Questions tagged [symbolic]

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

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3 answers
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RowReduce for symbolic matrices

I'd like to invoke RowReduce on some matrices with a time parameter. For example consider A = {{1, 0}, {0, t}} If ...
user8774's user avatar
9 votes
2 answers
230 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 = \frac{1}{2\...
Pillsy's user avatar
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9 votes
1 answer
1k 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 ...
Elaeum's user avatar
  • 111
9 votes
2 answers
995 views

How to symbolically differentiate an infinite series without evaluating the series itself

I'm dealing with finite sums of infinite series. Each of the infinite series possesses a different starting index, i.e. each of the series begins at n = 0, n = 1, or n = 2. As a result, it's important ...
Rob's user avatar
  • 91
9 votes
1 answer
293 views

Nice use case for symbolic tensors?

I come from before the times of symbolic tensors in Mathematica, and am used to working with concrete tensors and custom commands to contract them using Transpose, Dot, etc. I recently realized that ...
Stijn's user avatar
  • 320
9 votes
1 answer
533 views

Verifying and deriving basic (block) matrix identities

How can I use the new symbolic matrix/tensor capabilities to verify matrix identities, such as (1) or (2) Even better, how can I ask Mathematica to derive expressions for X, Y, Z, and U like ...
Eric's user avatar
  • 333
9 votes
1 answer
347 views

Comparing exact expressions for equality -- is it really OK if I get wrong answer?

Bug introduced in 7.0 or earlier and fixed in 10.2.0 I found an unexpected behavior (that I think of as a bug) in evaluation of the equality operator applied to mathematical functions with exact ...
Vladimir Reshetnikov's user avatar
9 votes
2 answers
1k views

Bug in Integrate for Mathematica

Bug introduced in 8.0.0 and fixed in 9.0.0 Consider the following: ...
Per Alexandersson's user avatar
9 votes
1 answer
142 views

DSolve fails with four variables

How is that DSolve has no trouble solving this: DSolve[{ D[G[x1,x2,x3],x1]==0, D[G[x1,x2,x3],x2]==0, D[G[x1,x2,x3],x3]==0 },G[x1,x2,x3],{x1,x2,x3}] but it fails ...
wxtou's user avatar
  • 91
9 votes
1 answer
2k 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 ...
Y.X's user avatar
  • 321
9 votes
0 answers
184 views

Symbolically evaluating gradients/Hessians

I'm taking a machine learning course, which involves taking a lot of analytical gradients and Hessians. It would be ideal if I could perform these calculations in Mathematica. However, I am only aware ...
user48151's user avatar
9 votes
0 answers
883 views

Symbolic Weak Form

Usually I write the weak form by hand for my FEM code, but it's a little annoying and mechanic sometimes. So, I wonder, is there any way to generate the symbolic weak form in Mathematica? For ...
senseiwa's user avatar
  • 515
9 votes
0 answers
154 views

When and why are Assuming and Assumptions not equivalent? [duplicate]

In this question there's an example of an integral where using Assuming and Assumptions give different results: ...
Szabolcs's user avatar
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8 votes
8 answers
1k views

Given a symbolic expression how to find if starts with a minus or not?

I am using a Mathematica function which returns some error term in symbolic form. I needed a way to determine if this term starts with a minus sign or not. There will be only one term. This is to ...
Nasser's user avatar
  • 143k
8 votes
3 answers
1k views

Exact Differentials

I just started using Mathematica so my apologies if this is a very basic question. I tried to find related questions on this forum but couldn't, so here goes. I have an equation, $\quad \quad dp =\...
xandrella's user avatar
8 votes
6 answers
243 views

Adding elements to some sublists of unequal length

Complicated title for a simple problem: I have list a = {{1, 3, 5, 2}, {2, 6, 2}, {3, 5, 6, 1, 2}, {4, 2}} In which the first element of each sublist is ...
Mockup Dungeon's user avatar
8 votes
2 answers
538 views

Can I get rid of the noise in my differential equation solution?

I am solving a differential equation: ...
blogoliubov's user avatar
8 votes
3 answers
587 views

Series expansion wrong

I had to work with some series expansions lately, and at some point I realised that something was becoming inconsistent at some point. It seems that applying Factor ...
Stan's user avatar
  • 951
8 votes
2 answers
375 views

Calculating sum of BesselJ[n, x]

My friend has a sum in his research paper that looks like this $$ \sum_{n=-\infty}^{\infty}\frac{J_n^2(x)}{n-\kappa}. $$ He was able to calculate this sum analytically, by substituting the ...
hayk's user avatar
  • 215
8 votes
2 answers
3k views

Piecewise differential equation

Say I have a very trivial function $$ V\left(r\right)=\begin{cases} -V_{0} & 0\leq r\leq R\\ 0 & r>R \end{cases} $$ with $V_{0}>0$ and $R>0$. I would like to let Mathematica solve ...
anthony2005's user avatar
8 votes
2 answers
301 views

How to represent $f(x) = (y-x)^k \log(y-x)$ as a summation of the form $f(x) = \sum\limits_{j=0}^\infty \cdots$?

I am having a lot of trouble working with summations in Mathematica, and this is unfortunate as it is my main use case for the application My latest summation issue is the following. I am trying to ...
ManUtdBloke's user avatar
8 votes
3 answers
712 views

Is this solution to nonlinear first order ODE correct?

Mathematica 11.3. I am not sure if this solution given by Mathematica is correct. But I'd like to ask the experts. ...
Nasser's user avatar
  • 143k
8 votes
2 answers
241 views

Issue with Upvalues

I want to introduce two variables (I call them EXt and EXtC, where "C" stands for complex conjugate) which would mimic the behavior of a phase of a complex number. For that, I use the following tags: ...
user43283's user avatar
  • 245
8 votes
2 answers
571 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 ...
Vladimir Reshetnikov's user avatar
8 votes
1 answer
481 views

Implement abstract algebraic structure

I would like to implement algebraic structures in Mathematica such as groups, algebras, Lie-algebras, Hopf-algebras, ... In particular, after initialising such a structure, I would like to have ...
Gert's user avatar
  • 1,510
8 votes
1 answer
279 views

How to assign up-values for `Derivative`?

I have defined several custom analytic functions. Here is the simplest example: ln[x_, a_?NumericQ] := Piecewise[{{Log[x], Re[a] > 0}, {-Log[1/x], True}}] ...
QuantumDot's user avatar
  • 19.6k
8 votes
2 answers
274 views

Representing a value in an output as a self defined variable

I'm trying to find a way to have Mathematica always represent a numerical value as a self defined variable that I define using lhs=rhs. For example, if I execute <...
David K.'s user avatar
  • 213
8 votes
1 answer
11k views

How to Make a change of variables

I have the following expresion $$\hat{M}^2=-\left[\frac{1}{\sin\beta}\frac{\partial}{\partial\beta}\sin\beta\frac{\partial}{\partial\beta}+\frac{1}{sin^2\beta}\left(\frac{\partial^2}{\partial\alpha^2}...
shadraws's user avatar
  • 139
8 votes
2 answers
252 views

Finding sub-expressions that simplify larger formula

If I use FullSimplify on a large formula it will consequently return a much smaller expression. However, suppose I notice the simplified expression can benefit from ...
user120911's user avatar
  • 2,655
8 votes
1 answer
209 views

Available Methods for DSolve?

I would like to know, apart from Method->Automatic what are available methods for DSolve. ...
drgrujic's user avatar
  • 299
8 votes
3 answers
628 views

Zero result from a positive integral

Bug introduced in 12.2 or earlier and persisting through 13.0.1. How to calculate the following symbolic integral in MMA? Every variable is real. Although the integrand is always positive, MMA (mine ...
xiaohuamao's user avatar
  • 4,708
8 votes
2 answers
360 views

Two-dimensional Laplacian coupled with another equation leading to a BVP with integral bc(s)

I have the two-dimensional Laplacian $(\nabla^2 T(x,y)=0)$ coupled with another equation. The Laplacian is defined over $x\in[0,L], y\in[0,l]$. On manipulating the second equation (which I have ...
Avrana's user avatar
  • 297
8 votes
2 answers
535 views

DEigensystem gives x-dependent eigenvalues

Bug introduced in Version 11 or earlier and persisting through 12.1. Reported to Wolfram Technical Support as CASE:4532301. I am considering the eigenvalue problem associated with the double-well ...
Fabio's user avatar
  • 1,357
8 votes
1 answer
279 views

Unexpected Behavior from Integrate with PrincipalValue -> True

Bug introduced in 9.0 or earlier and persisting through 12.1 or later. Reported to Wolfram, Inc. as CASE:4544446. The following code, taken from my answer to 97024, ...
bbgodfrey's user avatar
  • 61.4k
8 votes
3 answers
1k views

Symbolic integration in real domain only ( assumptions and ComplexExpand don't work)

Integrate[m^2/((x - m^2)^2 + y^2), m] mathematica gives me a complex-valued reuslt, but maple 17 gives me what I want. I tried using assumptions, but it doesn't ...
xinxin guo's user avatar
  • 1,273
8 votes
1 answer
808 views

Simplification of double symbolic sums containing a DiscreteDelta without explicit summation range

I am trying to get Mathematica to automatically do simplifications like the following: $$\sum\limits_{q}^{q\in qV}\sum\limits_{q'}^{q'\in q'V}{f(q)g(q')\delta(q-q')}=\sum_{q}^{q\in qV}{f(q)g(q)}.$$ ...
Paco's user avatar
  • 783
8 votes
1 answer
168 views

DSolve leaks internal error messages when attempting to solve two first order autonomous ODEs

Issue reported to Wolfram, Inc as a possible bug in Version 12.1.1; CASE:4630268. With Mathematica "12.1.1 for Microsoft Windows (64-bit) (June 19, 2020)", ...
bbgodfrey's user avatar
  • 61.4k
8 votes
1 answer
2k 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 ...
Vladimir Reshetnikov's user avatar
8 votes
1 answer
169 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 ...
David Z's user avatar
  • 4,911
8 votes
2 answers
465 views

How to implement a formal expectation operator over an unknown distribution?

I need to do some simplification of an expression involving averages over a stochastic variable (in order to verify a long analytical calculation). The easiest way to do that, I figured, were if I ...
Sooner's user avatar
  • 387
8 votes
1 answer
140 views

Order of boundary condition inside DSolve matters?

Bug introduced in 11.1.1 or earlier, fixed in 12.3.1 or earlier. Consider the following example: ...
xzczd's user avatar
  • 65.9k
8 votes
1 answer
409 views

Obtaining both Solutions of Linear, Second-Order ODE using DSolve

Bug introduced in 10.4 or earlier and persisting through 11.3 Reported as CASE:3849226. While attempting to provide a general answer for question 138321, I obtained a result, ...
bbgodfrey's user avatar
  • 61.4k
8 votes
0 answers
164 views

Is there a way to submit new closed form solutions to Wolfram? [closed]

I seem to keep coming across formulae that are not evaluated by Mathematica. For instance, today I was checking $$\sum_{k=1}^\infty\frac{(-1)^{k-1}}{k}\sum_{n=0}^\infty \frac{1}{k2^n+1}$$ (from this ...
Grant B.'s user avatar
  • 181
8 votes
0 answers
276 views

Spurious DSolve Solution

Bug introduced in 8.0.4 or earlier, persisting through 13.2. DSolve quickly returns solutions to the following PDE (which is the homogeneous portion of the PDE in ...
bbgodfrey's user avatar
  • 61.4k
7 votes
4 answers
601 views

What is wrong with my approach to solving a heat transfer PDE?

I wanna solve the following heat transfer PDE using Mathematica. $\qquad u_{xx}=u_{t}$ with following conditions: $\qquad \begin{cases}u(x,0)=sin(x) &0<x<\pi &,t>0\\u_{x}(0,t)=1\\...
Moreza7's user avatar
  • 83
7 votes
3 answers
513 views

Iterated differential operator

I would like to implement the following differential operator in Mathematica, $$ \prod_{j=1}^n \left({\mathrm d \over \mathrm d x}-j\right) $$ On a case by case basis, I can just expand it out and ...
B. Erenu's user avatar
7 votes
2 answers
3k views

Why Can't `DSolve` Find a Solution for this ODE?

I wanted to find a basis for the set of solutions of the following ODE. $$y^{''}+\frac{1}{x^2+1}y^{'}(x)+\left[-1-\frac{1}{x^2+1}\right]y(x)=0$$ But when I try to use ...
Hosein Rahnama's user avatar
7 votes
3 answers
2k views

How to implement Einstein summation convention with differential operators

Statement of this problem: In the textbook, the following differential equilibrium equations can be expressed by tensors: Using Einstein's summation convention, the formula in the figure above can be ...
A little mouse on the pampas's user avatar
7 votes
2 answers
357 views

How to generate a horizontal histogram with words?

I have a dataset of the type: ...
SAC's user avatar
  • 1,335
7 votes
3 answers
486 views

Symbolic manipulation of expression with undefined function

I have an expression which is a sum of undefined function v[n1,n2,n3,n4] with 4 arguments (n_i are integers): ...
Mario Krenn's user avatar
  • 2,172

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