You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
70 lines
1.9 KiB
70 lines
1.9 KiB
12 months ago
|
#ifndef _RATIONAL_FACTORIZATION_H_
|
||
|
|
#define _RATIONAL_FACTORIZATION_H_
|
||
|
|
|
||
|
|
#include <libqi/rpl/bigint.h>
|
||
|
|
#include <vector>
|
||
|
|
#include <iostream>
|
||
|
|
|
||
|
|
// \file rational_factorization.h
|
||
|
|
|
||
|
|
namespace rpl {
|
||
|
|
//! rational_factorization
|
||
|
|
/*! this class implements the decomposition
|
||
|
|
* in prime factors for bigints of small size
|
||
|
|
* At the prototype stage, we only implements
|
||
|
|
* the trialdiv algorithm (an Eratosthen sieve)
|
||
|
|
* with prime number knows until 10000
|
||
|
|
* the factorisation is implemented trough
|
||
|
|
* the factor method and could also be called
|
||
|
|
* trough the trialdiv method
|
||
|
|
* In mathematical terms we want to compute for a bigint \f$n\f$
|
||
|
|
* the following decomposition
|
||
|
|
* \f[
|
||
|
|
* n = \prod_{i}^{d} b_i^{e_i}
|
||
|
|
* \f]
|
||
|
|
* with \f$b\f$ is the bases vector and \f$e\f$ is the exponent vector
|
||
|
|
* note that in case of partial factorisation (typically if we limit
|
||
|
|
* the maxfactor with calling trialdiv )
|
||
|
|
* the factor $b_d$ is not prime, and it is called cofactor
|
||
|
|
*/
|
||
|
|
class rational_factorization {
|
||
|
|
public:
|
||
|
|
rational_factorization(const bigint & n = 1)
|
||
|
|
: number(n),
|
||
|
|
cofactor(n),
|
||
|
|
bases(0),
|
||
|
|
expos(0),
|
||
|
|
maxfactor(10000) {}
|
||
|
|
|
||
|
|
void assign(const bigint & n) { number = n; cofactor = n; }
|
||
|
|
|
||
|
|
size_t no_of_comp() const { return bases.size(); }
|
||
|
|
|
||
|
|
size_t exponent(size_t i) const { return expos[i]; }
|
||
|
|
|
||
|
|
bigint base(size_t i) const { return bases[i]; }
|
||
|
|
|
||
|
|
bigint cofact() const { return cofactor; }
|
||
|
|
|
||
|
|
void trialdiv(const bigint & maxfact) { maxfactor = maxfact; factor(); }
|
||
|
|
|
||
|
|
void factor();
|
||
|
|
|
||
|
|
~rational_factorization() {}
|
||
|
|
|
||
|
|
friend std::ostream & operator << (std::ostream & o , const rpl::rational_factorization & r);
|
||
|
|
|
||
|
|
private :
|
||
|
|
|
||
|
|
bigint number; /*!< the bigint we want to factorize*/
|
||
|
|
bigint cofactor;
|
||
|
|
std::vector<bigint> bases; /*<! the bases vector b */
|
||
|
|
std::vector<size_t> expos; /*<! the exponents vector e*/
|
||
|
|
bigint maxfactor; /*!< currently 10000 or a smaller integer */
|
||
|
|
|
||
|
|
};
|
||
|
|
|
||
|
|
|
||
|
|
};
|
||
|
|
#endif
|