Questions on the functionality operating on polynomials
5
votes
3answers
462 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 ...
6
votes
4answers
2k 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 ...
6
votes
1answer
344 views
Finding the characteristic polynomial of a matrix modulus n
Given a square matrix, is it possible to calculate its characteristic polynomial modulo n?
Unfortunately, this function ...
1
vote
2answers
222 views
4
votes
2answers
283 views
expanding a polynomial and collecting coefficients
I'm trying to expand the following polynomial
...
7
votes
3answers
446 views
Checking if the roots of a function are real
I'm trying to determine if the roots of a function are real. How would you do that?
(In particular I'm interested in verifying that the roots of LegendreP[6, x] ...
0
votes
3answers
273 views
Creating simple procedure for The Least-Square $m^\text{th}$ Degree Polynomials
I am CS major, taking Computational Numerical Analysis course. Instructor gave us freedom of choice, we were allowed to use anything or any computer language we picked, I picked Mathematica.This is my ...
9
votes
3answers
199 views
Any efficient way to make complete homogeneous symmetric functions in Mathematica?
We do have elementary symmetric functions, SymmetricPolynomial[k, {x_1, ..., x_n}] .
But I didn't find complete homogeneous symmetric functions.
The induction ...
2
votes
2answers
161 views
How to find solutions that yield of root of unity?
I have a polynomial with coefficients that are integer polynomials in another (complex) variable. For example:
1 + (1 - v^2) #1 + (-3 - v^2) #1^2 + #1^3 &
I ...
10
votes
3answers
660 views
Computing the genus of an algebraic curve
How-to compute the genus of an algebraic curve in Mathematica ?
In my case the algebraic curve is explicitly defined by a polynomial.
6
votes
2answers
400 views
11
votes
2answers
374 views
Surprises simplifying simple polynomials
I came across some somewhat surprising behavior of Simplify today, on something very simple. Let's take two cubic polynomials that we know have the same value:
...
10
votes
2answers
372 views
Factorizing polynomials over fields other than $\mathbb{C}$
I'd like to take a polynomial in $\mathbb{Z}_5[x]$ of the form $ax^2+bx+c$ and factor it into irreducible polynomials.
For example:
Input...
x^2+4
Output...
...
10
votes
1answer
344 views
Find roots of polynomial in field extension $GF(2^n)$?
How can I find roots of polynomial in extension field $GF(2^n)$?
26
votes
6answers
2k 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 ...
10
votes
1answer
279 views
Funny behaviour when plotting a polynomial of high degree and large coefficients
I am trying to plot a polynomial of degree 29 on the domain [0,1], with fairly large coefficients:
...
7
votes
1answer
147 views
GroebnerBasis without specifying variables
All the examples in the Mathematica documentation specify that the syntax for the GroebnerBasis command is
...
9
votes
1answer
285 views
Gröbner basis on a particular set of equations
This question is very similar in gist to equation solving with GroebnerBasis, but hopefully when I say that I make the system a little larger I mean little. I have ...
11
votes
1answer
292 views
Rearranging a Polynomial
In Mathematica 8.04 on Windows, I want to display a formula in standard textbook format. The formula is the variance of an $N$-security portfolio. For two securities it is:
...
7
votes
6answers
774 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
415 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 ...
3
votes
2answers
114 views
Better use of Mathematica's PolynomialReduce[]?
I've been using
scPhiDecomp[expr_]:= PolynomialReduce[expr, {x^2-y^2,2 x y}, {x,y}]
which works great on
...
