On Mon, 14 Aug 2006, David Wagner wrote:
Here's an example. Suppose we have the equations:
x*y + z = 1
x^3 + y^2 * z = 1
x + y + z = 0
Step 1: Find all solutions modulo 2. This is easy: you just have to try
2^3 = 8 possible assignments and see which one satisfy the
Ariel wrote:
A root that you lift using Hensel to Z_{p^n} looks
like a_0 + a_1 p + a_2 p2 +... +a_n p^n where a_i is
in Z_p. What will happen in your case
is that at first, in (Z_2)3 you can have at most 8
roots, once you lift to Z_{22} some of these roots
can
be split into more roots (if p=2
Danilo Gligoroski writes:
[...] solve a system of 3 polynomials of order 3
with 3 variables x1, x2 and x3 in the set Z_{2^32}
and
coeficients also in Z_{2^32} [...]
David Wagner wrote:
Here is a trick that should solve these kinds of
equations extremely quickly. First, you solve the
system of
Hi,
In order to solve a system of 3 polynomials of order 3
with 3 variables x1, x2 and x3 in the set Z_{2^32} and
coeficients also in Z_{2^32} I used the Mathematica
5.1 function Reduce[...,{x1,x2,x3},Modulus-2^32]. It
is giving the solutions but it is not very fast. I
wanted to programe a
Hi Danilo,
Maybe you should use some other function in Mathematica. Symbolic
solving polynomial equations is a very difficult task (e.g.,
doubly-exponential worst case time complexity). But in this case it
shouldn't take that much time.
Let me notice that Z_{2^32} is not the same as F_{2^32}
Danilo Gligoroski writes:
[...] solve a system of 3 polynomials of order 3
with 3 variables x1, x2 and x3 in the set Z_{2^32} and
coeficients also in Z_{2^32} [...]
Here is a trick that should solve these kinds of equations extremely
quickly. First, you solve the system of equations modulo 2.
