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

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3
votes
0answers
33 views

Wrong limit: Limit[(1 + (-1)^n/n)^n, n -> Infinity]=1 (Mathematica 10.4 and W-Alpha)

Since $(1-\frac{1}{n})^n\to 1/e$ and $(1+1/n)^n\to e$, the sequence $(1+\frac{(-1)^n}{n})^n$ has no limit as $n\to\infty$, but has limits for odds and even numbers. If $n$ were taken to be real, there ...
1
vote
1answer
86 views
0
votes
1answer
60 views

How to do symbolic logic in Mathematica

I'm currently in Symbolic Logic with homework assignments (not asking for people to do my homework for me) with questions such as the following: (derive the conclusion using the eighteen rules of ...
1
vote
2answers
223 views

How to compute this integral?

I'm trying to calculate this integral : $$I(z,k,a)= \displaystyle\int_{1}^{\infty} t^2\, \text{ArcTanh} \left(\sqrt{\frac{t^2-1}{t^2}} \dfrac{k}{z}\right)\, e^{-a\,t} \, dt$$ Where : ...
1
vote
4answers
90 views

Symbolic calculation on roots of polynomial

Given a polynomial like $x^3 + a_2 x^2 + a_1 x + a_0$ with roots $r_i$, I would like to symbolically compute the coefficients of a polynomial whose roots are $r_i^3 + r_i + 1$. How can I do this in ...
2
votes
0answers
44 views

Unexpected imaginary term in the asymptotic expansion of DawsonF

FullSimplify[Series[2 DawsonF[x], {x, ∞, 8}]] (* -I Exp[-x^2] √π + (1/x + 1/(2 x^3) + 3/(4 x^5) + 15/(8 x^7) + O[1/x]^9) *) What is the reason the term ...
0
votes
0answers
26 views

Ordering of Eigensystem in symbolic computations [duplicate]

Suppose I have a symbolic 4x4 matrix for which I am finding the Eigenvectors and Eigenvalues. My question is whether Mathematica ...
3
votes
0answers
74 views

What is the good source to study advanced custom coding in Mathematica [duplicate]

My question is, probably, too general ... I deal a lot with complicated symbolic evaluations, integrations, plotting. I have troubles with optimizing my codes. They come out way too slow. Google and ...
2
votes
0answers
40 views

Replacement rule for summation with Kronecker delta

I want to perform some symbolic computations in index notation, without explicit reference to sums, so that in expressions of the type f[i,j]g[j,k] summation over ...
2
votes
1answer
76 views

Unexpected behavior of FindGeneratingFunction

FindGeneratingFunction will give up to computer sometimes?Such as FindGeneratingFunction[{1, 4, 6, 4, 1}, x] But actually the ...
1
vote
1answer
76 views

Remove part within square brackets for function

So I've defined a variable as follows: q = {{x[t]}, {Φ[t]}} V=0.5*x[t]^2*m^2+0.5*Φ[t]^2*I I've had to differentiate with respect to time so: ...
2
votes
0answers
67 views

Unexpected behavior from applying ToRadicals to eigenvalues [closed]

I am trying to get the symbolic form of a $10 \times 10$ matrix (I know, that is generally too large). ...
0
votes
1answer
47 views

Symbolic Maximization: does not work with symbolic power?

Simple question from a beginner: I seem to be unable to do maximization if the variable has a power specified symbolically instead of numerically? ...
5
votes
4answers
93 views

Multi-index variable depending on signature of permutation of indices

I do have some multi-indexed variable, e.g. like this \begin{align*}f_{123} &= 1\\f_{345} &= 1/2\end{align*} where $f$ is antisymmetric under permutation of any pair of indices, i.e. e.g. ...
1
vote
0answers
50 views

Can Mathematica solve Kuhn-Tucker Equations with arbitrary functional form (up to 2nd order derivative)

I am in a business of solving a 5-variables optimization with inequality constraints, and I would like to maintain the functional form as arbitrary as possible. So far, I am assuming that the ...
2
votes
2answers
65 views

Symbolic calculation of the rank of jacobian matrix

I would like to symbolically determine the rank of a jacobian matrix. In the help, I have seen that the MatrixRank function can be used for this purpose. However, when I use this function, the ...
2
votes
2answers
54 views

Why does ExpandAll not work within a symbolic sum?

If I evaluate Sum[(x + Subscript[y, n])^2, n] + (y + z)^2 // ExpandAll then the expression within the Sum is not expanded, yet ...
0
votes
1answer
38 views

Expansion on sums of NonCommutativeMultiply

Following the MMa's documentations, the ExpandNCM[] function expands a**(b+c) without efforts (although I don't have very good ...
2
votes
1answer
57 views

Rewriting terms as perfect derivative

I am trying to find conservation laws of a system, and I'd like to rewrite terms of the form $$A\frac{dA^*}{dt}+A^*\frac{dA}{dt}$$ as $$\frac{d}{dt}|A|^2,$$ where $A$ is a complex valued function ...
3
votes
2answers
66 views

Creating Boolean expressions over a set of indexed variables

I've read lots of examples here on how to set one matrix Equal to another, but how do you nest And and ...
0
votes
1answer
72 views

How to transfer symbolic expression to code? [closed]

I have a lot of messy things in Mathematica in a form like this: Mathematica perfectly solves all these symbolic equations. But I'm in trouble when using Excel link with Mathematica. I really need ...
4
votes
2answers
205 views

General solution for a linear ODE set with complicated coefficient

This is the original problem that motivated me to ask this question. I encountered it when trying to reproduce the deduction in this paper. (I'll paste the relevant part below to make this question ...
6
votes
1answer
121 views

Issue in Det[…] when computing determinants of polynomials?

When I form a matrix of at least size $12 \times 12$ of second order polynomials in $w$ and I calculate the determinant of that, I get something that is a rational expression in $w$. Since the ...
3
votes
2answers
122 views

Computing powers of the operator using symbolic computation

Suppose $t\in\mathbb{R_+}$ - some parameter, $V: \mathbb{R}\to\mathbb{R}$ - some function. I have an operator $S:f\mapsto S[f]$ that maps a function $f$ to a function $S[f]$: $$ S[f](x) = ...
1
vote
1answer
98 views

New data type, interval, and overloading operators (+,-,*,/) [duplicate]

How can I create a new data type, interval, with different behavior than the built-in one. I want to write [a, b] and perform operator overloading, as in C ++? (I ...
1
vote
1answer
47 views

Unexpected behavior in symbolic integration with GenerateConditions->False

Consider the following two symbolic integrations: ...
2
votes
0answers
32 views

Polynomial kernel expansion

I am trying to calculate the polynomial kernel expansion using Mathematica. I have tried the Expand and Simplify functions with ...
5
votes
2answers
122 views

Problem summing an infinite series

Calculating this sum on Mathematica 10.3 Sum[(-1)^(r - 1)/((a^2 + r^2)r), {r, 1, Infinity}] gives the answer ...
3
votes
2answers
82 views

Problem with Custom Sort/Split/Gather

Please help me Sort/Split/Gather/Group(by) a set of symbolic expressions! (extreme TL;DR at bottom) I have a set of symbols (which represent 2-vectors in a plane, ultimately) and I want to ...
2
votes
0answers
45 views

Mathematica for dynamics and controls [closed]

I am new to Mathematica and want it to use for dynamic and control systems. To begin with, I would want to be limited to symbolic computation for linear and nonlinear control systems - including ...
1
vote
2answers
89 views

Closed form solution equations involving finite sums

I am a beginner in Mathematica, so take this into account. I could not find anything similar in the internet so far. I am trying to find a closed form solution for ...
40
votes
2answers
744 views

Why does Mathematica report that $\int_1^\infty\frac{\sin(\sqrt{x})}{\sqrt{x}}dx$ = $2\cos(1)$?

Bug introduced in 7.0 or earlier and persisting through 10.4 or later Mathematica 10 gives the following very odd result, ...
0
votes
2answers
87 views

Expression of an integral

I am doing the following integral in Mathematica with $a>0$: $$\iint e^{-\frac{(x_{1}+x_{2}-2b)^2}{4a}}dx_{1}dx_{2}$$ My code is ...
3
votes
1answer
75 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
56 views

Identity Matrix in symbolic Tensor Product [closed]

I am trying to simplify symbolic tensor products. E.g. ...
-3
votes
1answer
107 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
2answers
87 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 ...
4
votes
0answers
64 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 ...
3
votes
1answer
118 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: ...
0
votes
1answer
82 views

Calculate Dot product of a TensorProduct

Using this answer ...
0
votes
0answers
35 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 ...
2
votes
2answers
72 views

Permuting symbols

Suppose I have a list like {a, b, a, c}. How can I apply a "symbolic permutation" of the symbols a, ...
8
votes
1answer
129 views

What should I learn from DSolve working better with a named constant than a number in this case?

I have an equation $$\bigl(r''(\phi)r(\phi) - r'(\phi)^2\bigr)\bigl(b + r(\phi)\bigr) = r(\phi)\bigl(r'(\phi)^2 + r(\phi)^2\bigr)$$ Here $b$ and $r$ are lengths, and $\phi$ is an angle (in radians, so ...
3
votes
2answers
53 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, ...
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 ...
33
votes
3answers
604 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 10.4 or later When I try to evaluate the following: $$\sum_{k=1}^{\infty }\Bigg\lfloor\frac{5}{5^k}\Bigg\rfloor$$ using ...
13
votes
5answers
252 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}. ...
3
votes
2answers
101 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 ...
5
votes
1answer
188 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 $$ ...