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

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16
votes
1answer
156 views

No analogue for Maple's dchange?

Maple owns an interesting function called dchange which can change the variables of differential equations, but there seems to be no such function in Mathematica. ...
5
votes
1answer
41 views

How do I perform exact unit conversions with irrational conversion factors?

Suppose I want to express $3h$ in units of $\hbar$ (where $h$ and $\hbar$ are the Planck constant and reduced Planck constant, respectively). By definition, $h = 2\pi\hbar$, but when I attempt this ...
4
votes
1answer
82 views

Checking if a symbolic matrix is positive semi-definite

As far as I can tell, there is no way to tell the builtin PositiveSemidefiniteQ about assumptions on symbols. For example, the matrix ...
0
votes
1answer
40 views

Is there a function or option to collect factors under one radical sign?

One of the things that frustrates me most about Mathematica's symbolic manipulations is the fact that output is often presented quite differently than most humans would write it. This is especially ...
1
vote
0answers
26 views

How can I get symbolic orthonormal eigenvectors for 3 by 3 hermitian matrix?

Using the following syntax, I can obtain the symbolic eigenvalues and eigenvectors of the following Hermitian matrix (a,b,c,d are all real parameters): ...
2
votes
1answer
106 views

Can Mathematica solve this type of recurrence?

I have the following recursively defined equation: ...
0
votes
1answer
26 views

How to get the modulus of following complex number

I want to get the modulus of following (1+(x+I*y)/2+(x+I*y)^2/12)/(1-(x+I*y)/2+(x+I*y)^2/12) I use ...
15
votes
2answers
3k views

How do I work with Root objects?

I want to solve the trigonometric equation : $$(3-\cos 4x )\cdot (\sin x - \cos x ) = 2.$$ I tried Solve[(3 - Cos[4*x])*(Sin[x] - Cos[x]) == 2, x] It returns the ...
20
votes
2answers
260 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 ...
23
votes
3answers
622 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 ...
-3
votes
0answers
39 views

How to use the Mathematica to simplify a vector symbolic computation?

I'm working with a rigidbody dynamic problem,and I have listed the "Newton-Euler" equation for a system.The equation I listed is very long and many items are included.I want to use the Mathematica to ...
0
votes
0answers
23 views

Find out domain after change of variable in integral of d dimensions

Is there a way to tell Mathematica the change of variable you want to do and getting back the corresponding domain? The specific problem I am trying to solve is $\quad \quad\int_{-1}^0 ...
0
votes
1answer
31 views

Using Coefficient to pick combinations of parameters in an expression

I have the expression $$ c \partial_{\chi} u = \mu u - \nu v - (u + \beta v)|A|^2 + (\partial_{\chi}^2 u - \alpha \partial_{\chi}^2 v) + \gamma u \\ c \partial_{\chi} v = \mu v + \nu u - (v - \beta ...
4
votes
2answers
118 views

Well-defined symbolic integral leading to ConditionalExpression

I would like to determine a closed-form expression for the following symbolic integral $$ \int_{-1/2}^{1/2} \!\!\!\! \mathrm{d} x \int_{-1/2}^{1/2} \!\!\!\! \mathrm{d} y \, \frac{1 + b x + c y}{1 + e ...
10
votes
1answer
377 views

Symbolic Integration along contour: branch cut problem?

Context Following this question on path integrals in the complex plane, having defined again a numerical and symbolic integrator along a path as ...
1
vote
1answer
64 views

Working with derivative of conjugate of a complex number

I have a complex function, lets say $g(x)$. I want to take its and its conjugate's derivative. I need the solution of derivative which must be symbolically and computationally efficient. Lets take an ...
5
votes
1answer
55 views

Rearrange an algebraic expression so that each variable appears only once

Mathematica gave me a solution to an equation in this form: ans1 = (b c)/(a - a c + b c) $\text{ans1} = \frac{b c}{a - a c + b c}$ From solving the same equation ...
7
votes
1answer
219 views

Is it possible to implement symbolic sub matrices?

The accepted answer in the following link: http://stackoverflow.com/questions/5708208/symbolic-matrices-in-mathematica-with-unknown-dimensions provides a functionality to create symbolic matrices ...
3
votes
3answers
88 views

How to Integrate trivial products of DiracDelta

A long while ago I was able to integrate with Mathematica: $$\int_0^1 \delta(1-x)\delta(x) f(x) \,dx = 0$$ using ...
4
votes
1answer
48 views

Simplify complex answer given by DSolve[]

I tried the technique in this question, but that did not work for the solution given by the MWE: DSolve[{f'[t] + f[t]*g[t] == h[t], f[0] == f0}, {f[t]}, t] How ...
2
votes
1answer
85 views

simplifying integrals for multiple exponentials

This is somewhat related to this question, but applied to products of Exp[]. For example, I have a symbolic expression containing terms like $Exp[\int_0^1 ...
0
votes
1answer
37 views

Working with symbolic values in Quantities [duplicate]

I have the following expression: x Quantity[y, ("Milliwatts"*"Seconds"^2)/"Joules"] If I try to convert this to the SI unit, I would expect to get ...
5
votes
1answer
100 views

Slow-down encountered when using NMinimize with a compiled function

I'm minimizing a large function. Evaluating the function is very slow symbolically but using Compile I can get ~100x speed-up on this step. However, despite this, the NMinimize process is only ...
0
votes
1answer
68 views

How to make Mathematica show intermediate steps in integral [duplicate]

I want to know how Mathematica evaluates this integral: $PV \int _ {0} ^ {i \infty} d \tau \, \frac{e^{-\frac{\tau^2}{2 M^2}}(b^2 - 3 τ^2)^2 (|b^2+\tau^2|-(b^2-\tau^2))}{\tau (\tau^2 - b^2)}$, where ...
26
votes
1answer
669 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 $S^2$ ...
0
votes
0answers
131 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 $a,b \in \mathbb{R}^l$ ...
2
votes
1answer
86 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 ...
0
votes
0answers
38 views

Minimize doesn't solve a problem with many symbols

I am trying to solve a simple constrained optimization problem. I am running the code ...
1
vote
1answer
61 views

SymbolicC Simplified Displayed

How might I display a simplified SymbolicC below. For example in the following example ...
10
votes
2answers
494 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 ...
4
votes
7answers
407 views

Given a symbolic expression how to find if starts with a minus or not?

I am using a Mathematica function which returns some error term in symbolic form. I needed a way to determine if this term starts with a minus sign or not. There will be only one term. This is to ...
0
votes
0answers
34 views

Substitute all known values in matrix [duplicate]

There is probably a very simple way of doing the following, but I cannot find it. I have a an array of symbolic variables: coefficients = Array[c, 3] I then ...
1
vote
1answer
55 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 ...
3
votes
3answers
113 views

Differential equation with a Heavisidetheta function running for ever

So I'm trying to get the solution of the following differential equation: ...
18
votes
1answer
486 views

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 ...
1
vote
1answer
82 views

Strange timings of integrals involving Hermite's polynomials

I have used Mathematica to calculate tunneling for quantum harmonic oscillator. The code is simple: ...
13
votes
1answer
369 views

What is the confidence limit on this convergence?

When I run this, Product[n^MoebiusMu[n],{n,1,Infinity}] I get $\frac{1}{4 \pi^{2}}$ Over on Math Overflow they are saying it shouldn't happen. So, how do ...
2
votes
2answers
91 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 ...
2
votes
1answer
108 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 ...
1
vote
1answer
309 views

Import symbolic variables from Matlab with MATLink

I'm trying to manipulate with Mathematica symbolic expression created in Matlab. I'm using the MATLink package, and I've succedeed in importing numerical variables, but not symbolic ones : ...
27
votes
1answer
578 views

How to augment the realm of functions Mathematica thinks it knows how to integrate symbolically

My question involves extending the functionality of Integrate over specific integrals in the most generic manner. Specifically, is it possible to "hack into" ...
0
votes
1answer
56 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 ...
0
votes
1answer
726 views

How to find the inverse a symbolic matrix that Mathematica thinks might be singular

I have a square matrix depending on a parameter "a". When "a" has a numeric value (eg 2.1 * 10 ^ 8) through the inverse function Inverse[] I can invert the matrix. If I write the matrix as a function ...
1
vote
1answer
34 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 ...
20
votes
3answers
368 views

Negative probability?

Bug introduced in 9.0.1 and fixed in 10.0.2 I am trying to get the sum of the squares of seven random variables, all uniformly distributed. This is what I tried. ...
11
votes
1answer
199 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 ...
3
votes
2answers
204 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 ...
0
votes
0answers
73 views

Is it possible to get a symbolic expression from FindRoot?

I need to have an expression where the solution from FindRoot (or another solver) depends on one or more parameters. Let's say I have a polynomial of second ...
3
votes
2answers
108 views

Eigenvectors of large symbolic matrix

I have large symbolic matrix of order 32 x 32 given as ...