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

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0
votes
2answers
69 views

Expression of an integral

I am doing the following integral in Mathematica with $a>0$, $\iint e^{ -\left ( x_{1}+x_{2}-2b \right )^2/\left ( 4a \right )}dx_{1}dx_{2}$. My code is ...
19
votes
2answers
4k 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 ...
1
vote
2answers
58 views

Permuting symbols

Suppose I have a list like {a, b, a, c}. How can I apply a "symbolic permutation" of the symbols a, ...
1
vote
1answer
47 views

Factor a polynomial Root into Roots of smallest possible degree

Suppose I have a polynomial Root representing an algebraic number. I want to represent it (if possible) as a product of several polynomial ...
2
votes
0answers
42 views

Identity Matrix in symbolic Tensor Product

I am trying to simplify symbolic tensor products. E.g. ...
-3
votes
1answer
79 views

How to symbolically integrate 2D exponential function? [duplicate]

Is it possible to symbolically solve a 2D integral of the following form $$\int d \vec{r}e^{-\frac{\left| \vec{r} - \vec{r}' \right|^2}{2c}}e^{-i \vec{k} \cdot \vec{r}} $$ where $\vec{r} = (x,y)$ and ...
1
vote
1answer
73 views

Simplify fractions and square roots

I would like to 'Simplify' Sqrt[5/6]/2 to Sqrt[5/24] I've tried to penalize Times and Rational using ComplexityFunction, ...
1
vote
1answer
140 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 ...
4
votes
2answers
143 views

symbolic summation involving kronecker delta

I have to perform symbolically summations of this kind $\sum_{ijkl} V_{ijkl} c_i c_j c_k \delta_{l,m}$ where $V_{ijkl}$ are quantities which depend on 4 indices and $\delta_{l,m}$ is the kronecker ...
4
votes
0answers
56 views

Create an adequate 'training set' to train a ClassifierFunction which performs the role of the built-in `SubsetQ`

I am trying to "grow" my own SubsetQ function using Machine Learning methods. My cSubsetQ when given two lists (listA and ...
1
vote
2answers
71 views

Symbolic derivatives and substitution [duplicate]

I have troubles substituting functions when I have symbolic derivatives and I need to substitute more symbolic derivatives in my expression. Take for example ...
18
votes
3answers
2k views

How to deal with complicated Gaussian integrals in Mathematica?

As we know, for most Gaussian integrals, we can get the analytical result. Now I have many Gaussian integrals to treat, which have the following general form, ...
1
vote
1answer
104 views

The basic primitive recursive functions

How can the basic primitive recursive functions be expressed in the Wolfram Language? Apparently here's an example for primitive recursion: ...
26
votes
1answer
365 views

$\sum _{k=1}^{\infty } \left\lfloor \frac{5}{5^k}\right\rfloor$ giving wrong answer?

Bug introduced in 7.0 or earlier and persisting through 10.3.1 or later When I try to evaluate the following: $$\sum _{k=1}^{\infty } \Bigg\lfloor \frac{5}{5^k}\Bigg\rfloor$$ using ...
0
votes
1answer
70 views
27
votes
4answers
2k views

What is a type in Wolfram Mathematica programming language?

"Everything is an expression" is a popular citation from many Mathematica guidebooks. So, what is type in Mathematica? How does it relate to common types from Haskell, for example? I did some ...
0
votes
0answers
33 views

Symbolic root computation of a function that depens on parameters

I'm given list of real numbers $a_i, i=1,N$, where usually $N \le 100$. Consider a function $f_N = f_N(x,a_1,...,a_n)$. I need to find the roots of $f_N(x)$ on $[-1,1]$, assuming that $a_i \notin ...
3
votes
2answers
50 views

How to avoid 0 OverVector[F] to be evaluated as 0?

I am fairly new in Mathematica and I am trying to work with scalars and vectors. I decided to denote vectors using OverVector (as example, ...
3
votes
1answer
515 views

Mathematica 9 and later behavior with derivative of a sum

Bug introduced in 9.0 or earlier and persisting through 10.3.0 or later ...
2
votes
1answer
62 views

Finding the expansion of $\sin(a_{1}+a_{2}+a_{3})$ on Mathematica [closed]

How to find the expansion of $\sin(a_{1}+a_{2}+a_{3})$ on Mathematica, using $$ \sin(a+b) = \sin a \cos b + \sin b \cos a$$ to the end? I tried FunctionExpand ...
3
votes
1answer
291 views

Sum of positive terms gives negative answer

Bug introduced in 7.0 and fixed in 9.0 Mathematica evaluates Sum[((n - y - 1)*(n - y)^2*n^y)/y!, {y, 0, n - 2}] as -2 e^n n. ...
10
votes
1answer
143 views

Bug in GeneratingFunction?

Bug introduced in 7.0 and fixed in 9.0.0 According to the documentation GeneratingFunction[a[n],n,x]==Sum[a[n]x^n,{n,0,Infinity}] However, for $a_n=1/(n+2)$ I ...
12
votes
5answers
237 views

Prevent Plus from threading

This is probably a very simple question, but I couldn't find a duplicate. As everybody knows, {x, y} + v gives {x + v, y + v}. ...
5
votes
1answer
155 views

How to write polynomial expression as commutator form?

I want to write some polynomial expressions as commutator form. For example : $$ \frac{\text{BA}}{2}-\frac{\text{AB}}{2} = -\frac{1}{2}[A,B] $$ or $$ ...
3
votes
2answers
93 views

How to make algebraic substitutions?

I would like to simplify complicated expressions by defining some variable that is a combination of other variables that appear in the expression, but without eliminating the original variables. As a ...
0
votes
0answers
35 views

Series Manipulation [duplicate]

How do I get Mathematica to realize that it should simplify the expression Sum[f[t],{t,1,Infinity}]-Sum[f[t],{t,2,Infinity}] to ...
7
votes
1answer
55 views

Non-commutative algebra (NCAlgebra): How to properly SetCommutingOperators

I am starting to work with non-commutative algebra in Mathematica and had a look at the NCAlgebra package. I installed it and can use its functions. However, what I am struggling with is the ...
3
votes
0answers
57 views

Simplifying between set theory and logical connectives

I'm trying to find out how to switch between set notation and logic, but am having difficulty. For instance, I know that the following two expressions are equivalent ...
0
votes
0answers
107 views

Recognizing a generalized function as zero

Consider the following expression: HeavisideTheta[x]HeavisideTheta[-x] Mathematica will not simplify it further. But $\Theta(x)\Theta(-x)$ is zero if considered ...
0
votes
0answers
44 views

Simplify and compare two complex polynomial formulas

I have two formulas about variance estimation given order statistics $X_{1}\leqslant X_{2} \leqslant ...\leqslant X_{n} $ from a random sample of arbitrary distribution. My simulation in R already ...
1
vote
0answers
38 views

How to find symbolic greatest common divisor? [closed]

How can I use Mathematica to find the greatest common divisor of symbols? For example, is there some way that I could input $GCD[a,a+ba]$ and have Mathematica output $a$ as the greatest common ...
1
vote
1answer
253 views

How to minimize the sum of squares of deviations from the mean?

I am trying to minimize the sum of squares of a deviation from the mean applying the following: Minimize[Sum[(Subscript[x, i] - μ)^2, {i, 0, n}], x] It returns ...
0
votes
0answers
268 views

Symbolic tensor product calculation

I am trying to calculate the a symbolic tensor product $\langle \nabla f\otimes f,\nabla g\otimes g\rangle ^2+(\langle \nabla f\otimes g,\nabla f\otimes g\rangle +\langle \nabla g\otimes f,\nabla ...
0
votes
0answers
93 views

Series of square root of exponential

my problem concerns the Series command applied to Sqrt of an exponential, and it can be presented in a simplified version as ...
0
votes
0answers
72 views
0
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0answers
243 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 ...
0
votes
0answers
131 views

Alternative to Series

Here is a sample of my code: ...
0
votes
0answers
63 views
1
vote
1answer
66 views

Subtracting Series

When I input the following $$\sum_{n=0}^{m+1}x[n]-\sum_{n=0}^{m}x[n]$$ which in InputForm is: ...
5
votes
1answer
193 views

A triple sum related question

I'm trying to compute the triple sum Sum[ 1/(i! j! k! ), {i, 1, Infinity}, {j, i + 1, Infinity}, {k, j + 1, Infinity}] but Mathematica doesn't return any value. ...
2
votes
1answer
96 views

Two different results for same symbolic integral

I am trying to compute the following integral $\int_0^\infty dk \frac{e^{i k a}}{k^2}[\sin(kb)-kb\cos(kb)]$ When computing it as-is, i.e, with the code ...
1
vote
3answers
117 views

Identify a scalar, a list

I have a symbolic scalar m2 and a symbolic list (representing a 3x3 matrix) A. I want a function which does something like: ...
18
votes
2answers
350 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 ...
22
votes
1answer
959 views

Analogue for Maple's dchange - change of variables in differential expressions

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. ...
0
votes
1answer
52 views

Unexpected result from Sort with symbolic values

I think Sort should be able to sort symbolic values that are reducible to numerical values, but this example seems to get a wrong answer (here is a simplified ...
0
votes
0answers
141 views

No solution with DSolve

I have been trying to solve the following system of ODEs: \begin{eqnarray} ...
7
votes
6answers
1k views
6
votes
1answer
304 views

Using FunctionExpand to evaluate symbolic derivatives

Some symbolic derivatives of certain special functions are not expanded automatically, but FunctionExpand often helps to get a derivative-free closed form ...
3
votes
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: ...