blackbox/smith.C File Reference

mod m Smith form by elmination More...

#include <iostream>
#include <string>
#include <vector>
#include <list>
#include "linbox/util/timer.h"
#include "linbox/field/unparametric.h"
#include "linbox/field/local2_32.h"
#include "linbox/algorithms/2local-smith.h"
#include "linbox/algorithms/local-smith.h"
#include "linbox/algorithms/iliopoulos-elimination.h"
#include "linbox/field/PIR-modular-int32.h"

Include dependency graph for blackbox/smith.C:

Functions
template<class PIR >
void	Mat (DenseMatrix< PIR > &M, PIR &R, int n, string src, string file, string format)
	Output matrix is determined by src which may be: "random-rough" This mat will have s, near sqrt(n), distinct invariant factors, each repeated twice), involving the s primes 101, 103, ... More...
template<class I1 , class Lp >
void	distinct (I1 a, I1 b, Lp &c)

Detailed Description

mod m Smith form by elmination

Author

bds & zw

Function Documentation

Mat()

void Mat	(	DenseMatrix< PIR > &	M,
		PIR &	R,
		int	n,
		string	src,
		string	file,
		string	format
	)

Output matrix is determined by src which may be: "random-rough" This mat will have s, near sqrt(n), distinct invariant factors, each repeated twice), involving the s primes 101, 103, ...

"random" This mat will have the same nontrivial invariant factors as diag(1,2,3,5,8, ... 999, 0, 1, 2, ...). "fib" This mat will have the same nontrivial invariant factors as diag(1,2,3,5,8, ... fib(k)), where k is about sqrt(n). The basic matrix is block diagonal with i-th block of order i and being a tridiagonal {-1,0,1} matrix whose snf = diag(i-1 1's, fib(i)), where fib(1) = 1, fib(2) = 2. But note that, depending on n, the last block may be truncated, thus repeating an earlier fibonacci number. "file" (or any other string) mat read from named file with format "sparse" or "dense". Also "tref" and file with format "kdense"

Examples:

examples/mats.C, and examples/smith.C.

distinct()

void distinct	(	I1	a,
		I1	b,
		Lp &	c
	)

Bug:

this already exists elsewhere

Bug:

this already exists elsewhere

Examples:

examples/smith.C, and examples/smithsparse.C.