Questions tagged [symbolic]

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

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3
votes
1answer
106 views

Simplifying algebraically

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
28 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
319 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
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0answers
31 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
84 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
34 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
82 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
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0answers
46 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
31 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
90 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
2answers
40 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
183 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
39 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
94 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
101 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
163 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
90 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
100 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
70 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
78 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
32 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 ...
1
vote
2answers
60 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
51 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
46 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
53 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 ...
1
vote
1answer
124 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
3answers
555 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 be ...
2
votes
2answers
78 views

Conditional statement in function

It seems the equality condition does not work as expected. ...
0
votes
0answers
69 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 ...
3
votes
4answers
263 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
227 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) ...
2
votes
1answer
115 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
56 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
94 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
215 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 ...
1
vote
0answers
86 views

Element: True,False,Maybe,,,

I have a question about Element[] Element[3/2,Rationals] True OK ...
0
votes
1answer
68 views

Simple nested sum giving ridiculous answer [closed]

I have produced a minimum working example of the issue I'm facing. I would like to evaluate the following symbol sum, with $n\geq0$: $$\sum_{k=0}^n \sum_{m=0}^{2(n-k)} x^m$$ If I evaluate this sum ...
4
votes
2answers
168 views

`Series` gives wrong result

Bug introduced in 10.0 or earlier and persisting through 12.0. The following code shows that Series gives different results depending on whether one simplifies the ...
4
votes
3answers
241 views

How to simplify this formula?

$$ \int \frac{1}{\sqrt{1-2 x^3}} \, dx $$ Integrate[1/Sqrt[1 - 2 x^3], x]// FullSimplify The result is very complex. Then I want to differentiate it with the ...
5
votes
1answer
143 views

Implement abstract algebraic structure

I would like to implement algebraic structures in Mathematica such as groups, algebras, Lie-algebras, Hopf-algebras, ... In particular, after initialising such a structure, I would like to have ...
1
vote
3answers
682 views

How would I solve this math problem on Mathematica?

$(3t^2 + 5t + a ) (4t^2 + bt - 2) = 12t^4 +26t^3 - 8t^2 - 16t + 6$ What is a + b? The answer would be: $6=-2a$ $a=-3$ $-16t=(5t\cdot-2)+a\cdot bt\Longrightarrow-16t=-10t+(-3)bt\Longrightarrow b=...
1
vote
1answer
58 views

Refine Max[#] with assumptions breaks with more elements

Can someone please explain the following phenomenon to me? I am using Refine to evaluate a symbolic Max expression with a ...
0
votes
0answers
41 views

PlanarAngle symbolic equalities return contradictory results

PlanarAngle[OO->{A,B}]==PlanarAngle[OO->{B,A}]/.{OO->{0,0},A->{1,0},B->{1,1}} False ...
2
votes
1answer
89 views

Using chain rule to calculate a second-order partial derivative in spherical polar co-ordinates

I have a function $f$ and I am supposed to calculate its second-order partial derivative first in cartesian co-ordinates, which is fine. However, I am stuck while solving the problem in spherical ...
0
votes
1answer
175 views

How to calculate integration with undefined functions?

There are two functions inside the integral symbol, one is related to the independent variable and the other is independent of the independent variable. Both are the derivative and Tload is a ...
4
votes
1answer
166 views

How to get DAE representation from equations?

Update2: Thank you for all of your answers. I would like to clarify the question as I did a bit of research on DAE representations and their applications in software. There are 2 representations used ...

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