Questions tagged [symbolic]
For questions about symbolic computation, as opposed to numerical computations.
1,340
questions
3
votes
2answers
51 views
Compare the coefficient in same part of the equations
I want to use Mathematica to do certain calculations. Below is a minimal example, my goal is to solve the equations that result from comparing the coefficients of both polynomials
...
0
votes
0answers
36 views
Take a specific part of a matrix, excluding the external brackets [duplicate]
I have a little manipulation problem.
I have the following matrix:
...
1
vote
1answer
47 views
Symbol compute of Euler-Lagrange equation
If i have the Lagrange density function $$L(x,\dot{x}) = \frac{1}{2}x^2+ \frac{1}{2}\dot{x}^2,$$
The Euler-Lagrange equation is very simple by
$$ \frac{d}{dt}\frac{\partial L}{\partial \dot{x}} - \...
0
votes
0answers
31 views
How to simply this maximization problem with too many variables and parameters?
I'm someone who is trying to teach himself economics. My training in math is minimal. Forgive any inexact and/or irregular notations and terminologies below.
I'm trying to find out if the following ...
0
votes
0answers
43 views
Extracting powers of variables from an expression
I have some expression which I want to simplify by extracting powers of variables and precomputing them, while substituting the new variables in the expression:
...
0
votes
0answers
67 views
Can't create matrix function of symbolic functions and assign values to elements
So I have a problem regarding the symbolic matrix value assignment.
Say I create a matrix function as:
P[t_]:= {{P1[t]}, {P2[t]}, {P3[t]}};
Then I want to assign ...
5
votes
2answers
211 views
How to handle excluded values in a summation or product in Mathematica
I want help to writ that on Wolfram Mathematica :
How can I handle the $i \ne j$ part?
0
votes
0answers
46 views
Replace Array on symbolic expression
Following my previous question: Go back to a symbolic expression to evaluate derivative
I've changed my code to keep the symbolic expression.
My question now is if there is a way of replacing L1 and ...
0
votes
0answers
56 views
Inverse of symbolic hyperbolic function
I have a function
$$u = 1/4*\cosh(x)^2$$
Entered in Mathematica as
1/4*Cosh[x]^2
Inverted using
...
0
votes
0answers
41 views
Define multivariate even general function
I want to define a multivariate even function. This question shows how to do it for a single variable function Defining general odd function but I don't see how to generalize the syntax to multiple ...
1
vote
0answers
96 views
Incorrect result of Integrate
Let us consider in 12.3.1 on Windows 10
k = Integrate[a^(I*x)*Log[x]/x, {x, b, Infinity}, Assumptions -> a > 1 && b > 0]
...
-1
votes
1answer
102 views
How to solve that logarithmic equation? [closed]
I mean an equation
$$ \log _{2 \sqrt{\sqrt{3}+2}}\left(x^2-2 x-2\right)=\log _{\sqrt{3}+2}\left(x^2-2 x-3\right).$$
The result of
...
0
votes
0answers
33 views
Collecting coefficients of non-commutative products from an expression
I am trying to manipulate a Hamiltonian with non-commutative operators, $a_j,a_j^\dagger$. After some algebra using NCAlgebra package in Mathematica, I have an expression like, $$H = C_1 (b**a) + C_2 (...
0
votes
1answer
96 views
How to solve this infinite family of equations?
Is there any way to do a problem like this with MMa? I have an infinte set of coupled equations. j is a real integer index where $-\infty<j<\infty$. {a,b,c,d,f} are variables, and K's are ...
1
vote
1answer
102 views
Ordinary differential equation with variable (polynomial) coefficients -form of solution
If you have a differential equation with polynomial coefficients then quite remarkably Mathematica can find a solution. For example for the second order differential equation
$ y''(t)+b y'(t)+\left(\...
3
votes
2answers
99 views
Limit of $a^x$ when $x\rightarrow\infty$ does not output all conditional solutions depending on parameter $a$
I'm trying to compute the limit $\lim_{x\rightarrow \infty}a^x$ for $a>0$ in Mathematica and I would want it to give me the conditional solutions depending on the value of the paramter $a$. However,...
1
vote
2answers
45 views
System of rules transformingn a multivariate polynomial onto corresponding partial derivative operator
I take a complex multivariate polynomial, and I want to transform it into the corresponding differential operator. I.e., I am looking for the set of rules transforming variables to derivation, ...
4
votes
2answers
167 views
Get rid of a certain variable in a fraction's numerator
Consider expression $\frac{a - b}{a + b}$. When I apply $FullSimplify[\frac{a - b}{a + b}]$, I get $-1 + \frac{2a}{a+b}$, effectively getting rid of $b$ in the numerator. However, I want to get rid of ...
2
votes
1answer
89 views
Does every function know about other function? [closed]
The Mathematica function Area knows about Sphere. For example the following output.
...
2
votes
0answers
97 views
Solving a complicated, non-polynomial dispersion relation
I am quite new to Mathematica, so I apologise if the following question is very basic; I can't seem to find an appropriate answer anywhere!
I am trying to solve a quite complicated dispersion relation ...
3
votes
1answer
108 views
What is the scope of the bug where Piecewise breaks DSolve?
Bug introduced after 9.0.1, persisting through 12.3.1.
I have identified a bug in DSolve when differential equation includes a ...
5
votes
1answer
79 views
DSolve inconsistently able to evaluate expression
I am trying to use DSolve to evaluate a coupled system of ODEs as follows
DSolve[{Y0[X] + Y0''[X] == 0, Y1[X] + Y1''[X] == X Y0[X]}, {Y0[X], Y1[X]}, X]
However, ...
2
votes
1answer
41 views
1
vote
1answer
70 views
Symbolic Vector calculus
Can mathematica perform symbolic vector calculus? Say I want to find
$$\mathbf{v} = \mathbf{a} \exp(\mathbf{b}\cdot\mathbf{x})$$
$$\nabla \cdot \mathbf{v} = \mathbf{b}\cdot \mathbf{v}$$
If I try
...
0
votes
1answer
95 views
With Intel Xeon(R) E5-2667 v4 and 250GB RAM: still automatically quitting kernel when doing symbolic integrations
[![Here is the configuration for my calculation. Guess it can't be affected by this.][1]][1]
I was in trouble when solving the algebraic equations for q1 and q2.
\begin{equation}\label{eq:18}
\begin{...
0
votes
0answers
42 views
Symbolic 3x3 Jacobian matrix not being computed as expected
First question I have ever typed in a stackexchange forum so I hope you'll forgive me if i make rookie mistakes.
I'm try to compute the symbolic expression of a 3x3 Jacobian of a vector
...
-4
votes
1answer
136 views
How to write a really complicated formula into mathematica and do symbolic computation?
I want write the following formula $a$ into mathematica and do symbolic computation like $a^2$. $a$ is defined as follows:
\begin{multline*}
a=\sum_{t=0}^{T-1}f_1^2(t)+11\sum_{t=0}^{T-1}f_2^2(t)+\\
\...
0
votes
4answers
102 views
Integration challenge
For positive real $a \leq \pi$ and $b \leq \pi$
$\int_{-a/2}^{a/2} \frac{\sin{(b/2)}}{\sqrt{1+\cos^2 (b/2)\tan^2 (\phi )}} \; d \phi = 2 \arcsin \left[ \sin (a/2) \sin (b/2) \right] $
as can be ...
3
votes
1answer
213 views
RootReduce and Simplify for an algebraic expression
The American Invitational Mathematics Exam (AIME) 2006 asked contestants to reduce this expression:
$$\sqrt{104 \sqrt{6} + 468 \sqrt{10} + 144 \sqrt{15} + 2006}$$
The answer is $13 \sqrt{2} + 4 \sqrt{...
1
vote
0answers
38 views
Vectan.m in Mathematica12 - returns VPValue instead of VP (same with SP etc) [closed]
for years I was using Vectan.m to do analytical vector calculations. There seem to be a problem in Mathematica 12 (on Mac). All loads well, but then instead of VP[a,b] it returns VPValue[a, b]:
<&...
1
vote
1answer
92 views
Problem with Analytical Integration with Constant
Could you help me out on how to integrate this long equation with constant as it is indefinite integral so I assumed I could not use numerical integration (eg: Simpsons's 3/8 Rule or Trapezoidal Rule) ...
1
vote
1answer
63 views
GeneratedParameters in Integrate
I defined a function of two variables, let's say
u[x_, y_] := 4 x^4 + 6 x y - 24 x^2 y^2 + 4 y^4
I want to partial integrate (with respect to y) the partial derivative of u with respect to x obtaining ...
3
votes
1answer
77 views
Pattern matching problems involving FullForm and Plus and Times
I am trying to match an expression that will be a sum of more than one terms, with the last one being a product. For example, the objecta+b+x*y. I am using the ...
3
votes
1answer
42 views
Type formation rules for 1-position expressions
I made a summary of the rules for formation of types for simple 1-position expressions, as I understand them.
Here it is in textual form:
A symbol, say, α, is a discrete entity, represented by a ...
0
votes
0answers
25 views
Why does explicit Dirichlet Transform of Liouville Lambda not evaluate?
I have four expressions for the Dirichlet Transform of the Liouville-Lambda function, but one form does not evaluate, any ideas why and what could be done?
3
votes
2answers
72 views
How to symbolically evaluate expression within If[]?
I have a function, say f, that needs to take one of two symbolic forms depending on the value of its inputs. This function is part of a very large expression, and I'...
3
votes
0answers
67 views
2D Poisson equation with Piecewise RHS - symbolic solution?
I'm trying to solve the following 2D Poisson equation symbolically:
$$
-\nabla^2 u(x,y) =
\begin{cases}
1-\text{sech}\left(\frac{w}{2 d}\right) \cosh \left(\frac{x}{d}\right)
& -w/2 \leq ...
2
votes
1answer
56 views
Recursive computation of symbolic series
I don't have experience in Mathematica and I would like to use the ability it has to do symbolic computations to find the terms of a series of functions recursively. The terms I want to find are given ...
1
vote
0answers
56 views
Alternatives to NumericQ that allow symbols to be considered numeric
I am writing a program in which I am using NumericQ. I am trying to allow symbols to also be considered Numeric, so I have been using NumericQ[a]=True for all of ...
0
votes
1answer
48 views
Reduce coefficients from constraints in a set of equations
Total beginner here. I am chaining 4 quadratic equations $f_i(x)$ at 4 knots $k_i$ (where $0 < k_i < 1$ and $k_{i+1} > k_i$) on a wrapped unit interval (i.e. $0 \leq x \leq 1$):
$$ f_i(x) = ...
1
vote
2answers
112 views
Mathematica's evaluation of nested summations
As suggested there, here is a copy of the question I've posted on Math.Stackexchange.
Suppose we want to count the number of instructions executed by the following Python code:
...
4
votes
3answers
464 views
Useless result of Integrate
Considering a Fourier sine series, I calculate
int = Integrate[Log[1 + Sin[x]]*Sin[i*x], {x, 0, Pi}, Assumptions -> i ∈ PositiveIntegers]
...
1
vote
1answer
40 views
Changing expression using a new variable definition
If I have an expression that looks like the following:
$$ \frac{i \sqrt{\frac{\sigma _2}{\sigma _1}} \left(-\sigma _2 q_1(t){}^2+\sigma _1 q_2(t){}^2+\left(\omega _2-\omega _1\right) q_2(t) q_1(t)\...
0
votes
1answer
92 views
How to derive all KKT points of a parametric optimization problem
Suppose we have a symbolic optimization problem where all parameters and decision variables are nonnegative like the following problem. I would be thankful to know if there is any method to find all (...
0
votes
0answers
35 views
Getting the coefficients of an expression with Solve
I have a very lengthy expression (600+ terms) with derivatives of several functions, which I want to write in a compact way. I would like to get the coefficients of terms I know exist in this ...
0
votes
1answer
84 views
Symbolic partial differentiation of a Lagrangian function including a summation
I'm using Mathematica to double-check that I correctly derived first order conditions for the models I'm researching. Before I get started, I wanted to actually teach myself how to use Mathematica, ...
0
votes
2answers
186 views
Is it possible to calculate the desired area analytically?
I have the three two-variable curves $f,g,h$ with $0\leq x\leq \frac {\pi}{2} $ and $0 \leq y \leq \pi$
I use ContourPlot as
...
2
votes
0answers
29 views
Removing function arguments from expressions with derivatives
( This question is basically the opposite of this one: Variable dependency...easy one )
I would like to be able to output expressions in Mathematica that look more like pen-and-paper math. In ...
0
votes
0answers
18 views
Partially activate a derivative
Is there a way to make an inactive derivative do some amount of simplification? For instance, say I have
Inactive[D][{{f,g},{u,v}},x]
I would like ...
0
votes
1answer
57 views
How to simplify for a ratio of two variables
Say I have an equation like
$$2 z \ln[\frac{a v_{2}^{2}}{b_{2}}]+(v_{1}-2v_{2}) - z \ln[\frac{a v_{1}^{2}}{b_{1}}]\geq0$$
...
