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

learn more… | top users | synonyms

4
votes
1answer
90 views

When to use GenerateConditions -> True

Many functions, usuallly those involving integration, take a GenerateConditions option which often defaults to False, or at ...
4
votes
1answer
141 views

Volume within parameter space

Imagine a parameter space with variable 0<p<1, 0<e1<1/2 and 0<e2<1/2. ...
4
votes
1answer
771 views

Symbolic integration in the complex plane

Context While answering this question, I defined (symbolic and numerical) path integrations as follows ...
4
votes
1answer
79 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} ...
4
votes
3answers
244 views

Running out of variables

I am running symbolic calculations with Mathematica. Simplification of algebraic expressions is an important part of them as very often final results can be simplified considerably. Typically my ...
4
votes
2answers
245 views

How do I evaluate a symbolic integral involving Hermite polynomials?

I want to test a difficult integral : Integral on all reals of some complicated function involving the Hermitian polynomials, exponentials, squares, factorials, and being general considering any ...
4
votes
1answer
131 views

Identical code, different answers?

I'm having some trouble with identical code giving different answers. On a fresh kernel (MM 9.0.0.0, Windows 64-bit), running the same code, copy-paste, gives two different answers: ...
4
votes
1answer
612 views

Computation of parametric integral

I am trying to compute the integral Integrate[(g^(u^(g - 1)))/(1 + u^g), {u, 0, t}] but as an answer I get my input expression. There must be something wrong ...
4
votes
1answer
275 views

How to extract a possible closed form from WolframAlpha[] output

To find a possible closed form of a number, I can use the function WolframAlpha["6.38905609893065", IncludePods -> "PossibleClosedForm"] It returns a result ...
4
votes
2answers
200 views

Problem with adding vector to symbolic function (for NDSolve)

I'm trying to set up a system of differential equations for passing to NDSolve. Note that my initial conditions are vector valued so Mathematica should know that ...
4
votes
1answer
227 views

Is it possible to create a compiled function with some symbolic arguments?

I am trying to create a compiled function that takes in several arguments. However, some of the arguments contain symbolic entries and thus I get the following error message when executing the cell ...
4
votes
1answer
238 views

How to check if a given expression is an “explicit algebraic number”?

The documentation for PossibleZeroQ says: With the setting Method...
4
votes
1answer
90 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 ...
4
votes
2answers
405 views

Problems with Symbolic summation over unknown values

I'm having some real trouble with Mathematica wrongly evaluating various symbolic sums at the moment. I have this function: $$h_{ij}(x) = ...
4
votes
0answers
484 views

Analytically solve the eigenvalue problem with infinite dimensions by Mathematica?

If I am given a symbolic expression of all the matrix elements in an infinite-dimensional space, e.g., the Hamiltonian of a quantum mechanical system, is it possible to get the symbolic expression for ...
4
votes
0answers
87 views

Using Resolve and ForAll to prove takes a really long time

I've been trying to prove a lemma for my paper using Mathematica... basically that $$\forall \{n, d_i, d_j\} \in \mathbb{Z},\ n \ge d_i > d_j \ge 2$$ it's true that $$V[1, n, d_i-1, d_j-1] ...
3
votes
3answers
390 views

Symbolic derivative of $n$-term product

I want to determine the relationship that must exist between the $x_i$ and $y_i$ such that $$ \frac{\partial}{\partial\theta} \prod_{i=1}^n \frac{f(x_i,\theta)}{f(y_i,\theta)} = 0, $$ where $$ ...
3
votes
1answer
443 views

How do I solve $1 - (1 - (A x)^2)^\frac{3}{2} - B(1 - \cos(x))= 0$?

Consider the equation $$ 1 - (1 - (A x)^2)^\frac{3}{2} - B(1 - \cos(x)) = 0 $$ where $A,B \in \mathbb{R}$ are constants. What is the analytic solution?
3
votes
2answers
149 views

A suspicious result of an integral

I integrated this term in Mathematica: $$\int_{-\infty}^{\infty} d\omega*\sin(s*\omega)*\frac{1}{e^{\beta*\hbar*\omega}-1}*\frac{\omega}{\omega^{2}+\gamma^{2}}$$ The code in Mathematica: ...
3
votes
2answers
260 views

Can Mathematica identify formulae or sequences of numbers?

Can Mathematica suggest what a formula means? For example if I input $$\sum_{i=0}^n i$$ can it infer that this is a sum of integer values from $0$ to $n$? Or if I enter $0,1,1,2,3,5,8,13$, can ...
3
votes
1answer
222 views

What properties make this equation difficult to symbolically solve?

I tried to solve the following equation with Mathematica's solve: Solve[K*(2*Tan[L/2*Sqrt[P/(EI)]]-L*Sqrt[P/(EI)])+4*P*Sqrt[P/(EI)] == 0, P] It gave the ...
3
votes
3answers
616 views

Superscript prime symbol

x\[Prime] looks like $x_'$, ugly right? Is there a way to make a symbol with prime to look like $x'$? That's what I'm trying right now: ...
3
votes
1answer
726 views

Non-commutative algebra

I'm constantly dealing with non-commutative algebras. ** is inbuilt, non-commutative and associative. That's good :-) But it is not distributive. Rats. ...
3
votes
5answers
145 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 ...
3
votes
2answers
141 views

How to define the irrational domain or any other arbitrary domain?

I have found no way to define the domain of Irrational numbers. I can easily define a test to see if a number is irrational by defining: ...
3
votes
1answer
169 views

Symbolic Integration of Special Functions

Sorry in advance if this formatting comes out strange, this is my first question! I can't find a way to integrate, e.g., a function of the Hermite polynomials for general (still integer) order. For ...
3
votes
2answers
147 views

How to define even permutations correctly?

I define even permutations as following, but there may be some error. I use it in two different way and get different output. ...
3
votes
1answer
76 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 ...
3
votes
2answers
112 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 ...
3
votes
1answer
171 views

Covariant derivative for symbolic tensors

I want to define a "prefix" (D_i) covariant derivative operator CD[] for symbolic tensors in form of a function, i.e. for ...
3
votes
2answers
274 views

Tweaking Solve for systems of polynomial equations

I am trying to solve the following system of $6$ quadratic equations in $6$ variables: ...
3
votes
2answers
92 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 ...
3
votes
1answer
177 views

Strange behavior of Reduce with a cubic equation

This equation: $(\frac{-a}{x})^2=\sqrt{\frac{1}{x}}$ at $a > 0$ and $x > 0$ has a clear solution $x=a^{4/3}$, doesn't it? However, ...
3
votes
2answers
190 views

Mixed product identity between tensors in Mathematica 9

How can we simplify tensor expressions in Mathematica 9 using the mixed-product identity $(A\otimes B)(C \otimes D) \equiv AC \otimes BD$ ? Is it possible to implement this kind of evaluations using ...
3
votes
1answer
304 views

How can I get Mathematica to recognize equality of symbolic matrix expressions?

I have two matrix expressions: X.Transpose[T].Transpose[X] and X.T.Transpose[X] I want Mathematica to recognize that ...
3
votes
1answer
408 views

Non commutative multiply- expand expression

I began to use Mathematica a few days. My problem is: How to expand expression like $(a+b)*(a+b)$, where this multiplication is non commutative? Mathematica can do this?
3
votes
1answer
203 views
3
votes
1answer
130 views

How to do this complex integration on the real line?

$m, r$ are parameters in the following integral: Integrate[z Exp[I z r]/Sqrt[z^2 + m^2], {z, -∞, ∞}] How to do this integration directly? The result should be ...
3
votes
1answer
85 views

Problem with limit that requires L'Hôpital's rule to compute

Consider the following limit. Limit[(a - Sqrt[a^2 + x])/(a^2 - a*Sqrt[a^2 - x]), x -> 0, Assumptions -> {a > 0}] Mathematica 9.0.1.0 gives ...
3
votes
1answer
100 views

Check that a relational expression is true for all complex numbers

How can I use Mathematica to check if a statement like $$\left| \frac{\sqrt{1+2z}-2}{2z-3} \right| \le 1$$ is true for all complex numbers $z$? Also, how can I use Mathematica to check such a ...
3
votes
1answer
211 views

Define operator algebra

My objective is to work out commutators like this $$[f(x,y)\partial_x^2+g(x,y)\partial_x+h(x,y),a(x,y)\partial_x^2+b(x,y)\partial_x+c(x,y)]$$ or ...
3
votes
1answer
272 views

n-fold symbolic integral in Mathematica

I am trying to compute symbolically a n-fold integral (n is a parameter of a function) over, say, the cube [0,a]^n. My code looks like this ...
3
votes
1answer
99 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. ...
3
votes
1answer
74 views

Symbolic Output after numerical computation

I have a small question about the symbolic output. I started to write a program that generates the coordinates of n-dimensional polytopes by Wythoff construction. For crystallographic groups, all is ...
3
votes
0answers
62 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 ...
3
votes
0answers
53 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 ...
3
votes
0answers
115 views

Fourier transformation of HeavisideTheta functions

I want to find 2D-Fourier transformation of the function given below f = HeavisideTheta[y1]*HeavisideTheta[y2 - y1] For the purpose, I use built-in function in ...
3
votes
0answers
104 views

What is so special about variable s$?

I found a nice bug in Mathematica 9.0.1.0. Could anyone check to reproduce it? Create a file temp.txt with one line: ...
3
votes
0answers
120 views

Do a gauge transformation for a Chern-Simons theory?

Suppose we have the following Lagrangian density: $$ L=\epsilon^{\mu\nu\rho}\big(\sum_a A^a_{\mu}(x) \partial_\nu A^a_{\rho}(x)-\sum_{a,b,c}\frac{1}{3} f^{bca} A^a_{\mu}(x) A^b_{\nu}(x) ...