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

learn more… | top users | synonyms

6
votes
2answers
235 views
+100

Symbolically prove that two expressions are identical

I encountered this problem when trying to reproduce the result of this paper. (The relevant parts are all included in the preview i.e. the 1st page of the article. This link is just given as ...
4
votes
0answers
175 views

Version 8.0 integrates but Version 9.0.1 doesn't

I am trying to run the following integral in version 9.0, but it fails: ...
0
votes
1answer
48 views

Can this expression be calculated symbolically?

I want to do definite integration of the following expression ...
0
votes
0answers
26 views

Expectation of summation with symbolic indices

I am working on symbolic computations with mathematica. I faced an issue with taking expectation of a large expression involving summations with symbolic indices. Is it possible to take expectation ...
3
votes
1answer
54 views

How to assume all variables in my code are reals

I won't have any occasion to have any imaginary number in my code. If there are any, that is an error. So allowing the imaginary case simply hinders the equation manipulation and simplification. I ...
2
votes
2answers
117 views

Symbolic linear algebra gradients/matrix calculus

Can Mathematica generate symbolic expressions for gradients? For example, if $x_1$ and $x_2$ are two points, could I get Mathematica to generate expressions similar to the following? $\frac{\partial ...
0
votes
0answers
46 views

NCAlgebra: define a scalar variable

I have a linear operator L and a scalar h, and would like to expand L[f + h phi] to ...
2
votes
1answer
94 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 ...
5
votes
1answer
134 views

Evaluating standard functions of general quaternions symbolically

Mathematica can easily compute exponentials and logarithms of concrete quaternions: ...
0
votes
0answers
59 views

Scalar from tensor contraction

I'm trying to calculate the Kretschmann scalar in mathematica, it is given by: $c = R^{abcd} R_{abcd}$ Where $R^{abcd}$ is the Riemann tensor. I'm following this MSE post so I modified it to ...
3
votes
1answer
82 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 ...
5
votes
2answers
92 views

Defining a symbolic inner product

So I have some rules for a symbolic inner product that work for quite a lot of cases: ...
0
votes
0answers
33 views

Mathematica can't simplify disguised expression [duplicate]

When I simplify the following quartic polynomial with a linear constraint; Simplify[x y z a + x y z b , a + b + c == 0] // Expand I get what to me seems like the ...
19
votes
2answers
470 views

Calculating probabilities symbolically

Is there a way to solve for statistical quantities analytically/symbolically in Mathematica? example 1: Lets say that I want to do a calculation that requires Bayes theorem. I know p(a), p(b) and p(...
2
votes
1answer
71 views

Symbolic vector addition

I'm trying to figure out a nice way to add a mix of symbolic and explicit vectors/matrices without mathematica treating the symbolic vectors as scalars and promoting them to constant arrays. For ...
-1
votes
1answer
65 views

How to correctly calculate symbolic eigenvectors

I give a minimalistic example of my problem: I have a matrix: m[a_,b_]:={{0,-a+b},{b,0}}; I define the eigenvectors as: ...
9
votes
1answer
162 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 ...
2
votes
0answers
40 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, ...
1
vote
2answers
231 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 : $\textrm{...
14
votes
3answers
284 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: ...
1
vote
1answer
79 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: ...
1
vote
4answers
97 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 ...
2
votes
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
votes
1answer
78 views

Unexpected behavior of FindGeneratingFunction

FindGeneratingFunction will give up to computer sometimes?Such as FindGeneratingFunction[{1, 4, 6, 4, 1}, x] But actually the ...
0
votes
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
votes
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
votes
0answers
44 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
votes
1answer
469 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
votes
0answers
68 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
votes
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
votes
1answer
50 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
votes
4answers
96 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
vote
0answers
53 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
votes
2answers
70 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
votes
2answers
60 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
votes
1answer
75 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
136 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
votes
1answer
58 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
votes
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
votes
2answers
216 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
votes
1answer
127 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
votes
2answers
611 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
68 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
votes
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
votes
2answers
123 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) = f(x+\sqrt{t})...
0
votes
2answers
88 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
107 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
votes
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, ...