Questions tagged [symbolic]

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

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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
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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 $0\leq \gamma < 1$. ...
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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
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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
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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
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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
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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
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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
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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
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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 ...
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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
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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 ...
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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
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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 ...
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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
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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 ...
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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 ...
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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
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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 ...
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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
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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
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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, \...
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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, ...
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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
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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 ...
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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 ...
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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}{...
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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 <...
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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
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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
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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 ...
2
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2answers
78 views

Conditional statement in function

It seems the equality condition does not work as expected. ...
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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 ...
3
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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 $$ \int\limits_{-\pi}^{\pi} \mathrm{e}^{\mathrm{i}x\sin t} \mathrm{d}t $$ ...
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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
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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
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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
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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
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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 ...

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