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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 357 of file misc_ip.cc.

358{
359 int i;
360 int index=0;
361 mpz_t nn; number2mpz(n, coeffs_BIGINT, nn);
362 lists primes = (lists)omAllocBin(slists_bin); primes->Init(1000);
363 int* multiplicities = (int*)omAlloc0(1000*sizeof(int));
364 int positive=1;
365
366 if (!n_IsZero(n, coeffs_BIGINT))
367 {
369 {
370 positive=-1;
371 mpz_neg(nn,nn);
372 }
373 factor_gmp(nn,primes,multiplicities,index,pBound);
374 }
375
376 lists primesL = (lists)omAllocBin(slists_bin);
377 primesL->Init(index);
378 for (i = 0; i < index; i++)
379 {
380 primesL->m[i].rtyp = primes->m[i].rtyp;
381 primesL->m[i].data = primes->m[i].data;
382 primes->m[i].rtyp=0;
383 primes->m[i].data=NULL;
384 }
385 primes->Clean(NULL);
386
387 lists multiplicitiesL = (lists)omAllocBin(slists_bin);
388 multiplicitiesL->Init(index);
389 for (i = 0; i < index; i++)
390 {
391 multiplicitiesL->m[i].rtyp = INT_CMD;
392 multiplicitiesL->m[i].data = (void*)(long)multiplicities[i];
393 }
394 omFree(multiplicities);
395
397 L->Init(3);
398 if (positive==-1) mpz_neg(nn,nn);
399 L->m[0].rtyp = LIST_CMD; L->m[0].data = (void*)primesL;
400 L->m[1].rtyp = LIST_CMD; L->m[1].data = (void*)multiplicitiesL;
401 setListEntry(L, 2, nn);
402
403 mpz_clear(nn);
404
405 return L;
406}
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 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:491
static FORCE_INLINE BOOLEAN n_IsZero(number n, const coeffs r)
TRUE iff 'n' represents the zero element.
Definition: coeffs.h:461
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:327
void setListEntry(lists L, int index, mpz_t n)
Definition: misc_ip.cc:74
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