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

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2
votes
1answer
44 views

A question about expanding complex functions of real arguments

I have the following problem. There is such an expression as: P[x_,y_] := z[y] E^(I beta x) + Conjugate[z[y] E^(I beta x)]; The variables ...
1
vote
1answer
99 views

How to simplify symbolic matrix multiplication using the associativity of scalar multiplication?

My input is (2A).(3B). Is there a way to get 6A.B? All I could get back from Mathematica was ...
0
votes
0answers
71 views

No solution with DSOLVE

I have been trying to solve the following system of ODEs: \begin{eqnarray} ...
1
vote
0answers
31 views

Symbolic computation under certain assumptions [duplicate]

Assume that I have a matrix $M$ and I'm doing some operations on it. Is there a way to specify that two variables satisfy an equation say $x=y^2$ and then let Mathematica compute under that ...
5
votes
3answers
341 views

Different results of a definite integral $\int_0^{\cosh ^{-1}(a)} \frac{1}{\sqrt{a^2 \text{sech}^2(x)-1}}\, dx$

fixed in 10.0.2 Update I have tried like these. I think there is a bug. ...
4
votes
2answers
178 views

Coordinate free differential forms package

I am looking for a package in Mathematica which can handle differential forms in a coordinate free manner. I am aware of several packages which do differential forms, but it seems that for all of them ...
3
votes
2answers
162 views

How to define even permutations correctly?

I define even permutations as following, but there may be some error. I use it in two different way and get different output. ...
6
votes
1answer
77 views

How to assign up-values for `Derivative`?

I have defined several custom analytic functions. Here is the simplest example: ln[x_, a_?NumericQ] := Piecewise[{{Log[x], Re[a] > 0}, {-Log[1/x], True}}] ...
3
votes
1answer
85 views

Pulling powers to the outside of expressions (inverting PowerExpand)

Is there something like an inverse of PowerExpand that pulls powers to the outside of expressions: $$ x^2 y^2 \leadsto (x y)^2 \\ x^2/y^2 \leadsto (x/y)^2 $$ I ...
19
votes
2answers
575 views

Symbolic integration error

I'm running Mathematica 10.0.0 and encountered a disturbing error in the symbolic integration of a rather simple function ...
1
vote
0answers
100 views

Giving hints to Integrate

I working with the integral ...
7
votes
1answer
122 views

How to find a recurrence relation for a sequence?

I have a sequence given by an explicit formula for n-th term: ...
2
votes
1answer
78 views

Typing (and executing) expressions with multiple superscripts

I am trying to type (and evaluate) expressions of the following form: $$ G^{a,b} $$ into a mathematica. I've tried the obvious G^(a, b) or ...
0
votes
0answers
122 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 below, but it doesn't ...
3
votes
2answers
125 views

Expectation of a composite Markov-Gamma distribution

In a model I have a discrete two-state first order Markov process, defined by a (2x2) transition matrix with two free parameters. If the first state occurs then the process outputs zero for that ...
2
votes
0answers
97 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: ...
3
votes
5answers
169 views

Algebraic expressions on pure functions

I would like to know how to perform algebraic operations with pure functions. Simple version: Here's a silly toy model: I want to transform the algebraic expression Sin*Cos into the function ...
26
votes
1answer
643 views

Proving the hairy ball theorem using xAct

I would like to formally prove the hairy ball theorem in Mathematica, initially just for $S^2$, and then see about generalizing. An approach I thought about to use the xAct package to define $S^2$ ...
2
votes
1answer
45 views

Imaginary term in Integration procedure

How do you remove the imaginary term in the integrated output? Compare the outcome from the operations below. The first operation yields an imaginary term, while the second one has none. ...
0
votes
0answers
53 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 ...
4
votes
1answer
97 views

Avoid writing explicit form of operator

I would like to evaluate the following (simplified) expression with Mathematica : $\frac{\delta}{\delta J} \exp[(J(x)+K(x)) \Delta (J(x)+K(x))]$ where $\Delta$ is a differential operator independent ...
2
votes
0answers
41 views

Evaluating standard functions of general quaternions symbolically

Mathematica can easily compute exponentials and logarithms of concrete quaternions: ...
0
votes
1answer
123 views

Elegant way to do series expansion around x+$\epsilon$

Suppose I have a function $p(x+\epsilon,y-\epsilon,t)$, and I want to expand it around $(x,y)$ like $$ p(x+\epsilon,y-\epsilon,t)=p(x,y,t)+\dfrac{\partial p}{\partial x}\epsilon+\dfrac{\partial ...
3
votes
1answer
112 views

Expected graph distance in random graph

I am trying to use the functionality of Expectation and Probability for random graphs, in particular for percolation models. ...
2
votes
1answer
113 views

Extracting rational coefficients from an irrational sum [closed]

I have a function that returns results that always can be represented as $p+q\,\pi^2+r\ln2+s\ln^22+t\sqrt2$ where $p,q,r,s,t\in\mathbb Q$. But the actual Mathematica expression returned not always in ...
3
votes
0answers
67 views

Symbolic integration of elliptic functions

Is there some clever way to integrate products of elliptic functions $\wp(z;g_2,g_3)$ or $\zeta(z;g_2,g_3)$ in Mathematica? Mathematica seems to be able to integrate functions like ...
0
votes
3answers
102 views

how could I repalce Sqrt[x^2+y^2+z^2] back to r

do a calculation in mathematica r = Sqrt[x^2+y^2+z^2] D[D[E^(I (-k r + t \[Omega]))/r, x], y] but how could I get back to repalce Sqrt[x^2+y^2+z^2] back to r ...
1
vote
0answers
94 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 ...
4
votes
0answers
59 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 ...
1
vote
0answers
203 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 ...
2
votes
1answer
150 views

Check for holomorphy of a function

Given a (rather complicated) function H(z), what is the best approach to check symbolically whether it is holomorphic? What I tried is checking explicitly the ...
1
vote
1answer
44 views

Automatic substitution of fractions

I have several equations with many variables, and here and there I would like to do a variable substitution. For example, in the equation: a (b + 42 c / d) I ...
3
votes
2answers
148 views

Lookup in Inverse Symbolic Calculator+ from Mathematica

There is a useful feature in WolframAlpha that allows to find a possible closed form for approximate numeric values. It can be used, for example, to guess the value of an integral that Mathematica ...
1
vote
1answer
204 views

Computational complexity of symbolic determinant

I'm using the Det function in Mathematica to compute the determinant of an $n\times n$ matrix $A$ with entries of the form $a+bt$ with $a,b$ integers and $t$ a variable, and I would like to know what ...
8
votes
1answer
152 views

Expanding derivatives of hypergeometric functions

Sometimes Mathematica expresses results of integration or summation in terms of symbolic derivatives of Hypergeometric2F1 function, and cannot further simplify ...
5
votes
1answer
317 views
1
vote
0answers
106 views

Solving PDEs with complicated boundary conditions

The system I'm trying to solve is $$\nabla^2 C_{(r,\theta)} =0$$ $$C_{(\infty,\theta)}=C_0$$ $$ [ \frac{\partial C_{(r,\theta)}}{\partial r} \cos(\theta)+\frac{1}{r}\frac{\partial ...
25
votes
3answers
1k views

Symbolic solution(s) to generalized Heat equation

Symbolic solution(s) to Heat equation? or more generally,(eventually) Green functions to known PDEs I am interested in variations of the heat equation: or more generally or even more generally ...
4
votes
1answer
110 views

Factoring a differential equation into an operator product

Following the fundamental theorem of algebra, I can (as stated here in Sec. 1.1.4) factor an $n$th-order linear ordinary differential equation $$ a_n \frac{d^n x}{dt^n} + a_{n-1} \frac{d^{n-1} ...
0
votes
1answer
70 views

Compute integral symbolically

I want to compute the following integral: ...
18
votes
1answer
477 views

Transform Root objects into Trigonometric expressions

Consider the Root objects roots = Table[Root[-1 + 27 #1^2 - 162 #1^4 + 243 #1^6 &, i],{i,1,6}] These can be expressed in terms trigonometric functions as ...
2
votes
2answers
253 views

Finding Expectation of function of a Log-normal distribution

Say $Y=g(X)$ and $p_X = \frac{e^{-\frac{(\mu -\log (x))^2}{2 \sigma ^2}}}{\sqrt{2 \pi } x \sigma }$ is Log-normal density function: [Wiki] Find E[Y]? Since $E[Y] = \int_0^\infty y f_Y \ dy = ...
8
votes
0answers
182 views

Calculating probabilities symbolically

Is there a way to solve for statistical quantities analytically/symbolically in Mathematica? example 1: Lets say that I want to do a calculation that requires Bayes theorem. I know p(a), p(b) and ...
1
vote
1answer
116 views

Generate conditions seems to not work [closed]

I am trying to compute the following integral Integrate[E^(I*k*Omega*t), {t,0,T}, GenerateConditions->True] for which Mathematica returns ...
2
votes
1answer
146 views

What's the differences between the shift-enter and MakeBoxes running?

I know the example usages of MakeBoxes in the Tutorial like this. but I want to know a subtle distinction between (1) and (3) ...
0
votes
0answers
102 views

Define an operator with commutative, associative and distributive properties

I need to define a symbolic operator with commutative, associative and distributive properties, in the same way as the sum and product operator for real numbers. I have started with: ...
1
vote
1answer
137 views

Factoring terms out of a polynomial

I don't do much algebra in Mathematica and was surprised to discover, while attempting to answer this question, that I had no idea how to factor out an expression from a polynomial. The question was, ...
3
votes
1answer
85 views

Symbolic Output after numerical computation

I have a small question about the symbolic output. I started to write a program that generates the coordinates of n-dimensional polytopes by Wythoff construction. For crystallographic groups, all is ...
0
votes
0answers
82 views

A derivative encountered in matrix factorization using gradient descent

I want to factorize a matrix $a_{ij}$ as $$ a_{ij} = \sum_k u_{ik} v_{jk} $$ using variational method for some reason. That is, I want to minimize the cost function $$ F = \sum_{ij} b_{ij}^2 $$ with ...
1
vote
1answer
152 views

Symbolic evaluation of the sum of KroneckerDelta

I want to evaluate this simple expression $$ \sum_n f(n)\delta_{mn} = f(m) $$ using this: Sum[KroneckerDelta[m, n] f[n], {n, Infinity}] However Mathematica ...