For questions about symbolic computation, as opposed to numerical computations.
0
votes
0answers
38 views
Symbolically implementing the following product
I have two products I hope to compare symbolically and I am hoping to use Mathematica for this. They are as follows:
$$
\prod_{1 \leq i < j \leq n} {(a_i + ...
4
votes
1answer
363 views
Wallis Formula and Pippenger Product---How do we get symbolic output?
The Wallis Formula computes $\frac{\pi}{2}$ OEIS and the Pippenger Product computes $\frac{e}{2}$ OEIS. Here is a combined formula:
...
4
votes
1answer
140 views
Mathematica 9 can't integrate this function but earlier versions could
Integrate[ ArcTan[x]/(1 + x) Log[(1 + x^2)/2], {x, -1, 1}]
I used Mathematica 9.0.1 on Windows7 32bit, Mathematica 9 cannot compute this, but Mathematica 8 gives ...
2
votes
1answer
89 views
Reducing exponential inequalities fails
I am quite stumped by this problem :
Reduce[ N^(x-y) <1 && N > 0 , x, Reals]
gives the expected result
...
-3
votes
0answers
59 views
Symbolic constrained optimization with general/unknown objective function [closed]
I am fairly new to Mathematica and would like to solve the following problem:
$$\max\limits_{w,l,c} U(w,l,c)$$
such that $1=w+l, c = yl, w \geq 0, l \geq 0$ and I don't want to define any functional ...
5
votes
2answers
114 views
How to check an algebraic number for membership in a list
I need to check an algebraic number for membership in a list of algebraic numbers. The numbers can be expressed in different forms (combinations of radicals, Root ...
1
vote
0answers
69 views
Problems with Simultaneous Equation Solving
Let me first explain what I am doing and then I will explain the problem that I can't figure out. I am basically trying to solve 2 equations for 2 unknowns (a1 and ...
3
votes
1answer
196 views
n-fold symbolic integral in Mathematica
I am trying to compute symbolically a n-fold integral (n is a parameter of a function) over, say, the cube [0,a]^n. My code looks like this
...
0
votes
1answer
64 views
Pattern match with Table for matrix dimension check
In Mathematica, often an expression involving matrices will encounter dimension mismatch errors, like we are multiplying a 3x2 matrix to a 3x4 matrix. Below we define a new symbol Dim, which can be ...
4
votes
1answer
106 views
How to check if a given expression is an “explicit algebraic number”?
The documentation for PossibleZeroQ says:
With the setting Method...
4
votes
1answer
77 views
How to decompose a complex expression containing repeated subexpressions? [duplicate]
Suppose I have an expression like
...
0
votes
1answer
68 views
Extract Positive Solutions in Logical Expand
I am using Mathematica version 7. I have an expression named fd and I took the derivative of fd with respect to ...
1
vote
1answer
90 views
Comparative Statics on Mathematica
Let me first explain what I am doing then I will mention my little problem that I could not figure out. I am using Mathematica version 7. I have an equation named "fd" and I took the derivative of ...
2
votes
1answer
109 views
How to get (fg)' = f'g + g'f?
I am new to Mathematica so the my questions might be pretty much at the pupil's level.
If I want to use differentiation to derive:
(fg)' = f'g + g'f
How can ...
3
votes
0answers
85 views
Analytically solve the eigenvalue problem with infinite dimensions by Mathematica?
If I am given a symbolic expression of all the matrix elements in an infinite-dimensional space, e.g., the Hamiltonian of a quantum mechanical system, is it possible to get the symbolic expression for ...
7
votes
2answers
79 views
How do I invoke the default complexity function?
Documentation on ComplexityFunction says:
With the default setting ComplexityFunction->Automatic, forms are
ranked ...
5
votes
1answer
98 views
Is it possible to find a limit of a sequence given by its recurrence relation?
I need to calculate a limit of a sequence given by its recurrence relation. I tried the following:
...
13
votes
2answers
233 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?
6
votes
1answer
105 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 ...
5
votes
4answers
194 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 ...
1
vote
2answers
159 views
Write a function that returns the logarithmic derivative
How can we write a function that if we input an expression f, it returns the log derivative $\frac{1}{f} \frac{df}{dx}$. We have to use a conditional or pattern test so that the function accepts any ...
7
votes
2answers
107 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$$
To check this, I used the following code and the result is as what I expected.
...
3
votes
1answer
395 views
Definite and Indefinite integral give different results for piecewise function
I have the following function:
$$
f(q,y)=
\begin{cases}
\tfrac{11720+p}{37791360} & -11720<p<-7720 \\
0 & \text{True}
\end{cases}
$$
where $p = 443\ y-777600\ \sin^{-1}\left(\frac{q ...
6
votes
0answers
122 views
Symbolic integration in real domain only ( assumptions and ComplexExpand don't work)
Integrate[m^2/((x - m^2)^2 + y^2), m]
mathematica gives me a complex-valued reuslt, but maple 17 gives me what I want.
I tried using assumptions, but it doesn't ...
2
votes
2answers
105 views
Mass Symbolic Manipulation with Subscripts? (from plaintext Input)
The simplest example of the change being sought is a greek letter, typed in as plaintext nu, and its may be replaced by the symbol, ν:
expr = 3nu*kx*ky+ ...
9
votes
2answers
223 views
Find closed form expression for series expansion coefficients [duplicate]
Is there a built-in function that will find a general expression for the coefficient of the series expansion of a function?
Series will only give the explicit ...
5
votes
1answer
83 views
How do I expand StirlingS2[n, 10] in terms of elementary functions?
I know that it is possible to expand StirlingS2[n, 10] in terms of elementary functions of n. I tried ...
1
vote
1answer
108 views
Improve performance for finding Fibonacci number which have divisibility property
In this post, the OP requires finding a Fibonacci number having some divisibility property with Mathematica and Maxima. I tired tried that Mathematica code on Mathematica 9.0 and it's still slow ...
4
votes
2answers
92 views
Problem with adding vector to symbolic function (for NDSolve)
I'm trying to set up a system of differential equations for passing to NDSolve. Note that my initial conditions are vector valued so Mathematica should know that ...
4
votes
3answers
302 views
Why the difference?
When I do the double sum using the sigma notation I get
$$1 + \sum_{n=0}^{\infty}\sum_{k = n}^{\infty} \frac{1}{(k+2)k!}$$
$1 + e - \cosh[1]$
When I do the sums as below, I get the expected ...
-1
votes
3answers
209 views
Sqrt — how to get negative branch?
One of the many attractions of Mathematica is that integers are generally treated as exact symbolic entities, and not just as numbers. I was just playing with Sqrt, and was puzzled by what appeared to ...
1
vote
1answer
84 views
Why is a non-convergent series simplified to zero?
Sum[Sin[n*x]*Sin[n] /. x -> 1, {n, 1, Infinity}] ==
Sum[Sin[n*x]*Sin[n], {n, 1, Infinity}] /. x -> 1
Sum::div: Sum does not converge. >>
...
1
vote
1answer
71 views
Generating a list of symbolic coefficients [duplicate]
I am trying to do something which I assume should be very simple: I want to generate a list with symbolic coefficients that looks like this:
...
3
votes
1answer
48 views
Non commutative multiply- expand expression
I began to use Mathematica a few days. My problem is: How to expand expression like $(a+b)*(a+b)$, where this multiplication is non commutative? Mathematica can do this?
0
votes
2answers
77 views
Dropping Higher Order Terms in symbolic evaluation
I have a series of symbolic manipulations (along with some coefficients).
As a sample, here is one of the intermediate forms
...
15
votes
1answer
294 views
Speeding up trigonometric integral
Context
On a possible non trivial toric topology for the Universe (nothing less!).
Problem
I would like to carry out the following integral for $\ell=2,4\cdots 20$.
$$\int _0^{\pi }\int _0^{2 \pi ...
0
votes
0answers
18 views
Symbolic Calculations with formal matrices [duplicate]
I want to make calculations with matrices in the form (for lovers of statistical mechanics, is just the first step replica symmetry breaking)
...
2
votes
1answer
101 views
Is it possible to create a compiled function with some symbolic arguments?
I am trying to create a compiled function that takes in several arguments. However, some of the arguments contain symbolic entries and thus I get the following error message when executing the cell ...
2
votes
1answer
61 views
Differentiating with respect to vectors of unspecified length
Given a function defined by
f[x_,y_] := Sum[ x[[i]] (g[y[[i]]] - g[Total[y]] - Log[x[[i]]]), {i, 1, Length[x]}]
I can easily calculate the derivative for a fixed ...
0
votes
1answer
91 views
Alleviating a bottleneck involving a function call with symbolic derivatives
I have a bottleneck problem involving a function call with symbolic derivatives.
I don't have much experience with Mathematica (or any dynamic language) and I'm certain that the way I've set this up ...
1
vote
1answer
64 views
Only perform a symbolic differentiation once
I want to define a function that involves a differentiation step that Mathematica can do easily, which might be of the form
...
4
votes
4answers
136 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:
...
5
votes
4answers
204 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 (...
7
votes
1answer
247 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 ...
3
votes
3answers
215 views
Efficient code for solve this equation
We have know $a*b*c=-1$, $\frac{a^2}{c}+\frac{b}{c^2}=1$, $a^2 b+a c^2+b^2 c=t$,
What's the value of $a^5 c+a b^5+b c^5$?
I tried
...
4
votes
1answer
95 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:
...
2
votes
1answer
133 views
Variable name string to expression
I'm not sure how to name this problem appropriately. But anyway.
I have, say, three variables (arrays in my case), which I call:
A1, A2, A3
I would like to ...
3
votes
1answer
161 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.
...
1
vote
0answers
59 views
Symbolic Integration of Boole [closed]
Why is
Integrate[Boole[x < 1], q]
resulting in
Piecewise[{{x, x <= 1}}, 1]
I'd expect
...
2
votes
3answers
295 views
How to calculate partial derivative of an unknown function
How can I force Mathematica to calculate symbolically the partial derivative of a function u[x,y] with respect to a variable ...
