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

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4
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1answer
154 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
147 views

What is the inside? [closed]

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 ...
0
votes
2answers
206 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, ...
2
votes
1answer
82 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
1answer
233 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
146 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: ...
5
votes
1answer
1k views
8
votes
1answer
237 views

Speed up MinimalPolynomial

My Mathematica code runs slowly MinimalPolynomial[Sqrt[2] + Sqrt[3]+ Sqrt[5]+ Sqrt[7]+ Sqrt[11]+ Sqrt[13], x] runs slowly, but the Maple version ...
0
votes
1answer
101 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
134 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 ...
1
vote
0answers
117 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 ...
13
votes
2answers
294 views

Transform an expression to remove the singularity

I have the expression Sin[c x]/c. Clearly it is undefined at $c=0$, but that is merely a removable singularity, since $$\frac{\sin(cx)}c=x\frac{\sin(cx)}{cx}= ...
7
votes
1answer
706 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
158 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
347 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
100 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 ...
1
vote
2answers
99 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 ...
3
votes
1answer
98 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: ...
2
votes
2answers
143 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 ...
6
votes
1answer
210 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: ...
9
votes
2answers
608 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 ...
4
votes
2answers
418 views

How can I simplify $\log(512)$ to $9\log(2)$?

Can you explain me about the result of Integrate. ...
1
vote
1answer
96 views

How to transform the polynomial in this way?

I have two functions f and g and a polynomial ...
3
votes
0answers
190 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) ...
7
votes
1answer
470 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 ...
13
votes
1answer
1k 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
464 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 ...
9
votes
3answers
2k views

How to extract expression from ConditionalExpression

p1 := y /. {First[Solve[x^2 + y^2 + x == 1, y, Reals]]} ...
2
votes
2answers
368 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 ...
13
votes
1answer
869 views

Block Matrix Algebra with Mathematica

I have come up with some BlockMatrix Algebra for Mathematica to make notations easier. I have the following: ...
6
votes
1answer
189 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 ...
0
votes
1answer
65 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 ...
6
votes
2answers
327 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 ...
3
votes
1answer
267 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
268 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 ...
1
vote
1answer
126 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
157 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 ...
4
votes
2answers
180 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): ...
12
votes
4answers
374 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, ...
0
votes
0answers
35 views

Solving an algebraic equation with one or more constraints? [duplicate]

Just as a simple example, say I wanted to solve Sin[x] == a for x with the constraints -1<=a<=1 and 0 < x < Pi. Is there any way to do this?
0
votes
1answer
109 views

how to permute bit strings and manipulate their elements

I want to write a function(has 2 paremeter, n=range,k=number of 1 digits) which finds all probable combinatorics of arbitrary bit strings and evaluate sum of tensor ...
0
votes
0answers
113 views

Unexpected result from InverseFunction

Given the following two equivalent inverse functions, why does one simplify (using inverse functions that are acceptable to me) and the other doesn't? Is there an assumption or setting I can give ...
0
votes
2answers
120 views

Rearranging a simple algebraic equation

Suppose I have a simple algebraic equation like: ChebyshevT[4, p] == 0 1 - 8 p^2 + 8 p^4 == 0 and I want to solve for the ...
0
votes
1answer
125 views

Why do I get a different answer from the use of TrigExpand?

This is an old post but I get two different answers from Mathematica 9.0.1.0 ...
1
vote
1answer
142 views

Problem about Solve

See this example : ...
3
votes
3answers
241 views

Speed up Eliminate

I have a set of trig equations, c1,c2,c3 are constants, I excepted the result is c1 c2 c3 r^2 + (c1^2 + c2^2 + c3^2 - 1) r + c1 c2 c3 == 0 but following code ...
2
votes
2answers
181 views

Trigonometry expansion of a product

The following command does what I want: ...
0
votes
1answer
1k views

How to neglect higher power terms in a polynomial expression

I have a polynomial expression of order n (say n=20). F(x)=1+x+x^2+x^3++...x^20. I want to approximate the polynomial for order 3 only. So I need to make the ...
-5
votes
1answer
575 views

Solving Det[matrix] == 0 with an 8 x 8 matrix [closed]

I want to solve the equation Det[matrix] == 0 which came from the consistency of solutions of a set of 8 equations. This matrix has two constants λ and μ and two variables $P$ and $q$. I want to get ...
4
votes
1answer
2k views

What do the hashtags represent in the result of Solve, and how should I use them? [duplicate]

There is a function that I'm trying to get the inverse of. My function is a simple polynomial: Tn[T_] := 4/9 T^3/Tc^2 + 5/9 T Now I tried to find ...