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

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0
votes
1answer
225 views

Is the formula $\sum _{m=1}^{n-1} \prod _{k=m+1}^n x_k x_m$ wrong in the wiki's page

SymmetricPolynomial[2, {Subscript[x, 1], Subscript[x, 2], Subscript[x, 3], Subscript[x, 4]}] $$\begin{align*}x_1 x_2+x_3 x_2+x_4 x_2+x_1 x_3+x_1 x_4+x_3 ...
5
votes
5answers
173 views

Is there an analogue of the Variables command for general expressions?

The command Variables[poly] gives me a list of all variables that appear in the expression poly, which involved sums, ...
1
vote
3answers
404 views

RowReduce for symbolic matrices

I'd like to invoke RowReduce on some matrices with a time parameter. For example consider A = {{1, 0}, {0, t}} If ...
3
votes
1answer
460 views

How do I solve $1 - (1 - (A x)^2)^\frac{3}{2} - B(1 - \cos(x))= 0$?

Consider the equation $$ 1 - (1 - (A x)^2)^\frac{3}{2} - B(1 - \cos(x)) = 0 $$ where $A,B \in \mathbb{R}$ are constants. What is the analytic solution?
6
votes
1answer
161 views

Symbolic tensor simplifications and the identity matrix

How can I get Mathematica to simplify the following expressions, with $Assumptions including Element[n,Integers], n > 0, and ...
-4
votes
1answer
426 views

Symbolic Definite Integration

How do I perform Integrate[Sin[x]^2/(z^2 + R^2 - 2 zRCos[x])^(3/2), {x, 0, Pi}] where z and ...
2
votes
0answers
123 views

Changing bounds of summation after differentiating symbolic sums

Suppose, I have a function written as Taylor-Maclaurin series f = Sum[c[n]*x^n, {n, 0, Infinity}] Now, I wish to differentiate this expression with respect to ...
5
votes
0answers
981 views

Solve huge symbolic system of linear equations

I have a system of 76 symbolic linear equations (i.e. some coefficients are symbolic) with a sparse coefficient matrix. However, neither Solve[] nor ...
5
votes
1answer
80 views

Why is NHoldFirst not propagated to symbolic derivatives?

I encountered a nasty problem that N cannot evaluate expressions containing a symbolic Derivative of a multi-parameter function ...
3
votes
0answers
231 views

Malliavin Derivative with Mathematica is it possible?

Is it possible to define a Malliavin calculus with Mathematica 9? Consider a random variables on the Wiener-space $\Omega=\mathcal{C}([0,1])$ of the form ...
5
votes
1answer
221 views

VariationalD giving the wrong solution?

EDIT: As pointed out in the comments, VariationalD gives a variational derivative (which I don't want), not a derivative with respect to a function (i.e. ...
0
votes
1answer
91 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 + ...
7
votes
1answer
402 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
0answers
186 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 ...
5
votes
1answer
558 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
250 views

How to check if a given expression is an “explicit algebraic number”?

The documentation for PossibleZeroQ says: With the setting Method...
5
votes
2answers
162 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 ...
0
votes
1answer
155 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
225 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
347 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 ...
4
votes
0answers
521 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
148 views

How do I invoke the default complexity function?

Documentation on ComplexityFunction says: With the default setting ComplexityFunction->Automatic, forms are ranked ...
9
votes
1answer
365 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: ...
0
votes
1answer
164 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 ...
19
votes
4answers
907 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?
8
votes
2answers
351 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
4answers
812 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 ...
2
votes
2answers
369 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 ...
8
votes
2answers
207 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. ...
5
votes
2answers
391 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 ...
8
votes
2answers
629 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
397 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+ ...
10
votes
1answer
129 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
169 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
218 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
384 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
vote
3answers
508 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
175 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. >> ...
3
votes
1answer
483 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?
1
vote
1answer
246 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: ...
0
votes
2answers
423 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 ...
0
votes
0answers
36 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) ...
4
votes
1answer
264 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
129 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 ...
1
vote
1answer
114 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 ...
0
votes
1answer
166 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 ...
9
votes
2answers
608 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 ...
8
votes
4answers
758 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: ...
8
votes
1answer
335 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 ...