To execute the main file
- Type "make main" into the directory to complile the file
- Type "./main to execute the program

//Major functions 
 
//This preforms hensel lifting on n factors to factor polynomial A (using our Cubic complexity algorithm)
int HenselLiftCubic(LONG *A, int dx, int dy, LONG *F0, int n, int du, LONG *F, LONG alpha, LONG *W, LONG p ){
/*
n - number of factors
du - degree bound of initial factors (could be extended to an array later) //max(degree(f_i,x)) for i = 1..n
dx - degree bound on variable x of A
dy - degree bound on variable y of A

A[x][y]- polynomial you wish to factor. This is an array of size (dx+1)*(dy+1). It's oriented in the following way.
The first dx+1 spaces stores the coefficients for the polynomial coeff(A,y^0). The second dx+1 spaces stores the coefficients for the polynomial coeff(A,y^1), and so on.

F0 - set of initial n factors s.t. A-F0_1*F0_2*...*F0_n mod p = 0. This is an array of size n*(du+1). It's oriented in the following way.
The first du+1 spaces stores the coefficients for the first factor. The second dx+1 spaces stores the coefficients for the second factors, and so on.

F - array that will store the final polynomials. must be of size n*(dx+1)*(dy+1)
W - working array for calculations. The space is allocated during the program
alpha - LONG integer - Solves the factors in the form f_i = f_{i,0} + f_{i,1}*(y-alpha)^1 + ...
p - prime 
*/

The first dx+1 spaces stores the coefficients for the polynomial coeff(A,y^0). The second dx+1 spaces stores the coefficients for the polynomial coeff(A,y^1).


//This preforms hensel lifting on n factors to factor polynomial A (using Bernardin's Quartic complexity algorithm)
int HenselLiftQuartic(LONG *A, int dx, int dy, LONG *F0, int n, int du, LONG *F, LONG alpha, LONG *W, LONG p ){

//The variables are denoted the same as in the cubic function



//calculates A - F_1*F_2*...*F_n. It will output 0 if correct
void ComparePolyFactorsBivar(LONG *A,LONG *F,int dx,int dy,int n,LONG alpha,LONG p){

A[x][y]- polynomial you wish to factor. This is an array of size (dx+1)*(dy+1). It's oriented the same as in the cubic algorithm
F - arry of size n*(dx+1)*(dy+1). Holds the n factors of A. The first (dx+1)*(dy+1) spaces holds the first factor, and so on...
dx - degree bound of A in x // deg(A,x)
dy - degree bound of A in y // deg(A,y)
n - number of factors
alpha - for the taylor representation of the factors. 
p - prime.