Questions tagged [symbolic]
For questions about symbolic computation, as opposed to numerical computations.
1,285
questions
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
votes
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
votes
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
vote
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
votes
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
votes
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
votes
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
vote
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:
$$\text{expr} = \omega_1 Q_1^2 Q_2 + \frac{Q_1^3}{\...
0
votes
0answers
33 views
Identity operator of unspecified dimensions
I would like to create a function which can can take a symbolic square matrix $m$ and returns
$m \otimes I$. Where $I$ is the idenity operator of same dimensions as $m$. The actual function I am ...
0
votes
3answers
92 views
Simplification with User defined rules and assumptions
The results of DSolve are usually expressions that can be further simplified. For instance, consider the following expression for a co-ordinate of a particle in ...
0
votes
2answers
99 views
DSolve to obtain a tanh solution
We are given a simple ODE with BCs:
$\xi^2 \frac{df^2}{dx^2} + f - f^3 = 0$
$f(x=0) = 0$
$\\f(x\to\infty) = 1$
On paper this is quite easy to solve. One can obtain the solution
$f(x) = \operatorname{...
1
vote
1answer
88 views
how to define unit vectors in mathematica
I'm struggling a little bit trying to understand how to address this problem, I would like to do this in mathematica: is just that I don't know how to do the dot product between $\mathbf{J}$ and $\...
1
vote
1answer
133 views
Help with an integral
I want to know if the following integral can be evaluated in Mathematica:
$$ 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)$$
...
0
votes
0answers
21 views
How do I get actual solutions from MaxValue?
Say I want to calculate the maximum value of a simple function of two variables:
f[r_, t_]:= r Cos[t]^3 (1 + r Sin[t])
with respect to the variable ...
0
votes
0answers
58 views
WolframAlpha gives small imaginary part for real integral $\int_0^\infty \log(1 - 2xe^{-x} - e^{-2x})\,dx$
Putting the integral $$\int_0^\infty \log(1 - 2xe^{-x} - e^{-2x})\,dx$$ into Wolfram|Alpha gives ...
0
votes
1answer
57 views
Help with the evaluation of an integral in Mathematica
I have the following (m and n are integers)
$$ 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}]$$
I also need the aymptotic ...
0
votes
0answers
89 views
Why can't Mathematica integrate my function?
I am very new to Mathematica and have been trying to integrate a function p[f] that is expressed as follows
...
0
votes
0answers
42 views
How to declare a list of symbols as Real numbers?
I have a list of symbols :
gammaVecs =Table[Symbol[StringJoin["gamma", ToString@j, ToString@i]], {j,7}, {i, 40)}];
Which I want to use later in ...
0
votes
0answers
48 views
Strange behavior of FindInstance
I try to solve a problem from Kazakhstan math school competition (see it here in Russian) by
...
0
votes
0answers
37 views
Splitting product of $\gamma$-matrices into symmetric and anti-symmetric part
The $\gamma$-matrices satisfy the relation
$$\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
votes
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
votes
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
votes
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
votes
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
votes
1answer
31 views
Simplifying cross product expressions II
This is related to Simplifying cross product expressions
Consider the following:
...
0
votes
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
votes
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
votes
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 =...
1
vote
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
...
