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9
votes
2answers
486 views

Solving/Reducing equations in $\mathbb{Z}/p\mathbb{Z}$

I was trying to find all the numbers $n$ for which $2^n=n\mod 10^k$ using Mathematica. My first try: Reduce[2^n == n, n, Modulus -> 100] However, I receive ...
11
votes
2answers
523 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... ...
3
votes
0answers
253 views

Parallel PowerMod

Is there anyway to parallelize the PowerMod function? Here is my Left-To-Right modular exponentation: ...
6
votes
1answer
571 views

How to Simplify equations over a Ring with Mathematica?

For example, when we work over a ring, the equation x^3=0 does not imply x^2=0 or x=0, but ...
4
votes
2answers
532 views

Inverse of a polynomial in a polynomial ring

Let $N$ be a prime, and $q$ be a positive integer. Given a polynomial $f(x)$ in $R = \mathbb Z[x]/(x^N-1)$, I want to find another polynomial $f_q(x)$ in $R_q = \mathbb Z_q[x]/(x^N-1)$, such that ...
2
votes
1answer
570 views

Linear Solve with Modular Arithmetic

I am interested in using LinearSolve[m,b] which will find a solution to the equation $m.x=b$, where I am in mod 2 arithmetic. Is there any way to perform this ...
1
vote
1answer
251 views

Faster GCD Implementation

Is there any chance to write a faster GCD than the built-in one in Mathematica? @Mr.Wizard has written one in this question (although it's not for this purpose) which is 6 times slower on a 100k ...