Questions tagged [symbolic]
For questions about symbolic computation, as opposed to numerical computations.
1,205
questions
81
votes
6answers
5k 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, ...
63
votes
4answers
17k 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 ...
53
votes
1answer
5k 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.
...
44
votes
4answers
14k 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 ...
44
votes
3answers
4k 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 (<...
42
votes
2answers
1k 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 fixed in 11.0
Mathematica 10 gives the following very odd result,
Integrate[Sin[Sqrt[x]]/Sqrt[x], {x, 1, ∞}]
(* 2 Cos[1] *)
...
40
votes
4answers
1k views
Some indefinite integrals evaluate in 11.2 but not in 11.3 - what can be done?
Bug introduced in 11.3 and fixed in 12.0.0
Reported to Wolfram: [CASE:4032137]
These integrals evaluate in version 11.2 on windows but
when I tried them under version 11.3 they returned unevaluated.,...
40
votes
1answer
2k views
How can I define a new symbolic constant like Pi?
There are a few builtin symbolic constants which behave like numbers, e.g. E, Pi, EulerGamma,...
37
votes
2answers
858 views
$\sum_{k=1}^{\infty }\left\lfloor\frac{5}{5^k}\right\rfloor$ giving wrong answer?
Bug introduced in 7.0 or earlier and fixed in 11.0.1
When I try to evaluate the following:
$$\sum_{k=1}^{\infty }\Bigg\lfloor\frac{5}{5^k}\Bigg\rfloor$$
using
...
37
votes
1answer
907 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" ...
35
votes
4answers
3k 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 ...
33
votes
1answer
31k 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:
...
33
votes
1answer
1k 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 $S^2$
...
30
votes
3answers
5k views
How to symbolically do matrix “Block Inversion”?
Consider a block (partitioned) matrix
matrix = ArrayFlatten[{{a, b}, {c, d}}]
where, a, b,...
28
votes
6answers
15k 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., ...
28
votes
3answers
4k 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,
...
28
votes
3answers
2k 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
...
26
votes
1answer
874 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 ...
25
votes
5answers
5k 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:
...
24
votes
3answers
514 views
Backslide of Limit
Backslide introduced in 9.0, and persisting through 12.0.
A friend of mine showed me this example:
Limit[Sum[Sin[Pi*k/n]/(n + 1/k), {k, 1, n}], n -> Infinity]
...
22
votes
5answers
5k views
Why this real integral yields imaginary results?
This integral yields -1-4Iπ/3 in Mathematica:
Integrate[(y - y^2 + x - x^2 + 2*x*y)/(1 - x - y), {x,0,1}, {y, 0, 1}]
Since ...
22
votes
2answers
666 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 for ...
21
votes
4answers
3k 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?
21
votes
3answers
2k views
Wrong answer from DSolve when solving a differential equation
Bug introduced in 12.0.0, fixed in 12.1.1.
I was trying to solve the following differential equation: $$\frac{dy}{dx}=x^2+y^2-1 \quad \text{and} \quad y(0)=1$$
and I used the code below:
...
21
votes
4answers
487 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
541 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 ...
21
votes
2answers
2k 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(...
20
votes
1answer
1k views
Incorrect result from Integrate
Bug introduced in 8.0 and fixed in 10.0
I attempted to calculate the following integral:
...
20
votes
1answer
559 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 ...
20
votes
1answer
337 views
Mathematica v12 Integration bug?
Bug introduced in 12.0 and fixed in 12.1
After upgrading to mathematica 12, this integral gives the wrong result, also with other types of similar integrals.
...
19
votes
2answers
1k 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 ...
19
votes
1answer
5k 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 ...
18
votes
6answers
2k 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 ...
18
votes
3answers
5k 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 ...
18
votes
6answers
390 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}. ...
18
votes
3answers
365 views
Coordinate-free derivative
Given the function
\begin{align*}
f \colon \mathbb{R}^n &\to \mathbb{R}^n\\
v&\mapsto \dfrac{v}{\|v\|},
\end{align*}
I would like to compute the derivative of $f$, that is $df(v)$. It is ...
18
votes
1answer
972 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:
$$\theta(x)=\...
18
votes
1answer
709 views
Speeding up trigonometric integral
Context
On a possible non trivial toric topology for the Universe (nothing less!).
Problem
I would like to carry out the following integral for $\ell=2,4\cdots 20$.
$$\int _0^{\pi }\int _0^{2 \pi }...
17
votes
2answers
1k 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:
...
17
votes
2answers
2k 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:
...
17
votes
1answer
10k 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 ...
17
votes
1answer
634 views
Mathematica incorrectly giving zero for partial derivative
Bug introduced in 9.0 and fixed in 11.1
Mathematica is incorrectly reporting that the partial derivative of a certain expression is zero.
I try to compute the following:
...
16
votes
7answers
665 views
Missing solution - system of equations
Attention! This example already works as expected in Wolfram Mathematica 12.1.1.0 for function Solve.
The problem was in version 12.1.0.0. Check out answer of Bob ...
16
votes
3answers
1k 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 perimeter ...
16
votes
2answers
825 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 ...
16
votes
1answer
6k views
Non-commutative algebra
I'm constantly dealing with non-commutative algebras. ** is inbuilt, non-commutative and associative. That's good :-) But it is not distributive. Rats.
...
16
votes
3answers
1k 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 ...
16
votes
1answer
488 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 ...
15
votes
5answers
1k 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 ...
15
votes
5answers
3k 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 ...
