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: Mathematica, Maple, Wolfram Alpha, GAP. For questions about Mathematica please see the ...

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Is there CAS design wisdom regarding categorizing expressions?

Is there CAS design wisdom regarding categorizing expressions? For instance. A user types in the expression $X^2 + X + 1$. Would it be best to classify it as a member of $R[X]$ (for some R, yet to ...
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Generating a 2D coordinate from a 1D Index

Imagine you have a 5x5 matrix (zero indexed), where only the upper right coordinates are valid. I am unsure if this is the terminology to use, so the following coordinates should be the valid ones: ...
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Understanding BlowUp Computation in Singular

Many of us might know that "Singular" is a computer algebra system for Algebraic Geometry, Commutative Algebra and Non-commutative algebra. This is a procedure in "Singular" for computing blowups. ...
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Is there some database or software to look for patterns in polynomials?

Like if I am looking at these polynomials, $$x^8-8x^6+20x^4-16x^2+3$$ $$x^{10}-12x^8+48x^6-72x^4+33x^2$$ $$x^{12}-16x^{10}+88x^8-192x^6+138x^4$$ And I want to know if they are members of some ...
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Lower bounds on possible integer relations from the PSLQ algorithm

For the equation: $$ \sum_{i=1}^na_ix_i=0 $$ where all $x_i$ are real numbers and all $a_i$ are integers, the PSLQ algorithm can either find an integer relation or give lower bounds on the norm of ...
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Is there any efficient progam or software to calculate the fractional chromatic number?

The fractional chromatic number $\chi_f(G)$ is a generation of the chromatic number of a graph $G$. It can be formulated as a linear programming question: Let $\mathcal{I}(G)$ be the set of all ...
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70 views

How to detect carry and overflow?

Let's say that 0011 + 0111 = 1010 How to detect whether the operation generate carry and overflow?
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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 ...
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Boolean Expression simplification help

Hi I am new to the board. Taking a computer architecture course and I am having trouble understanding further simplification on a question I got on a previous quiz. When I type in the expression ...
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128 views

In SAGE, what function factors a polynomial whose coefficients are parameters?

In SAGE the function "factor" will factorize elementary polynomials with coefficients in $\Bbb Q$. For example: x,y = var('x,y') poly = x^3-y^2*x factor(poly) SAGE: x*(x-y)*(x+y) ...
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Silverman exercise 3.1 proving that two polynomials are relatively prime iff the discriminant is non-zero

Silverman, p. 104: Show that the polynomials $$f=x^4−b_4x^2−2b_6x−b8 \qquad \text{and}\qquad g=4x^3+b_2x^2+2b_4x+b_6$$ appearing in the duplication formula (III.2.3d) are relatively prime if ...
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Help in understanding risch algorithm

This is an excerpt from the paper that explains risch algorithm for symbolic integration. I do not understand how do we get to the residue directly and also how does it help us in the integration. ...
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Revealing output slowly in Magma

When working in Magma, is there a command to gradually reveal the output. For example, if you have a finite group $G$ and you want to calculate SubgroupLattice(G), then the output may be thousands of ...
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Tools for optimizing asymptotic bounds.

Is there any tool for this task ? Given the asymptotic bound in term of $n$ and other paramaters $t_1,\dots,t_r$, then return the value for each $t_i$ which optimizes the expression in term of $n$, ...
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Flatten kronecker product in CAS?

I am a new user of Maxima, and I need to trace the elements of a big messy kronecker product of symbolic matrices. I tried the following to get my feet wet, but I don't get a simple, flat matrix -- ...
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Looking for a binomial system solver

I am interested in solving binomial systems of the form $$ \begin{cases} a_1 x_1^{d_{11}} x_2^{d_{12}} \cdots x_n^{d_{1n}} + b_1 x_1^{d_{11}} x_2^{d_{12}} \cdots x_n^{d_{1n}} &= 0 \\ ...
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CAS for counting points of varieties over finite fields

I am looking for a computer algebra system, which is able to some of the following (in theory equivalent) things for a smooth projective variety defined over a finite field: -Count the number of ...
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832 views

Simple example application of Karush-Kuhn-Tucker conditions to minimization problem

I am wondering if there is a simple example application of the Karush-Kuhn-Tucker conditions to show that a minimum exists for a multivariate minimization/optimization problem. Could anyone suggest a ...
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Interpreting a chain of m's and o's from Macaulay2

This has been crossed referenced here as well in case a software developer understands this language. I am using Macaulay2 and does anyone know how to read the following? Example 1: -- ...
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Computing relations on the columns of a matrix

Given an $m\times n$ (with $n>m)$ matrix $M$ over a polynomial ring $R=k[x_1,...,x_n]$, suppose that every column of $M$ is an $R$-linear combination of $m$ specified columns. I would like to ...
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169 views

Any software package with Mordell equations implemented?

I admit I have no idea how to tag this post, but I'm looking for a CAS/number theory software package that would implement a decent algorithm for computing the integral solutions to $x^2 = y^3 - k$, ...
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Does MAPLE not simplify correctly or am I goofing?

While attempting to answer this question with help of MAPLE, something very strange happened, at least according to me. We have the following function: $$ \phi(x,y) = ...
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158 views

The mathematics underlying this baroque expression of the double-factorial

On the OEIS page for the double factorial, there are three ways of getting the sequence in PARI. One of them is this curious bit of PARI code: ...
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Plot Y-Range on Mathematica

I have a plot that I would like to slightly manipulate in Mathematica. Here is the code I am entering: Plot[{x, 2^x, log_2(x)}, {x, -1, 3}] As you can see $x$, $2^x$, and $log_2(x)$ are all ...
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Evaluating the real and imaginary parts of a nasty complex number

This seems like an elementary question, but I was unable to find an clear answer to it. Generally, the real and imaginary parts of a complex number comprised of radicals are not expressible by ...
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Postfix notation in MAPLE

I usually use MATHEMATICA as a computer algebra system and there I heavily employ the postfix notation (achieved by "//" at the end of some command), e.g. ...
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Semi directProduct and Maximal subgroup in gap [closed]

Let $P$ be a quaternion of order 8 and $Q$ a cyclic group of order 9 and $G=[p]Q$, a semidirect product ($P$ is normal in $G$). Let $M$ be a maximal subgroup of $G$ such that $Q<M$. I want to ...
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finding roots of polynomial in MAGMA or GAP

Please hint me. I want to find the roots of $x^3+(1-2n)x^2-(1+4n)x+8n^2-10n-1$ with Magma or GAP. In Magma: $P<x> := PolynomialRing(Rationals())$; $P<n>:= ...
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131 views

How to expand quadratic equations in Octave/Matlab?

I have some column vectors, and I put them in a row, so I have $[a \, b \, c]$. Now I want to get a matrix of the form $[a^2 \, b^2 \, c^2 \, ab \, ac \, bc]$. It is like expanding $(a+b+c)^2$, but ...
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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} ...
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What “meta-dimension” do algebraic numbers have?

actually what I am asking for is "how many ways do there exist to create a real number out of a sequence of coefficients?" there is the solution of polynomials through radicals, some polynomials can ...
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Solving an equation in charcateristic 2 in sage OR finding 3-torsion points of an elliptic curve over field with char 2

Problem: show that an elliptic curve over a field of char 2 has nontrivial 3-torsion points Method: I used SAGE to unwind the duplication formula for an elliptic curve given in short Weierstrass form ...
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102 views

Symbolic manipulations of integral equations

I was trying to learn about solving integral equations using symbolic algorithms. After a quick web search, I mostly found items like this Mathematica journal article that mostly focuses on how to use ...
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solving a matrix equation $X-I=a \cdot (X\cdot U^T + U \cdot X)$

I am trying to solve the $n \times n$ diagonal matrix $X$ in the following equation: $$X-I=a \cdot (X\cdot U^T + U \cdot X)$$ where $0<a<1$ is a given scalar, $U$ is a $n \times n$ given ...
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Get the closed form of Taylor series with Maple

Is it possible to get the closed form of Taylor series with Maple? The series command can give any given number of terms, but the question is about the closed form ...
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146 views

Solve nolinear system of equaion with c/c++ [closed]

My system of equation is like this: (x-a1)^2 + (y-b1)^2 = c1 (x-a2)^2 + (y-b2)^2 = c2 I know it is simple using matlab: ...
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56 views

Any algorithm or theorem to decide whether two functions are equivalent? [duplicate]

Any algorithm or theorem to decide whether two functions that are polynomials,rationals and analytic over $\mathbb{N}$ or $\mathbb{Q}$ or $\mathbb{R}$ or $\mathbb{C}$ are equivalent ?
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Decomposition of a polynomial over generators of an ideal

Let $f$ be a polynomial in six variables, say, over complex numbers, and $l_1$, $l_2$ are some linear forms in the same variables. If I know that polynomial $f$ belong to the ideal generated by $l_1$ ...
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Relationship between the Carmichael function and Euler's totient function

Let $\lambda$ denote the Carmichael function and $\varphi$ Euler's totient function. Furthermore, let $p$ denote any prime number and $k\in\mathbb{N}$. The wikipedia article about $\lambda$ states: ...
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Simplify basic expression

Please, does anyone know which tool can simplify expressions like: $$a^4 - 4a^3b + 6a^2b^2 - 4ab^3 - a + b^4$$ into: $$(a - b)^4 - a$$ I tried SymPy, Maxima and W|A without success. PS: I'm ...
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How to get 2 percentages to a 100%

First of im new to this site and I've never been the sharpest at math, im a web developer by trade. My question is math related but ill just give you a quick background about my website so that you ...
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68 views

Printing long lines in MAGMA without line break

In MAGMA, how do I print a long list of items to a file without automatic line breaks? It seems to me that there is an internal length limit and anything longer than it will result in a automatic ...
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33 views

software with a routine for the vanishing ideal of a finite set of points

I am looking for an algebraic software package that provides a routine that computes the vanishing ideal of a finite set of points. So far i am working with Macaulay2 but i have not been able to find ...
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300 views

Solving a nonlinear equation for one of variables with the help of a computer algebra system

Are there any solutions out there that can take a wide variety of equations with variables, like the one below, and transpose or isolate variables to other sides of the equation automatically? For ...
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How to iterate over power set in MAGMA?

I want do something for all subsets J of a certain cardinality of {1,2,...,n}, for a (previously declared) number n. It seems magma is not happy with: for J in PowerSet([1..n]) do To which MAGMA ...
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Maple: How to turn a set of vectors into a matrix?

In Maple the command NullSpace turns a given matrix into a set of vectors -- a basis for its null space. This is precisely what it should in a mathematical sense. However, for computations using the ...
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Changing versions of MAGMA [on hold]

I have to use some very long code (not written by me) which works on an earlier version of MAGMA (v2.19-4) but not on the current one my university has (v2.21-2). Is there any way I can switch to ...
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Discrete Fourier Transform using WolframAlpha

I tried to verify a calculation with WolframAlpha. I want to compute the DFT of $[2,3,-3,1]$. So in particular one entry of the result vector should be $2+3-3+1=3$. I don't understand why I get ...
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How does the factor command on the TI-89 works?

So to put my question in context, I am working on the following problem. Let $N=1291233941$. Eve's magic box tells her the following three encryption/decryption pairs for $N$: $$(1103927639, ...