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// Copyright (C) 1996 The New York Group Theory Cooperative
// See magnus/doc/COPYRIGHT for the full notice.
// Contents: Definition of the PrimeNumbers and IntProblems classes
//
// Principal Author: Alexey Myasnikov
//
// Status: in progress
//
// Usage:
//
// Special Notes:
//
// Revision History:
//
#ifndef _PRIMENUMBERS_H_
#define _PRIMENUMBERS_H_
#include "Integer.h"
#include "Vector.h"
#include "DArray.h"
// IntProblems involces some methods to deal with Integers
struct IntProblems
{
Integer gcdOfVector(const VectorOf<Integer>& vc)const;
// Computes and returns the gcd of integers in
// vector vc.
Integer powerOf(const Integer& o, const Integer& p)const;
// Returns the power e if p^e = o, if not returns -1
void findCoeff(Integer p, Integer q, Integer& x, Integer& y, Integer mod)const;
// Computes the coefficients x, y such that xp + yq = 1 (modulo mod)
};
// Class with methods in which prime numbers are involved
class PrimeNumbers {
public:
PrimeNumbers() : currentNumber(2) {}
const Integer& current() const {
return currentNumber;
}
// Gives thee next prime number from current
const Integer& nextNumber(){
while (true){
currentNumber+=1;
if (isPrime(currentNumber))
return currentNumber;
}
}
// Sets the current number
void setCurrent(const Integer& num){
currentNumber = num;
}
// True if number is prime
bool isPrime(Integer num) const
{
for (int i=2;i<=sqrt(num);i++){
if (num%i==0)
return false;
}
return true;
}
// returns primary decomposition of num. First column - primes,
// second their powers.
DArray<Integer> getPrimeDecom(const Integer& num);
// Prints primary decomposition of num in ostr. 2^3 + 3^2 + 5 ...
void printPrimeDecom(ostream& ostr,const Integer& num);
private:
Integer currentNumber;
// current prime number
};
#endif
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