The art of manipulating an algebraic expression into the desired form.
3
votes
3answers
211 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 ...
3
votes
3answers
238 views
Limiting form of a polynomial expression
When simplifying an expression by hand, a trick that is often used is to remove terms that are lower powers of the independent variable, for instance, as $x \rightarrow \infty$,
$x^2 + x$
becomes ...
4
votes
1answer
162 views
Finding mappings between expressions
Suppose we have an expression of the form:
$j=\frac{A\left(t\right)}{B\left(t\right)}=\frac{C\left(s\right)}{D\left(s\right)}$
That is, $j$ can be expressed either as a function of $t$, or as a ...
5
votes
3answers
460 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 ...
7
votes
1answer
187 views
RootSum result manipulation/simplification
Consider the sum
sum1 = Sum[ k/( k^7 - 2 k + 3), {k, Infinity}]
...
8
votes
4answers
299 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 ...
3
votes
2answers
1k 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) :
...
2
votes
2answers
160 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:
...
4
votes
2answers
278 views
expanding a polynomial and collecting coefficients
I'm trying to expand the following polynomial
...
6
votes
4answers
854 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'' ...
10
votes
6answers
900 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., ...
11
votes
4answers
407 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 ...
7
votes
3answers
253 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
279 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
171 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
293 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 ...
8
votes
2answers
261 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, ...
14
votes
2answers
294 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:
$$\begin{align*}
0+0&=0\\
0+1&=1\\
...
7
votes
6answers
761 views
How do I replace a variable in a polynomial?
How do I substitue z^2->x in the following polynomial z^4+z^2+4?
z^4+z^2+4 /. z^2->x
...
9
votes
2answers
474 views
Expand modulus squared
Is it possible to make a function in Mathematica that expands expressions of the form
$$|z + w|^2 = |z|^2 + 2\text{Re} \overline{z}w + |w|^2?$$
Preferably it should also be able to handle things ...
