Questions tagged [symbolic]
For questions about symbolic computation, as opposed to numerical computations.
1,083
questions
0
votes
1answer
52 views
Finding an eigenvector for a specific eigenvalue of a symbolic matrix
The relevant matrix is
$$M=\left( \begin{matrix} p^3+\frac{1}{\sqrt{3}}p^8 & p^1-ip^2 & p^4-ip^5 \\
p^1 +i p^2 & -p^3 + \frac{1}{\sqrt{3}}p^8 & p^6-ip^7\\
p^4+i p^5 & p^6+i p^7 &...
1
vote
1answer
60 views
complex number from the integration of a real integrand
Consider this integral:
$$
\int_0^\pi d\theta \sin\theta\, {1 \over \gamma^q}\left((1-\gamma^2)^2\sqrt{1 \over 1-\left(1-(1-\gamma^2)^4\right)\cos^2\theta} - 1\right)^q
$$
for $0\leq \gamma < 1$. ...
0
votes
0answers
44 views
Can anyone help me to get symbolic expression for the following code?
Using Mathematica I did some manipulation on the function $\sum _{s=-m}^{m} e^i \lambda ^{-(2-d) s} \left(1-e^{i y \lambda ^s}\right)$.
And got the following output:
(1) when I took $\text{m}$ in ...
2
votes
0answers
33 views
Summing with assumptions provides unexpected output
I am computing a closed form of a number of sums having generally the following form: $$ \sum_{i = 0}^{m/2}\sum_{\substack{0\leq k \leq i \\ 2k \equiv i + m \, \text{mod } 3}} k $$
It looks like ...
5
votes
2answers
325 views
Why doesn't Integrate evaluate an elliptic integral?
My code is
Integrate[ 1/Sqrt[(x - a) (x - b) (x - c) (x - d)], {x, a, ∞},
Assumptions -> 0 < d < c < b < a]
I know this can be ...
1
vote
1answer
44 views
Plotting a function rescaled by a parameter along x axis
I would like to know, how to plot a graph, for example of this function:
$f(t)=-\frac{4 \sin \left(\frac{\gamma t}{2}\right)}{\gamma ^2 t}-\frac{4 \sin ^2\left(\frac{\gamma t}{4}\right)}{\gamma }-\...
2
votes
0answers
19 views
Define an operator with the distributive property that works in general expressions
This is a follow up to this question. In that question they use TagSetDelayed to give a symbol the distributive property. In my case this becomes
...
5
votes
2answers
155 views
Evaluate integrals with parameters
I'm new to Mathematica so I apologize if the answer to my question is trivial.
I need to calculate the following integral
$$ \int_{-\infty}^{0}\frac{dx}{\sqrt{(x-a)(x-b)(x-c)(x-d)}} $$
with
$$ 0 < ...
3
votes
1answer
91 views
Replace derivative terms with finite difference symbols
I would like to replace the derivative terms in an expression with their finite difference approximations. Note, I don't want to actually evaluate the approximations at a given point, just display the ...
2
votes
1answer
38 views
Defer evaluation of function but not of its derivative
Sometimes, the derivative of a function can be simplified nicely using the definition of the function itself. For example, if $f(x) = e^{x^2}$, then
$$f'(x) = 2x \cdot f(x).$$
How can I perform this ...
0
votes
1answer
68 views
Can I simplify a PDE with Mathematica?
I'm a beginner in Mathematica and I search for help with a calculation problem with some derivatives and basic operations.
I need to simplify a PDE that depends of a smooth function $f:U\subset\...
2
votes
1answer
90 views
Simplifying algebraically [closed]
Is there a way to derive an simplified expression from other equations. Or create an alternate form such that the main equation takes other equations and manipulates the main function.
Here is what I ...
2
votes
0answers
25 views
Computations with OptimizedExpressions without completely expanding them
I have to manipulate huge expressions that are rational functions of many (∼30) variables with integer coefficients. Storing them just as a ratio of two polynomials would be impractical. But they can ...
5
votes
3answers
290 views
DSolve fails to handle summation involving DiracDelta
Executing
s = DSolve[{y''[x] + y[x]==Sum[DiracDelta[x-2^n]/2^n,{n,0,Infinity}],y[-Pi/2]==-1,y'[-Pi/2]== 0}, y[x], x]
, I obtained ...
1
vote
0answers
29 views
Tackling variational problem with constraints [closed]
I need to minimize (preferably symbolically) functional with constraints:
$$
F = \int_{0}^{\pi/2} f(x)cos{x}dx\,\\
1.1 \geq f(x) \geq 0\\
2.\int_{0}^{\pi/2} f(x)dx=Const\\
3. f(0) =1\\
4.f(\pi/2) = 0\...
2
votes
1answer
77 views
Correcting HeavisideTheta in MM11.3 for generating the same results with UnitStep in MM5.2
The UnitStep was replaced with the HeavisideTheta after the version 6.0 (reference here), but some differences confused me ...
0
votes
1answer
31 views
Simplification of an integral through product manipulation under the integration symbol
Consider an integral of the form
Integrate[
f[a*x]
g[c1*z1+c2*z2+c3*z3]
h[e*x]
k[d1*z1+d2*z2+d3*z3]
,{x,0,1}
,{z1,0,2}
,{z2,0,3}
,{z3,0,4}
]
Assume that ...
0
votes
0answers
10 views
How can I obtain the traditional form of variable defined by Notation?
I use Mathematica to deduce the equation. My formula contains many derivative, for example I have a variable $\sigma_x=\frac{\partial u_0}{\partial x}$. I want to directly copy the deduced formula to ...
6
votes
1answer
75 views
How to use RiccatiSolve with symbolic matrix
According to the RiccatiSolve documentation the Eigensystem method can apply to symbolic matrices.
However, I can not get it to ...
0
votes
0answers
37 views
Does Solve work with symbolic tensors?
I am considering the usefulness of Mathematica's symbolic tensors to handle algebra which I encounter in acoustics of solids. Is there a way to solve equations written in symbolic tensors? This is ...
2
votes
1answer
30 views
How to state nontrivial tensor symmetry assumptions?
For example dddg, the third derivative of the metric tensor, in dimension $4$.
I need to state that it is symmetric in the first two indices and symmetric in the ...
3
votes
2answers
82 views
Two identities involving contour integrals in the presence of a branch point where the integrand explodes, and the Kummer function
I need to understand how to establish two identities. The first is
$$ \int_{C} z^{-1-q}(1-z)^{-1-\lambda } dz=\frac{2 \pi \Gamma (q+\lambda +1)}{\Gamma
(\lambda +1) \Gamma (q+1)}, q\geq 0, \...
0
votes
1answer
29 views
Assuming a root and simplify
I want to simplify an expression assuming a given value is a root. Say s[v] is a root of f[x,u]-f[x,v]. Sometimes Assuming works, for example,
...
1
vote
0answers
40 views
Are two equations equal
I have a two vector laplacians which have very long equations and I have to verify that they are equal, and doing that by hand would take an hour, I have tried using LHS == RHS, which should print ...
3
votes
2answers
170 views
Defining a*b=-b*a
I am fairly new to using Mathematica and was wondering if it's possible to define something along the lines of:
$a*b=-b*a$
a sort of antisymmetry or skew symmetry if you will. I would like to do ...
0
votes
1answer
48 views
Using subscripted symbol affects integration — why?
Below is a sample program that shows that Integrate is giving different results depending on whether I name the variable duration1 or ...
0
votes
1answer
37 views
Keeping equations in terms of specific variable
I'm new to Mathematica and really struggling with something seemingly simple. I'm trying to do an integration and keep the results in terms of the symbol $T_1$ and $A_i$:
$$ T_1=\frac{\text{pi} A_i}{...
0
votes
1answer
91 views
How to perform the following complex integration in two variable?
$$\int_{-\infty}^\infty\int_{-\infty}^\infty\frac{\mathrm dx\mathrm dy}{xy}\sinh(\pi x)\sinh(\pi y)e^{\pi i(2x^2+y^2)}\sin(\pi x y)$$
Here both integration variables $x$ and $y$ run from $-\infty$ to ...
5
votes
1answer
91 views
Discrepancy between the results of NDSolve and DSolve (equations related to one step processes)
Bug introduced in 12.0 and fixed in 12.1
The following are the dimensionless equations of a one-step random walk with an "impure" reflecting boundary assuming only four possible states, i.e., n=0, 1, ...
7
votes
2answers
140 views
DEigensystem gives x-dependent eigenvalues
Bug introduced in Version 11 or earlier and persisting through 12.1. Reported to Wolfram Technical Support as CASE:4532301.
I am considering the eigenvalue problem associated with the double-well ...
3
votes
2answers
86 views
Maximizing the global minimum of a simple parameterized trigonometric sum
I want to maximize the minimum of a simple (Sin/Cos based) parameterized trigonometric sum over all real values of ...
3
votes
2answers
98 views
Why Mathematica gives me different results depending on the order I set the parameters when I solve this differential equation?
I am asking Mathematica to solve a differential equation using DSolve, with two different parameters, q and m, and then evaluate at a point.
So I write the ...
0
votes
1answer
34 views
Sleeping Symbolic Term in and Expression
Hello I have some code that have terms that look like g2''[y] E^[n I x] where n is 0,1,2,... I would like for when ...
4
votes
1answer
63 views
Is it possible to take into account recurrence relations using FullSimplify?
There is the identity,
$$\frac{\partial}{\partial x}\left(e^{-x}x^{a}L_n^{\lambda}(x)\right)=(n+1)e^{-x}x^{a-1}L_{n+1}^{\lambda-1}(x)$$
I would like to simplify expression
$$\frac{\partial}{\partial x}...
0
votes
3answers
75 views
System of non-linear equations - Symbolic solution
I've been running this code for more than 12 hours and still can't find a symbolic solution for this. Maybe there is a way to simplify it or something might be wrong with the code. Do someone have a ...
0
votes
0answers
27 views
Using NCAlgebra for Matrix Calculus
I have the following expression:
$$
F = \| \mathbf{1} \text{diag}(G)^\top P S+(\mathbf{1} \text{diag}(G)^\top P S)^\top - 2 S^\top P^\top G P S - D \|_F^2
$$
where $S\in \mathbb{R}^{M\times N}$, $P\in ...
2
votes
2answers
57 views
Is there any way to define the Pauli matrices eigenstates symbolically in Mathematica?
I've been trying to define the kets $|+\rangle$ and $|-\rangle$ with no sucess with
...
2
votes
1answer
50 views
select the symbolic terms of an array
is it possible to extract the symbolic variables from an array ?. For example:
s = {(1+0.1I)a*b*c,4*a*b*c,(0.5-2i)*j*k^3,0.88*b*d^2}
I would like to have another ...
2
votes
1answer
45 views
odd output from DifferenceDelta
I would appreciate an explanation of why DifferenceDelta produces a complicated expression for a simple quadratic. I see that this is caused by the Real value <...
1
vote
0answers
50 views
What is the symbol for Matrix inverse operator? [closed]
I tried to take inverse of a matrix A using Inverse[A] and it gave me the right result. But when I tried using notation form A-1 by using typesetting superscript, it gives me wrong result (element ...
2
votes
1answer
123 views
Symbolic solution of an iterative system
I am not an expert in Mathematica. I want to keep off from tedious calculation
I want to solve (in symbolic sens) this system: $\quad AU^{j+1}+BU^{j}=F^{j}$
where:
$*$ ${U}^{j}$ a $(N;1)$ vector $\...
6
votes
2answers
420 views
How to implement Einstein summation convention with differential operators
Statement of this problem:
In the textbook, the following differential equilibrium equations can be expressed by tensors:
Using Einstein's summation convention, the formula in the figure above can ...
asked Mar 22 at 10:48
Please Correct GrammarMistakes
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2
votes
2answers
78 views
1
vote
0answers
66 views
Is there an Mathematica version of Structural Mechanics Solver Based on symbol system?
I want to write a structural mechanic's solver similar to the following one. The difference is that only numerical parameters are accepted below. I want to write a symbolic solver system with the help ...
asked Mar 20 at 4:37
Please Correct GrammarMistakes
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3
votes
4answers
235 views
Evaluate the defining Integral of the Bessel functions of the first kind
I am trying to evaluate the integrals
$$ \int\limits_{-\pi}^{\pi} \mathrm{e}^{\mathrm{i}(x\sin t - nt)} \mathrm{d}t $$
and
$$ \int\limits_{-\pi}^{\pi} \mathrm{e}^{\mathrm{i}x\sin t} \mathrm{d}t $$
...
1
vote
2answers
218 views
Making Integrate find an integral involving logarithms
I need to simplify the following integrand to make it work with Integrate, I've tried to make a substitution with u = x ln(x) ...
3
votes
1answer
112 views
Solving delay differential equation. DSolve returns `Indeterminate`
I want to solve the following systems of delay differential equations
$$
\text{SYSTEM 1}\\
x'(t) = -y'(t)-z'(t)\\
y'(t) = -z'(t) + x(t)y(t) \tanh(t)\\
z'(t) = -\Theta(t-2)x'(t-2)
$$
and
$$
\text{...
1
vote
1answer
54 views
Table of Variables within Manipulate
Given a certain number n, I want to define n controls within Manipulate with the correct ...
4
votes
1answer
90 views
Pattern matching natural powers as products
I thought that Mathematica would be smart enough to know that f[t]^2 should match a_ * b_ with ...
6
votes
1answer
196 views
Laplace transform of a rectangle function
I defined a rectangle function as below:
rect[t_, T_] := (Sign[t] - Sign[t - T])/2
The laplace transform should be
$$
\frac{1-e^{-sT}}{s}
$$
But the code below ...
