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

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2
votes
1answer
102 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
58 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
63 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
311 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
98 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
165 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
36 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
112 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
115 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
91 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
105 views

Boundary condition not fully taken into account in DEigensystem?

Context Mathematica 10.3 now has the very nice DEigensystem function. ...
6
votes
1answer
107 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
146 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
61 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
125 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
110 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
257 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
88 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
125 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
171 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
52 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
91 views

Symbolic Integration gives wrong answer [closed]

I have tried to integrate the following expression in Mathematica 10.1 ...
5
votes
1answer
127 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 ...
1
vote
0answers
71 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 ...
0
votes
1answer
125 views

Integrating 2d exponential function symbolically with polynomials of 2nd order running for days

I'm trying to integrate this function by Mathematica ...
58
votes
5answers
2k views

Advice for Mathematica as Mathematician's Aid

I use Mathematica mainly as an aid in symbolic attacks on problems, usually intermediate or harder and often number theoretic. While Reduce, ...
3
votes
2answers
110 views

How to deduce the Ramanujan's summation of this series?

I have already asked a similar question about Ramanujan's summation in general but received no good answers. Now I am interested in this exact series: $$\sum _{n\ge1}^\Re (24 n + 12 n^2)$$
4
votes
0answers
105 views

Simplest identity that cannot be proved by FullSimplify [closed]

Apparently, FullSimplify is not able to prove all true identities, but usually it does pretty well when it comes to elementary functions. I'd like to know what are ...
6
votes
3answers
252 views

How to simplify symbolic expressions with KroneckerProduct

Having $X,Y$ being symbols for matrices, I was wondering if there is a way to simplify expressions like KroneckerProduct[X, X] + KroneckerProduct[-X, X] to ...
2
votes
2answers
189 views

Solve a symbolic underdetermined Linear System

Dear StackExchange Community, I'm trying to solve an indeterminate linear system of equations, with $n+1$ variables and $n$ equations; therefore, I need to express all $n$ other variables a function ...
4
votes
0answers
58 views

How to take the second derivative of a complicated function using limits [closed]

I have a very complicated function of one variable consisting of exponential and error functions combined in various ways. Mathematica can't take the derivative of this function in the usual way ...
1
vote
1answer
131 views

How does one verify the derivative of $ f(x) = \sum^{K_2}_{k_2=1} c_{k_2} \exp\left(- \big(a^{(2)} - t^{(2)}_{k_2}\big)^2\right)$

I wanted to verify the derivative of the following equation: $$ f(x) = \sum^{K_2}_{k_2=1} c_{k_2} \exp\left(- \big(a^{(2)} - t^{(2)}_{k_2}\big)^2\right)$$ for that I wanted to write a symbolic ...
1
vote
0answers
55 views

How can I find the formal derivative of a polynomial w.r.t. to its coefficients [duplicate]

I want to define a function $f(x)$ as in $\quad \quad f(x) = \sum^{n}_{i=0} c_i x^i$ as a symbolic expression. Then I'd like to do operations on it. For example, take derivatives of it with respect ...
0
votes
1answer
56 views

Why can not the vector be transposed in integrating over a region? [duplicate]

Clear[x, A]; A = {{2, -1, 0}, {-1, 2, -1}, {0, -1, 1}}; Integrate[Exp[-x.A.{x}\[Transpose]/2], x \[Element] FullRegion[3]] This code raises an error ...
0
votes
1answer
79 views

Multivariate Equation solving [closed]

I have the following equation: r^(1 + Rho) - r^Rho (-1 + Mu) - z Rho == 0 I searched the list but I couldn't come up with a solution. Any help is appreciated. ...
2
votes
1answer
64 views

Dropping rational coefficients

I have a list of expressions (they all are exact numeric quantities, not containing any variables), some of them have integer or rationals coefficients, or complex coefficients with rational or ...
1
vote
1answer
60 views

How to apply Simplify only to elements of list that cause specific Warning

I have a set of replacement rules I use to analytically compute nested integrals of very long symbolic expressions since Integrate literally takes forever. To do ...
2
votes
0answers
106 views

Parallel evaluation of symbolic matrix eigenvalues

I'm trying to find eigenvalues of symbolic hermitian 40x40 block matrix. It is made from 20 2x2 matrices like this: ArrayFlatten[Table[M[m,n],{m,1,20},{n,1,20}]] ...
1
vote
3answers
133 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: ...
3
votes
0answers
76 views

Analytical Fourier Transforms with convolution rule [closed]

The task is the following, how to extend Mathematica's FourierTransform command in order to be able to analytically deal with non-linear differential equations. To do so it should be able to deal with ...
14
votes
2answers
438 views

Symbolic area calculation for a parametric self-intersecting closed curve

The parametric equation of the curve is: $$\begin{cases} x &= -9 \sin (2 t)-5 \sin (3 t) \\[6pt] y & = 9 \cos (2 t)-5 \cos (3 t) \end{cases}\quad t\in[0,2\pi]$$ which can be easily ...
1
vote
1answer
158 views

How to speed up an optimization with very long symbolic expressions?

I have 8 very long symbolic expressions (each having around 200,000 summands) - Simplify will run forever, so that is unfortunately not an option. Each of those ...
2
votes
2answers
169 views

MaxValue of a periodic function

I want to find the maximum of a periodic function on the interval [-Pi,Pi]. What I tried is the following: ...
6
votes
1answer
192 views

Defining a function implicitly and calculating its derivatives

I'm interested in using Mathematica's symbolic manipulation to obtain, for a particular function $f$, derivatives of arbitrary order evaluated at zero. Normally I'd use the ...
2
votes
1answer
136 views

How to convert a rational parametric plane curve into implicit form?

This problem is generated from another Green's theorem related question of mine. And here is a forward of the same problem in math.stackexchange. The original equation of the plane curve is not in ...
15
votes
3answers
539 views

Solve a trig equation system

Background of the problem In the same plane, P is a fixed point, A,B,C are moving point, PA=a, PB=b, PC=c, find the maximize perimeter of △ABC. let ∠BPC=A, ∠CPA=B, ∠APB=2*Pi-A-B, then the ...