The art of manipulating an algebraic expression into the desired form.

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7
votes
4answers
503 views

Distances between points in periodic cube

How can one implement more efficiently/elegantly/memory savvily the following function which returns a matrix of all Euclidian distances between points in 3D within a cube of width ...
12
votes
1answer
286 views

ToNumberField won't recognize Root as an explicit algebraic number

In Mathematica 9.0.1, it appears that ToNumberField will not always recognize a Root object as an explicit algebraic number. ...
0
votes
0answers
54 views

Ordering oscillators with negative powers: Infinite loops

I have been working with ordering of oscillators for example $[a,a^\dagger]=1$ and I have a fairly stable code. I have needed to use inverse oscillators for example expressions like $a^m ...
4
votes
1answer
177 views

Infinite expression encountered when simplifying ArcTan sums although the result is finite

If I attempt to simplify the sum ArcTan[1/x] + ArcTan[x] with ArcTan[ Simplify[ TrigExpand[ Tan[ ArcTan[1/x] + ArcTan[x]]]]] ...
1
vote
1answer
150 views

Factoring terms out of a polynomial

I don't do much algebra in Mathematica and was surprised to discover, while attempting to answer this question, that I had no idea how to factor out an expression from a polynomial. The question was, ...
2
votes
2answers
138 views

Choosing a branch of the square root when performing a series expansion

I have the following problem. Consider expression f=Sqrt[(x-2y)^2] There is an obvious ambiguity in the definition of f ...
1
vote
1answer
78 views

If statement and elements of an imported data

I import a data file: SetDirectory["C:\\Users\\SE7EN\\Desktop\\mathematica\\test"]; dd = Import["data.dat", "Table"] Out[2] = {{1}, {2}, {3}, {4}, {5}, {6}, {7}} ...
4
votes
1answer
138 views

Generate expressions equivalent to rooted trees

I would like to know how to generate all rooted trees on $n$ vertices using Mathematica? More precisely, I am interested in generating algebraic expressions equivalent to rooted trees and constructed ...
1
vote
1answer
123 views

What is the inside?

What is the inside of the Mathematica command, solve, for a system of equations like the following? $$\eqalign{ (x +2\phantom{3} z)^2 + (y +\phantom{3} w)^2 &= 52\cr (x + 30z)^2 + (y + 3w)^2 ...
-2
votes
1answer
99 views

Algebra problem [closed]

I have recently run into an algebra problem that goes as follows. Using the numbers 1-9 A + B + C + D = EF E + F + G + H = CJ B + G + J = ?D total = B? where ...
2
votes
1answer
65 views

How to distribute PermutationProduct over the sum

Assuming I have two elements of the permutation group algebra $a_1$, $a_2$ such that $a_i=\sum_{p\in S_n}\alpha_pp$, I want to define a linear product $\odot$ that distributes over the sum and pulls ...
0
votes
2answers
144 views

Expand expression into quotient of negative power series

I have a function T(z) and want to expand it to the following form: At the end I want to have a list of equations, which can calculate a0, a1, a2, b0, b1 and b2 with different values of h1, h2, ...
6
votes
1answer
316 views

Maple like collect command in Mathematica

In Maple I often simplify expressions for functions of same argument using the collect command: > collect(a*f(x)+f(y)+x*f(x), f, factor) (a+x)*f(x)+f(y) where ...
0
votes
1answer
157 views

Impose an specific Trigonometric expansion with TrigExpand

Is there a way to impose in mathematica an specific trigonometric expansion with TrigExpand? I have various double-angle expressions for cosine and sine in my ...
0
votes
1answer
129 views

Replacement rules in combination with pure functions to make a change of variables

I have defined my function in this way w = f[r,Θ] ; After some calculations i obtained my results with respect to the previous function. For instance: ...
0
votes
1answer
82 views

Manipulating formal vectors

I want to work with a formal vector space spanned by integer triplets: $$ V=\text{span}\{(a,b,c):a,b,c\in\mathbb N^3\}, $$ such that Mathematica can do additions for me. For example,if I input ...
1
vote
0answers
73 views

How to make noncommutative multiplication agree with commutative multiplication

I need a noncommutative multiplication that is Associative Distributive $A**0=0$, $A**1=A$ Agrees with the commutative multiplication ($A**(k B)=(k A)**B=k (A**B)$) I have found a code ...
13
votes
1answer
612 views

Block Matrix Algebra with Mathematica

I have come up with some BlockMatrix Algebra for Mathematica to make notations easier. I have the following: ...
1
vote
0answers
95 views

Define inverse for the custom operator

I want to define simple matrix algebra (inspired by the following posts: Block Matrix Algebra with Mathematica ; How to define custom operators ). I assume the funtion ...
6
votes
1answer
145 views

Is there a version of Together that doesn't cancel common factors?

I'm running code that produces a long combination of rational functions with free constants that need to be tuned such that the combination vanishes. My current method is to put the combination over ...
12
votes
7answers
3k views

How do I replace a variable in a polynomial?

How do I substitue z^2->x in the following polynomial z^4+z^2+4? z^4+z^2+4 /. z^2->x ...
1
vote
2answers
95 views

How to get a rule for, e.g., (x + y) to apply to (-x - y), etc.?

For example, the substitution (x + y) -> s fails here: In[1]:= (-x - y) /. (x + y) -> s Out[1]= -x - y Of course, I ...
7
votes
1answer
328 views

How to substitute the following conditions into an expression?

I have an expression: $p=a\;b\; x + b^2\; y + a\;c\; z$. I want to substitute $a\;b=1$, $b^2 = 2$ and $a\;c = 4$ to obtain $p = x + 2y + 4z$. How can I tell Mathematica to do that? I dont know how to ...
3
votes
2answers
147 views

Exploiting a relation among constants

Say I have two arbitrary real constants $p,q$ that satisfy $p^2+q^2=1$. Is there any way to easily declare this relation in Mathematica? Edit More specifically I have this (among others) expression: ...
5
votes
5answers
340 views

Isolating characters in a string

I'm struggling to find the right function in mathematica to isolate specific characters in a string. I have got a formula as string (I imported it from an excelfile) like this: y = 0.97*x1 + ...
1
vote
2answers
93 views

Grouping constants in expressions

Starting from the general expression: i A(a x + b y + c z + ...) + j B(a' x + b' y + c' z + ...) + k C(a'' x +b'' y + c'' z + ...) I'd like to rearrange it to ...
2
votes
2answers
129 views

Simplification with assumptions

I'm trying to make Mathematica do some simplifications for me. I have the expression ((1 + s[1]) (-1 + s[2]) )/(-1 + s[1] s[2]) and want to simplify this with ...
3
votes
1answer
81 views

How to order lexicographically the monomers of a parametrized polynomial?

I want to order lexicographically the monomials in a "parametrized polynomial", i.e. polynomials whose "symbolic bits" may be either "variables" or "parameters". For example: ...
9
votes
2answers
553 views

Memory leak issues

I am working with noncommuting objects and basically I am using Mathematica to sort large expressions by normal ordering and simplifying them. To this end, I first create an object called ...
6
votes
1answer
179 views

Working with a system of differential equations that cannot be solved explicitly

I have to work a lot with three functions $\;o_1(t), o_2(t), o_3(t)\;$ that are solutions to the certain system of differential equations: ...
4
votes
2answers
353 views
1
vote
1answer
96 views
3
votes
0answers
147 views

Do a gauge transformation for a Chern-Simons theory?

Suppose we have the following Lagrangian density: $$ L=\epsilon^{\mu\nu\rho}\big(\sum_a A^a_{\mu}(x) \partial_\nu A^a_{\rho}(x)-\sum_{a,b,c}\frac{1}{3} f^{bca} A^a_{\mu}(x) A^b_{\nu}(x) ...
8
votes
3answers
876 views
11
votes
1answer
645 views

What is the proper way to verify that two expressions are equivalent?

First of all, it appears to me that $$\left|\frac{1}{x} + x^2\right| \Leftrightarrow \frac{|1 + x^3|}{|x|}$$ is true. I don't know why, but my attempt to verify it in Mathematica failed. ...
4
votes
1answer
285 views

Plot a cone in spherical co-ordinates

As we all know in spherical coordinates a function phi = π/3 gives us a cone. The cone makes an angle of π/3 with the imagined ...
2
votes
2answers
274 views

Pulling out common terms when simplifying complicated equations

I have a complicated expression where common terms are apparent but Simplify[] and FullSimplify[] don't appear able, even with plenty of assumptions added, to reduce down to a simpler form with common ...
0
votes
1answer
62 views

Using Collect with equations

Is it possible to somehow use the expression that Mathematica has collected once the Collect command has been used? What I mean is, I have an expression like this ...
7
votes
4answers
2k views

Checking if two trigonometric expressions are equal

Say I have two trigonometric expressions which are a bit complicated. Is there a quick way to check if they reduce to the same thing (that they are equal) using Mathematica? I was solving this: $y'' ...
6
votes
2answers
250 views

How to implement a formal expectation operator over an unknown distribution?

I need to do some simplification of an expression involving averages over a stochastic variable (in order to verify a long analytical calculation). The easiest way to do that, I figured, were if I ...
4
votes
2answers
166 views

HornerForm of polynomials in terms of E^(i x)

I want to know how to get the HornerForm of the following expression in terms of E^(I x): ...
3
votes
3answers
224 views

How can I expand a inequality with Abs

I want Abs[x] + Abs[y] <= 1 to be convert to ...
12
votes
3answers
2k views

How can I convert a complex number a+b I to the exponent form A Exp(I phi)?

When I have an expression such as: (1/4 + I/4) ((1 - 2 I) x + Sqrt[3] y) it is hard to get an intuition of the number. So I want to convert it to the complex ...
1
vote
0answers
159 views

Multivariate resultant in Mathematica?

Is there any command in Mathematica 7 which can compute the (McCaulay) resultant of a parametric system of multivariate polynomial equations? In fact, it would be great if there is also a way to ...
4
votes
4answers
265 views

How to compute MIN$(A(x), B(x))$

I have two polynomials: $\;A(x) = \sum a_i\;x^i$, $\quad B(x) = \sum b_i\;x^i$. Given $A(x)$, $B(x)$, I want to compute $\;C(x) = $MIN$(A(x), B(x)) = c_i\;x^i$ where $c_i = $MIN$(a_i, b_i)$. How can ...
11
votes
4answers
346 views

How to replace every possible $A+B$ and $AB$ in expansion of $(A+B)^{10}-A^{10}-B^{10}$ with $x$ and $y$, respectively?

I would like to replace every possible $A+B$ and $AB$ in expansion of $(A+B)^{10}-A^{10}-B^{10}$ with $x$ and $y$, respectively. How to do it with the simplest code in Mathematica? For example, ...
1
vote
1answer
104 views

How accurate is Collect?

Background: I am trying to compute the Lyapunov exponent for the logistic map given by \begin{equation*} x_{n+1}=F(x_n)=ax_n(1-x_n) \end{equation*} The formula for the Lyapunov exponent for a given ...
6
votes
2answers
124 views

Why is ToRadicals[] not able to handle all cases? Is there a workaround?

The documentation for the function ToRadicals says: ♦ There are some cases in which expressions involving radicals can in principle be given, but ...