Questions tagged [symbolic]
For questions about symbolic computation, as opposed to numerical computations.
981
questions
0
votes
0answers
45 views
Long computation time for solving two algebraic expressions
I am having two equations algebraic equations in two variables and 12 parameters
However, the Solve command is failing to provide any result even after running it for 5 hours.
How much time should I ...
0
votes
0answers
31 views
Why can Mathematica detect a linear term in a series expansion only in special cases?
The series expansion
Series[Sqrt[2 - 2 Cos[d k]], {k, 0, 5}]
Is in odd powers of Abs[k], or more precisely ...
0
votes
1answer
88 views
Minimize fails to find a minimum [on hold]
I am trying to find, analytically, the $\theta,\phi$ that minimize the function U($\theta,\phi$)
...
0
votes
0answers
30 views
Exact Solution to Maximum with constraint, no output
I am new to Mathematica. I am trying to solve a maximum problem with several constraints.
Here is my input.
...
2
votes
2answers
76 views
Definite Integration with Exponental Heaviside Step Funtions
As part of an equation of state calculator that I am working on, I have to handle a virial expansion for the equation of state. As such I have to solve for the virial coefficent, $B(T)$, which is ...
3
votes
3answers
51 views
Assign Values from Array to Array [duplicate]
I am trying to simply do the following
cVec = {a,b,c,d}
From another expression, I obtain another vector, say,
...
0
votes
1answer
36 views
How to force Mathematica to give answer in certain functional form?
I want Mathematica to evaluate $$0=\psi (x) \left(\frac{k x^2}{2}-\text{En}\right)-\frac{\hbar ^2 \psi ''(x)}{2 m}$$ and give me answer in terms of the Hermite polynomials but it gives me result in ...
5
votes
1answer
56 views
1
vote
1answer
60 views
Solution of a system of ODE with Dsolve
I am trying to solve following ODE with Dsolve.
a1[t_] = 2 - 3*Exp[-2*t];
a2[t_] = 1 + Exp[-3*t];
a3[t_] = 4 + Exp[-5*t]
$B=\begin{bmatrix}a1[t] & a2[t] &...
1
vote
1answer
75 views
How to obtain the symbolic expression for the integral?
I need to evaluate the following expression,
$\frac{1}{\Gamma(1-\alpha)} \frac{d}{d x} \int_{0}^{x}(x-t)^{-\alpha}(\exp(\lambda t)) d t, 0<\alpha<1, \lambda\in \mathbb{C}$
using Mathematica to ...
3
votes
1answer
56 views
Can Mathematica check ansatz for solutions of differential equations?
I'm just a beginner learning Mathematica. I'd like to do something with it, but I don't know if it is possible.
Suppose I want to solve a system of differential equations, maybe a nonlinear one, and ...
1
vote
1answer
89 views
RecurrenceTable runs very slowly when doing exact arithmetic [closed]
I am a newbie to Mathematica. I wanted to generate a sequence of numbers with the following command:
...
3
votes
1answer
85 views
n-th derivative of an arbitrary polynomial / power series
How can I tell mathematica to give me the symbolic derivative of the following sum
$$ \frac{\partial^n}{\partial x^n}\sum_{j=0}^N\gamma_jx^j=\sum_{j=n}^N\frac{j!}{(j-n)!} \gamma_jx^{j-n} $$
I only get ...
0
votes
0answers
34 views
How to convert a symbolic recursive formula to a non-recursive one
I am new to Mathematica. I want to convert a recursive formula to a non-recursive one using symbolic math. Specifically, I have a recursive formula similar to this:
$a_n = f_a(c_{n-1}, x_{n-1})$
$...
1
vote
1answer
92 views
Symbolic matrix equation with summation
Considering a set of points:
Let Matrix A be:
And B:
Where $\bar{x}$ is given by:
And the same goes for $\bar{y}$ and $\bar{z}$. I want to solve this equation:
But without specifying any values. ...
0
votes
0answers
58 views
Simplifying a differential equation acting on a product of functions
I have a function $f(x_1, \ldots , x_n)$ in $n$-variables that satisfies a fourth order linear differential equation (say $Df=0$). The function $f(x_1, \ldots, x_n)$ is of the form $f(x_1, \ldots, x_n)...
5
votes
3answers
172 views
Adding elements to some sublists of unequal length
Complicated title for a simple problem:
I have list
a = {{1, 3, 5, 2}, {2, 6, 2}, {3, 5, 6, 1, 2}, {4, 2}}
In which the first element of each sublist is ...
0
votes
1answer
41 views
Reversing the flow of the equation sign. Compacting an equation. Choosing which variables to show
Here's a simple example of what I'm trying to get at with that mysterious title.
I start off with a Hermitian matrix that I derived analytically
...
1
vote
3answers
103 views
Inverting series with symbolic coefficients?
I am trying to invert the series symbolically. Is this possible in Mathematica?
Example 1 -
Let $p = u + au^2 + bu^3$, where $a,b$ are symbolic variables. I am trying to invert the series around $u=...
1
vote
1answer
124 views
Help speeding up solution of system of differential equations using Laplace transform
I'm trying to speed up this code that seems to take forever to evaluate. I'm solving a system of 9 coupled differential equations using a Laplace transform (a version of this code that works perfectly ...
4
votes
1answer
83 views
Is it possible to make Decompose work with coefficients containing radicals?
It appears that Decompose works reliably only on polynomials with integer coefficients, although it seems to be not mentioned in the docs. Can I make it work (or ...
2
votes
0answers
34 views
Integrate Twice over Symbolic Interval [closed]
I would like to solve:
$$
\int _0^1\int _y^11dxdy
$$
In one function call to Integrate[]. However, evaulating
Integrate[1, {x, y, 1}, {y, 0, 1}] (*1-y*)
Gives ...
0
votes
0answers
51 views
How to multiply the elements of each site of tensor products to each other while using symbolic representation?
If I have, say three sites in a symbolic operator which is of the form A = a⊗1⊗c and I want it to act on another operator B = a1⊗b⊗1 in order to find the commutator A.B - B....
5
votes
1answer
94 views
Why DSolve gives different answer depending on order of variables: $u(x,t)$ vs. $u(t,x)$?
Using V12 on windows 10.
I would think it should not matter if one uses $u(x,t)$ or $u(t,x)$ in the specification of the PDE, as long as everything else is consistent (keeping the initial condition ...
4
votes
1answer
100 views
How to set up a Fourier transform?
I am having trouble figuring out how to set up the Fourier transform to:
...
0
votes
1answer
29 views
Get Conditions for Variable to be Real
I have a complex definition of a few variables (that I got using s = Solve[1 - a x^2 - x^3 == 0, x]) and I now want to know under what conditions of "a" will each ...
0
votes
1answer
50 views
How to define a cross product of two orthogonal vectors?
t[s], n[s] and b[s] are three orthogonal vectors. I define a cross product ...
2
votes
0answers
72 views
Lambda calculus reduction in Mathematica
Are there any built-in functions for reducing lambda terms in Mathematica? If not, how might one do it? I've heard of Function, which is good for $\beta$-reduction, ...
2
votes
1answer
38 views
Replace sub-expressions matching a pattern unless located under specific heads
Suppose I have some rule, e.g. Re[x_] :> (x + Conjugate[x])/2. I want to apply it to all matching sub-expressions in some expression, excluding any sub-...
12
votes
3answers
507 views
How to evaluate $ \int_0^1{\mathrm e^{\mathrm i\pi x}x^x(1-x)^{1-x}\mathrm dx} $ and get $ \frac{\mathrm i\pi \mathrm e}{2\cdot3\cdot4} $?
The following definite integral identity holds
$$
\int_0^1{\mathrm e^{\mathrm i\pi x}x^x(1-x)^{1-x}\mathrm dx} = \frac{\mathrm i\pi \mathrm e}{2\cdot3\cdot4}
$$
and is easy to verify numerically. ...
3
votes
2answers
54 views
Limit of an infinite summation
The above is from Maple 2019.1. Is there a way to achieve the same result from MMA12?
Tried
Limit[Sum[Sqrt[1 + k^2/n^3] - 1, {k, 1, n}], {n -> Infinity}]
...
3
votes
1answer
53 views
Simplifying symbolic expression with Heaviside step function
When inputing
Integrate[HeavisideTheta[s - t], {s, 0, 1}, Assumptions -> {t > 0}]
Mathematica correctly simplifies if to
-(-1 + t) HeavisideTheta[1 - ...
0
votes
1answer
53 views
Get Mathematica to factor constants out of definite integral [duplicate]
Say we have
Integrate[a f[x],{x,-Infinity,Infinity}]
And want Mathmatica to factor out a to get
...
0
votes
0answers
107 views
Need help with symbolic integration
I have
f[x_] := g[x]/g'[x]
FullSimplify[Integrate[f[x], x]]
I'm trying to get F[x] in terms of ...
2
votes
1answer
173 views
Solving infinite coupled equations
I need to solve symbolically an infinite system of coupled algebraic equations that I tried to do analytically but I could not.
Solutions of these equations, $V_l^m$, define the coefficients of a some ...
1
vote
1answer
40 views
Symbolic equation pair with two unknowns [closed]
I am a beginner with Mathematica, so hopefully my problem is clearly presented.
My problem is solving two unknowns from equation pair with five symbolic parameters. Baghdadi et al. (2016) created ...
0
votes
1answer
71 views
Matrix of functions
I want to create a matrix of functions. As explained in this question, I can create a matrix of variables:
...
4
votes
1answer
67 views
find a maximum parameter for a range of target eigenvalues as a function of matrix dimension
I have a symbolic tridiagonal matrix of this form
...
2
votes
2answers
45 views
How to obtain a variable in terms of another variable?
I'm new to Mathematica and would like to ask a question about equation systems. I have a linear equation system given in the link. I would like to obtain kappa1 in terms of psi1, kappa2 in terms of ...
3
votes
1answer
96 views
Implementing the Peano-Baker Series with Mathematica
I would like to calculate the Peano-Baker series with mathematica, namely an integral expansion to approximate the state transition matrix:
Say I have a matrix $A(t)$ and I want to calculate:
$\Phi(...
1
vote
1answer
32 views
Mixed partial derivatives with respect to n variables
I have the following generic set of variables:
x = {x1, x2, ..., xn}
nu = {0, 1, 2, ..., n - 1}
order(nu) := Total @ nu;
I would like to calculate:
$$ \frac{\...
0
votes
0answers
41 views
Algebraic manipulation on removing common factor outside
d[i,j] and M[i,j] are elements of size arrays of size 2x2
After some manipulations I get this as Output
...
0
votes
0answers
39 views
Analytically integrating bivariate Gaussian PDF
I have this somewhat complicated expression in terms of the following 8 variables (note: actually, $X$ and $Y$ are variables, and $a,b,c,d,e,f$ are longer expressions as a funtion two other variables, ...
0
votes
0answers
39 views
Why does Refine not use transformation rules for a user-defined function?
I defined a transformation rule for a symbol L that takes a sequence of numbers
...
1
vote
1answer
43 views
Generating examples by applying conditions to symbolic expressions
For example,
Given a list of symbolic expressions:
...
7
votes
0answers
89 views
DSolve fails with four variables
How is that DSolve has no trouble solving this:
DSolve[{
D[G[x1,x2,x3],x1]==0,
D[G[x1,x2,x3],x2]==0,
D[G[x1,x2,x3],x3]==0
},G[x1,x2,x3],{x1,x2,x3}]
but it fails ...
4
votes
1answer
98 views
Symbolic multiplication of tensors
I am trying to do symbolic calculations on Pauli Matrix Algebra. I want to find some way of making CircleTimes[a,b] ** CircleTimes[c,d] map to CircleTimes[a.c,b.d] for every a,b,c,d. I would also like ...
4
votes
4answers
147 views
Find maximum according to a parameter
I am new to Mathematica. I want to find the maximum of the functions:
...
2
votes
1answer
119 views
Evaluating an integral symbolically
I am trying to integrate following integral symbolically via integrate command:
$$(0.09)\Bigg[1 + \Bigg\{ \int_{3t-4k-7}^{2k+7/3} (0.09) \text{exp}\Bigg(\int_{3s-...
0
votes
3answers
98 views
How can I calculate the expected value of the sum of “n” i.i.d. variables with any distribution?
Particulary, I would like to find the expected value of the sum of $n$ variables distributed like ParetoDistribution[1,1.14]. For example, this works for the sum of two vars with Gamma distribution:
<...
