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

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0answers
24 views

How do I prevent Root and RootSum from expanding over quadratic roots?

For quadratics, RootSum[a #^2 + b # + c &, Cos[#] &] Immediately turns into and also, ...
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0answers
35 views

Rotation of basis system [on hold]

I have a 16x16 matrix HCF hamiltonian with symbolic entries depending on 8 parameters Bxx. Now I add anoter hamiltonian which is a zeeman hamiltonian HZ with a symbolic angle [\theta] entry .But if i ...
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0answers
32 views

Parallelization or other speed-up of the algebraic evaluation of Eigensystem

I am calculating the eigen system of a 16 x 16 matrix HCF[B02, B04 …] of 8 variables in it. The matrix is Hermitian and has many 0 elements and only a few ...
5
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0answers
94 views

Wrong limit: Limit[(1 + (-1)^n/n)^n, n -> Infinity]=1 (Mathematica 10.4 and W-Alpha)

Since $(1-\frac{1}{n})^n\to 1/e$ and $(1+1/n)^n\to e$, the sequence $(1+\frac{(-1)^n}{n})^n$ has no limit as $n\to\infty$, but has limits for odds and even numbers. If $n$ were taken to be real, there ...
0
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1answer
61 views

How to do symbolic logic in Mathematica

I'm currently in Symbolic Logic with homework assignments (not asking for people to do my homework for me) with questions such as the following: (derive the conclusion using the eighteen rules of ...
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2answers
224 views

How to compute this integral?

I'm trying to calculate this integral : $$I(z,k,a)= \displaystyle\int_{1}^{\infty} t^2\, \text{ArcTanh} \left(\sqrt{\frac{t^2-1}{t^2}} \dfrac{k}{z}\right)\, e^{-a\,t} \, dt$$ Where : ...
14
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3answers
277 views

Symbolic sum of Stirling numbers gives wrong answer

Bug introduced in 9.0.1 or earlier and fixed in 10.4.1 This issue originated from my attempt to answer a question on MathOverflow: ...
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1answer
76 views

Remove part within square brackets for function

So I've defined a variable as follows: q = {{x[t]}, {Φ[t]}} V=0.5*x[t]^2*m^2+0.5*Φ[t]^2*I I've had to differentiate with respect to time so: ...
3
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1answer
75 views

Factor a polynomial Root into Roots of smallest possible degree

Suppose I have a polynomial Root representing an algebraic number. I want to represent it (if possible) as a product of several polynomial ...
1
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4answers
90 views

Symbolic calculation on roots of polynomial

Given a polynomial like $x^3 + a_2 x^2 + a_1 x + a_0$ with roots $r_i$, I would like to symbolically compute the coefficients of a polynomial whose roots are $r_i^3 + r_i + 1$. How can I do this in ...
5
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1answer
113 views

Evaluating standard functions of general quaternions symbolically

Mathematica can easily compute exponentials and logarithms of concrete quaternions: ...
2
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0answers
44 views

Unexpected imaginary term in the asymptotic expansion of DawsonF

FullSimplify[Series[2 DawsonF[x], {x, ∞, 8}]] (* -I Exp[-x^2] √π + (1/x + 1/(2 x^3) + 3/(4 x^5) + 15/(8 x^7) + O[1/x]^9) *) What is the reason the term ...
2
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1answer
76 views

Unexpected behavior of FindGeneratingFunction

FindGeneratingFunction will give up to computer sometimes?Such as FindGeneratingFunction[{1, 4, 6, 4, 1}, x] But actually the ...
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0answers
26 views

Ordering of Eigensystem in symbolic computations [duplicate]

Suppose I have a symbolic 4x4 matrix for which I am finding the Eigenvectors and Eigenvalues. My question is whether Mathematica ...
3
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0answers
74 views

What is the good source to study advanced custom coding in Mathematica [duplicate]

My question is, probably, too general ... I deal a lot with complicated symbolic evaluations, integrations, plotting. I have troubles with optimizing my codes. They come out way too slow. Google and ...
2
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0answers
41 views

Replacement rule for summation with Kronecker delta

I want to perform some symbolic computations in index notation, without explicit reference to sums, so that in expressions of the type f[i,j]g[j,k] summation over ...
10
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1answer
452 views

Compute inverse Laplace transform with Integrate

Since inverse Laplace transform is just an integral, while we already have InverseLaplaceTransform built in, can we compute it with ...
2
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0answers
67 views

Unexpected behavior from applying ToRadicals to eigenvalues [closed]

I am trying to get the symbolic form of a $10 \times 10$ matrix (I know, that is generally too large). ...
9
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6answers
2k views

Superscript prime symbol

x\[Prime] looks like $x_{'}$, ugly right? Is there a way to make a symbol with prime to look like $x'$? That's what I'm trying right now: ...
0
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1answer
47 views

Symbolic Maximization: does not work with symbolic power?

Simple question from a beginner: I seem to be unable to do maximization if the variable has a power specified symbolically instead of numerically? ...
5
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4answers
93 views

Multi-index variable depending on signature of permutation of indices

I do have some multi-indexed variable, e.g. like this \begin{align*}f_{123} &= 1\\f_{345} &= 1/2\end{align*} where $f$ is antisymmetric under permutation of any pair of indices, i.e. e.g. ...
1
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0answers
50 views

Can Mathematica solve Kuhn-Tucker Equations with arbitrary functional form (up to 2nd order derivative)

I am in a business of solving a 5-variables optimization with inequality constraints, and I would like to maintain the functional form as arbitrary as possible. So far, I am assuming that the ...
2
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2answers
65 views

Symbolic calculation of the rank of jacobian matrix

I would like to symbolically determine the rank of a jacobian matrix. In the help, I have seen that the MatrixRank function can be used for this purpose. However, when I use this function, the ...
2
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2answers
54 views

Why does ExpandAll not work within a symbolic sum?

If I evaluate Sum[(x + Subscript[y, n])^2, n] + (y + z)^2 // ExpandAll then the expression within the Sum is not expanded, yet ...
0
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1answer
72 views

How to transfer symbolic expression to code? [closed]

I have a lot of messy things in Mathematica in a form like this: Mathematica perfectly solves all these symbolic equations. But I'm in trouble when using Excel link with Mathematica. I really need ...
5
votes
1answer
131 views

Define an operator with the distributive property

I would like to define the operator with distributive, associative, and commutative properties - so that Mathematica can symbolically simplify expressions I use ...
2
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1answer
57 views

Rewriting terms as perfect derivative

I am trying to find conservation laws of a system, and I'd like to rewrite terms of the form $$A\frac{dA^*}{dt}+A^*\frac{dA}{dt}$$ as $$\frac{d}{dt}|A|^2,$$ where $A$ is a complex valued function ...
0
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1answer
38 views

Expansion on sums of NonCommutativeMultiply

Following the MMa's documentations, the ExpandNCM[] function expands a**(b+c) without efforts (although I don't have very good ...
4
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2answers
205 views

General solution for a linear ODE set with complicated coefficient

This is the original problem that motivated me to ask this question. I encountered it when trying to reproduce the deduction in this paper. (I'll paste the relevant part below to make this question ...
6
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1answer
121 views

Issue in Det[…] when computing determinants of polynomials?

When I form a matrix of at least size $12 \times 12$ of second order polynomials in $w$ and I calculate the determinant of that, I get something that is a rational expression in $w$. Since the ...
33
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3answers
604 views

$\sum_{k=1}^{\infty }\left\lfloor\frac{5}{5^k}\right\rfloor$ giving wrong answer?

Bug introduced in 7.0 or earlier and persisting through 10.4 or later When I try to evaluate the following: $$\sum_{k=1}^{\infty }\Bigg\lfloor\frac{5}{5^k}\Bigg\rfloor$$ using ...
3
votes
2answers
67 views

Creating Boolean expressions over a set of indexed variables

I've read lots of examples here on how to set one matrix Equal to another, but how do you nest And and ...
2
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2answers
72 views

Permuting symbols

Suppose I have a list like {a, b, a, c}. How can I apply a "symbolic permutation" of the symbols a, ...
3
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2answers
122 views

Computing powers of the operator using symbolic computation

Suppose $t\in\mathbb{R_+}$ - some parameter, $V: \mathbb{R}\to\mathbb{R}$ - some function. I have an operator $S:f\mapsto S[f]$ that maps a function $f$ to a function $S[f]$: $$ S[f](x) = ...
0
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2answers
87 views

Expression of an integral

I am doing the following integral in Mathematica with $a>0$: $$\iint e^{-\frac{(x_{1}+x_{2}-2b)^2}{4a}}dx_{1}dx_{2}$$ My code is ...
1
vote
1answer
98 views

New data type, interval, and overloading operators (+,-,*,/) [duplicate]

How can I create a new data type, interval, with different behavior than the built-in one. I want to write [a, b] and perform operator overloading, as in C ++? (I ...
19
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3answers
2k views

How to deal with complicated Gaussian integrals in Mathematica?

As we know, for most Gaussian integrals, we can get the analytical result. Now I have many Gaussian integrals to treat, which have the following general form, ...
24
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1answer
1k views

Analogue for Maple's dchange - change of variables in differential expressions

Maple owns an interesting function called dchange which can change the variables of differential equations, but there seems to be no such function in Mathematica. ...
40
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2answers
746 views

Why does Mathematica report that $\int_1^\infty\frac{\sin(\sqrt{x})}{\sqrt{x}}dx$ = $2\cos(1)$?

Bug introduced in 7.0 or earlier and persisting through 10.4 or later Mathematica 10 gives the following very odd result, ...
2
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0answers
32 views

Polynomial kernel expansion

I am trying to calculate the polynomial kernel expansion using Mathematica. I have tried the Expand and Simplify functions with ...
5
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2answers
122 views

Problem summing an infinite series

Calculating this sum on Mathematica 10.3 Sum[(-1)^(r - 1)/((a^2 + r^2)r), {r, 1, Infinity}] gives the answer ...
1
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1answer
95 views

How can I get symbolic orthonormal eigenvectors for 3 by 3 hermitian matrix?

Using the following syntax, I can obtain the symbolic eigenvalues and eigenvectors of the following Hermitian matrix (a,b,c,d are all real parameters): ...
3
votes
2answers
82 views

Problem with Custom Sort/Split/Gather

Please help me Sort/Split/Gather/Group(by) a set of symbolic expressions! (extreme TL;DR at bottom) I have a set of symbols (which represent 2-vectors in a plane, ultimately) and I want to ...
8
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1answer
129 views

What should I learn from DSolve working better with a named constant than a number in this case?

I have an equation $$\bigl(r''(\phi)r(\phi) - r'(\phi)^2\bigr)\bigl(b + r(\phi)\bigr) = r(\phi)\bigl(r'(\phi)^2 + r(\phi)^2\bigr)$$ Here $b$ and $r$ are lengths, and $\phi$ is an angle (in radians, so ...
2
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0answers
45 views

Mathematica for dynamics and controls [closed]

I am new to Mathematica and want it to use for dynamic and control systems. To begin with, I would want to be limited to symbolic computation for linear and nonlinear control systems - including ...
1
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2answers
89 views

Closed form solution equations involving finite sums

I am a beginner in Mathematica, so take this into account. I could not find anything similar in the internet so far. I am trying to find a closed form solution for ...
20
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2answers
4k views

How do I work with Root objects?

I want to solve the trigonometric equation : $$(3-\cos 4x )\cdot (\sin x - \cos x ) = 2.$$ I tried Solve[(3 - Cos[4*x])*(Sin[x] - Cos[x]) == 2, x] It returns the ...
2
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0answers
56 views