humans. For example, if you type in an integral, it can show you step by step on how to solve the integration. What are the algorithms behind all this?