Questions tagged [symbolic]
For questions about symbolic computation, as opposed to numerical computations.
6
votes
4answers
118 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
39 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 ...
0
votes
1answer
44 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
36 views
On using ConditionalExpression inside Integrate vs. getting the result, then applying Assuming on result
I thought at first that
sol = Integrate[ ConditionalExpression[ integrand, conditions],....] (1)
Is equivalent to and should give the same answer as
...
-1
votes
0answers
62 views
Analytic solution for two coupled Partial Differential Equations using DSolve [closed]
I am looking for an analytic solution to the following two coupled equations for $v(x,t)$ and $u(x,t)$:
$$\frac{\partial v}{\partial x}=-m \frac{\partial u}{\partial t}$$
$$\frac{\partial u}{\partial ...
0
votes
1answer
62 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
24 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
39 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
59 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
70 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
37 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
69 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
70 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
33 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
146 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
328 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
72 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
61 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
74 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
61 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
77 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
338 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
76 views
Collecting w.r.t. long expression
Sorry for a probably naive question.
I have the following expression
...
4
votes
1answer
142 views
why this PDE causes internal 1/0 division?
Assigned WRI Case number 4210941
Using 11.3 on widnows 10, this input
...
0
votes
0answers
63 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
votes
1answer
45 views
5
votes
1answer
105 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 applies to neural networks?
If ...
0
votes
1answer
54 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
vote
3answers
83 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
votes
0answers
64 views
1
vote
1answer
68 views
1
vote
0answers
85 views
Finding root of symbolic function
I'm trying to find a root of the following equation
$$\theta^\frac{t}{s}-\theta-\sqrt{1-p},$$
where $0<t\leq1\leq s$ and $0<p<1$.
I've tried FindRoot and Reduce, but somehow they don't ...
0
votes
0answers
36 views
Define some variables to be real within the whole notebook
I want to define some variables to be real within the whole notbook? How can I do this? In the following you can find my code. I think the last step will be computed in seconds when I tell mathematica ...
1
vote
1answer
136 views
On double summation with Mathematica
Today I wanted to evaluate this sum using Mathematica:
$$f(a,b):=\sum_{(k,l)\in\mathbb{Z}^2,\ l\ne0}\frac{1}{(2 i k a \pi +
l b) (2 i (k - l) a \pi + l b)}$$
...
2
votes
2answers
68 views
Plotting solution to Differential Equation with separable variables [closed]
Got this differential equation $$y'=\frac{-x^2(y+1)}{y^2(x-1)}$$
If I try directly to DSolve it
...
1
vote
1answer
43 views
Extracting parts of symbolic expressions
I've searched around and found things that could help me only in cases that are simpler than the one I had in mind. I would like to extract polynomials from expressions that schematically look like
$$...
12
votes
1answer
308 views
Symbolic integration of potential over a disc : branch cut problem?
Context
I am trying to explore the geometry of a crystal made of irregular bubbles.
See animation here.
very vaguely in the spirit of this post (it is in fact motivated by cosmology and galaxy ...
1
vote
1answer
87 views
ODE which can be solved without parametrisation [closed]
I want to solve the following differential equation, which can be solved without parametrisation
$\qquad y^2y'^2-2xyy'=x^2-2y^2$
I need the solution for my student research project.
When I try to ...
4
votes
2answers
108 views
RSolve not reducing for a certain recurrence relation
I'm trying to use RSolve as follows to solve a recurrence relation:
...
1
vote
1answer
29 views
Why does the Symbol stringification operation appear to work with only single argument strings? [closed]
I'm trying to label my symbolic object's using Symbol
Works as expected
Symbol["M" <> ToString[5]]
Output
...
7
votes
2answers
446 views
Symbolic Quaternion Multiplication
It is possible to do the symbolic multiplication $qq^*$ of a quaternion $q=a+bi+cj+dk$ by its conjugate $q^*=a-bi-cj-dk$ using Mathematica? It seems that Quaternion package only works with numeric ...
3
votes
1answer
80 views
Symbolic decomposition of a tensor given an assumption
I am relatively new to Mathematica. Suppose I have a matrix
M = {{a^2, a b, 0}, {a b, b^2, 0}, {0, 0, 0}}
How can I get Mathematica to decompose this into an ...
1
vote
1answer
62 views
Calculate angle between skew vectors
I want to use Mathematica to calculate the angle between two vectors (say a and b) that don't lie in the same plane. The vectors ...
4
votes
1answer
218 views
estimation of values using NMaximize over symbolic array entries
I'm trying to generate instances of a dataset that satisfy specific conditions, based on the following equation:
Each of four non-zero terms (term 1, A; term 3, B; term 4, C; term 5, D) is a scalar. ...
1
vote
1answer
101 views
Save and use results of LinearSolve for symbolic large system (28 equations)
I need to solve system of 28 linear equations, for 28 variables, symbolicly.
The coefficient matrix is sparse, and is composed from 8 parameters (symbols).
After that I need to use 6 of the variables ...
1
vote
1answer
63 views
How to change the integral variable and integral upper/lower limit?
I am dealing with the symbolic operation of taking the antiderivative, e.g., Integrate[f, x] (where $f$ represents a complicated function which cannot return ...
6
votes
2answers
280 views
How do I verify a vector identity using Mathematica?
I am trying to verify well known Frenet–Serret formulas in general setting using Mathematica.
I need to consider a general space curve $r(s)=(x(s),y(s),z(s))$ in $\mathbb{R}^3$ and define its unit ...
2
votes
2answers
125 views
Newbie PDE Question
I downloaded Mathematica trial in order to try to solve a PDE that Matlab symbolic couldn't handle. I don't know all the bells and whistles but going along with online documentation.
I am trying to ...
0
votes
1answer
75 views
Mathematica can't solve system of equations but doesn't show error
I try to solve a system of equations:
...
