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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.
 

Detailed Description

This file provides miscellaneous functionality.

ABSTRACT: This file provides the following miscellaneous functionality:

  • prime factorisation of bigints with prime factors < 2^31 (This will require at most 256 MByte of RAM.)
  • approximate square root of a bigint

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 empty 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 358 of file misc_ip.cc.

359{
360 int i;
361 int index=0;
362 mpz_t nn; number2mpz(n, coeffs_BIGINT, nn);
363 lists primes = (lists)omAllocBin(slists_bin); primes->Init(1000);
364 int* multiplicities = (int*)omAlloc0(1000*sizeof(int));
365 int positive=1;
366
367 if (!n_IsZero(n, coeffs_BIGINT))
368 {
370 {
371 positive=-1;
372 mpz_neg(nn,nn);
373 }
374 factor_gmp(nn,primes,multiplicities,index,pBound);
375 }
376
377 lists primesL = (lists)omAllocBin(slists_bin);
378 primesL->Init(index);
379 for (i = 0; i < index; i++)
380 {
381 primesL->m[i].rtyp = primes->m[i].rtyp;
382 primesL->m[i].data = primes->m[i].data;
383 primes->m[i].rtyp=0;
384 primes->m[i].data=NULL;
385 }
386 primes->Clean(NULL);
387
388 lists multiplicitiesL = (lists)omAllocBin(slists_bin);
389 multiplicitiesL->Init(index);
390 for (i = 0; i < index; i++)
391 {
392 multiplicitiesL->m[i].rtyp = INT_CMD;
393 multiplicitiesL->m[i].data = (void*)(long)multiplicities[i];
394 }
395 omFree(multiplicities);
396
398 L->Init(3);
399 if (positive==-1) mpz_neg(nn,nn);
400 L->m[0].rtyp = LIST_CMD; L->m[0].data = (void*)primesL;
401 L->m[1].rtyp = LIST_CMD; L->m[1].data = (void*)multiplicitiesL;
402 setListEntry(L, 2, nn);
403
404 mpz_clear(nn);
405
406 return L;
407}
int i
Definition cfEzgcd.cc:132
int rtyp
Definition subexpr.h:91
void * data
Definition subexpr.h:88
sleftv * m
Definition lists.h:46
INLINE_THIS void Init(int l=0)
static FORCE_INLINE void number2mpz(number n, coeffs c, mpz_t m)
Definition coeffs.h:984
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:498
static FORCE_INLINE BOOLEAN n_IsZero(number n, const coeffs r)
TRUE iff 'n' represents the zero element.
Definition coeffs.h:468
STATIC_VAR unsigned short primes[]
primes, primes_len: used to step through possible extensions
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:328
void setListEntry(lists L, int index, mpz_t n)
Definition misc_ip.cc:75
slists * lists
#define omAllocBin(bin)
#define omFree(addr)
#define omAlloc0(size)
#define NULL
Definition omList.c:12
static int index(p_Length length, p_Ord ord)
VAR coeffs coeffs_BIGINT
Definition polys.cc:14
@ LIST_CMD
Definition tok.h:118
@ INT_CMD
Definition tok.h:96