Questions tagged [symbolic]

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

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4
votes
1answer
94 views

How to speed up the calculation process of a symbolic matrix?

There are a symbolic matrix and a real number list. I'm going to replace the symbols of the matrix with all the elements of the list, and then to get the Eigenvalues...
0
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0answers
45 views

Why is ArgMax/ArgMin so bad at working out closed formed solutions? [closed]

Mathematica can't even work out this one: ArgMax[{e^(-c (b - x)^2), c > 0}, x, Reals] . The result is the same as the expression: ...
4
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2answers
652 views

Where I am wrong?

I have an ODE: ( I want to write a code for Manuel solution algorithm) ...(Eq.4) STEP 1: Assume that the solution of ODE can be expressed by ...
1
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1answer
42 views

How to generate assumptions automatically for definite integrals?

In Mathematica, a trick to speed up the process of definite integrals is by adding assumptions. For example, the following codes run faster if we add such assumptions: ...
5
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2answers
170 views

Factorising blinear forms with Mathematica

Say I have some symbolic output that looks like the following: expr = A a1 b1 + B a1 b2 + C a2 b1 + D a2 b2 I would like to factorise this in the following way: ...
5
votes
3answers
319 views

How do you find information regarding the derivative?

I have been struggling with an issue that I believe has a simple way to solve. Given that I have extracted a term of a partial differential equation: f(1,2,0) [x,y,z]. In this case, it is similar to ...
0
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0answers
52 views

Can mathematica solve this analysis difficult problem ? “Functional” equation

Given two continuous functions $G,H: \mathbb R^+ \rightarrow \mathbb R$ such that $\frac{G}{H}$ is positive and strictly increasing, I am looking for two continuous functions $f_0, f_1 :[0,1] \...
5
votes
1answer
152 views

DSolve - incorrect solution to PDE

Bug introduced in 12.2, persisting through 12.3.0. I'm trying to solve a simple Schrödinger equation in external field: ...
0
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1answer
45 views

Solving coupled ODE symbolically for the parameters

I'm trying to solve the following system: $$ \dot{x_1} = -i w_1 x_1+ i s_1 x_2 $$ $$ \dot{x_2} = -i w_2 x_2- i s_2 x_1 $$ For $X(t)_{1,2}$, where $x_{1,2} = X(t)_{1,2}\cdot e^{ip(t)_{1,2}}$ I know ...
1
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0answers
38 views

Derivative of unknown functions and constants [closed]

I'm trying to do symbolic differentiation with Mathematica for expressions with unkown functions and constans. For example the following expression: $$\text{expr} = \omega_1 Q_1^2 Q_2 + \frac{Q_1^3}{\...
0
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0answers
33 views

Identity operator of unspecified dimensions

I would like to create a function which can can take a symbolic square matrix $m$ and returns $m \otimes I$. Where $I$ is the idenity operator of same dimensions as $m$. The actual function I am ...
0
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3answers
92 views

Simplification with User defined rules and assumptions

The results of DSolve are usually expressions that can be further simplified. For instance, consider the following expression for a co-ordinate of a particle in ...
0
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2answers
99 views

DSolve to obtain a tanh solution

We are given a simple ODE with BCs: $\xi^2 \frac{df^2}{dx^2} + f - f^3 = 0$ $f(x=0) = 0$ $\\f(x\to\infty) = 1$ On paper this is quite easy to solve. One can obtain the solution $f(x) = \operatorname{...
1
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1answer
88 views

how to define unit vectors in mathematica

I'm struggling a little bit trying to understand how to address this problem, I would like to do this in mathematica: is just that I don't know how to do the dot product between $\mathbf{J}$ and $\...
1
vote
1answer
133 views

Help with an integral

I want to know if the following integral can be evaluated in Mathematica: $$ g(t)= c\int_{0}^{1-t} t^{m-1}\left[(u+t)^{m}-u^{m}\right]^{n-2}(u+t)^{m-1} d u$$ where $$ c= m^2n(n-1)$$ ...
0
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0answers
21 views

How do I get actual solutions from MaxValue?

Say I want to calculate the maximum value of a simple function of two variables: f[r_, t_]:= r Cos[t]^3 (1 + r Sin[t]) with respect to the variable ...
0
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0answers
58 views

WolframAlpha gives small imaginary part for real integral $\int_0^\infty \log(1 - 2xe^{-x} - e^{-2x})\,dx$

Putting the integral $$\int_0^\infty \log(1 - 2xe^{-x} - e^{-2x})\,dx$$ into Wolfram|Alpha gives ...
0
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1answer
57 views

Help with the evaluation of an integral in Mathematica

I have the following (m and n are integers) $$ f[t] =\frac{ m^2n(n-1)}{2}t^2 \left(1 - (1 - t)^m \right)^{(n - 2)} (1 - t)^{(m - 1)} $$ $$ \text{Integrate}[f[t], {t, 0, 1}]$$ I also need the aymptotic ...
0
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0answers
89 views

Why can't Mathematica integrate my function?

I am very new to Mathematica and have been trying to integrate a function p[f] that is expressed as follows ...
0
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0answers
42 views

How to declare a list of symbols as Real numbers?

I have a list of symbols : gammaVecs =Table[Symbol[StringJoin["gamma", ToString@j, ToString@i]], {j,7}, {i, 40)}]; Which I want to use later in ...
0
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0answers
48 views

Strange behavior of FindInstance

I try to solve a problem from Kazakhstan math school competition (see it here in Russian) by ...
0
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0answers
37 views

Splitting product of $\gamma$-matrices into symmetric and anti-symmetric part

The $\gamma$-matrices satisfy the relation $$\gamma^\mu \gamma^\nu +\gamma^\nu\gamma^\mu=2\eta^{\mu\nu}\mathrm{id},$$ where $\eta$ is the Minkowski metric. Consider now the following process $$\begin{...
0
votes
1answer
51 views

A doubt about symbolic rational expression

I have this expression: $$PB=\frac{(R3 + R4) R6}{R4 R5 + R4 R6 + C2 R2 R3 R5 S + C2 R2 R4 R5 S + C1 C2 R1 R2 R3 R5 S^2 + C1 C2 R1 R2 R3 R6 S^2}$$ I need to put it in this form: $$PB=\frac{\frac{(R3 + ...
0
votes
1answer
47 views

How can I get the equation solution in the form of y1/y2 [closed]

I have some trouble getting the equation solution in the variable fraction form. If there is an equation set shows below: ...
4
votes
1answer
352 views

Some doubts about symbolic equations in Wolfram Mathematica

I need to perform the following operations using Wolfram Mathematica. I have these equations: $$a b = c+d+e$$ $$\frac{d}{f}=g h + i$$ $$k=\frac{a}{c}$$ I need to obtain $k$ as a function of: $a,b,c,e,...
2
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1answer
97 views

Getting Mathematica to solve a system of two second order nonlinear ordinary differential equations

I tried solving a system of two second order nonlinear ordinary differential equations using the DSolve command. First, I tried like this: ...
3
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3answers
190 views

Why such a big difference between results of Integrate and NIntegrate?

Studying an interesting article of Daniel Lichtblau, I consider a variation of an example from it, calculating an improper integral ...
0
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2answers
37 views

Fast fourier coefficients for a long sum

I have a very long expression involving a sum of exponentials, say: Sum[(RandomReal[] + RandomReal[] a) Exp[2 I ii x Pi], {ii, -10, 10}] I want the fastest way to ...
0
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0answers
29 views

Standard way to define a linear operator?

Say I want to define some simple linear operator. I can do this by f[c_?NumericQ x_] := c f[x] f[x_ + y_] := f[x] + f[y] Or let's define a bi-linear operator ...
0
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1answer
31 views

Simplifying cross product expressions II

This is related to Simplifying cross product expressions Consider the following: ...
0
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1answer
26 views

exclude terms from expansion

Suppose I define F1[R + a] = F1[R] + a D[F1[R],R] F2[R + 2 a] = F2[R] + 2 a D[F2[R],R] and I want to expand the square of their sum keeping only first order terms ...
2
votes
1answer
96 views

Simplifying cross product expressions

Suppose I want to calculate: Cross[A1 + B1, A2 - B2] + Cross[A1 - B1, A2 + B2] which is equal to 2 A1xA2 - 2 B1xB2 Using ...
0
votes
1answer
52 views

Surd factors do not auto cancel each other out

Simplify[Sqrt[Pr] - (Sqrt[Pr/Ra])*Sqrt[Ra]] The above command should give me 0 as the simplified outcome, but it keeps ...
0
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0answers
43 views

How to find eigenvalues of 8x8 matrix?

I am new to Mathematica, and was trying to find the eigenvalues of an 8x8 matrix using Mathematica. I have fairly simplifies the matrix A into a mathematical expression and I know the final ...
1
vote
1answer
51 views

How to define distributivity of CenterDot on bras and kets

I am working on a code for a coupled quantum harmonic oscillator and found myself in a hiccup when trying to evaluate the inner product of linear combinations of bras and kets. I have initially ...
0
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0answers
25 views

Replacement of functions bound by sums and integrals in NCAlgebra

I want to use the NCAlgebra package to do some simplification on non commutative expressions involving integrals. For example, one such expression would be $$ I=\left(\int f(x)g(x) dx\right) * h $$ ...
3
votes
1answer
79 views

How to get True for X^2>= 0? [closed]

How to get true when introducing the expression $x^2 \geq 0$ in mathematica ? how do I specify that x is real ? GreaterEqual[x^2, 0, Element[x, Reals]]
2
votes
2answers
93 views

Does a positive real solution exist to this problem?

I wrote the following code for getting the solution. I am not sure if the code I wrote is correct. The problem is further intensified by the fact that I don't know if a solution exists to this problem ...
0
votes
0answers
38 views

Cancel common factors in symbolic product

Suppose I have the following function G[n_, k_] := Product[g[n + i]/g[i], {i, 0, k}] where $n,k$ are assumed to be natural numbers and $g$ is a nonzero symbolic ...
1
vote
1answer
34 views

Difficulty in evaluating the constants of simultaneous equations

How to find the constants A1, A2, B1, B2 using linear solve or null space function in Mathematica. ...
0
votes
1answer
92 views

How to properly attempt to express a function in terms of new variables

I have a specific problem in mind, but I am more interested in how to "properly" convey to Mathematica the result that I want. To start with, I have a function $G$ that can be represented ...
3
votes
1answer
105 views

Solve system of trigonometric polynomials

I am trying to solve a real system of trigonometric polynomials, which contain 7 symbols {b[1],b[2],b[3],b[4],a[2],a[3],a[4]} between 7 equations: ...
0
votes
1answer
80 views

Finding the exact symbolic formula for a function defined recursively

Let me introduce the problem. I have the following functions; The first one is defined recursively $h(i,j):=\frac{i-1}{j+1}h(i+2,j-2)$ and $h(i,0)=1$ where $i$ and $j$ are even integers, greater than $...
0
votes
2answers
110 views

Incorrect results of differentiation

Let us consider the derivative D[Floor[x]*Sin[Pi*x]^2, x] // Simplify ...
0
votes
1answer
97 views

Why are the results of integrations of a DiracDelta related integrand and its approximations strikingly different?

Let us consider a double integral, treating it as a functional which corresponds a number to a function, ...
0
votes
2answers
107 views

Solving a non-linear system of equations symbolically [closed]

How would I solve this systems of non-linear equations symbolically: $$ \mu N -\frac{\beta S I}{N} - \nu S = 0 \qquad (1)$$ $$\frac{\beta S I}{N} -\gamma I - \nu I = 0 \qquad (2)$$ $$\gamma I - \nu R =...
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0answers
35 views

Four dimensional symbolic integration using HalfSpace

Consider the regions $r1 and $r2 defined as follows, ...
0
votes
2answers
58 views

Error in Integration of special functions using mathematica 12.0

When I try to integrate the following, Integrate[-GegenbauerC[22,-1/2,x]/(1+k*x),{x,-1,1}] where -1<k<1 and k!=0, Mathematica gives different results if I ...
2
votes
0answers
46 views

Piecewise PDE Over 3 Regions with Continuity Boundary Conditions

I am using Wolfram Language for the first time for my research and could really use some help! I am trying to find the analytical solution of a PDE which has piecewise constants and a piecewise input. ...
7
votes
0answers
142 views

Series with ArcTan gives wrong symbolic answer in Wolfram Language

Bug introduced after 9, persisting through 12.2. Recently, I have found a very bad problem with Wolfram Language. It gives the wrong answer for a quite simple expression! When calculating ...

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