Questions tagged [symbolic]

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

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42 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 ...
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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 ...
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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($\theta,\phi$) ...
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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. ...
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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
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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, ...
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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 ...
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1answer
56 views
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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] &...
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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
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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
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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
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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 ...
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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: $a_n = f_a(c_{n-1}, x_{n-1})$ $...
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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. ...
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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
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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 ...
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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 ...
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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
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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
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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
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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 ...
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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
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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
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1answer
100 views

How to set up a Fourier transform?

I am having trouble figuring out how to set up the Fourier transform to: ...
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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 ...
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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
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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
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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
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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
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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
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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 - ...
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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 ...
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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
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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
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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 ...
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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
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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
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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
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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
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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{\...
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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 ...
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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, ...
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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 ...
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1answer
43 views

Generating examples by applying conditions to symbolic expressions

For example, Given a list of symbolic expressions: ...
7
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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
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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
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4answers
147 views

Find maximum according to a parameter

I am new to Mathematica. I want to find the maximum of the functions: ...
2
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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
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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: <...