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misc_ip.h File Reference

This file provides miscellaneous functionality. More...

#include "kernel/mod2.h"
#include "coeffs/si_gmp.h"
#include "coeffs/coeffs.h"
#include "Singular/lists.h"

Go to the source code of this file.

Functions

lists primeFactorisation (const number n, const int pBound)
 Factorises a given bigint number n into its prime factors less than or equal to a given bound, with corresponding multiplicities. More...
 

Detailed Description

This file provides miscellaneous functionality.

ABSTRACT: This file provides the following miscellaneous functionality:

Most of the functioanlity implemented here had earlier been coded in SINGULAR in some library. Due to performance reasons these algorithms have been moved to the C/C++ kernel.

Author
Frank Seelisch

Definition in file misc_ip.h.

Function Documentation

◆ primeFactorisation()

lists primeFactorisation ( const number  n,
const int  pBound 
)

Factorises a given bigint number n into its prime factors less than or equal to a given bound, with corresponding multiplicities.

The method finds all prime factors with multiplicities. If a positive bound is given, then only the prime factors <= pBound are being found. In this case, there may remain an unfactored portion m of n. Also, when n is negative, m will contain the sign. If n is zero, m will be zero. The method returns a list L filled with three entries: L[1] a list; L[1][i] contains the i-th prime factor of |n| as int or bigint (sorted in ascending order), L[2] a list; L[2][i] contains the multiplicity of L[1, i] in |n| as int L[3] contains the remainder m as int or bigint, depending on the size,

We thus have: n = L[1][1]^L[2][1] * ... * L[1][k]^L[2][k] * L[3], where k is the number of mutually distinct prime factors (<= a provided non- zero bound). Note that for n = 0, L[1] and L[2] will be emtpy lists and L[3] will be zero.

Returns
the factorisation data in a SINGULAR-internal list
Parameters
[in]nthe bigint > 0 to be factorised
[in]pBoundbound on the prime factors seeked

Definition at line 365 of file misc_ip.cc.

366 {
367  int i;
368  int index=0;
369  mpz_t nn; number2mpz(n, nn);
370  lists primes = (lists)omAllocBin(slists_bin); primes->Init(1000);
371  int* multiplicities = (int*)omAlloc0(1000*sizeof(int));
372  int positive=1;
373 
374  if (!n_IsZero(n, coeffs_BIGINT))
375  {
376  if (!n_GreaterZero(n, coeffs_BIGINT))
377  {
378  positive=-1;
379  mpz_neg(nn,nn);
380  }
381  factor_gmp(nn,primes,multiplicities,index,pBound);
382  }
383 
384  lists primesL = (lists)omAllocBin(slists_bin);
385  primesL->Init(index);
386  for (i = 0; i < index; i++)
387  {
388  primesL->m[i].rtyp = primes->m[i].rtyp;
389  primesL->m[i].data = primes->m[i].data;
390  primes->m[i].rtyp=0;
391  primes->m[i].data=NULL;
392  }
393  primes->Clean(NULL);
394 
395  lists multiplicitiesL = (lists)omAllocBin(slists_bin);
396  multiplicitiesL->Init(index);
397  for (i = 0; i < index; i++)
398  {
399  multiplicitiesL->m[i].rtyp = INT_CMD;
400  multiplicitiesL->m[i].data = (void*)(long)multiplicities[i];
401  }
402  omFree(multiplicities);
403 
405  L->Init(3);
406  if (positive==-1) mpz_neg(nn,nn);
407  L->m[0].rtyp = LIST_CMD; L->m[0].data = (void*)primesL;
408  L->m[1].rtyp = LIST_CMD; L->m[1].data = (void*)multiplicitiesL;
409  setListEntry(L, 2, nn);
410 
411  mpz_clear(nn);
412 
413  return L;
414 }
int i
Definition: cfEzgcd.cc:132
int rtyp
Definition: subexpr.h:91
void * data
Definition: subexpr.h:88
Definition: lists.h:24
sleftv * m
Definition: lists.h:46
INLINE_THIS void Init(int l=0)
static FORCE_INLINE BOOLEAN n_GreaterZero(number n, const coeffs r)
ordered fields: TRUE iff 'n' is positive; in Z/pZ: TRUE iff 0 < m <= roundedBelow(p/2),...
Definition: coeffs.h:495
static FORCE_INLINE BOOLEAN n_IsZero(number n, const coeffs r)
TRUE iff 'n' represents the zero element.
Definition: coeffs.h:465
STATIC_VAR unsigned short primes[]
primes, primes_len: used to step through possible extensions
VAR coeffs coeffs_BIGINT
Definition: ipid.cc:50
VAR omBin slists_bin
Definition: lists.cc:23
static void factor_gmp(mpz_t t, lists primes, int *multiplicities, int &index, unsigned long bound)
Definition: misc_ip.cc:335
void setListEntry(lists L, int index, mpz_t n)
Definition: misc_ip.cc:82
static FORCE_INLINE void number2mpz(number n, mpz_t m)
Definition: misc_ip.cc:78
slists * lists
Definition: mpr_numeric.h:146
#define omAllocBin(bin)
Definition: omAllocDecl.h:205
#define omFree(addr)
Definition: omAllocDecl.h:261
#define omAlloc0(size)
Definition: omAllocDecl.h:211
#define NULL
Definition: omList.c:12
static int index(p_Length length, p_Ord ord)
Definition: p_Procs_Impl.h:592
@ LIST_CMD
Definition: tok.h:118
@ INT_CMD
Definition: tok.h:96