Questions tagged [symbolic]

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

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3
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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

Calculating number of nonzero elements in any symbolic matrix

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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
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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
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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 $$2 z \ln[\frac{a v_{2}^{2}}{b_{2}}]+(v_{1}-2v_{2}) - z \ln[\frac{a v_{1}^{2}}{b_{1}}]\geq0$$ ...

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