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

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2
votes
3answers
255 views

Is it possible to use Composition for polynomial composition?

I want to do this: $P = (x^3+x)$ $Q = (x^2+1)$ $P \circ Q = P \circ (x^2+1) = (x^2+1)^3+(x^2+1) = x^6+3x^4+4x^2+2$ I used Composition for testing if that could ...
7
votes
1answer
253 views

RootSum result manipulation/simplification

Consider the sum sum1 = Sum[ k/( k^7 - 2 k + 3), {k, Infinity}] ...
8
votes
4answers
458 views

“Evaluating” polynomials of functions (Symbols)

I want to implement the following type evaluation symbolically $$(f^2g + fg + g)(x) \to f(x)^2 g(x) + f(x) g(x) + g(x)$$ In general, on left hand side there is a polynomial in an arbitrary number of ...
6
votes
3answers
525 views

What function can I use to evaluate $(x+y)^2$ to $x^2 + 2xy + y^2$?

What function can I use to evaluate $(x+y)^2$ to $x^2 + 2xy + y^2$? I want to evaluate It and I've tried to use the most obvious way: simply typing and evaluating $(x+y)^2$, But it gives me only ...
2
votes
2answers
191 views

What does MinimalPolynomial do?

suppose $x^5-x-1=0$, $y^7-y-1=0$ and $z=x+y$. I want to find a minimal polynomial expression of $z$, such that $p(z)=0$, and the code can be written like this: ...
3
votes
2answers
2k views

How to convert a system of parametric equations to a normal equation?

For example, I have a system of parametric equations (R is a constant number) : ...
8
votes
4answers
4k views

Factoring polynomials to factors involving complex coefficients

I've run into some problems using Factor on polynomials with complex coefficient factors. Reading the documentation it looks like it only factors over the ...
4
votes
2answers
598 views

expanding a polynomial and collecting coefficients

I'm trying to expand the following polynomial ...
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'' ...
7
votes
3answers
320 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 ...
2
votes
2answers
450 views

How do I make Mathematica understand roots of unity?

Try the following: z = Exp[2 \[Pi] I / 5] Z = { { z, 1 }, { 0, 1/z } } Simplify[MatrixPower[Z, 5]] //MatrixForm Of course, this should return a 2 x 2 identity ...
2
votes
4answers
218 views

I need to move all the variables(x,y,z) to one side of an equality for the equation of a plane

I have 5(x-1)-(y+1)-(z+1)==0. If I use FullSimplify on it it returns 5x==7+x+y. This is not ...
7
votes
2answers
429 views

Manipulating an equation into standard quadratic form?

Say I have an equation of the form $$u s + \frac{1}{v} + \frac{1}{p s + q} = 0$$ (or any form that can be written as a standard quadratic, really, the above form is just an example; they'll all be ...
9
votes
2answers
384 views

Shaping/simplifying equations in a certain way

A problem I am occasionally facing is to simplify an equation not to it's shortest form but to a form that is simple by other means. Often, this is grouping the term according to certain functions, ...
15
votes
2answers
502 views

How to define a non-standard algebra in Mathematica?

I want to define an algebra, where there are three elements: 0, 1 and $\infty$ and two operations, addition and multiplication defined, both commutative: $$\begin{align*} 0+0&=0\\ 0+1&=1\\ ...
12
votes
4answers
1k views

Is it possible to have Mathematica move all terms to one side of an equation?

I have an inequality expression that I would like to express in terms of the relation of the parameters to zero. More simply, I want to have mathematica move all the terms to one side of the ...
10
votes
2answers
2k views

Why doesn't Mathematica expand Cos[x]^3 Sin[x]^2?

I found some examples of Mathematica's commands usage in an old manual but the program gives me different result than expected ...
31
votes
6answers
4k views

Finding real roots of negative numbers (for example, $\sqrt[3]{-8}$)

Say I want to quickly calculate $\sqrt[3]{-8}$, to which the most obvious solution is $-2$. When I input $\sqrt[3]{-8}$ or Power[-8, 3^-1], Mathematica gives the ...
13
votes
6answers
2k 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., ...
9
votes
2answers
731 views

Expand modulus squared

Is it possible to make a function in Mathematica that expands expressions of the form $$|z + w|^2 = |z|^2 + 2\text{Re} \overline{z}w + |w|^2?$$ Preferably it should also be able to handle things ...
10
votes
7answers
2k 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 ...
11
votes
4answers
603 views

Is there a way to Collect[] for more than one symbol?

Oftentimes you find yourself looking for polynomials in multiple variables. Consider the following expression: a(x - y)^3 + b(x - y) + c(x - y) + d as you can ...