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

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0
votes
2answers
65 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 ...
1
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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
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 ...
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
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: ...
0
votes
1answer
70 views

Calculate Dot product of a TensorProduct

Using this answer ...
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 ...
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, ...
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, ...
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 ...
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 ...
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}. ...
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 ...
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 $$ ...
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 ...
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 ...
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
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, ...
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 ...
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 ...
2
votes
0answers
59 views

Subscript vs. Brackets [duplicate]

I'm used to using Ctr+_ to create indexes for variables (which evaluates to something like Subscript[a,i,j]), but on this site I ...
18
votes
2answers
283 views

Derivative of a pure function with SlotSequence

I can live with this but I can't figure out why the following is 0: Derivative[1][f[##] &][x] 0 From documentation ...
1
vote
1answer
94 views

Find function tracing the maximum of a 2D function

I'd like to solve the following problem: Given MI[o_, n_] := Log2[1 + 4 o (Sqrt@n + Sqrt[1 + n])^2] Find a function f[n_] ...
9
votes
1answer
160 views

How can I make FourierCoefficient et al. handle the zero-order term correctly?

Say that I would like to use Mathematica to step through one of the most famous solutions to the Basel Problem, using Parseval's Identity, $$ \sum_{n = -\infty}^\infty \left|c_n\right|^2 = ...
0
votes
0answers
35 views

Manipulating a symbol via its name [duplicate]

I'm trying to change the entries of a list. The problem here is that I only know the symbolname of the list for example name="x" , where x is defined as ...
1
vote
0answers
91 views
4
votes
1answer
93 views

Is it possible to find the vectors that span the nullspace of a large, symbolic matrix

My problem is composed of two parts, a large sparse matrix $L$ ($m$x$n$ where $m=10^3$, and $n=10^5$, with $10^7$ non-zero complex numbers), and a dense, symbolic matrix $F$ ($m$x$m$ where $m=10^3$), ...
3
votes
0answers
90 views

Is it possible to simplify an expression in vector form, which involves crossproduct and dot product?

I often need to simplify expressions involving cross product and dot product, for example: f = Dot[Cross[Cross[p1 - p, e1], Cross[p2 - p, e2]], Cross[p3 - p, e3]] ...
1
vote
1answer
86 views

Help with singular integral

I'm new in Mathematica. I need solve a singular integral like $$\int_a^b \frac{A_0 + A_1 s + A_2 s^2 + A_3 s^3}{(B_0 + B_2 s^2 + B_4 s^4)(t-s)}ds$$ where $A's$ and $B's$ are reals and ...
2
votes
1answer
88 views

Boundary condition not fully taken into account in DEigensystem?

Context Mathematica 10.3 now has the very nice DEigensystem function. ...
6
votes
1answer
105 views

Relevant help page for: Sum`?

When I type Sum into Mathematica, it also offers Sum` in the autocomplete dropdown, but when I click the little menu button next ...
10
votes
1answer
144 views

How to predict the degree of the first series coefficient?

Given an expression f that is a function of x and a number x0, what is the least integer ...
3
votes
1answer
60 views

Need help understandig the output of `DSolve`

I give Mathematica (10) the following command: DSolve[I D[P[x], {x, 2}] f[x] - (P'[x])^2 f[x] + 2 I P'[x] f'[x] == 0, P, x] And I have the following output: ...
0
votes
2answers
117 views

Why does Integrate[] return an expression with 'True' in it?

I am running Mathematica 10 on Windows 10. I'm trying to analytically evaluate a definite, principal value integral: ...
2
votes
1answer
101 views
2
votes
1answer
104 views

Is there a good way to check, whether a small value produced numerically is a symbolic zero?

I have a complicated 4x4 matrix and need to know the eigenvalues. I expect a zero eigenvalue for physical reasons. Giving numerical values first gives me an eigenvalue of $\mathcal O(10^{-15})$. Now ...
13
votes
3answers
251 views

Symbolic sum of Stirling numbers gives wrong answer

Bug introduced in 9.0.1 or earlier and persisting through 10.3.0.0 or later This issue originated from my attempt to answer a question on MathOverflow: ...
1
vote
0answers
73 views

General suggestions to accelerate Simplify and FullSimplify

To my understanding, the function Simplify[] and FullSimplify[] work by applying a series of built-in transformation rules to ...
7
votes
0answers
99 views

Examples of using Mathematica to solve matrix equations symbolically

Suppose we want to solve a linear system like $$\left\lbrack\begin{array}{cc}M& S\\ -S^\mathrm{T}&0 \end{array} \right\rbrack \left\lbrack \begin{array}{c} x\\y\end{array}\right\rbrack = ...
2
votes
1answer
89 views

How does this code work to substract a set A from a set B?

In an answer to a question (as given here: code), the proposed function was to to subtract a set B from a Set A: ...
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 ...
1
vote
1answer
35 views

ReplaceAll - Position of list arguments not displayed properly [closed]

This code A[1, 2, 4, 5] /. A[a___] -> Position[{a}, 4] return {} Why this code not return 3 (a position of number 4) ? I ...
3
votes
1answer
48 views

How to get Mathematica to make further simplifications to conditional expressions than it has already made?

I have the following Mathematica result under the assumption that {ax, bx, px, ay, by, py} \[Element] Reals, and after refinement by ...
1
vote
1answer
90 views

Symbolic Integration gives wrong answer [closed]

I have tried to integrate the following expression in Mathematica 10.1 ...
4
votes
1answer
93 views

Define an operator with the distributive property

I would like to define the ⊕ operator with distributive, associative, and commutative properties so that Mathematica can symbolically simplify expressions I use it in. For example: ...
1
vote
0answers
56 views

Legendre expansion of functions [closed]

I am given the expansion for the Legendre function of the first kind. It is just $$f(x)=\sum_{n=0}^{\infty}A_{n}P_{n}(x).$$ I have found the expression for the coefficient $A_{n}$. However I would ...