Questions tagged [symbolic]

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

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52 views

Solve method in Mathematica, symbolically solving method

I am looking for a way to solve this equation symbolically with Mathematica. ...
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1answer
74 views

How to get Mathematica to return more accurate symbolic eigenvectors

This code: Eigenvectors[{{Cos[t], Sin[t]}, {Sin[t], -Cos[t]}}] returns this output: ...
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1answer
79 views

speed up symbolic summation

I have the following summation L=24; sind=Range[-Pi,Pi,2*Pi/L]; Sum[f, {x, sind}, {y, sind}, {x1, sind}, {y1, sind}, {x2, sind}, {y2, sind}] where ...
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3answers
149 views

Initial-boundary value problem of 2nd order linear PDE with variable coefficient

Today I was studying partial differential equations and I tried to check if my solution was correct, I thought Mathematica code would be easy, but it wasn't. Here is my problem: Solve $u_{xx}-2tu-u_t=...
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1answer
39 views

Normal ordering of operators multiplied by scalars

I have the following code for normal ordering of two Boson operators $a(x),\,b(y)$: ...
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1answer
62 views

Extracting von Neumann neighbors from a list of lists [duplicate]

I want to be able to implement a rule that extracts the von Neumann neighbors from a given list of lists, that act as the entries of a rectangular matrix. Say a list of lists is given: ...
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2answers
57 views

Creating a Symbolic Matrix

Probably very simple, but I don't know where to start with this. How do I go about creating a symbolic matrix, such as the one below? I want to be able to use this so that any list of lists that are ...
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1answer
27 views

Expand product of symbolic sums (with identically named indices)

I have an expression that is a product of two symbolic sums. Sum[a[k], {k, 1, n}]*Sum[b[k], {k, 1, n}] How can I expand this expression? I want to see something ...
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0answers
78 views

How reliable is AsymptoticIntegrate?

In new mathematica 12 there is a new function AsymptoticIntegrate. However, it seems that it gives me incorrect results in some cases. To be completely honest, it ...
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1answer
39 views

NonCommutativeMultiply question- syntax question

if I define id as: id /: NonCommutativeMultiply[id, x_] := x id /: NonCommutativeMultiply[y_, id] := y then ...
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3answers
277 views

Solving a Sturm-Liouville problem

Ello, I would like to reproduce the analytical solution of the following eigenvalue problem, or at the least confirm them numerically (especially the eigenvalues): $$ - \frac{1}{2} y^{\prime \prime} ...
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0answers
29 views

summation involving Kronecker Deltas

I see that: Sum[u[q] u[k] v[k1] v[k + k1 + q] KroneckerDelta[k1 - q], {k1, -\[Infinity], \[Infinity]}] produces the correct result: ...
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2answers
57 views

Better way to do a replacement to define a function

I have a long analytical process where I have defined a stand in function Int[] to act as a placeholder for either NIntegrate[] ...
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1answer
84 views

Game of Life (GoL) in 3D cellular automaton and its rule numbers

I walked through How to calculate CellularAutomaton rule numbers in higher dimensions? to produce the following code for the Advent of Code, day 17, which asks for "Life, but in 3D". More ...
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3answers
118 views

How do I solve this integral in Mathematica?

I am trying to solve this integral in Mathematica $$ I=\int_{0}^{1} d x e^{iax} K_{0}\left(\sqrt{\left[q x(1-x)+m\right] b}\right) $$ where $a$, $b$, $m$, and $q$ are real positive constants. I want ...
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0answers
31 views

Symbolic min max optimization

I have the following seemingly simple optimization problem Minimize[{Max[p^(c - 3) , a p^(c - 1) , b p^c], d <= p <= 1}, p] but the Mathematica does nothing. ...
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0answers
66 views

How to get an asymptotic of the real-valued branch of the inverse function?

Consider function $f:\mathbb R^+\to\mathbb R^+$, defined as $f(x) = x + x^2\left(1 + \log x\right)$. I need to find an asymptotic approximation of its inverse function $f^{\small(-1)}\!:\mathbb R^+\to\...
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0answers
26 views

Importing equations generated in subpackage to be solved in another subpackage

I have a package which contains two subpackages: one ("`MOTSimulator`MOTGenerator") which generates a systems of differential equations of the form ...
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1answer
129 views

Nice use case for symbolic tensors?

I come from before the times of symbolic tensors in Mathematica, and am used to working with concrete tensors and custom commands to contract them using Transpose, Dot, etc. I recently realized that ...
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1answer
87 views

How to perform symbolic integration of six variable function?

I have a function of six variables in total - x1, x2, x3, x11, x22, x33 and I need to perform symbolic integration to get a symbolic expression. Before showing my ...
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0answers
53 views

Implementing the symbolic identity matrix $I$

I am working with symbolic tensors within Mathematica and I wanted to ask if there is a way to have a symbolic identity tensor.
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2answers
584 views

Three coupled PDEs to be solved semi-analytically/analytically

I have been trying to solve the following three coupled PDEs where the final objective is to find the distributions $\theta_h, \theta_c$ and $\theta_w$: $x\in[0,1]$ and $y\in[0,1]$ $$\frac{\partial \...
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1answer
86 views

Having problem in evaluating the eigenvalues of an $11\times11$ symmetric matrix in Mathematica [closed]

I am solving an $11\times11$ matrix in Mathematica. I am facing problem when I try to find the determinant or eigenvalues of this matrix. The error (Det::matsq/<...
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3answers
65 views

Solve function used symbolic computation yields all the coefficients value zeros

I am trying to compute the symbolic coefficients of using Solve function. But this is yielding all the coefficients values zeros. What are the other ways to find ...
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2answers
94 views

Can't compute the Integral

I tried to calculate an integral with the function Integrate, but it runs for a long long time without any answer. I have been checking the integrand and it seems ...
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1answer
47 views

TensorExpand, TensorProduct and Distribution over Scalars

Consider: TensorExpand[( b1 x )\[TensorProduct] (b1 x + b2), Assumptions -> x ∈ Reals] (*x^2 b1\[TensorProduct]b1 + x b1\[TensorProduct]b2*) This works as ...
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2answers
78 views

Solving Simultaneous equations of matrices

I am in a precarious situation where I have two equations: eq1 = α1 + αt12.t1 + αr11.r1 == 0; eq2 = γ1 + γt12.t1 + γr11.r1 == 0; Where each variable is a 3x3 ...
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3answers
93 views

Table over array indices

I want to generalize the following table to a summation over $s[1], \ldots, s[N]$ and $t[1], \ldots t[N]$, where each variable sums over $\{-1, 1\}$. ...
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3answers
241 views

A question on the exact value [closed]

Could anyone help me find the exact value of ...
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0answers
35 views

How to define function in Mathematica

I have a 3 by 3 symbolic matrix M(x,y,z). Question:1 First, I want to find its eigenvalues and eigenvectors. After that I want to make each eigenvalue and eigenvector a function of x,y, and z i.e. <...
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2answers
51 views

How to make calculations involving symbolic summation?

I want to minimize a function involving the sum of $n$ fixed (but indetermined) $x$ values, for example: Minimize[Sum[(x[i] - a)^2, {i, 1, n}], a] Expected answer: ...
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0answers
73 views

Symbolic equation solving: Inverse functions are being used by Solve

I'm quite new to mathematica, so apologies if the question it soo trivial. I'm trying to symbolically solve an equation for R, and would like at the same time to mix in a second equation. What I've ...
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1answer
66 views

How &@ and &/@works?

I have the following expression: (Join[#, Reverse[#, {2}]] &@Partition[#, 2, 1, 1]) & /@ Vec (* where: *) Vec={{2,0},{1,1},{0,2}}, but I am not sure how ...
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26 views

Is there any formula to get the IRR from the slope of the Cumulative Cash Flow?

I've simulated a monthly regular cash flow with Excel, and the Internal Rate of Return (IRR) calculated from the first date to the current row. The curve of the IRR is very similar to the Transfer ...
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2answers
151 views

Trying to solve transient semi-infinite 1D Fick's Law with decay, getting constant for answer

I'm trying to find the solution to $$\frac{\partial f(x,t)}{\partial t} = a\frac{\partial^2 f(x,t)}{\partial x^2} - bf(x,t)$$ where $$f(0,t)=1, \lim_{x\to\infty}f(x,t)=0,f(x,0)=0.$$ I tried: ...
6
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1answer
175 views

Why can't this simple second-order differential equation be solved?

I'm trying to solve the following partial differential equation: $$ f(x,y) = \partial_x^2f(x,y)-\partial_y^2f(x,y) $$ for which one obvious solution would be: $$ f(x,y)=e^{2x+\sqrt{3}y} $$ An even ...
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0answers
18 views

Is substitution of symbolic expressions for JordanDecomposition correct?

Is it correct if I substitute letters A-Z for 25 expressions that are in a 5x5 matrix, run JordanDecomposition and then substitute expressions back? The process makes no progress after a day with ...
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1answer
63 views

Trouble evaluating this definite integral, either directly or with indefinite + limits

I have the function $$ \Sigma(x) = \frac{\sqrt{R^2-x^2}(\left| R\right| -1)}{\left(R^2-1\right) \left(x^2-1\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{R^2-x^2}}{\sqrt{R^2 \left(1-x^2\right)}}\right)-\...
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0answers
66 views

Very slow (days…) computation of JordanDecomposition of symbolic matrix

I am aware there may exist a similar topic, but I haven't found anything. Is there any way to speed up computation of JordanDecomposition for a symbolic 5x5 matrix with about symbolic variables? After ...
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1answer
54 views

Substitution of expressions in a symbolic expression

I define tables of symbolic variables in the following form (for convenience) ...
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1answer
50 views

Plotting symbolic functions

I want to plot the following Gaussian function Is there a way that I can do this symbolically without giving values to the constants.
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3answers
126 views

The symbolic result does not give a proper answer when inputs are specified

Define F by F[m_, k_, i_, j_] := (-1)^(m+k)/(m!*k!)*2^m*Binomial[m, i]*Binomial[k+1,j] I am trying to find this sum: ...
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1answer
46 views

Symbolically evaluating jump conditions of expressions across interfaces

I am dealing with a problem in electromagnetism involving problems in different regions, and there is something that I haven't been able to figure out yet. What I would like to be able to do is take ...
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0answers
36 views

Simplifying symbolic products of matrices

(This is probably a trivial question, but I could not find the answer in the documentation.) I would like to be able to use (functions similar to) Simplify, ...
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1answer
87 views

Symbolic solution of system of equations 12x12 takes very long time and the answer is complex too

I am trying to solve a system of equation symbolically. It works fine for 6x6, however for 12x12 system it takes very long and the answers are complex. I am using "Solve" or "Reduce&...
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2answers
91 views

Creating an Array with Subscripts and Superscripts

I would like to figure out how to construct an array using subscripts and superscripts based on the following info: ...
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0answers
82 views

Why does Mathematica give the wrong answer for this integral, and how can I correct it?

Mathematica is getting the following integral completely wrong: $Assumptions = a > 0; Integrate[1/k (E^-(k + a)^2 - E^-(k - a)^2), {k, 0, ∞}] (* I E^-a^2 π *) ...
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1answer
127 views

Bug in DSolve when solving a system of two second order PDEs?

I'm solving a simple system of PDEs in Mathematica 11.1: DSolve[{D[f[x, y], x, y] == 0, D[g[x, y], x, y] == 0}, {f[x, y], g[x, y]}, {x, y}] This gives: ...
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2answers
186 views

DSolve does not return solution to simple system of second order PDEs

I'm trying to solve a simple system of second order PDEs with Mathematica 11.1. Here is the system: ...
2
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1answer
62 views

Concatenation of Distributions

I would like to calculate mean, variance, ... of a concatenation of distributions (is this the correct technical term?). For an easy example I am trying to calculate the mean of a PoissonDistribution ...

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