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

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58
votes
5answers
2k views

Advice for Mathematica as Mathematician's Aid

I use Mathematica mainly as an aid in symbolic attacks on problems, usually intermediate or harder and often number theoretic. While Reduce, ...
40
votes
2answers
747 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, ...
34
votes
3answers
2k views

Symbolic solution(s) to generalized Heat equation

Symbolic solution(s) to Heat equation? or more generally,(eventually) Green functions to known PDEs I am interested in variations of the heat equation: or more generally or even more generally ...
33
votes
1answer
736 views

How to augment the realm of functions Mathematica thinks it knows how to integrate symbolically

My question involves extending the functionality of Integrate over specific integrals in the most generic manner. Specifically, is it possible to "hack into" ...
33
votes
3answers
605 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 ...
30
votes
3answers
8k views

Can Mathematica do symbolic linear algebra?

For instance, is there some way I can say "let A and B be arbitrary real $m\times n$ and $k\times m$ matrices, Simplify[Transpose[Transpose[A].Transpose[B]]]" and ...
29
votes
1answer
779 views

Proving the hairy ball theorem using xAct

I would like to formally prove the hairy ball theorem in Mathematica, initially just for $S^2$, and then see about generalizing. An approach I thought about to use the xAct package to define $S^2$ ...
28
votes
4answers
2k views

What is a type in Wolfram Mathematica programming language?

"Everything is an expression" is a popular citation from many Mathematica guidebooks. So, what is type in Mathematica? How does it relate to common types from Haskell, for example? I did some ...
26
votes
3answers
873 views

Symbolic integration error

fixed in 10.1 (windows) I'm running Mathematica 10.0.0 and encountered a disturbing error in the symbolic integration of a rather simple function ...
24
votes
3answers
3k views

How to symbolically do matrix “Block Inversion”?

Consider a block (partitioned) matrix matrix = ArrayFlatten[{{a, b}, {c, d}}] where, a, ...
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. ...
22
votes
1answer
579 views

Transform Root objects into Trigonometric expressions

Consider the Root objects roots = Table[Root[-1 + 27 #1^2 - 162 #1^4 + 243 #1^6 &, i],{i,1,6}] These can be expressed in terms trigonometric functions as ...
21
votes
4answers
440 views

Negative probability?

Bug introduced in 9.0.1 and fixed in 10.0.2 I am trying to get the sum of the squares of seven random variables, all uniformly distributed. This is what I tried. ...
21
votes
2answers
322 views

Backslide of Limit

A friend of mine showed me this example: Limit[Sum[Sin[Pi*k/n]/(n + 1/k), {k, 1, n}], n -> Infinity] This sample calculates well in v8.0.4: but not in ...
20
votes
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 ...
20
votes
4answers
2k views

How to calculate the volume of a convex hull?

Given a spatial curve represented by a parametric equation, is it possible in Mathematica 9 to calculate symbolically (or at least numerically) the volume of its convex hull?
20
votes
1answer
633 views

Incorrect result from Integrate

Bug introduced in 8.0 and fixed in 10.0 I attempted to calculate the following integral: ...
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, ...
19
votes
2answers
318 views

Derivative of a pure function with SlotSequence

I can live with this but I can't figure out why the following is 0: Derivative[1][f[##] &][x] 0 From documentation ...
19
votes
2answers
359 views

What does f_[whoCalled]^:=f really mean?

I came across the following post by John Doty in this Google Groups discussion: On Friday, January 11, 2013 8:23:16 PM UTC-7, amzoti wrote: It is clear the Mathematica uses Lisp as one ...
17
votes
6answers
6k views

Replacing composite variables by a single variable

To replace a single variable by another variable, one can simply use the the replace all (/.) operator (e.g., ...
17
votes
3answers
2k views

Is learning to use Mathematica useful for pure theoretical research in Mathematics and Computer Science?

I am looking for opinions from Mathematica users about Mathematica itself. After reading the faq, I thought that in some sense I "wish to solve a problem using Mathematica" ... although I understand ...
16
votes
2answers
1k views

Why do certain values in ArcSin not fully evaluate?

This is a continuation of: Why do certain fractional values in TriangleWave not evaluate? The analysis by R.M and rasher revealed that problem to reduce to the behavior of: ...
16
votes
1answer
566 views

How to represent a continuous monotonic phase of Airy functions?

Note: In this question I am concerned only with real-valued variables and functions. DLMF, §9.8 Airy Functions, Modulus and Phase, formula $9.8.4$ defines the phase of Airy functions: ...
16
votes
1answer
516 views

Speeding up trigonometric integral

Context On a possible non trivial toric topology for the Universe (nothing less!). Problem I would like to carry out the following integral for $\ell=2,4\cdots 20$. $$\int _0^{\pi }\int _0^{2 \pi ...
16
votes
1answer
452 views

What does “suitable for symbolic manipulation” in the documentation mean?

This question is related to this other one I posted on Stack Overflow some time ago. There, in a beautiful answer, acl (with some unhumble editing done by me) showed that the derivative of ...
15
votes
6answers
790 views

How can I evaluate only a single step of a recursive function?

Let's say have a simple recursive function for the Fibonacci sequence f[0] := 1 f[1] := 1 f[n_] := f[n - 1] + f[n - 2] but I want to see how it will expand in a ...
15
votes
3answers
554 views

Solve a trig equation system

Background of the problem In the same plane, P is a fixed point, A,B,C are moving point, PA=a, PB=b, PC=c, find the maximize perimeter of △ABC. let ∠BPC=A, ∠CPA=B, ∠APB=2*Pi-A-B, then the ...
15
votes
1answer
2k views

How does Mathematica integrate?

Basically, this question can be considered to be an extenstion to my other question. What I wanted to do was this integral as homework (it is indefinite BTW so no approximations using Simpson's Rule ...
15
votes
1answer
424 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 ...
15
votes
1answer
368 views

Polynomial expectations of generic distributions

Summary Polynomial expectations depend only moments and cross moments of a multivariate distribution. I would like to use Expectation to compute polynomial ...
14
votes
2answers
446 views

Symbolic area calculation for a parametric self-intersecting closed curve

The parametric equation of the curve is: $$\begin{cases} x &= -9 \sin (2 t)-5 \sin (3 t) \\[6pt] y & = 9 \cos (2 t)-5 \cos (3 t) \end{cases}\quad t\in[0,2\pi]$$ which can be easily ...
14
votes
1answer
12k views

Extract real part of a complex expression better than Re does

I have a complex expression with real positive variables only. Mathematica Input Style: ...
14
votes
1answer
650 views

Incorrect results for elementary integrals when using Integrate

There is a rather simple integral ($K_0$ is the 0-th order MacDonald function) $$\int_0^\infty e^{-x \cosh\xi}\, d\xi = K_0(x)$$ which mathematica cannot solve. This even though the documentation ...
14
votes
3answers
278 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: ...
13
votes
5answers
821 views

Does $x>0$ imply that $x\in\mathbb{R}$?

Let’s assume I input Assuming[x > 0, expression] Is it assumed by Mathematica that $x$ is a real number? Or that the real part of $x$ is positive? Something ...
13
votes
2answers
345 views

How to do algebra on summations of variable expressions?

Is there any easy, general way to handle algebra on variable Sums? For examples, Gaussian Mixtures or Fourier Series: ...
13
votes
5answers
253 views

Prevent Plus from threading

This is probably a very simple question, but I couldn't find a duplicate. As everybody knows, {x, y} + v gives {x + v, y + v}. ...
13
votes
1answer
610 views

Does anyone have experience with performing symbolic regression using Mathematica?

I understand that there is at least one Mathematica package, DataModeler commercially available for symbolic regression. I'm seeking any observations with this or any other similar tool. I'm ...
13
votes
1answer
407 views

What is the confidence limit on this convergence?

Bug introduced in 7.0 and fixed in 10.0.0 When I run this, Product[n^MoebiusMu[n],{n,1,Infinity}] I get $\frac{1}{4 \pi^{2}}$ Over on Math Overflow ...
12
votes
2answers
648 views

Surprises simplifying simple polynomials

I came across some somewhat surprising behavior of Simplify today, on something very simple. Let's take two cubic polynomials that we know have the same value: ...
12
votes
1answer
262 views

Symbolic computations with already assigned variables

For example I have assigned some variables that could defined in terms of each other. Then I for some reason need to derive some formula using this variables. How to show the result of this ...
12
votes
2answers
420 views

Why Mathematica cannot apply The Fundamental Theorem of Calculus automatically?

For some reason Mathematica cannot evaluate this definite integral: ...
11
votes
4answers
2k views

Extracting variables from an expression

I'm looking for a way to extract a list of variables from an expression, for example with an input like: ...
11
votes
5answers
2k views

How to get exact roots of this polynomial?

The equation $$ 64x^7 -112x^5 -8x^4 +56x^3 +8x^2 -7x - 1 = 0 $$ has seven solutions $x = 1$, $x = -\dfrac{1}{2}$ and $x = \cos \dfrac{2n\pi}{11}$, where $n$ runs from $1$ to $5$. With ...
11
votes
2answers
1k views

Non-commutative symbolic linear algebra

I am fairly new to Mathematica but I thought I would be a helpful tool to carry out a few simple linear algebra calculations. It seems like an easy task but I cannot figure out how to do it. For ...
11
votes
1answer
350 views

Why does Assuming[x > 0, TrueQ[x > 0]] return False?

Assuming[x>0,TrueQ[x>0]] should, as I understand it, test TrueQ[x>0] after assuming ...
11
votes
2answers
288 views

How to implement symbolic Ramanujan's summation in Mathematica?

How to implement Ramanujan's summation in symbolic form in Mathematica? For instance, I want as input the function $f(x)=x$, as output $-1/12$, as input $f(x)=1/x$, as output $\gamma$ (Euler's ...
11
votes
1answer
978 views

Managing Exclusions in Plot[ ]

When I do: ...
11
votes
1answer
408 views

How can I eliminate a function in a system of PDEs, Maple-style?

Maple can separate and eliminate a function in a system of PDE equations, with casesplit in the PDEtools package. How to do ...