For questions about symbolic computation, as opposed to numerical computations.

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9
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0answers
243 views

Improving the performance of a package for working with rational functions

As Mathematica gets slow for large symbolic calculations, the cost of putting terms over a common denominator (Together), in particular, gets too high. It occurred ...
7
votes
0answers
136 views

Examples of using Mathematica to solve matrix equations symbolically

Suppose we want to solve a linear system like $$\left\lbrack\begin{array}{cc}M& S\\ -S^\mathrm{T}&0 \end{array} \right\rbrack \left\lbrack \begin{array}{c} x\\y\end{array}\right\rbrack = \...
5
votes
0answers
78 views

Operator which can be interpreted as binary and unary

I'm a bit lost with the way how e.g. the + operator is implemented in Mathematica as binary (infix) and unary (prefix) operator depending on the context, since I would like to define a similiar ...
5
votes
0answers
2k views

Solve huge symbolic system of linear equations

I have a system of 76 symbolic linear equations (i.e. some coefficients are symbolic) with a sparse coefficient matrix. However, neither Solve[] nor ...
4
votes
0answers
68 views

Create an adequate 'training set' to train a ClassifierFunction which performs the role of the built-in `SubsetQ`

I am trying to "grow" my own SubsetQ function using Machine Learning methods. My cSubsetQ when given two lists (listA and listB)...
4
votes
0answers
77 views

Interval Arithmetic with Symbolic Intervals

I've run into a problem with IntervalUnion and IntervalIntersection when dealing with symbolic intervals. The following code ...
4
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0answers
84 views

Does it help to do any preprocessing before `FindSequenceFunction`?

I am always amazed how smart FindSequenceFunction can be in discovering general term formula for a sequence of rational numbers. The documentation says it can work ...
4
votes
0answers
728 views

Analytically solve the eigenvalue problem with infinite dimensions by Mathematica?

If I am given a symbolic expression of all the matrix elements in an infinite-dimensional space, e.g., the Hamiltonian of a quantum mechanical system, is it possible to get the symbolic expression for ...
4
votes
0answers
176 views

Version 8.0 integrates but Version 9.0.1 doesn't

I am trying to run the following integral in version 9.0, but it fails: ...
4
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0answers
96 views

Using Resolve and ForAll to prove takes a really long time

I've been trying to prove a lemma for my paper using Mathematica... basically that $$\forall \{n, d_i, d_j\} \in \mathbb{Z},\ n \ge d_i > d_j \ge 2$$ it's true that $$V[1, n, d_i-1, d_j-1] >...
3
votes
0answers
63 views

Simplifying between set theory and logical connectives

I'm trying to find out how to switch between set notation and logic, but am having difficulty. For instance, I know that the following two expressions are equivalent ...
3
votes
0answers
133 views

Is it possible to simplify an expression in vector form, which involves crossproduct and dot product?

I often need to simplify expressions involving cross product and dot product, for example: f = Dot[Cross[Cross[p1 - p, e1], Cross[p2 - p, e2]], Cross[p3 - p, e3]] ...
3
votes
0answers
88 views

Symbolically Minimizing a Max function

I'm having a tough time with seemingly simple symbolic Minimization/Maximization in Mathematica. I would like to use the Maximize function to work on some unknown random variables and so use min/max ...
3
votes
0answers
63 views

Derive logistic choice probabilities symbolically

More generally, I am interested in learning what the current limitations of Mathematica are when using it for doing pure mathematics. A recent blog post by Stephen Wolfram (see: http://blog....
3
votes
0answers
568 views

Symbolic matrix calculus: What's new in Version 9

I have seen some of the related posts, which ask about doing matrix calculation on tensors unknown dimensions. One of the posts mentioned that version 9 has some capability, but it was concerned about ...
3
votes
0answers
156 views

Fourier transformation of HeavisideTheta functions

I want to find 2D-Fourier transformation of the function given below f = HeavisideTheta[y1]*HeavisideTheta[y2 - y1] For the purpose, I use built-in function in ...
3
votes
0answers
113 views

What is so special about variable s$?

I found a nice bug in Mathematica 9.0.1.0. Could anyone check to reproduce it? Create a file temp.txt with one line: ...
3
votes
0answers
195 views

Do a gauge transformation for a Chern-Simons theory?

Suppose we have the following Lagrangian density: $$ L=\epsilon^{\mu\nu\rho}\big(\sum_a A^a_{\mu}(x) \partial_\nu A^a_{\rho}(x)-\sum_{a,b,c}\frac{1}{3} f^{bca} A^a_{\mu}(x) A^b_{\nu}(x) A^c_{\rho}(x)...
3
votes
0answers
84 views

How to combine DifferenceRoot objects for odd and even-indexed terms

I'm trying to analyze a certain infinite sequence $S$, indexed by positive integers starting from $1$. It can be split into two subsequences: $S^{odd}$ by removing all even-indexed elements and ...
3
votes
0answers
250 views

Malliavin Derivative with Mathematica is it possible?

Is it possible to define a Malliavin calculus with Mathematica 9? Consider a random variables on the Wiener-space $\Omega=\mathcal{C}([0,1])$ of the form $$F=F(\omega)=\displaystyle\int_{0}^{T}h_{t}...
3
votes
0answers
247 views

Numerical-Symbolical Integration (Calculus)

I created a simple numeric-symbolic integration. Here you can use symbolical and numerical techniques at the same time. You can also interpolate numerical integrals. The problem with my function is ...
2
votes
0answers
40 views

How do I prevent Root and RootSum from expanding over quadratic roots?

For quadratics, RootSum[a #^2 + b # + c &, Cos[#] &] Immediately turns into and also, ...
2
votes
0answers
44 views

Unexpected imaginary term in the asymptotic expansion of DawsonF

FullSimplify[Series[2 DawsonF[x], {x, ∞, 8}]] (* -I Exp[-x^2] √π + (1/x + 1/(2 x^3) + 3/(4 x^5) + 15/(8 x^7) + O[1/x]^9) *) What is the reason the term ...
2
votes
0answers
44 views

Replacement rule for summation with Kronecker delta

I want to perform some symbolic computations in index notation, without explicit reference to sums, so that in expressions of the type f[i,j]g[j,k] summation over <...
2
votes
0answers
33 views

Polynomial kernel expansion

I am trying to calculate the polynomial kernel expansion using Mathematica. I have tried the Expand and Simplify functions with ...
2
votes
0answers
99 views

General suggestions to accelerate Simplify and FullSimplify

To my understanding, the function Simplify[] and FullSimplify[] work by applying a series of built-in transformation rules to ...
2
votes
0answers
121 views

Parallel evaluation of symbolic matrix eigenvalues

I'm trying to find eigenvalues of symbolic hermitian 40x40 block matrix. It is made from 20 2x2 matrices like this: ArrayFlatten[Table[M[m,n],{m,1,20},{n,1,20}]] ...
2
votes
0answers
82 views

Integrate with Subscript: does this crash your kernel too?

I encountered some strange behaviour running v10.0.1 on a Mac Pro, while working with Integrate and Subscript. Starting from a ...
2
votes
0answers
98 views

Result of symbolic integration changed drastically by making assumptions

I would like to know the underlying reason for different outcomes for the two integration operation below. One of them includes a few assumptions, otherwise both have the same integrand: ...
2
votes
0answers
415 views

Eigenvectors for a large symbolic matrix

I'm trying to compute the eigenvectors for a 42x42 symbolic matrix (with one variable) in Mathematica. I get the following error: Eigenvectors::eivec0: Unable to find all eigenvectors. >> and the ...
2
votes
0answers
166 views

Changing bounds of summation after differentiating symbolic sums

Suppose, I have a function written as Taylor-Maclaurin series f = Sum[c[n]*x^n, {n, 0, Infinity}] Now, I wish to differentiate this expression with respect to <...
2
votes
0answers
216 views

Problems with Simultaneous Equation Solving

Let me first explain what I am doing and then I will explain the problem that I can't figure out. I am basically trying to solve 2 equations for 2 unknowns (a1 and <...
1
vote
0answers
53 views

Can Mathematica solve Kuhn-Tucker Equations with arbitrary functional form (up to 2nd order derivative)

I am in a business of solving a 5-variables optimization with inequality constraints, and I would like to maintain the functional form as arbitrary as possible. So far, I am assuming that the ...
1
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0answers
91 views
1
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0answers
78 views

CharacteristicPolynomial returns 0

I have a following matrix. ...
1
vote
0answers
77 views

Computing symbolic surface normal of a surface point on a semialgebraic set

Consider a semialgebraic set; such as reg below: ...
1
vote
0answers
112 views

Summing the probability distribution to 1 to convince myself

I have worked out a probability distribution and want to check its sum which is necessarily 1. First we write $$ r \triangleq \frac{(2 \lambda + \mu)^2}{2(\mu + \lambda)^2}, \quad s \triangleq \...
1
vote
0answers
145 views

Symbolic Nullspace computation in parallel

I am trying to determine the nullspace of a large symbolic matrix. The single core evolution seems to take too long. I tried Parallelize[] on the commands ...
1
vote
0answers
47 views

Why does integration of a radical times HeavisideTheta give a conditional expression?

If I want to compute an integral over x^p HeavisideTheta[y-x] where p is some fraction, I do not get the desired result, but ...
1
vote
0answers
118 views

Giving hints to Integrate

I working with the integral ...
1
vote
0answers
249 views

Calculate the power spectral density of a Markov chain

I would like to calculate the symbolic power spectral density of a two state Markov process with a symbolic transition matrix characterised by two parameters. I have tried the code below, but it ...
1
vote
0answers
80 views

Getting long complex-valued integrals when simpler real-valued expressions exist

I have a long list of real-valued functions I'd like to integrate symbolically. For many of them, Mathematica gives me results with long complex-valued expressions involving weird functions such as <...
1
vote
0answers
347 views

specifying a list (vector) of arbitrary length

When trying to do symbolic calculations in mathematica involving a space of dimension n, which is arbitrary but fixed, I'd often like to work with vectors that have ...
1
vote
0answers
146 views

Find the values of parameters so that the matrix is symmetric positive definite

Good evening , I have a matrix 20x20 in symbolic form. The matrix depends on 5 parameters (a,b,c,d,e). I would like to get the interval of each parameters that ensures that the matrix S is symmetric ...
1
vote
0answers
117 views

Computing residues of matrix valued functions symbolically

I have a somewhat specific application in mind, but I've run into this kind of problem a few times and never found an elegant solution. Is there an efficient way to get Mathematica to recognize that ...
1
vote
0answers
188 views

ExpToTrig transforms solution to 4th order ODE into unwanted form

Mathematica gives the solution of the second order differential equation DSolve[a y''[x] + b*y[x] == 0, y[x], x] in trigonometric form ...
1
vote
0answers
233 views

Speeding up inversion of symbolic matrices by invoking caching

Is it possible to reduce the computation time taken to find inverse of symbolic matrices USING CACHING TECHNIQUES accessible (if any)? I am trying to compute inverse of symbolic matrices of size ...
1
vote
0answers
165 views

(Symbolic) LinearSolve is slower/different after upgrading to Mathematica 9

Yesterday I upgraded from mathematica 8.0.4.0 to 9.0.1.0. Trying to run the same notebook I used many times before, it takes ages to evaluate a symbolic (linearsolve) expression which before was ...
1
vote
0answers
44 views

Matching Root[…] objects with patterns, unexpected hidden argument

I needed to write patterns that could distinguish between arbitrary-function and polynomial forms of Root objects, for example, ...