Questions on the functionality operating on polynomials

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15
votes
3answers
1k 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
833 views

Why does Expand not work within a function?

I'm writing this fairly simple function: ...
12
votes
2answers
643 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: ...
13
votes
2answers
709 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
825 views

Find roots of polynomial in field extension $GF(2^n)$?

How can I find roots of polynomial in extension field $GF(2^n)$?
39
votes
6answers
7k 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 ...
27
votes
3answers
1k 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
234 views

GroebnerBasis without specifying variables

All the examples in the Mathematica documentation specify that the syntax for the GroebnerBasis command is ...
9
votes
1answer
562 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 ...
12
votes
1answer
729 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: ...
12
votes
7answers
5k 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 ...
14
votes
4answers
2k 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 ...
4
votes
2answers
293 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 ...