For questions about symbolic computation, as opposed to numerical computations.
22
votes
1answer
406 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" ...
20
votes
3answers
1k 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 ...
18
votes
3answers
822 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 ...
16
votes
3answers
1k views
How to symbolically do matrix “Block Inversion”?
Consider a block (partitioned) matrix
matrix = ArrayFlatten[{{a, b}, {c, d}}]
where, a, ...
16
votes
1answer
275 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
1answer
289 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 $\ell=2,4\cdots 20$.
$$\int _0^{\pi }\int _0^{2 \pi ...
15
votes
1answer
194 views
Polynomial expectations of generic distributions
Summary
Polynomial expectations depend only moments and cross moments of a multivariate distribution. I would like to use Expectation to compute polynomial ...
13
votes
5answers
626 views
Does $x>0$ imply that $x\in\mathbb{R}$?
Let’s assume I input
Assuming[x > 0, expression]
Is it assumed by Mathematica that $x$ is a real number? Or that the real part of $x$ is positive? Something ...
12
votes
1answer
171 views
Symbolic computations with already assigned variables
For example I have assigned some variables that could defined in terms of each other. Then I for some reason need to derive some formula using this variables. How to show the result of this ...
11
votes
3answers
540 views
Is learning to use Mathematica useful for pure theoretical research in Mathematics and Computer Science?
I am looking for opinions from Mathematica users about Mathematica itself. After reading the faq, I thought that in some sense I "wish to solve a problem using Mathematica" ... although I understand ...
11
votes
2answers
372 views
Surprises simplifying simple polynomials
I came across some somewhat surprising behavior of Simplify today, on something very simple. Let's take two cubic polynomials that we know have the same value:
...
11
votes
1answer
436 views
Incorrect results for elementary integrals when using Integrate
There is a rather simple integral ($K_0$ is the 0-th order MacDonald function)
$$\int_0^\infty e^{-x \cosh\xi}\, d\xi = K_0(x)$$
which mathematica cannot solve. This even though the documentation ...
11
votes
1answer
666 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 ...
10
votes
6answers
911 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., ...
10
votes
2answers
557 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 ...
10
votes
1answer
168 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 ...
10
votes
1answer
631 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,
...
9
votes
2answers
203 views
Find closed form expression for series expansion coefficients [duplicate]
Is there a built-in function that will find a general expression for the coefficient of the series expansion of a function?
Series will only give the explicit ...
9
votes
1answer
257 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 ...
8
votes
2answers
139 views
Representing a value in an output as a self defined variable
I'm trying to find a way to have Mathematica always represent a numerical value as a self defined variable that I define using lhs=rhs. For example, if I execute
...
8
votes
1answer
158 views
Verifying and deriving basic (block) matrix identities
How can I use the new symbolic matrix/tensor capabilities to verify matrix identities, such as
(1)
or
(2)
Even better, how can I ask Mathematica to derive expressions for X, Y, Z, and U like ...
8
votes
2answers
660 views
7
votes
2answers
383 views
Why aren't these additions of integrals and summations equal?
I have the following code:
Simplify[Integrate[f[x] + g[x], x] == Integrate[f[x], x] + Integrate[g[x], x]]
To test:
$$\int{\left(f(x) + ...
7
votes
2answers
101 views
How to simplify an expression with special functions to zero
The following is a well-known Bessel function identity:
$$J_{-n}(z)=(-1)^n J_n(z),\qquad n\in\mathbb Z$$
To check this, I used the following code and the result is as what I expected.
...
7
votes
1answer
2k 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:
...
7
votes
1answer
244 views
What is the confidence limit on this convergence?
When I run this,
Product[n^MoebiusMu[n],{n,1,Infinity}]
I get $\frac{1}{4 \pi^{2}}$
Over on Math Overflow they are saying it shouldn't happen. So, how do ...
7
votes
1answer
237 views
Symbolic Integration along contour: branch cut problem?
Context
Following this question on path integrals in the complex plane, having defined again a numerical and symbolic integrator along a path as
...
7
votes
1answer
270 views
6
votes
3answers
467 views
Using D to find a symbolic derivative
I need to do the following:
Define a function
Take the derivative of this function and have a look at the symoblic representation
Substitute in some values
With the bonus that I want to use the ...
6
votes
3answers
852 views
How to solve an overdetermined system in Mathematica
I would like to understand the reasons and find a way to avoid such behaviour of the Solve function in Mathematica 8.
...
6
votes
2answers
304 views
Symbolic manipulation with unevaluated sums
If I have two expressions with sums in them, like this:
$$\begin{align*}
b&=\frac{\sum_{i} (x_i - \bar{x})(y_i -\bar{y})}{\sum_{i}(x_i -\bar{x})^2}\\
r&=\frac{\sum_{i} (x_i - \bar{x})(y_i ...
6
votes
1answer
141 views
Sophistication of Series[…]
I'll give a concrete example and I hope that my general question will be clear.
Say I have three variables, $f$, $g$, $h$, and I know that $f=\mathcal O(x)$, $g=\mathcal O(x^2)$, $h=\mathcal O(x^3)$ ...
6
votes
1answer
87 views
Telling mathematica to output * instead of space for multiplication, so I can copy as plain text
I am trying to get some symbolic expressions in Mathematica
which I would like to paste into my C/MATLAB codes. This can be accomplished
nicely by selecting the expression and right-clicking to ...
6
votes
1answer
492 views
Why does this sum not simplify properly?
I was trying to get Mathematica to simplify some moderately ugly sums and I ran into some pretty weird behaviour, which I tracked down to the following example. I'm working with ...
6
votes
0answers
109 views
Symbolic integration in real domain only ( assumptions and ComplexExpand don't work)
Integrate[m^2/((x - m^2)^2 + y^2), m]
mathematica gives me a complex-valued reuslt, but maple 17 gives me what I want.
I tried using assumptions, but it doesn't ...
5
votes
4answers
518 views
How to find the sum all even numbers of this sequence?
I have a sequence $(u_{n})$
$$u_1= 1, \quad u_2 = 2, \quad u_3 = 3, \quad u_{n}= -u_{n-3} + 3u _{n-2} +2 u_{n-1}, \quad \forall n \geqslant 4.$$
I want to list the first $20$ terms of this sequence ...
5
votes
1answer
213 views
Validating simplifications analytically
I have a rather complex expression which I would like to simplify and check my work along the way (Mathematica does not simplify very basic things and it is frustrating me). In the following example, ...
5
votes
4answers
529 views
How to get exact roots of this polynomial?
The equation $$ 64x^7 -112x^5 -8x^4 +56x^3 +8x^2 -7x - 1 = 0 $$
has seven solutions $x = 1$, $x = -\dfrac{1}{2}$ and $x = \cos \dfrac{2n\pi}{11}$, where $n$ runs from $1$ to $5$. With ...
5
votes
1answer
491 views
Complex number operations: telling Mathematica variables are real
I want to do Conjugate[a + b*I], but when I do that, the solution is
Conjugate[a] - I*Conjugate[b]; when for me, a and b are ...
5
votes
4answers
178 views
How do I obtain the correct double limit?
The command
Limit[(Sin[x^2] + Sin[y^2])/ (x - y) /. x -> 0, y -> 0]
(*
0
*)
I think that Mathematica finds the iterated limit instead of the double ...
5
votes
1answer
137 views
Finding ranges of a parameter for which a function is always positive
I have a complex function of a single variable expressed in analytical form, which also depends on a parameter. I would like to have Mathematica show me for which values of the parameter the real part ...
5
votes
1answer
74 views
How do I expand StirlingS2[n, 10] in terms of elementary functions?
I know that it is possible to expand StirlingS2[n, 10] in terms of elementary functions of n. I tried ...
5
votes
4answers
196 views
Prevent Part[] from trying to extract parts of symbolic expressions
If you have a list, e.g.
{1, 2, 3}
then you can extract the $k$th part using Part (...
4
votes
2answers
626 views
How do I work with Root objects?
I want to solve the trigonometric equation :
$$(3-\cos 4x )\cdot (\sin x - \cos x ) = 2.$$
I tried
Solve[(3 - Cos[4*x])*(Sin[x] - Cos[x]) == 2, x]
It returns the ...
4
votes
4answers
129 views
Extracting variables from an expression
I'm looking for a way to extract a list of variables from an expression, for example with an input like:
...
4
votes
3answers
292 views
Why the difference?
When I do the double sum using the sigma notation I get
$$1 + \sum_{n=0}^{\infty}\sum_{k = n}^{\infty} \frac{1}{(k+2)k!}$$
$1 + e - \cosh[1]$
When I do the sums as below, I get the expected ...
4
votes
4answers
547 views
Mathematica gives wrong answer for integral
When I execute the following,
Integrate[Exp[-w^2 + I w^3], {w, -\[Infinity], \[Infinity]}]
I get
...
4
votes
1answer
365 views
Does the Im function work with symbolic arguments?
Does the Im function work with symbolic arguments?
...
4
votes
1answer
201 views
Symbolic bit vectors
I'd like to see how addition and xoring bitvectors mix together. To do this, I implemented (a primitive) vec_add and vec_xor:
...
4
votes
1answer
94 views
Identical code, different answers?
I'm having some trouble with identical code giving different answers. On a fresh kernel (MM 9.0.0.0, Windows 64-bit), running the same code, copy-paste, gives two different answers:
...
