Questions tagged [symbolic]
For questions about symbolic computation, as opposed to numerical computations.
0
votes
0answers
29 views
How to pass lists as arguments in NMinimize or FindMinimum?
The following code runs in Mathematica 12. But, I have two problems that I would like to solve: (1) How to pass a list as an argument to the function g in such a way that it can be used seamlessly ...
0
votes
1answer
45 views
Multiple Assumptions for Symbolic Matrices
new to the forum and here's the question I'm pondering on:
I'm trying to use FindInstance in Mathematica to solve a symbolic matrix equation with quite a few assumptions. For example, quite ...
2
votes
0answers
48 views
4
votes
3answers
237 views
Alias for root of a polynomial
I need to work with a variable $u$ such that $u^2 + u + 1 = 0$. I don't want to find a root of the polynomial $u^2 + u + 1$. Rather, I have to work with $u$ symbolically so that a (polynomial) ...
4
votes
0answers
76 views
Can I use Mathematica ML capability to translate an image of a formula?
If I am given a pdf image of a mathematical symbolic formula can I translate it into Mathematica syntax using ML?
I tried using Classify, but I can only translate parts of the equation and I don't ...
19
votes
2answers
2k views
Wrong answer from DSolve when solving a differential equation
Bug introduced in 12.0.0
I was trying to solve the following differential equation: $$\frac{dy}{dx}=x^2+y^2-1 \quad \text{and} \quad y(0)=1$$
and I used the code below:
...
3
votes
0answers
38 views
Can I extract symbolic expression of neural network loss function?
Once we create a neural network with NetChain in Mathematica, can we extract the loss function in the symbolic form for Mathematica to play with symbolic manipulations using Mathematica's built-in ...
1
vote
1answer
28 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
votes
1answer
79 views
Symbolic Multivariate Distribution
If I try to input a symbolic multivariate distribution, I do not get a useful result.
...
5
votes
2answers
146 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
votes
0answers
29 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
votes
0answers
108 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
votes
0answers
118 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
vote
1answer
81 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
vote
1answer
21 views
Trying to apply Jensen's inequality to a complicated symbolic expression
I have a somewhat complicated inequality expression like this:
...
0
votes
2answers
41 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
vote
0answers
39 views
Finding symbolic solution to constrained optimization question
The code below is my attempt to solve a constrained optimization problem:
...
5
votes
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
vote
1answer
46 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
vote
1answer
103 views
2
votes
0answers
65 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
votes
0answers
54 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
votes
2answers
84 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
vote
1answer
117 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
vote
1answer
43 views
Rearranging similar terms in an equation
In a piece of code I am writing, I run into an equation of the form
...
6
votes
4answers
514 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
votes
2answers
62 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
votes
1answer
107 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
votes
1answer
107 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
votes
0answers
41 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
votes
1answer
69 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
votes
0answers
26 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
votes
0answers
27 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
votes
1answer
40 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
vote
2answers
62 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
vote
3answers
81 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
votes
1answer
41 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
votes
3answers
70 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
votes
2answers
72 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
vote
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
155 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
votes
2answers
335 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
votes
1answer
77 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
votes
1answer
68 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
vote
1answer
79 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
votes
1answer
64 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
vote
1answer
79 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
votes
4answers
351 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
votes
1answer
91 views
Collecting w.r.t. long expression
Sorry for a probably naive question.
I have the following expression
...
5
votes
1answer
171 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
<...
