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

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3
votes
2answers
159 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
74 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
84 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 ...
18
votes
2answers
545 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
98 views

Giving hints to Integrate

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

How to find a recurrence relation for a sequence?

I have a sequence given by an explicit formula for n-th term: ...
1
vote
0answers
62 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
115 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
109 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
164 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 ...
23
votes
1answer
582 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
44 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
52 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
95 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
39 views

Evaluating standard functions of general quaternions symbolically

Mathematica can easily compute exponentials and logarithms of concrete quaternions: ...
0
votes
1answer
113 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
109 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
111 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
101 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
77 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
58 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
175 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
141 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
40 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
141 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
183 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
134 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
304 views
1
vote
0answers
86 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
980 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
108 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
68 views

Compute integral symbolically

I want to compute the following integral: ...
18
votes
1answer
459 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
235 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
176 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
115 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
144 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
96 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
127 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
79 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
74 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
129 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 ...
0
votes
0answers
30 views

How to calculate this derivative? [duplicate]

Can Mathematica do the following simple calculation? $$F(x_0, x_1, x_2, ...) \equiv \sum_n x_n^2$$ I want to do the symbolic calculation: $$ \frac{\partial F}{\partial x_m} = \sum_n 2 x_n ...
2
votes
1answer
67 views

Defining a function (but not explicitly)

I have a question that must have a simple answer, but googling and searching this website did not produce an answer, so I'm asking it here. I'm working with three variables $x, y, \theta$, and I want ...
0
votes
1answer
218 views

Is this function convex?

How can I determine convexity of the function f = Log[ x, 1 + (x^a - 1) (x^b - 1)/(x - 1)] with the parameters $a,\,b$ belonging to the interval $(0,1)$ in ...
1
vote
2answers
342 views

How to make Mathematica use the chain rule?

Lets say I have the following PDE: $$x^2 u_{xx} - u_{yy} + u_y = 0$$ And I have the following change of variables: $$ s(x,y) = x e^y \, \, \, , \, \, t(x,y) = x e^{-y}$$ How can I use Mathematica ...
0
votes
0answers
54 views

Expectation taking unusually long to evaluate

I am trying to evaluate an expectation, but it is taking an extremely long time although the expression itself should not be too complicated. My code is ...
2
votes
1answer
130 views

Compute symbolic Expectation of a summation

I am required to computed following Expectations : $E[\displaystyle\sum\limits_{i=1}^N \frac{X_{i}}{N}] = \bar{x}_{0}$ & $E[\displaystyle(\sum\limits_{i=1}^N \frac{X_{i}}{N})^2] = ...