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

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1answer
42 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
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0answers
53 views

No solution with DSOLVE

I have been trying to solve the following system of ODEs: \begin{eqnarray} ...
0
votes
1answer
164 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 ...
5
votes
2answers
239 views

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

Update I have tried like these. I think there is a bug. Plot[1/Sqrt[-1 + 2^2 Sech[x]^2], {x, 0, ArcCosh[2]}, Ticks -> {{ArcCosh[2]}, Automatic}] This ...
2
votes
1answer
68 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 ...
1
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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 ...
3
votes
2answers
122 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. ...
8
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1answer
5k views

Extract real part of a complex expression better than Re does

I have a complex expression with real positive variables only. Mathematica Input Style: ...
6
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1answer
47 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}}] ...
17
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2answers
436 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 ...
3
votes
1answer
74 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 ...
1
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0answers
93 views
6
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1answer
88 views

How to find a recurrence relation for a sequence?

I have a sequence given by an explicit formula for n-th term: ...
6
votes
1answer
152 views

Symbolic tensor simplifications and the identity matrix

How can I get Mathematica to simplify the following expressions, with $Assumptions including Element[n,Integers], n > 0, and ...
1
vote
0answers
45 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 ...
17
votes
0answers
437 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 $S^2$ ...
3
votes
2answers
90 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 ...
0
votes
0answers
63 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 ...
2
votes
3answers
197 views

How to code the following product?

I am trying to examine the properties of the following product for a given tuple $\vec \lambda = (\lambda_1, \lambda_2, \dots, \lambda_n)$, then the product is as follows: $$ \dim \Gamma_\lambda = ...
3
votes
5answers
136 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 ...
4
votes
1answer
90 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 ...
1
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1answer
145 views

How to apply a tensor to a list of arguments

The problem I have is the following: Let C be a list of coordinates, say, C = {x1, x2, ..., xn} and ...
2
votes
0answers
89 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
1answer
43 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
50 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 ...
0
votes
3answers
84 views

Place symbols from small to big

I am wondering how to compare the different values of ω I derived in this code, and place them in order as follows. (use Print ...
2
votes
0answers
33 views

Evaluating standard functions of general quaternions symbolically

Mathematica can easily compute exponentials and logarithms of concrete quaternions: ...
0
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1answer
92 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
99 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
94 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
61 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 ...
25
votes
3answers
836 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 ...
0
votes
3answers
99 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 ...
8
votes
2answers
569 views

Symbolic integration in real domain only ( assumptions and ComplexExpand don't work)

Integrate[m^2/((x - m^2)^2 + y^2), m] mathematica gives me a complex-valued reuslt, but maple 17 gives me what I want. I tried using assumptions, but it doesn't ...
1
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0answers
48 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 ...
3
votes
0answers
49 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
1answer
130 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
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0answers
87 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 ...
1
vote
1answer
35 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
95 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
130 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 ...
0
votes
1answer
266 views

Solving a large system of non-linear equations

I am new to Mathematica, and I am currently trying to use it to solve a large symbolic system of non-linear equations. I began the code below about 30 hrs ago, and the Mathematica Kernal has been ...
7
votes
1answer
96 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 ...
3
votes
1answer
154 views

Covariant derivative for symbolic tensors

I want to define a "prefix" (D_i) covariant derivative operator CD[] for symbolic tensors in form of a function, i.e. for ...
1
vote
0answers
63 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 ...
18
votes
4answers
824 views

How to calculate the volume of a convex hull?

Given a spatial curve represented by a parametric equation, is it possible in Mathematica 9 to calculate symbolically (or at least numerically) the volume of its convex hull?
4
votes
1answer
77 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} ...
5
votes
5answers
564 views

Prevent Part[] from trying to extract parts of symbolic expressions

If you have a list, e.g. {1, 2, 3} then you can extract the $k$th part using Part (...
18
votes
2answers
274 views

Negative probability?

I am trying to get the sum of the squares of seven random variables, all uniformly distributed. This is what I tried. ...