Class misc.Utilities

public class Utilities {}

This class contains all the utility functions used by individual programs.

Constructor Index:

Utilities()

Method Index:

static int gcd( int a, int b )
This computes the greatest common divisor of a and b.
static boolean isprime( int p )
This checks whether p is a prime number.
static void swap( int[] arr, int i, int j )
This swaps the `i'th and `j'th values of arr[]. This is used by the sort()
method defined below.
static void sort( int[] arr, int low, int high )
This sorts the array arr between low and high.
static int order_in_Ugroup( int elt, int n )
This returns the order of the element elt in U(n). Returns -1 if there is an
error.
static int order_in_Ugroup( int elt, int n, vector vals )
This returns the order of the element elt in U(n) and stores the group
generated by elt in the vector vals. Returns -1 if there is an error.
static int order_in_Zgroup( int elt, int n )
This returns the order of elt in Z_n. Returns -1 if there is an error.
static boolean is_in_Ugroup( int elt, int n )
This checks whether elt is in U(n).
static boolean is_identity_in_ZxZ( int M, int N, Ordered_pair op )
This checks whether the element op is the identity element in Z_M + Z_N.
static int Order_in_ZxZ( int M, int N, Ordered_pair op )
This returns the order of op in Z_M + Z_N. Returns -1 if there is an error.
static boolean is_in_ZxZ( int M, int N, Ordered_pair op )
This checks whether op is in Z_M + Z_N.
static void prime_factorization( vector vect, int number )
This gives the prime-factorization of the integer 'number' and stores it in
the vector 'vect' as algebra.Ordered_pairs. Where the first component of
the Ordered_pair is the prime number and the second component is the power
of that prime_number.
static void partitions( int n, vector vect )
This computes the partitions of the integer 'n' and stores them in a vector as an
array of integers.
static void GxG( int n, vector G1, vector G2, vector G1XG2)
This computes the internal direct product of G1 and G2 and stores it in G1XG2.
Also, it is assumed that both G1 and G2 are subgroups of U(n).