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

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6
votes
1answer
336 views

How to solve this probability symbolically or numerically?

I am trying to calculate the following probability $$\mathbb{P} \big(\sum_{i=1}^{m} (A_i + S_i) \le L < \sum_{i=1}^{m+1} (A_i + S_i) \big)$$ where, $$A_i \sim \exp(\lambda), \quad S_i \sim ...
11
votes
2answers
267 views

How to do algebra on summations of variable expressions?

Is there any easy, general way to handle algebra on variable Sums? For examples, Gaussian Mixtures or Fourier Series: ...
1
vote
0answers
78 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
88 views

Symbolic and numeric calculations (and plots) simultanuosly

I use Mathematica to do a bunch of symbolic calculations (integrals, ...). This is good because I found that sometimes, if I plug in numeric values, Mathematica takes much longer. However, sometimes ...
21
votes
2answers
287 views

Backslide of Limit

A friend of mine showed me this example: Limit[Sum[Sin[Pi*k/n]/(n + 1/k), {k, 1, n}], n -> Infinity] This sample calculates well in v8.0.4: but not in ...
0
votes
1answer
92 views

Wrong Definite Integral result [closed]

When I calculate the definite integrate of (a+bt)*cos(nt). Integrate[(a + b t) Cos[n t], {t, t1, t2}] MMA gives a correct answer: ...
4
votes
2answers
134 views

Remove redundant parameters from equation

I have random expressions like (b1 x + b2 x)/(b3 + b4/b5 x) + Sin[b6 x] where $x$ is a variable and {b1, ..., b6} are parameters to be fitted. This expression is ...
0
votes
2answers
77 views

How to use Expected values in symbolic solving

How can I create a function that brackets off terms of an expectation value? For example, I have : f = a[x] + c1*b[x] + c2*c[x]; g = Expand[f*f]; ...
0
votes
1answer
57 views

Integral evalutation

I am trying to integrate the following expression over $L$. E^(-2 L n) (1 - L/(2 s))^(-1 + 4 n µ) (L/s)^(-1 + 4 n v) I did... ...
1
vote
0answers
44 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 ...
3
votes
1answer
109 views

Strange integration

Bug introduced in 9.0 or earlier and fixed in 10.1 Note: Beginning with V10.1, this integral returns unevaluated but without error messages. I tried to evaluate this line ...
4
votes
2answers
244 views

Why doesn't FullSimplify simplify expressions with DiracDelta?

I want to simplify a complicated expression with some Dirac delta distributions, but FullSimplify does not do what I want. Specifically, I want ...
5
votes
0answers
229 views

Integrate wrong for absolute value of trig function

I was trying to get $\int_0^1 \lvert \cos(2 \pi k x) \rvert \,\mathrm{d}x$ for $k \in \mathbb{Z}$, and was surprised by the result (using Mathematica 10.0.1.0): ...
14
votes
6answers
665 views

How can I evaluate only a single step of a recursive function?

Let's say have a simple recursive function for the Fibonacci sequence f[0] := 1 f[1] := 1 f[n_] := f[n - 1] + f[n - 2] but I want to see how it will expand in a ...
0
votes
1answer
103 views

About Symbolize and Variables

I do believe this sort of similar questions had been asked many times, so I have read a LOT. For example this and this as well as many other related posts. But a glance at what my main question is ...
0
votes
1answer
64 views

Algebraic manipulation of closed loop state space system [closed]

I have the following equations $$ \begin{align} x(k+1) &= A x(k) + B \tilde{u}(k) \\ y(k) &= C x(k) + D \tilde{u}(k) \\ w(k+1) &= E w(k) + F \tilde{e}(k) \\ u(k) &= G w(k) + H ...
1
vote
0answers
40 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: ...
10
votes
1answer
323 views

Is it possible to implement symbolic sub matrices?

The accepted answer in the question Symbolic matrices in Mathematica with unknown dimensions provides a functionality to create symbolic matrices which behave pretty much as the name suggests. ...
0
votes
1answer
57 views

A problem with getting a coefficient

I try Coefficient[E^(I a (t - b)), E^(I a t)] and expect the output E^(-I a b) but in fact I get ...
2
votes
1answer
50 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
177 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
92 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
374 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. ...
6
votes
2answers
299 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 ...
7
votes
1answer
87 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
109 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 ...
26
votes
3answers
702 views

Symbolic integration error

fixed in 10.1 (windows) I'm running Mathematica 10.0.0 and encountered a disturbing error in the symbolic integration of a rather simple function ...
1
vote
0answers
111 views

Giving hints to Integrate

I working with the integral ...
7
votes
1answer
176 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
103 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 ...
1
vote
0answers
177 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 ...
3
votes
2answers
150 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
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: ...
3
votes
5answers
189 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 ...
29
votes
1answer
729 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. ...
1
vote
0answers
65 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
103 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 ...
3
votes
0answers
57 views

Evaluating standard functions of general quaternions symbolically

Mathematica can easily compute exponentials and logarithms of concrete quaternions: ...
0
votes
1answer
145 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
124 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. ...
4
votes
0answers
97 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
110 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
170 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
71 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 ...
2
votes
0answers
346 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
186 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
48 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
195 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 ...