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Functions
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 372 of file misc_ip.cc.

373 {
374  int i;
375  int index=0;
376  mpz_t nn; number2mpz(n, nn);
377  lists primes = (lists)omAllocBin(slists_bin); primes->Init(1000);
378  int* multiplicities = (int*)omAlloc0(1000*sizeof(int));
379  int positive=1;
380 
381  if (!n_IsZero(n, coeffs_BIGINT))
382  {
383  if (!n_GreaterZero(n, coeffs_BIGINT))
384  {
385  positive=-1;
386  mpz_neg(nn,nn);
387  }
388  factor_gmp(nn,primes,multiplicities,index,pBound);
389  }
390 
391  lists primesL = (lists)omAllocBin(slists_bin);
392  primesL->Init(index);
393  for (i = 0; i < index; i++)
394  {
395  primesL->m[i].rtyp = primes->m[i].rtyp;
396  primesL->m[i].data = primes->m[i].data;
397  primes->m[i].rtyp=0;
398  primes->m[i].data=NULL;
399  }
400  primes->Clean(NULL);
401 
402  lists multiplicitiesL = (lists)omAllocBin(slists_bin);
403  multiplicitiesL->Init(index);
404  for (i = 0; i < index; i++)
405  {
406  multiplicitiesL->m[i].rtyp = INT_CMD;
407  multiplicitiesL->m[i].data = (void*)(long)multiplicities[i];
408  }
409  omFree(multiplicities);
410 
412  L->Init(3);
413  if (positive==-1) mpz_neg(nn,nn);
414  L->m[0].rtyp = LIST_CMD; L->m[0].data = (void*)primesL;
415  L->m[1].rtyp = LIST_CMD; L->m[1].data = (void*)multiplicitiesL;
416  setListEntry(L, 2, nn);
417 
418  mpz_clear(nn);
419 
420  return L;
421 }
number2mpz
static FORCE_INLINE void number2mpz(number n, mpz_t m)
Definition: misc_ip.cc:85
omFree
#define omFree(addr)
Definition: omAllocDecl.h:261
LIST_CMD
@ LIST_CMD
Definition: tok.h:118
primes
static unsigned short primes[]
primes, primes_len: used to step through possible extensions
Definition: gengftables-conway.cc:59
setListEntry
void setListEntry(lists L, int index, mpz_t n)
Definition: misc_ip.cc:89
omAllocBin
#define omAllocBin(bin)
Definition: omAllocDecl.h:205
n_IsZero
static FORCE_INLINE BOOLEAN n_IsZero(number n, const coeffs r)
TRUE iff 'n' represents the zero element.
Definition: coeffs.h:464
slists_bin
omBin slists_bin
Definition: lists.cc:23
i
int i
Definition: cfEzgcd.cc:125
INT_CMD
@ INT_CMD
Definition: tok.h:96
factor_gmp
static void factor_gmp(mpz_t t, lists primes, int *multiplicities, int &index, unsigned long bound)
Definition: misc_ip.cc:342
sleftv::data
void * data
Definition: subexpr.h:88
slists::m
sleftv * m
Definition: lists.h:45
slists
Definition: lists.h:23
coeffs_BIGINT
coeffs coeffs_BIGINT
Definition: ipid.cc:52
n_GreaterZero
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:494
sleftv::rtyp
int rtyp
Definition: subexpr.h:91
NULL
#define NULL
Definition: omList.c:10
lists
slists * lists
Definition: mpr_numeric.h:146
slists::Init
INLINE_THIS void Init(int l=0)
index
static int index(p_Length length, p_Ord ord)
Definition: p_Procs_Impl.h:592
omAlloc0
#define omAlloc0(size)
Definition: omAllocDecl.h:211