Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [computer-algebra-systems]

A computer algebra system (CAS) is a program which is able to carry out various symbolic manipulations with mathematical expressions. Some well-known computer-algebra systems are Mathematica, Maple, Wolfram Alpha, GAP, SAGE. Questions on this site about computer algebra systems should be mathematical in nature, and not just about the syntax or the mechanics of the CAS. Otherwise the question would be better suited for a different Stack Exchange site.

A computer algebra system (CAS) is a program which is able to carry out various symbolic manipulations with mathematical expressions. Typically they include simplification, differentiation, integration, solving equations etc.

Some well-known computer-algebra systems: Mathematica, Maple, Wolfram Alpha, GAP, SAGE.

Some of them have also separate tags: , , , ,

For Mathematica there is even a separate Stack Exchange site. Another related site is Computational Science (currently in beta).

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Recent benchmarks of CAS programs? (HNF, Groebner)

I've been trying to find recent benchmarks of CAS systems for computing the Hermite Normal Form as well as Groebner basis over both $\mathbb{Q}$ and $\mathbb{C}$. I've been unable to find anything useful and would hope that someone has experience…
Edvard Fagerholm
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Computer Algebra System for Homotopy Types of Finite Simplicial Sets

I hope this is the right place to ask the following question, if not please guide me towards the correct forum... I want to show that two certain finite simplicial sets are not weakly homotopy equivalent. They are too large to prove it by hand, so I…
Jonas Linssen
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Comparing expressions exactly

Suppose I have two expressions; call them $A$ and $B$. The following values of $A$ and $B$ are good examples for my question... $$ A = \pi e^2\\ B = \pi^2 e $$ Is there a method to determine the truth of comparisons such as $A \ge B$, $A \lt B$,…
thirtythreeforty
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Latex code questions for curly C

What is the latex code for the curly C? (on the second line of the picture)
신정연
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CAS that can simplify sums of integral powers?

Is there a CAS that can automatically apply the following simplification: Given $I_k = \int_a^b f_k(x) dx$, rewrite $$\sum_{k=1}^K I_k^m = \int_{[a,b]^m}\sum_{k=1}^K \prod_{i=1}^m f_k(x_i) dx_1\ldots dx_m$$ So e.g. $\Big(\int f(x)dx \Big)^2 +…
Hyperplane
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Any software for calculating Lie Group Quotients?

Are there any software packages out there that can do equations like: $$ \frac{SU(5)}{SU(3)}=SU(2)\times U(1)$$ or... $$\frac{E_8}{E_6} = SU(3)$$ or... $$ \frac{O(32)}{O(10)\times O(4)} = \text{?}$$ Probably you wouldn't need software to do this as…
zooby
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Resources for arithmetic in quantum integers.

I'm using the definition $$[n]=\frac{A^{2n}-A^{-2n}}{A^2-A^{-2}},$$ although the usual definition is recovered by substituting $q=A^2$. In trying to prove various identities (and also reading the literature) I've had a lot of problems passing…
Andres Mejia
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How does a computation engine or calculator give exact answers?

I've always wondered how sites like Wolfram Alpha or tools like TI-89 calculators can give exact answers to complex problems. I.e. irrational numbers or exact solutions to calculus problems. For example, take a simple problem of: $2\pi/4$. Wolfram…
ThePedestrian
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CAS expression - Solve equations with $\sum$ and $\infty$

Can a TI89 or other CAS calculators solve this? I tried it on my classpad 330 did not work solve for p $$p = \sum_{j=0}^\infty p^j \frac{2^je^{-2}}{j!}$$ solve for p $$p = \lim_{z \to \infty} \sum_{j=0}^z p^j \frac{2^je^{-2}}{j!}$$ Edit: The whole…
jacob
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Symbolic manipulation softwares that can work with sums

I am wondering if there is any CAS that can work with formal sums and formal products. For example, say is there any software that can comprehend expressions like $\sum_{n=1}^k (x-n)^2$ or $\prod_{n=1}^k(x-n)$ as an expression in terms of $x,n$ and…
daruma
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Renaming variables in FriCAS sandbox output

I'm playing with FriCAS in sandbox and the problem is, When asked to find indefinite integral (as well as in many other cases), FriCAS outputs auto-generated variables in a rather unsightly manner, for example, integrate(x^x, x) outputs…
Thehx
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What tools are there to factor multivariate polynomials over a field of characteristic 2

I would like to factor a multivariate polynomials over a field of characteristic 2. It is not that large (tens of variables and hundreds of terms). I tried Mathematica and Pari-GP, and googled around for open source options.
yberman
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Solve the following system of equations: $[x[i-1]-(2-h^2)x[i]+x[i+1]=0, \ x[1]=1, \ x[50]-x[49]=h$, where $h=0.1$

This is my attempt at the solution using MuPAD: $x[1]:=1;\ h:=0.1; \ x[50]-x[49]=h$ eqs:= $[x[i-1]-(2-h^2)x[i]+x[i+1]=0; \ i=2,...,49]$ vars:=$[x[i]; \ i = 1,...,50]$ numeric::linsolve(eqs,vars); The problem is that $x[50]$ and $x[49]$ are not…
Jens
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Use MuPAD to prove $(4^{(x-1)}+2^{(2x-4)})/(2^{(2x+1)}+5\cdot(2^{(2x-3)}))=5/42$

I attempted to answer this in the following way, but got stuck on being unable to cancel out $4^x$ and $2^{2x}$. Even though they are clearly mathematically the same, I failed to find a command that cancels these out in any of the expressions (I…
Jens
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how to solve two's complement question?

i tried 9 D + (-10 D) 9= 0000 1001 10= 0000 1010 Reverse 10 = 1111 0101 and add 1 become 1111 0110 after that add up 9 D + (-10 D) == 0000 1001 + 1111 0110 but the answer is equal to 1111 1111 whch is 255 in decimal but the answer should be -1…
Bilis
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