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

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496 views

Solving Symbolically Equations with Vectors and Matrices

I want to solve equations with vector variables and vector/matrix parameters symbolically. As a basic example I would like to be able to solve something like $[I-aG]x=b$ where $a,b \in \mathbb{R}^l$ ...
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0answers
131 views

Alternative to Series

Here is a sample of my code: ...
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0answers
269 views

Simplifying terms in a Sum expression

I have a sum in the form of pure function s = Sum[f[k], {k, 0, # - 1}] & of perhaps complicated terms f[k]. The terms ...
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2answers
523 views

Is there a way to identify a symbolic fraction?

Is there a way to use Head to detect a symbolic fraction? In particular I find, Head[a/b] Head[1/5] Times Rational ...
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1answer
68 views

Defining a matrix with the symmetry Transpose[A(q)]=A(-q)

I am trying to construct a symbolic matrix with the following property- $$ \left(D_{3\times3}(q)\right)^T = D_{3\times3}(-q) $$ Note that for $q\in \mathbb{R}$, $D(q)$ would be hermitian. So far i ...
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3answers
167 views

Differential equation with a Heavisidetheta function running for ever

So I'm trying to get the solution of the following differential equation: ...
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1answer
108 views

Strange timings of integrals involving Hermite's polynomials

I have used Mathematica to calculate tunneling for quantum harmonic oscillator. The code is simple: ...
2
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2answers
139 views

Let mathematica combine integral limits

Is there a way to teach mathematica to combine integral limits according to $\int_a^b f dx+\int_b^c f dx=\int_a^cf dx$ to simplify expressions like $\int_0^1 f[t] dt+\int_1^x (1+f[t]) dt$ to $\int_0^t ...
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1answer
155 views

Symbolic quadratic constrained maximization with non-negativity constraints?

Dear Mathematica users, I attempted to maximize the below quadratic function K, subject to x1+x2<=A, and a series of ...
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1answer
344 views

Issue with integration from 0 to infinity with constants [closed]

I am trying to take the integration for $\int_0^{+\infty}e^{-\alpha t}sin(\beta t)d t$. Here is a screen shot of what I did: The solution to this integeation should be ...
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1answer
42 views

hold specific pattern in symbolic calculation

I encounter some questions when I try to simplify a symbolic expression using Mathematica. For example, I got an intermediate expression ...
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2answers
355 views

What does f_[whoCalled]^:=f really mean?

I came across the following post by John Doty in this Google Groups discussion: On Friday, January 11, 2013 8:23:16 PM UTC-7, amzoti wrote: It is clear the Mathematica uses Lisp as one ...
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2answers
360 views

Help at speeding up simplification/nested symbolic integration

I have the following problem: I want to compute an integral of the form $$\int\limits_0^{t_g}\mathrm{d}t_2\int\limits_0^{t_2}\mathrm{d}t_1\left[A(t_1),A(t_2)\right],$$where $\left[B,C\right]=BC-CB$ is ...
3
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2answers
139 views

Eigenvectors of large symbolic matrix

I have large symbolic matrix of order 32 x 32 given as ...
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0answers
81 views

Integrate with Subscript: does this crash your kernel too?

I encountered some strange behaviour running v10.0.1 on a Mac Pro, while working with Integrate and Subscript. Starting from a ...
2
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3answers
116 views

Symbolic integration conditional bug?

I just ran across this: Assuming[x > 0, Integrate[1/t^2, {t, 1, x}]] gives the output ...
2
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1answer
87 views

How to define the symbolic expression $V = \frac{1}{N} \sum_{i=1}^N ( y_i(g) - z_i)^2$ in Mathematica?

I want to define this expression symbolically: $V = \frac{1}{N} \sum_{i=1}^N ( y_i(g) - z_i)^2$ in which $\{y_i(g)\}_{i=1}^N$ is to be understood as a symbolic sequence that depends on a vector $g$. ...
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1answer
68 views

Taking function output as shown, and processing it regardless of its history

I am making some symbolical calculations for my quantum chemistry class. I am supposed to build a wave function composed of multiple other functions, each of which is also composite of some lower ...
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0answers
110 views

Summing the probability distribution to 1 to convince myself

I have worked out a probability distribution and want to check its sum which is necessarily 1. First we write $$ r \triangleq \frac{(2 \lambda + \mu)^2}{2(\mu + \lambda)^2}, \quad s \triangleq ...
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0answers
139 views

How does Mathematica resolve symbolic systems of inequalities? [closed]

Before getting into my question, let me provide some context: I recently started using Mathematica to automatically perform stability analyses that I previously did by hand. A major part of the ...
5
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3answers
298 views

Comparison of Dispatch objects ureliable in Mathematica 10

In 2008 I wrote a group theory package. I've recently started using it again, and I found that one (at least) of my functions is broken in Mathematica 10. The problem is complicated to describe, but ...
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2answers
426 views

DSolve bvlim error due to Boundary condition at infinity

I am solving an Ode using Mathematica that has boundary condition at infinity which is why Mathematica is showing error message. Please help to tackle this problem. ...
3
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1answer
127 views

How to get a more compact form of this probability calculation?

Inspired by the probability calculation here, I am trying to solve a little general one: $$\mathbb{P} (\sum_{i=1}^{m-1} A_i + \sum_{i=1}^{m} S_i < L < \sum_{i=1}^{m} A_i + \sum_{i=1}^{m+1} ...
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2answers
86 views

Symbolic integration of a indexed product term?

I am trying to perform the symbolic integration of the following expression $$\int \prod_{i=1}^n p(x_i | z) p(z) dz$$ where $$p(x_i|z) = \frac{exp(\frac{-(x-z)^2}{2\sigma_i^2})}{\sqrt{2 \pi ...
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2answers
140 views

Symbolic matrice or vectors in Mathematica?

Suppose I would like to define an expression, containing and array or matrix of symbolic elements. Like this ...
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1answer
370 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 ...
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2answers
338 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: ...
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0answers
132 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
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0answers
120 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
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2answers
322 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 ...
4
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2answers
164 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 ...
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2answers
163 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]; ...
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1answer
67 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... ...
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0answers
46 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
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1answer
120 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
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2answers
393 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
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1answer
306 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): ...
15
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6answers
785 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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1answer
124 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 ...
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0answers
58 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: ...
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1answer
407 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. ...
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1answer
58 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
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1answer
78 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 ...
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1answer
335 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 ...
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0answers
148 views

No solution with DSolve

I have been trying to solve the following system of ODEs: \begin{eqnarray} ...
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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 ...
6
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3answers
416 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
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2answers
445 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
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1answer
101 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
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1answer
121 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 ...