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

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0answers
64 views

How does Mathematica resolve symbolic systems of inequalities?

Before getting into my (probably annoying) question, let me provide some context: I recently started using Mathematica to automatically perform stability analyses that I previously did by hand. A ...
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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: ...
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0answers
37 views

Evaluating standard functions of general quaternions symbolically

Mathematica can easily compute exponentials and logarithms of concrete quaternions: ...
2
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1answer
109 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 ...
2
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1answer
701 views

How to simplify symbolic matrix multiplication results?

I've defined three symbolic abstract matrices X, M and S as shown below. ...
2
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0answers
123 views

Changing bounds of summation after differentiating symbolic sums

Suppose, I have a function written as Taylor-Maclaurin series f = Sum[c[n]*x^n, {n, 0, Infinity}] Now, I wish to differentiate this expression with respect to ...
2
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0answers
186 views

Problems with Simultaneous Equation Solving

Let me first explain what I am doing and then I will explain the problem that I can't figure out. I am basically trying to solve 2 equations for 2 unknowns (a1 and ...
2
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0answers
229 views

Numerical-Symbolical Integration (Calculus)

I created a simple numeric-symbolic integration. Here you can use symbolical and numerical techniques at the same time. You can also interpolate numerical integrals. The problem with my function is ...
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1answer
197 views
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2answers
315 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 ...
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3answers
508 views

Sqrt — how to get negative branch?

One of the many attractions of Mathematica is that integers are generally treated as exact symbolic entities, and not just as numbers. I was just playing with Sqrt, and was puzzled by what appeared to ...
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2answers
145 views

Symbolic integral with distributions

Why is Integrate[ HeavisideTheta[1 - x^2] DiracDelta[1 - x^2] , {x, 0, 1} ] (*0*) It should be HeavisideTheta[0]?
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1answer
169 views

Improve performance for finding Fibonacci number which have divisibility property

In this post, the OP requires finding a Fibonacci number having some divisibility property with Mathematica and Maxima. I tired tried that Mathematica code on Mathematica 9.0 and it's still slow ...
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1answer
175 views

Why is a non-convergent series simplified to zero?

Sum[Sin[n*x]*Sin[n] /. x -> 1, {n, 1, Infinity}] == Sum[Sin[n*x]*Sin[n], {n, 1, Infinity}] /. x -> 1 Sum::div: Sum does not converge. >> ...
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1answer
443 views

How to define a derivative/Variation operation in Mathematica from scratch

I am looking for a method in Mathematica 8 to define my own derivative/variation (independent of built-in operations). I do not want to re-define built-in objects since I fear that this could cause ...
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1answer
114 views

Why do expressions with D and Derivative giving so different results for me?

I tried to express with Derivative the same I expressed earlier by D, but failed: ...
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2answers
44 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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1answer
119 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, ...
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2answers
239 views

Symbolically associate vectors and their norms

I am wondering how to handle the following situation: I do have vectors of known dimension that I would like to handle symbolically. I suppose I can do something like ...
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1answer
117 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 ...
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1answer
120 views

Calculate the algebraic multiplicity of known eigenvalues of a large, sparse matrix

I have a large (and sparse) matrix with size 1000x1000 -- 10000x10000. I believe i know all eigenvalues for the matrices. All entries are integers and so are the eigenvalues. I want to check this by ...
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1answer
129 views

Simplifying fractions

What ComplexityFunction (or other technique) can I use to have Mathematica pull things out of fractions? I have a rational function of several variables and I'd ...
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1answer
93 views

How can I check if one expression implies another?

Say I have one expression, for example $x^3-3 + c = y$, and I want to check if it implies another with some set of explicitly stated assumptions. With the previous example, assuming all variables are ...
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2answers
233 views

Expansion with binomial coefficients

How can I get binomial coefficients in expansion of $(n x+i) (1+i x)^n+(n x-i) (1-i x)^n$, where $i=\sqrt{-1}$ and $n$ is an integer. I have no idea how to coax Mathematica to do something remotely ...
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1answer
101 views

Linearity of a function in Mathematica

I have a function which has something like myFunc[q,a state[c,d]] a could be anything, and I want to tell Mathematica that ...
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3answers
405 views

RowReduce for symbolic matrices

I'd like to invoke RowReduce on some matrices with a time parameter. For example consider A = {{1, 0}, {0, t}} If ...
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1answer
247 views

Generating a list of symbolic coefficients [duplicate]

I am trying to do something which I assume should be very simple: I want to generate a list with symbolic coefficients that looks like this: ...
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1answer
114 views

Only perform a symbolic differentiation once

I want to define a function that involves a differentiation step that Mathematica can do easily, which might be of the form ...
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1answer
212 views

Symbolic calculation

Is there any software where this kind of symbolic calculation is possible? s = 0 for i = 1 to m j = 2 i + a - t if (j > 0) s = s + a I want s as a ...
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1answer
65 views

Strange integration

I tried to evaluate this line Integrate[((-I/2) (E^((-I) x) - E^(I x)) + ((E^((-I) x) + E^(I x)) x)/ 2)/((-1 + E^x) x), {x, 0, Infinity}] Then I get $14$ ...
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1answer
72 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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1answer
38 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 ...
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1answer
170 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 ...
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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 ...
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2answers
124 views

Symbolic solution of system

everyone! I am sorry, but I am an abcolute novice of Mathematica (to be more precise this is my first day of using it) and even after surfing the web and all documents I am not able to solve the ...
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1answer
85 views

Why TensorReduce not working here?

I would like to use TensorReduce to work on the tensor contraction $y_{ib}y_{ia}$ (where index $i$ is summed). However, ...
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1answer
303 views

Finding exact local extrema of simple functions

I want to exactly find all the local maxima of f[x_] := x^4/4 - x^2/2 over the interval [-Sqrt[2], 1 + Pi/10]. The correct ...
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1answer
225 views

Comparative Statics on Mathematica

Let me first explain what I am doing then I will mention my little problem that I could not figure out. I am using Mathematica version 7. I have an equation named "fd" and I took the derivative of ...
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1answer
137 views

How to perform a symbolic minimization?

Can Mathematica determine the symbolic expression in terms of τ that minimizes f[τ] ? ...
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1answer
147 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 ...
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0answers
56 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 ...
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0answers
71 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
40 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 ...
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0answers
49 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 ...
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0answers
38 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 ...
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0answers
26 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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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 ...
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0answers
97 views

Giving hints to Integrate

I working with the integral ...
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0answers
61 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 ...
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0answers
71 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 ...