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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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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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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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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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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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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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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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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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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how to use hilbert function in gap system with loadpackage singular

how to calculate hilbert function as it do in singular code singular code ...
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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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45 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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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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263 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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116 views

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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What is the “cost” of computation of two special CAS algorithms

Suppose I have an integer $n$ with e.g. a large number of say decimal digits. I would like to get some information about the runtime "cost" of standard CAS algorithm which factors $n$ into primes ...
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Interpolating transformation matrices

I read not to interpolate transformation matrices by linearly interpolating. Can someone explain to me why interpolating transformation matrices by linearly interpolating the matrix components is a ...
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defining an upper bound for n-tuple

Let we have $n-tuple ~~like ~ a=(a_1,...a_n) \in N_0^n ~and ~every ~a_j < (2^{m_j} -1). $ and let suppose we have another n-tuple like $b:=(b_1,...,b_n)$ such that $ b_i \leq (2^{m_j} -1)$. I ...
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Improvement of Buchberger's Algorithm

1) Let $S(F)$ be the subset of $(k[x_1,\dots,x_n])^s$ consisting of all syzygies on the leading terms of $F=\{f_1,\dots,f_s\}$. Then every element of $S(F)$ can be written uniquely as a sum of ...
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using wolfram alpha to solve a system of nonlinear differential equations

Will Wolfram Alpha solve a system of nonlinear differential equations with initial values and graph the solutions? Essentially, I want to hand Wolfram a first-order system with variables x_1, x_2, ...
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Question about multiple solutions to a polynomial

Assume that $f(X,Y,Z,V,W)\in \mathbb{Z}[X,Y,Z,V,W]$ is some polynomial and assume that $f(x,y,z,v,w)=0$. I would like to know if there is some way to figure out if there are non-trivial constants in ...
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Gram-Schmidt-procedure with PARI/GP

Can the Gram-Schmidt-procedure to find an orthogonal basis of a vector space spanned by given linear independent vectors be easily done in PARI /GP or do I have to program the procedure ?
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Can a Computer Algebra System 'experiment' with expressions?

I have recently been reading about software for symbolic manipulation, and I can see its use as a tool for performing large calculations that would be unfeasible otherwise. Given that these systems ...
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63 views

Marking the roots of a quadratic function in Scilab

I have 2D plotted a simple quadratic function in Scilab and now have to mark the roots with an X. Is there any simple way of doing that? I have written a function that calculates the roots and ...
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How to reduce a graph via decomposition?

Is there a Java / C# library that can be used to reduce a graph via decomposition? Or could someone point me to a good tutorial where I can learn all these? E.g.
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Risch differential equation algorithm by Bronstein

I was implementing the algorithm by Manuel Bronstein for solving the Risch differential equation. My question is: What does Bronstein mean by "Order" in the algorithm poly_DE (exponential case, ...
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Changing the “Type” of an object in Magma

The computer algebra system Magma can store groups as one of many different types. For example, using AbelianGroup([2,2]) we obtain the Klein $4$-group stored as type GrpAb. However, we can also ...
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Why $face_w(New(f))=New(in_w(f))$?

Is there anyone who can help me with this problem? Any hint to the solution would be appreciated! Let $f\in \Bbb K[x_1,\ldots,x_n], w\in \Bbb R^n$ and $New(f)$ be the Newton polytope of $f$. Why ...
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Why are these CAS calculated integrals equal

I let Wolfram evaluate this integral: $$\int\frac{-2\sin(x)\cos(x)}{2\cos^2(x)+\cos(x)-1}dx$$ 1st result from WolframAlpha online was $$\frac43 \log(\cos(\frac{x}2))+\frac{1}{3\log(1-2 \cos(x))}+C$$ ...
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Computing univariate resultant via modified Euclidean algorithm

In an answer to the question Resultant of Two Univariate Polynomials, a PDF of course slides was linked which describes a modification of Euclid's algorithm for computing univariate polynomial ...
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Canonical Separation of variables

Do the functions of the form $\psi(x)\phi(y)$ span $L^2(\mathbf{R}^6)$? Insert proper grammar here.
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Coercing a vector into a module in MAGMA.

Given a $1\times n$ row vector $v$ over a ring $R$, and an $n$-dimensional $R$-module $M$, is there any way to coerce the vector $v$ into $M$ (the obvious $M!v$ does not work).
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Can Maple solve recurrence relations when n is only certain numbers?

If you have an equation $a(n)=a_{n-1}+2a_{n-2}$ only defined when n is powers of 2, how would convey that to Maple that n has a restriction? What if you wanted only $n \ge 2$?