Questions tagged [symbolic]

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

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1answer
29 views

Verify that a PDE is satisfied by a matrix consisting of functions satisfying a different PDE

My problem is as follows: I have two matrices $P$ and $Q$ which are made up of algebraic expressions of a function $q(x,t)$ which solves a somewhat complicated pde, and its derivatives, for example, ...
2
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1answer
84 views

Symbolic Multivariate Distribution

If I try to input a symbolic multivariate distribution, I do not get a useful result. ...
5
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2answers
172 views

Solving a heat equation problem

I'm brand new to Mathematica. I am trying to solve a heat equation problem, but I keep getting back the input on the output line. The problem: Consider the equation $\qquad u_t = u_{xx} - 9 ...
2
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0answers
35 views

How to Simplify/Factorise symbolic non-commutative expressions?

It always strikes me as odd, that Mathematica seems to have a hard time with non-communative multiplications. I can use the horrible TensorExpand (or more performant Distribute) to get ...
3
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0answers
112 views

Evaluate $\int_0^1 \frac{\log \left( 1+x^{2+\sqrt{3}}\right)}{1+x}\mathrm dx$

Saw this post and noted that it was posted back in 2013. Just tried V11.3 and got no analytic solution. Just wondering if there is a way for Mathematica to give the desired result? Machine VS Human ...
2
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0answers
119 views

Substitution of expressions using Groebner basis

I know this topic came up numerous times (most of the results are detailed in the comments of this link Is there a way to to substitute for symbols, simplify, and back-substitute?). However, I have ...
1
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1answer
96 views

Definite Integration by parts

how do I code Integrate[u[x] D[v[x], x], {x, a, b}] to return the following straightforward undergraduate result? ...
1
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1answer
25 views

Trying to apply Jensen's inequality to a complicated symbolic expression

I have a somewhat complicated inequality expression like this: ...
0
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2answers
44 views

How to manipulate sequences of inequalities?

I am trying to write some symbolic inequality proofs in Mathematica. What would be a clean way to make the inference that a >= b and ...
1
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0answers
42 views

Finding symbolic solution to constrained optimization question

The code below is my attempt to solve a constrained optimization problem: ...
5
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1answer
1k views

Vector calculus integration identity problem

This is a follow up from another post. I was using the integration symbols available in the Basic Math Assistant palette. I am new to vector calculus operations. There is a known identity found in ...
1
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1answer
52 views

DSolve returns unevaluated

I am trying to find a solution to this system of differential equations but the program gives the same output without any messages. I would like help. Please find the Mathematica code posted here: <...
1
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1answer
105 views

Mathematica doesn't extract Re and Im parts properly

I have a code: ...
2
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0answers
81 views

Asymptotes of parabolic cylinder differential equations with boundaries at infinity

For context, I'm studying the paper Coulomb blockade in superconducting quantum point contacts by Averin from 1998. Specifically, I am trying to find how he obtains equation 11 from equation 10, which ...
3
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0answers
55 views

Problem solving first order ODE's with DSolve

The issue I am facing is the following. I am trying to solve a system of two coupled first order ODE's with DSolve: ...
3
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2answers
86 views

Keep element of formula as it is

I have ClearAll["Global`*"]; de = f''[y] - (n^2 \[Pi]^2)/(4 a^2) f[y]; DSolve[de == -q/S (4/(n \[Pi] b))(-1)^((n - 1)/2), f[y], y] and I would like the $(-1)^{(n ...
1
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1answer
142 views

Symbolic non-commutative algebra

Consider 3 non-commutative elements $A,B,C$ and we have the relation $CB=\alpha BC$. I want to compute things like : $(A\otimes BC ) ( B \otimes B) = AB \otimes \alpha B^2C$ Is there any package ...
1
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1answer
46 views

Rearranging similar terms in an equation

In a piece of code I am writing, I run into an equation of the form ...
6
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4answers
517 views

Sort with assumptions

I have a list which looks like this list = {0, Subscript[x,7], -Subscript[x,3]-Subscript[x,9], -Subscript[x,9]}; and all the $x_i$'s are positive semidefinite (i....
4
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2answers
71 views

Identifying total derivatives

I would like to identify which terms in my expression are a total derivative and which ones are not. For expressions in which all terms are a total derivative, one can simply use integrate to find ...
2
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1answer
130 views

System of coupled differential equations

I am trying to solve the following system of equations, but I get as the output the command itself. ...
0
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1answer
208 views

Part::pkspec1: The expression j cannot be used as a part specification

I want to do some stuff with symbolic arrays like this a[[j]] + a[[j + 1]] == a[[j - 1]] + a[[j - 2]] But upon declaring such an expression I get ...
3
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0answers
43 views

On using ConditionalExpression inside Integrate vs. getting the result, then applying Assuming on result [closed]

I thought at first that sol = Integrate[ ConditionalExpression[ integrand, conditions],....] (1) Is equivalent to and should give the same answer as ...
0
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1answer
78 views

Kronecker Delta manipulation

Is there a way to force mma expressions that have symbolic terms like KroneckerDelta[i,j]*KroneckerDelta[j,k] to simplify to ...
0
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0answers
34 views

Evaluating Fourier coefficients when Exponential terms are present

I am trying an analytical solution for a 3D Laplace equaition, and just wanted to know if I could use the symbolic calculation capabilities of Mathematica to calculate the Fourier coefficients ...
0
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0answers
28 views

Linear dependency of vectors of functions

I would like to find a symbolic way to obtain a Q-function (Boolean output) for the following problem. I have the following inputs: ...
0
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1answer
48 views

Substitution inside an expression [duplicate]

I'm trying to get mathematica to replace an expression with a reduced form. I wanted to replace $(k/w)$ with $h$ in a particular expression, and I've tried something like: ...
1
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2answers
64 views

Verifying equality

I am trying to test equalities involving integrals. What are the possible causes for not being able to test the following: ...
1
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3answers
92 views

3D Plot the result of local Minimize with varying parameter values

I'm faced with the following minimization problem: Find $r\in[0,1]$ that minimizes $\frac{d^2+k^2 (1-2r)r}{2(1-r)r}$, which is bounded by 0 and 1. In addition, $k<d$ holds and each of $d$ and $k$ ...
0
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1answer
46 views

Changing variables to obtain derivatives of new variables [duplicate]

Let's say that I have some symbolic expression of a function $x(t)$, and would like to obtain its derivative $x'(t)$. However, I also have the following two identities, $\xi = \omega t$, and $\eta = ...
2
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3answers
72 views

Exponentials don't cancel numerically [closed]

I'm trying something essentially like N[Exp[-x]*(D[Exp[x*y^2], y] /. y -> 1)] After differentiation and y -> 1 there is ...
0
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2answers
73 views

Having Mathematica automatically plug in the values for a system of equations

I have a set of pairs, such as {{8 a, 2 + 2 a}, {8 b, 1 + 3 a}}. This set encodes the fact that I want to put 8a == 2+2a and <...
1
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0answers
35 views

Generic symbols vs Generic functions arguments [closed]

I've got a lot recursion relation that takes multiple hours at a time to run. I'm looking for some subtle reasons why it takes so long, and hoping to be able to reduce the time it takes for the more ...
5
votes
4answers
169 views

Simplify $\tan^{-1}(\cot(a))$ to $\frac{\pi }{2}-a$ assuming $0<a<\frac{\pi }{2}$

I know Mathematica is not omnipotent, but still can't help feeling surprised when I encountered this example, and I think it's worth starting a question for it. The example is, ...
5
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2answers
337 views

How to find the sum with Mathematica?

That hard problem was invented by V. P. Beshkarev (Russia) in 1971: Sum[Tan[(4*j - 3)*Pi/180], {j, 1, 45}] // FullSimplify The result should be 45, but the ...
2
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1answer
81 views

Generalizing to N variables

I have a function of the following type where $p(i)$ is a variable on which the agent can optimize and $p(-i)$ a vector of variables that he has to take as parameters. This is a demand function and ...
0
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1answer
77 views

Determinant of the symbolic matrix is giving very large expression

I have a symbolic matrix of size 16 by 16. I tried to get the determinant of this symbolic matrix, but it turned out to be a very large expression. How to make this expression concise so that it ...
1
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1answer
90 views

Complex Inner Product and Orthogonalization

Orthogonalize[{E^x, E^(w^1*x), E^(w^2*x), E^(w^3*x)}, Integrate[#1 *Conjugate[#2], {x, -Pi, Pi}] &] I am trying to orthogonalize the first 4 expression ...
0
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1answer
66 views

Taking derivative of general order

How can I directly evaluate the following derivative? $$ \frac{\partial ^n}{\partial x^n}\bigg[\sum_{k=1}^{m} (m-k)! (ax+b)^k\bigg] = \sum_{k=1}^{m} (m-k)! \bigg[\frac{k!}{(k-n)!}a^n (ax+b)^{...
1
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1answer
81 views

How to distribute rules?

For example i want to have following equation : Det[A B C]=Det[A] Det[B] Det[C] What is the simplest way to distribute automatically?
6
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4answers
368 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\\...
2
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1answer
102 views

Collecting w.r.t. long expression

Sorry for a probably naive question. I have the following expression ...
5
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1answer
174 views

Why this PDE causes internal 1/0 division?

Bug introduced in 11.3 and persisting through 12.0.0 In 11.2 DSolve return unevaluated. Assigned WRI case number 4210941 Using 11.3 on Windows 10, this input <...
0
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0answers
83 views

How to sum over the variable in partial derivative operator?

I need to use the partial derivative operator in Wolfram Mathematica within a summation, specifically to define the D'Alembertian operator of scalar fields. I am having trouble summing over the D ...
0
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1answer
49 views

Characteristic Function of 2D Gaussian with Boole

Context Given the Probability Distribution ...
6
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1answer
188 views

Symbolic Neural Networks in Mathematica

Mathematica is very well known about its symbolic capabilities/functionality. Heavy users usually say that “everything is a symbolic expression”. Does this principle apply to neural networks? If not, ...
0
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1answer
74 views

FindRoot and symbolic evaluation

Following the Symbolic evaluation documentation, I am trying to solve the equation: $y'(x) = a*y(x), \quad y(0)=1$ where I later fix a via FindRoot, requiring that $y(2) = 2$: ...
1
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3answers
84 views

Evaluating complicated limits correctly

Let's say I have defined some function: a[x_] = x^2 Log[x^2]. If I try to evaluate a[0] Mathematica will complain that it is ...
0
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0answers
70 views

symbolic solution pde

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1
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1answer
79 views

solving coupled pde with conditions

I have two coupled PDE ...