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hilb.h File Reference
#include "polys/monomials/ring.h"
#include "kernel/polys.h"
#include "misc/intvec.h"

Go to the source code of this file.

Functions

intvechFirstSeries (ideal S, intvec *modulweight, ideal Q=NULL, intvec *wdegree=NULL)
 
intvechFirstSeries0 (ideal S, ideal Q, intvec *wdegree, const ring src, const ring Qt)
 
poly hilbert_series (ideal A, const ring src, const intvec *wdegree, const ring Qt)
 
intvechSecondSeries (intvec *hseries1)
 
void hLookSeries (ideal S, intvec *modulweight, ideal Q=NULL, intvec *wdegree=NULL)
 

Function Documentation

◆ hFirstSeries()

intvec * hFirstSeries ( ideal  S,
intvec modulweight,
ideal  Q = NULL,
intvec wdegree = NULL 
)

Definition at line 1947 of file hilb.cc.

1948{
1949 static ring hilb_Qt=NULL;
1950 if (hilb_Qt==NULL) hilb_Qt=makeQt();
1951 if (!isModule(A,currRing))
1952 return hFirstSeries0(A,Q,wdegree,currRing,hilb_Qt);
1953 intvec *res=NULL;
1954 int w_max=0,w_min=0;
1955 if (module_w!=NULL)
1956 {
1957 w_max=module_w->max_in();
1958 w_min=module_w->min_in();
1959 }
1960 for(int c=1;c<=A->rank;c++)
1961 {
1962 ideal Ac=getModuleComp(A,c,currRing);
1963 intvec *res_c=hFirstSeries0(Ac,Q,wdegree,currRing,hilb_Qt);
1964 id_Delete(&Ac,currRing);
1965 intvec *tmp=NULL;
1966 if (res==NULL)
1967 res=new intvec(res_c->length()+(w_max-w_min));
1968 if ((module_w==NULL) || ((*module_w)[c-1]==0)) tmp=ivAdd(res,res_c);
1969 else tmp=ivAddShift(res, res_c,(*module_w)[c-1]-w_min);
1970 delete res_c;
1971 if (tmp!=NULL)
1972 {
1973 delete res;
1974 res=tmp;
1975 }
1976 }
1977 (*res)[res->length()-1]=w_min;
1978 return res;
1979}
Definition: intvec.h:23
int length() const
Definition: intvec.h:94
CanonicalForm res
Definition: facAbsFact.cc:60
static BOOLEAN isModule(ideal A, const ring src)
Definition: hilb.cc:1931
static ring makeQt()
Definition: hilb.cc:1840
static ideal getModuleComp(ideal A, int c, const ring src)
Definition: hilb.cc:1920
intvec * hFirstSeries0(ideal A, ideal Q, intvec *wdegree, const ring src, const ring Qt)
Definition: hilb.cc:1863
intvec * ivAddShift(intvec *a, intvec *b, int s)
Definition: intvec.cc:279
intvec * ivAdd(intvec *a, intvec *b)
Definition: intvec.cc:249
STATIC_VAR jList * Q
Definition: janet.cc:30
#define NULL
Definition: omList.c:12
VAR ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
Definition: polys.cc:13
void id_Delete(ideal *h, ring r)
deletes an ideal/module/matrix
#define A
Definition: sirandom.c:24

◆ hFirstSeries0()

intvec * hFirstSeries0 ( ideal  S,
ideal  Q,
intvec wdegree,
const ring  src,
const ring  Qt 
)

Definition at line 1863 of file hilb.cc.

1864{
1865 A=id_Head(A,src);
1866 id_Test(A,src);
1867 ideal AA;
1868 if (Q!=NULL)
1869 {
1870 ideal QQ=id_Head(Q,src);
1871 AA=id_SimpleAdd(A,QQ,src);
1872 id_Delete(&QQ,src);
1873 id_Delete(&A,src);
1874 idSkipZeroes(AA);
1875 int c=p_GetComp(AA->m[0],src);
1876 if (c!=0)
1877 {
1878 for(int i=0;i<IDELEMS(AA);i++)
1879 if (AA->m[i]!=NULL) p_SetComp(AA->m[i],c,src);
1880 }
1881 }
1882 else AA=A;
1883 id_DelDiv_Sorted(AA,src);
1884 idSkipZeroes(AA);
1885 /* sort */
1886 if (IDELEMS(AA)>1)
1887 #ifdef HAVE_QSORT_R
1888 #if defined(__APPLE__) || defined(__FreeBSD__) || defined(__OpenBSD__) || defined(__NetBSD__) || defined(__CYGWIN__)
1889 qsort_r(AA->m,IDELEMS(AA),sizeof(poly),src,compare_rp);
1890 #else
1891 qsort_r(AA->m,IDELEMS(AA),sizeof(poly),compare_rp,src);
1892 #endif
1893 #else
1894 {
1895 ring r=currRing;
1896 currRing=src;
1897 qsort(AA->m,IDELEMS(AA),sizeof(poly),compare_rp_currRing);
1898 currRing=r;
1899 }
1900 #endif
1901 poly s=hilbert_series(AA,src,wdegree,Qt);
1902 id_Delete(&AA,src);
1903 intvec *ss;
1904 if (s==NULL)
1905 ss=new intvec(2);
1906 else
1907 {
1908 ss=new intvec(p_Totaldegree(s,Qt)+2);
1909 while(s!=NULL)
1910 {
1911 int i=p_Totaldegree(s,Qt);
1912 (*ss)[i]=n_Int(pGetCoeff(s),Qt->cf);
1913 if((*ss)[i]==0) Print("overflow at t^%d\n",i);
1914 p_LmDelete(&s,Qt);
1915 }
1916 }
1917 return ss;
1918}
int i
Definition: cfEzgcd.cc:132
static FORCE_INLINE long n_Int(number &n, const coeffs r)
conversion of n to an int; 0 if not possible in Z/pZ: the representing int lying in (-p/2 ....
Definition: coeffs.h:547
#define Print
Definition: emacs.cc:80
const CanonicalForm int s
Definition: facAbsFact.cc:51
poly hilbert_series(ideal A, const ring src, const intvec *wdegree, const ring Qt)
Definition: hilb.cc:1753
static int compare_rp_currRing(const void *pp1, const void *pp2)
Definition: hilb.cc:1739
#define p_GetComp(p, r)
Definition: monomials.h:64
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy
Definition: monomials.h:44
static void p_LmDelete(poly p, const ring r)
Definition: p_polys.h:725
static unsigned long p_SetComp(poly p, unsigned long c, ring r)
Definition: p_polys.h:249
static long p_Totaldegree(poly p, const ring r)
Definition: p_polys.h:1509
void id_DelDiv_Sorted(ideal id, const ring r)
delete id[j], if LT(j) == coeff*mon*LT(i) (j>i)
ideal id_Head(ideal h, const ring r)
returns the ideals of initial terms
ideal id_SimpleAdd(ideal h1, ideal h2, const ring R)
concat the lists h1 and h2 without zeros
void idSkipZeroes(ideal ide)
gives an ideal/module the minimal possible size
#define IDELEMS(i)
Definition: simpleideals.h:23
#define id_Test(A, lR)
Definition: simpleideals.h:78

◆ hilbert_series()

poly hilbert_series ( ideal  A,
const ring  src,
const intvec wdegree,
const ring  Qt 
)

Definition at line 1753 of file hilb.cc.

1759{
1760 int r=id_Elem(A,src);
1761 poly h=NULL;
1762 if (r==0)
1763 return p_One(Qt);
1764 if (wdegree!=NULL)
1765 {
1766 int* exp=(int*)omAlloc((src->N+1)*sizeof(int));
1767 for(int i=IDELEMS(A)-1; i>=0;i--)
1768 {
1769 if (A->m[i]!=NULL)
1770 {
1771 p_GetExpV(A->m[i],exp,src);
1772 for(int j=src->N;j>0;j--)
1773 exp[j]*=ABS((*wdegree)[j-1]);
1774 p_SetExpV(A->m[i],exp,src);
1775 #ifdef PDEBUG
1776 p_Setm(A->m[i],src);
1777 #endif
1778 }
1779 }
1780 omFreeSize(exp,(src->N+1)*sizeof(int));
1781 }
1782 h=p_One(Qt);
1783 p_SetExp(h,1,p_Totaldegree(A->m[0],src),Qt);
1784 p_Setm(h,Qt);
1785 h=p_Neg(h,Qt);
1786 h=p_Add_q(h,p_One(Qt),Qt); // 1-t
1787 int *exp_q=(int*)omAlloc((src->N+1)*sizeof(int));
1788 for (int i=1;i<r;i++)
1789 {
1790 //ideal J=id_Copy(A,src);
1791 //for (int ii=i;ii<r;ii++) p_Delete(&J->m[ii],src);
1792 //idSkipZeroes(J);
1793 ideal J=id_CopyFirstK(A,i,src);
1794 for(int ii=1;ii<=src->N;ii++)
1795 exp_q[ii]=p_GetExp(A->m[i],ii,src);
1796 for(int ii=0;ii<i;ii++) p_Div_hi(J->m[ii],exp_q,src);
1797 id_DelDiv_Sorted(J,src);
1798 // search linear elems:
1799 int k=0;
1800 for (int ii=IDELEMS(J)-1;ii>=0;ii--)
1801 {
1802 if((J->m[ii]!=NULL) && (p_Totaldegree(J->m[ii],src)==1))
1803 {
1804 k++;
1805 p_Delete(&J->m[ii],src);
1806 }
1807 }
1808 idSkipZeroes(J);
1809 poly h_J=hilbert_series(J,src,NULL,Qt);// J_1
1810 poly tmp;
1811 if (k>0)
1812 {
1813 // hilbert_series of unmodified J:
1814 tmp=p_One(Qt);
1815 p_SetExp(tmp,1,1,Qt);
1816 p_Setm(tmp,Qt);
1817 tmp=p_Neg(tmp,Qt);
1818 tmp=p_Add_q(tmp,p_One(Qt),Qt); // 1-t
1819 if (k>1)
1820 {
1821 tmp=p_Power(tmp,k,Qt); // (1-t)^k
1822 }
1823 h_J=p_Mult_q(h_J,tmp,Qt);
1824 }
1825 // forget about J:
1826 id_Delete(&J,src);
1827 // t^|A_i|
1828 tmp=p_One(Qt);
1829 p_SetExp(tmp,1,p_Totaldegree(A->m[i],src),Qt);
1830 p_Setm(tmp,Qt);
1831 tmp=p_Neg(tmp,Qt);
1832 tmp=p_Mult_q(tmp,h_J,Qt);
1833 h=p_Add_q(h,tmp,Qt);
1834 }
1835 omFreeSize(exp_q,(src->N+1)*sizeof(int));
1836 //Print("end hilbert_series, r=%d\n",r);
1837 return h;
1838}
static int ABS(int v)
Definition: auxiliary.h:112
int k
Definition: cfEzgcd.cc:99
int j
Definition: facHensel.cc:110
static void p_Div_hi(poly p, const int *exp_q, const ring src)
Definition: hilb.cc:1707
STATIC_VAR Poly * h
Definition: janet.cc:971
gmp_float exp(const gmp_float &a)
Definition: mpr_complex.cc:357
#define omFreeSize(addr, size)
Definition: omAllocDecl.h:260
#define omAlloc(size)
Definition: omAllocDecl.h:210
poly p_Power(poly p, int i, const ring r)
Definition: p_polys.cc:2193
poly p_One(const ring r)
Definition: p_polys.cc:1313
static poly p_Neg(poly p, const ring r)
Definition: p_polys.h:1109
static poly p_Add_q(poly p, poly q, const ring r)
Definition: p_polys.h:938
static poly p_Mult_q(poly p, poly q, const ring r)
Definition: p_polys.h:1116
static void p_SetExpV(poly p, int *ev, const ring r)
Definition: p_polys.h:1546
static unsigned long p_SetExp(poly p, const unsigned long e, const unsigned long iBitmask, const int VarOffset)
set a single variable exponent @Note: VarOffset encodes the position in p->exp
Definition: p_polys.h:490
static void p_Setm(poly p, const ring r)
Definition: p_polys.h:235
static long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset)
get a single variable exponent @Note: the integer VarOffset encodes:
Definition: p_polys.h:471
static void p_Delete(poly *p, const ring r)
Definition: p_polys.h:903
static void p_GetExpV(poly p, int *ev, const ring r)
Definition: p_polys.h:1522
ideal id_CopyFirstK(const ideal ide, const int k, const ring r)
copies the first k (>= 1) entries of the given ideal/module and returns these as a new ideal/module (...
#define id_Elem(F, R)
Definition: simpleideals.h:68

◆ hLookSeries()

void hLookSeries ( ideal  S,
intvec modulweight,
ideal  Q = NULL,
intvec wdegree = NULL 
)

Definition at line 776 of file hilb.cc.

777{
779
780 intvec *hseries1 = hFirstSeries(S, modulweight, Q, wdegree);
781 if (errorreported) return;
782
783 hPrintHilb(hseries1,modulweight);
784
785 const int l = hseries1->length()-1;
786
787 intvec *hseries2 = (l > 1) ? hSecondSeries(hseries1) : hseries1;
788
789 int co, mu;
790 hDegreeSeries(hseries1, hseries2, &co, &mu);
791
792 PrintLn();
793 hPrintHilb(hseries2,modulweight);
794 if ((l == 1) &&(mu == 0))
796 else
797 scPrintDegree(co, mu);
798 if (l>1)
799 delete hseries1;
800 delete hseries2;
801}
int l
Definition: cfEzgcd.cc:100
void mu(int **points, int sizePoints)
VAR short errorreported
Definition: feFopen.cc:23
void scPrintDegree(int co, int mu)
Definition: hdegree.cc:912
intvec * hSecondSeries(intvec *hseries1)
Definition: hilb.cc:697
static void hPrintHilb(intvec *hseries, intvec *modul_weight)
Definition: hilb.cc:750
intvec * hFirstSeries(ideal A, intvec *module_w, ideal Q, intvec *wdegree)
Definition: hilb.cc:1947
void hDegreeSeries(intvec *s1, intvec *s2, int *co, int *mu)
Definition: hilb.cc:732
void PrintLn()
Definition: reporter.cc:310
static short rVar(const ring r)
#define rVar(r) (r->N)
Definition: ring.h:593
#define id_LmTest(A, lR)
Definition: simpleideals.h:79

◆ hSecondSeries()

intvec * hSecondSeries ( intvec hseries1)

Definition at line 697 of file hilb.cc.

698{
699 intvec *work, *hseries2;
700 int i, j, k, t, l;
701 int s;
702 if (hseries1 == NULL)
703 return NULL;
704 work = new intvec(hseries1);
705 k = l = work->length()-1;
706 s = 0;
707 for (i = k-1; i >= 0; i--)
708 s += (*work)[i];
709 loop
710 {
711 if ((s != 0) || (k == 1))
712 break;
713 s = 0;
714 t = (*work)[k-1];
715 k--;
716 for (i = k-1; i >= 0; i--)
717 {
718 j = (*work)[i];
719 (*work)[i] = -t;
720 s += t;
721 t += j;
722 }
723 }
724 hseries2 = new intvec(k+1);
725 for (i = k-1; i >= 0; i--)
726 (*hseries2)[i] = (*work)[i];
727 (*hseries2)[k] = (*work)[l];
728 delete work;
729 return hseries2;
730}
#define loop
Definition: structs.h:75