Questions on the number-theoretic functionality of Mathematica.

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7
votes
0answers
415 views

Does Mathematica use the Elliptic Curve Method (ECM) in FactorInteger[]?

I'm not a mathematician, and I'm not even going to pretend that I understand anything of the ECM. But I know it can be a fast method for factorization. I benchmarked the factorization of ...
5
votes
0answers
98 views

Doing computations in a modulo ring

I need to perform some computations in a modulo ring, like Mod[Subfactorial[n], m] Mod[Binomial[n, k], m] However, this is obviously much too slow for large ...
4
votes
0answers
79 views

Simplifying expressions involving Divisible

FullSimplify[ Divisible[p^2 - 1, 24] , Element[p, Primes] && p > 3] Should evaluate to True, but I get ...
3
votes
0answers
238 views

Parallel PowerMod

Is there anyway to parallelize the PowerMod function? Here is my Left-To-Right modular exponentation: ...
2
votes
0answers
112 views

PowersRepresentations Algorithm

I'm trying to understand the mathematics behind counting the number of representations of a positive integer by $n$ distinct $k$th powers, i.e. I would really like to know how to do the Mathematica ...
0
votes
0answers
68 views

Elliptic curve cryptography in Mathematica

I can find no resources for doing elliptic curve cryptography. I have used the finite field package, but I find it cumbersome and it does not seem to have any builtin methods for ECC. How can I get ...
0
votes
0answers
69 views

How can I calculate all irreducible polynomials of 31 degree in $\mathbb Z_2[x]$?

How can I calculate all binary irreducible polynomials of degree 31? or how i calculate all irreducible $f$ in $\mathbb Z_2[x]$? (The irreducible polynomial in $\mathbb Z_2[x]$ and $\mathbb R$ are ...
0
votes
0answers
60 views

Is mathematica able to count all results?

I have N variables, say $V_1, V_2, ..., V_n$. and I have several logical conditions like $[(V_1 > V_2) \cap (V_2 + V_3 > V_1) \cap (V_1*V_1 > 2*V_2)] \cup [..]$ You can consider they are in ...