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

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3
votes
1answer
64 views

Issue with symbolic summation [duplicate]

Here is the sum: $$\sum_{j=0}^{n-1}r^{a+b}\cos^a\left(\frac{2\pi j}{n}+t\right)\sin^b\left(\frac{2\pi j}{n}+t\right)$$ Code: ...
3
votes
1answer
84 views

Need help understanding the output of `DSolve`

I give Mathematica 10 the following command: DSolve[I D[P[x], {x, 2}] f[x] - (P'[x])^2 f[x] + 2 I P'[x] f'[x] == 0, P, x] and I have the following output: ...
0
votes
1answer
67 views

Can this expression be calculated symbolically?

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

Opportunity for ordering mathematics through symbols

Hilbert came up with the idea of grounding all of mathematics in an a priori synthetic knowledge of symbols. Mathematica also pegs all mathematical operations down under a single roof aided by ...
-1
votes
0answers
56 views

Creating a Symbolic Singular Matrix

I am trying to differentiate an expression involving a matrix. When evaluating the input, Mathematica assumes the matrix is invertible, when it is not. How do I specify a symbolic singular matrix to ...
1
vote
1answer
46 views

How to symbolically solve the minimization problem in simple linear regression

I want to use mathematica to symbolically solve the minimization problem in simple linear regression: $${\text{Find }}\text{arg}\min _{\alpha ,\,\beta }Q(\alpha ,\beta ),\qquad {\text{for }}Q(\alpha ,...
3
votes
1answer
90 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 ...
24
votes
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. ...
3
votes
3answers
132 views

Symbolic integration conditional bug?

I just ran across this: Assuming[x > 0, Integrate[1/t^2, {t, 1, x}]] gives the output ...
0
votes
0answers
49 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 ...
9
votes
2answers
290 views

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
180 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: ...
3
votes
1answer
62 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
121 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
48 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
95 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
63 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 ...
5
votes
2answers
97 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
487 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
68 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
165 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
236 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
80 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
105 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
75 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
46 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
480 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
5answers
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
55 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
72 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
62 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
78 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
141 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
59 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
39 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
138 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 ...