# Tagged Questions

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

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### 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 ...
320 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): ...
798 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 ...
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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 ...
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### 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....
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### 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. However,...
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### 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 ...
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### 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 ...
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### 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 ...
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### No solution with DSolve

I have been trying to solve the following system of ODEs: \begin{eqnarray} \frac{d\pi_1(x_\mathrm{ref})}{dx_\mathrm{ref}}x_\mathrm{ref}&=&l_{10}+\pi_1(x_\mathrm{ref})(l_2+l_5)+\pi_2(x_\...
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### 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 assumption?...
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### 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. ...
496 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 ...
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### 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}}] ...
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### 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 ...
881 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 ...
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### Giving hints to Integrate

I working with the integral ...
242 views

### How to find a recurrence relation for a sequence?

I have a sequence given by an explicit formula for n-th term: ...
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### 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 ...
250 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 ...
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### 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 ...
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### 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: ...
218 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 ...
782 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 $S^2$ ...
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### 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. ...
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### 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 <...
113 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 ...
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### Evaluating standard functions of general quaternions symbolically

Mathematica can easily compute exponentials and logarithms of concrete quaternions: ...
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### 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 ...
160 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} x}{dt^{...
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### Compute integral symbolically

I want to compute the following integral: ...
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### 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 ...
451 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 = \int_0^\...
471 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 p(...