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stairc.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

void scComputeHC (ideal s, ideal Q, int k, poly &hEdge, ring tailRing=currRing)
 
intvecscIndIntvec (ideal S, ideal Q=NULL)
 
int scDimInt (ideal s, ideal Q=NULL)
 ideal dimension More...
 
int scDimIntRing (ideal s, ideal Q=NULL)
 scDimInt for ring-coefficients More...
 
int scMultInt (ideal s, ideal Q=NULL)
 
int scMult0Int (ideal s, ideal Q=NULL, const ring tailRing=currRing)
 
void scPrintDegree (int co, int mu)
 
void scDegree (ideal s, intvec *modulweight, ideal Q=NULL)
 
ideal scKBase (int deg, ideal s, ideal Q=NULL, intvec *mv=NULL)
 
int lp_gkDim (const ideal G)
 
int lp_kDim (const ideal G)
 
intveclp_ufnarovskiGraph (ideal G, ideal &standardWords)
 

Function Documentation

◆ lp_gkDim()

int lp_gkDim ( const ideal  G)

Definition at line 1839 of file hdegree.cc.

1840 {
1841  id_Test(_G, currRing);
1842 
1843  if (rField_is_Ring(currRing)) {
1844  WerrorS("GK-Dim not implemented for rings");
1845  return -2;
1846  }
1847 
1848  for (int i=IDELEMS(_G)-1;i>=0; i--)
1849  {
1850  if (_G->m[i] != NULL)
1851  {
1852  if (pGetComp(_G->m[i]) != 0)
1853  {
1854  WerrorS("GK-Dim not implemented for modules");
1855  return -2;
1856  }
1857  if (pGetNCGen(_G->m[i]) != 0)
1858  {
1859  WerrorS("GK-Dim not implemented for bi-modules");
1860  return -2;
1861  }
1862  }
1863  }
1864 
1865  ideal G = id_Head(_G, currRing); // G = LM(G) (and copy)
1866  idSkipZeroes(G); // remove zeros
1867  id_DelLmEquals(G, currRing); // remove duplicates
1868 
1869  // check if G is the zero ideal
1870  if (IDELEMS(G) == 1 && G->m[0] == NULL)
1871  {
1872  // NOTE: this is needed because if the ideal is <0>, then idSkipZeroes keeps this element, and IDELEMS is still 1!
1873  int lV = currRing->isLPring;
1874  int ncGenCount = currRing->LPncGenCount;
1875  if (lV - ncGenCount == 0)
1876  {
1877  idDelete(&G);
1878  return 0;
1879  }
1880  if (lV - ncGenCount == 1)
1881  {
1882  idDelete(&G);
1883  return 1;
1884  }
1885  if (lV - ncGenCount >= 2)
1886  {
1887  idDelete(&G);
1888  return -1;
1889  }
1890  }
1891 
1892  // get the max deg
1893  long maxDeg = 0;
1894  for (int i = 0; i < IDELEMS(G); i++)
1895  {
1896  maxDeg = si_max(maxDeg, pTotaldegree(G->m[i]));
1897 
1898  // also check whether G = <1>
1899  if (pIsConstantComp(G->m[i]))
1900  {
1901  WerrorS("GK-Dim not defined for 0-ring");
1902  idDelete(&G);
1903  return -2;
1904  }
1905  }
1906 
1907  // early termination if G \subset X
1908  if (maxDeg <= 1)
1909  {
1910  int lV = currRing->isLPring;
1911  int ncGenCount = currRing->LPncGenCount;
1912  if (IDELEMS(G) == lV - ncGenCount) // V = {1} no edges
1913  {
1914  idDelete(&G);
1915  return 0;
1916  }
1917  if (IDELEMS(G) == lV - ncGenCount - 1) // V = {1} with loop
1918  {
1919  idDelete(&G);
1920  return 1;
1921  }
1922  if (IDELEMS(G) <= lV - ncGenCount - 2) // V = {1} with more than one loop
1923  {
1924  idDelete(&G);
1925  return -1;
1926  }
1927  }
1928 
1929  ideal standardWords;
1930  intvec* UG = lp_ufnarovskiGraph(G, standardWords);
1931  if (UG == NULL)
1932  {
1933  idDelete(&G);
1934  return -2;
1935  }
1936  if (errorreported)
1937  {
1938  delete UG;
1939  idDelete(&G);
1940  return -2;
1941  }
1942  int gkDim = graphGrowth(UG);
1943  delete UG;
1944  idDelete(&G);
1945  return gkDim;
1946 }
static int si_max(const int a, const int b)
Definition: auxiliary.h:124
int i
Definition: cfEzgcd.cc:132
Definition: intvec.h:23
VAR short errorreported
Definition: feFopen.cc:23
void WerrorS(const char *s)
Definition: feFopen.cc:24
intvec * lp_ufnarovskiGraph(ideal G, ideal &standardWords)
Definition: hdegree.cc:1778
static int graphGrowth(const intvec *G)
Definition: hdegree.cc:1651
#define idDelete(H)
delete an ideal
Definition: ideals.h:29
STATIC_VAR TreeM * G
Definition: janet.cc:31
#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
static long pTotaldegree(poly p)
Definition: polys.h:282
#define pGetComp(p)
Component.
Definition: polys.h:37
#define pIsConstantComp(p)
return true if p is either NULL, or if all exponents of p are 0, Comp of p might be !...
Definition: polys.h:236
static BOOLEAN rField_is_Ring(const ring r)
Definition: ring.h:489
#define pGetNCGen(p)
Definition: shiftop.h:65
ideal id_Head(ideal h, const ring r)
returns the ideals of initial terms
void id_DelLmEquals(ideal id, const ring r)
Delete id[j], if Lm(j) == Lm(i) and both LC(j), LC(i) are units and j > i.
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

◆ lp_kDim()

int lp_kDim ( const ideal  G)

Definition at line 2089 of file hdegree.cc.

2090 {
2091  if (rField_is_Ring(currRing)) {
2092  WerrorS("K-Dim not implemented for rings");
2093  return -2;
2094  }
2095 
2096  for (int i=IDELEMS(_G)-1;i>=0; i--)
2097  {
2098  if (_G->m[i] != NULL)
2099  {
2100  if (pGetComp(_G->m[i]) != 0)
2101  {
2102  WerrorS("K-Dim not implemented for modules");
2103  return -2;
2104  }
2105  if (pGetNCGen(_G->m[i]) != 0)
2106  {
2107  WerrorS("K-Dim not implemented for bi-modules");
2108  return -2;
2109  }
2110  }
2111  }
2112 
2113  ideal G = id_Head(_G, currRing); // G = LM(G) (and copy)
2114  if (TEST_OPT_PROT)
2115  Print("%d original generators\n", IDELEMS(G));
2116  idSkipZeroes(G); // remove zeros
2117  id_DelLmEquals(G, currRing); // remove duplicates
2118  if (TEST_OPT_PROT)
2119  Print("%d non-zero unique generators\n", IDELEMS(G));
2120 
2121  // check if G is the zero ideal
2122  if (IDELEMS(G) == 1 && G->m[0] == NULL)
2123  {
2124  // NOTE: this is needed because if the ideal is <0>, then idSkipZeroes keeps this element, and IDELEMS is still 1!
2125  int lV = currRing->isLPring;
2126  int ncGenCount = currRing->LPncGenCount;
2127  if (lV - ncGenCount == 0)
2128  {
2129  idDelete(&G);
2130  return 1;
2131  }
2132  if (lV - ncGenCount == 1)
2133  {
2134  idDelete(&G);
2135  return -1;
2136  }
2137  if (lV - ncGenCount >= 2)
2138  {
2139  idDelete(&G);
2140  return -1;
2141  }
2142  }
2143 
2144  // get the max deg
2145  long maxDeg = 0;
2146  for (int i = 0; i < IDELEMS(G); i++)
2147  {
2148  maxDeg = si_max(maxDeg, pTotaldegree(G->m[i]));
2149 
2150  // also check whether G = <1>
2151  if (pIsConstantComp(G->m[i]))
2152  {
2153  WerrorS("K-Dim not defined for 0-ring"); // TODO is it minus infinity ?
2154  idDelete(&G);
2155  return -2;
2156  }
2157  }
2158  if (TEST_OPT_PROT)
2159  Print("max deg: %ld\n", maxDeg);
2160 
2161 
2162  // for normal words of length minDeg ... maxDeg-1
2163  // brute-force the normal words
2164  if (TEST_OPT_PROT)
2165  PrintS("Computing normal words normally...\n");
2166  long numberOfNormalWords = lp_countNormalWords(maxDeg - 1, G);
2167 
2168  if (TEST_OPT_PROT)
2169  Print("%ld normal words up to length %ld\n", numberOfNormalWords, maxDeg - 1);
2170 
2171  // early termination if G \subset X
2172  if (maxDeg <= 1)
2173  {
2174  int lV = currRing->isLPring;
2175  int ncGenCount = currRing->LPncGenCount;
2176  if (IDELEMS(G) == lV - ncGenCount) // V = {1} no edges
2177  {
2178  idDelete(&G);
2179  return numberOfNormalWords;
2180  }
2181  if (IDELEMS(G) == lV - ncGenCount - 1) // V = {1} with loop
2182  {
2183  idDelete(&G);
2184  return -1;
2185  }
2186  if (IDELEMS(G) <= lV - ncGenCount - 2) // V = {1} with more than one loop
2187  {
2188  idDelete(&G);
2189  return -1;
2190  }
2191  }
2192 
2193  if (TEST_OPT_PROT)
2194  PrintS("Computing Ufnarovski graph...\n");
2195 
2196  ideal standardWords;
2197  intvec* UG = lp_ufnarovskiGraph(G, standardWords);
2198  if (UG == NULL)
2199  {
2200  idDelete(&G);
2201  return -2;
2202  }
2203  if (errorreported)
2204  {
2205  delete UG;
2206  idDelete(&G);
2207  return -2;
2208  }
2209 
2210  if (TEST_OPT_PROT)
2211  Print("Ufnarovski graph is %dx%d.\n", UG->rows(), UG->cols());
2212 
2213  if (TEST_OPT_PROT)
2214  PrintS("Checking whether Ufnarovski graph is acyclic...\n");
2215 
2216  if (!isAcyclic(UG))
2217  {
2218  // in this case we have infinitely many normal words
2219  return -1;
2220  }
2221 
2222  std::vector<std::vector<int> > vvUG = iv2vv(UG);
2223  for (int i = 0; i < vvUG.size(); i++)
2224  {
2225  if (vvIsRowZero(vvUG, i) && vvIsColumnZero(vvUG, i)) // i is isolated vertex
2226  {
2227  vvDeleteRow(vvUG, i);
2228  vvDeleteColumn(vvUG, i);
2229  i--;
2230  }
2231  }
2232  if (TEST_OPT_PROT)
2233  Print("Simplified Ufnarovski graph to %dx%d.\n", (int)vvUG.size(), (int)vvUG.size());
2234 
2235  // for normal words of length >= maxDeg
2236  // use Ufnarovski graph
2237  if (TEST_OPT_PROT)
2238  PrintS("Computing normal words via Ufnarovski graph...\n");
2239  std::vector<std::vector<int> > UGpower = vvUG;
2240  long nUGpower = 1;
2241  while (!vvIsZero(UGpower))
2242  {
2243  if (TEST_OPT_PROT)
2244  PrintS("Start count graph entries.\n");
2245  for (int i = 0; i < UGpower.size(); i++)
2246  {
2247  for (int j = 0; j < UGpower[i].size(); j++)
2248  {
2249  numberOfNormalWords += UGpower[i][j];
2250  }
2251  }
2252 
2253  if (TEST_OPT_PROT)
2254  {
2255  PrintS("Done count graph entries.\n");
2256  Print("%ld normal words up to length %ld\n", numberOfNormalWords, maxDeg - 1 + nUGpower);
2257  }
2258 
2259  if (TEST_OPT_PROT)
2260  PrintS("Start mat mult.\n");
2261  UGpower = vvMult(UGpower, vvUG); // TODO: avoid creation of new intvec
2262  if (TEST_OPT_PROT)
2263  PrintS("Done mat mult.\n");
2264  nUGpower++;
2265  }
2266 
2267  delete UG;
2268  idDelete(&G);
2269  return numberOfNormalWords;
2270 }
int cols() const
Definition: intvec.h:95
int rows() const
Definition: intvec.h:96
#define Print
Definition: emacs.cc:80
int j
Definition: facHensel.cc:110
static std::vector< std::vector< int > > iv2vv(intvec *M)
Definition: hdegree.cc:1949
static void vvDeleteRow(std::vector< std::vector< int > > &mat, int row)
Definition: hdegree.cc:1992
static BOOLEAN vvIsColumnZero(const std::vector< std::vector< int > > &mat, int col)
Definition: hdegree.cc:2015
static void vvDeleteColumn(std::vector< std::vector< int > > &mat, int col)
Definition: hdegree.cc:1997
static int lp_countNormalWords(int upToLength, ideal M)
Definition: hdegree.cc:1757
static BOOLEAN isAcyclic(const intvec *G)
Definition: hdegree.cc:2062
static BOOLEAN vvIsZero(const std::vector< std::vector< int > > &mat)
Definition: hdegree.cc:2025
static BOOLEAN vvIsRowZero(const std::vector< std::vector< int > > &mat, int row)
Definition: hdegree.cc:2005
static std::vector< std::vector< int > > vvMult(const std::vector< std::vector< int > > &a, const std::vector< std::vector< int > > &b)
Definition: hdegree.cc:2035
#define TEST_OPT_PROT
Definition: options.h:102
void PrintS(const char *s)
Definition: reporter.cc:284

◆ lp_ufnarovskiGraph()

intvec* lp_ufnarovskiGraph ( ideal  G,
ideal &  standardWords 
)

Definition at line 1778 of file hdegree.cc.

1779 {
1780  long l = 0;
1781  for (int i = 0; i < IDELEMS(G); i++)
1782  l = si_max(pTotaldegree(G->m[i]), l);
1783  l--;
1784  if (l <= 0)
1785  {
1786  WerrorS("Ufnarovski graph not implemented for l <= 0");
1787  return NULL;
1788  }
1789  int lV = currRing->isLPring;
1790 
1791  standardWords = lp_computeNormalWords(l, G);
1792 
1793  int n = IDELEMS(standardWords);
1794  intvec* UG = new intvec(n, n, 0);
1795  for (int i = 0; i < n; i++)
1796  {
1797  for (int j = 0; j < n; j++)
1798  {
1799  poly v = standardWords->m[i];
1800  poly w = standardWords->m[j];
1801 
1802  // check whether v*x1 = x2*w (overlap)
1803  bool overlap = true;
1804  for (int k = 1; k <= (l - 1) * lV; k++)
1805  {
1806  if (pGetExp(v, k + lV) != pGetExp(w, k)) {
1807  overlap = false;
1808  break;
1809  }
1810  }
1811 
1812  if (overlap)
1813  {
1814  // create the overlap
1815  poly p = pMult(pCopy(v), p_LPVarAt(w, l, currRing));
1816 
1817  // check whether the overlap is normal
1818  bool normal = true;
1819  for (int k = 0; k < IDELEMS(G); k++)
1820  {
1821  if (p_LPDivisibleBy(G->m[k], p, currRing))
1822  {
1823  normal = false;
1824  break;
1825  }
1826  }
1827 
1828  if (normal)
1829  {
1830  IMATELEM(*UG, i + 1, j + 1) = 1;
1831  }
1832  }
1833  }
1834  }
1835  return UG;
1836 }
int l
Definition: cfEzgcd.cc:100
int k
Definition: cfEzgcd.cc:99
int p
Definition: cfModGcd.cc:4080
const CanonicalForm & w
Definition: facAbsFact.cc:51
const Variable & v
< [in] a sqrfree bivariate poly
Definition: facBivar.h:39
static ideal lp_computeNormalWords(int length, ideal M)
Definition: hdegree.cc:1737
#define IMATELEM(M, I, J)
Definition: intvec.h:85
#define pMult(p, q)
Definition: polys.h:207
#define pGetExp(p, i)
Exponent.
Definition: polys.h:41
#define pCopy(p)
return a copy of the poly
Definition: polys.h:185
BOOLEAN p_LPDivisibleBy(poly a, poly b, const ring r)
Definition: shiftop.cc:773
poly p_LPVarAt(poly p, int pos, const ring r)
Definition: shiftop.cc:835

◆ scComputeHC()

void scComputeHC ( ideal  s,
ideal  Q,
int  k,
poly &  hEdge,
ring  tailRing = currRing 
)

Definition at line 1078 of file hdegree.cc.

1079 {
1080  id_TestTail(S, currRing, tailRing);
1081  if (Q!=NULL) id_TestTail(Q, currRing, tailRing);
1082 
1083  int i;
1084  int k = ak;
1085  #ifdef HAVE_RINGS
1086  if (rField_is_Ring(currRing) && (currRing->OrdSgn == -1))
1087  {
1088  //consider just monic generators (over rings with zero-divisors)
1089  ideal SS=id_Copy(S,tailRing);
1090  for(i=0;i<=idElem(S);i++)
1091  {
1092  if((SS->m[i]!=NULL)
1093  && ((p_IsPurePower(SS->m[i],tailRing)==0)
1094  ||(!n_IsUnit(pGetCoeff(SS->m[i]), tailRing->cf))))
1095  {
1096  p_Delete(&SS->m[i],tailRing);
1097  }
1098  }
1099  S=id_Copy(SS,tailRing);
1100  idSkipZeroes(S);
1101  }
1102  #if 0
1103  printf("\nThis is HC:\n");
1104  for(int ii=0;ii<=idElem(S);ii++)
1105  {
1106  pWrite(S->m[ii]);
1107  }
1108  //getchar();
1109  #endif
1110  #endif
1111  if(idElem(S) == 0)
1112  return;
1113  hNvar = (currRing->N);
1114  hexist = hInit(S, Q, &hNexist, tailRing); // tailRing?
1115  if (k!=0)
1116  hComp(hexist, hNexist, k, hexist, &hNstc);
1117  else
1118  hNstc = hNexist;
1119  assume(hNexist > 0);
1120  hwork = (scfmon)omAlloc(hNexist * sizeof(scmon));
1121  hvar = (varset)omAlloc((hNvar + 1) * sizeof(int));
1122  hpure = (scmon)omAlloc((1 + (hNvar * hNvar)) * sizeof(int));
1123  stcmem = hCreate(hNvar - 1);
1124  for (i = hNvar; i>0; i--)
1125  hvar[i] = i;
1127  if ((hNvar > 2) && (hNstc > 10))
1129  memset(hpure, 0, (hNvar + 1) * sizeof(int));
1130  hPure(hexist, 0, &hNstc, hvar, hNvar, hpure, &hNpure);
1131  hLexS(hexist, hNstc, hvar, hNvar);
1132  if (hEdge!=NULL)
1133  pLmFree(hEdge);
1134  hEdge = pInit();
1135  pWork = pInit();
1136  hHedgeStep(hpure, hexist, hNstc, hvar, hNvar,hEdge);
1137  pSetComp(hEdge,ak);
1138  hKill(stcmem, hNvar - 1);
1139  omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon));
1140  omFreeSize((ADDRESS)hvar, (hNvar + 1) * sizeof(int));
1141  omFreeSize((ADDRESS)hpure, (1 + (hNvar * hNvar)) * sizeof(int));
1143  pLmFree(pWork);
1144 }
void * ADDRESS
Definition: auxiliary.h:119
static FORCE_INLINE BOOLEAN n_IsUnit(number n, const coeffs r)
TRUE iff n has a multiplicative inverse in the given coeff field/ring r.
Definition: coeffs.h:516
static void hHedgeStep(scmon pure, scfmon stc, int Nstc, varset var, int Nvar, poly hEdge)
Definition: hdegree.cc:1018
STATIC_VAR poly pWork
Definition: hdegree.cc:1004
monf hCreate(int Nvar)
Definition: hutil.cc:999
void hComp(scfmon exist, int Nexist, int ak, scfmon stc, int *Nstc)
Definition: hutil.cc:157
scfmon hInit(ideal S, ideal Q, int *Nexist, ring tailRing)
Definition: hutil.cc:31
VAR varset hvar
Definition: hutil.cc:18
void hKill(monf xmem, int Nvar)
Definition: hutil.cc:1013
VAR int hNexist
Definition: hutil.cc:19
void hLexS(scfmon stc, int Nstc, varset var, int Nvar)
Definition: hutil.cc:509
void hDelete(scfmon ev, int ev_length)
Definition: hutil.cc:143
VAR monf stcmem
Definition: hutil.cc:21
void hPure(scfmon stc, int a, int *Nstc, varset var, int Nvar, scmon pure, int *Npure)
Definition: hutil.cc:624
VAR scfmon hwork
Definition: hutil.cc:16
VAR scmon hpure
Definition: hutil.cc:17
void hStaircase(scfmon stc, int *Nstc, varset var, int Nvar)
Definition: hutil.cc:316
void hOrdSupp(scfmon stc, int Nstc, varset var, int Nvar)
Definition: hutil.cc:205
VAR int hNpure
Definition: hutil.cc:19
VAR scfmon hexist
Definition: hutil.cc:16
VAR int hNstc
Definition: hutil.cc:19
VAR int hNvar
Definition: hutil.cc:19
scmon * scfmon
Definition: hutil.h:15
int * varset
Definition: hutil.h:16
int * scmon
Definition: hutil.h:14
ideal id_Copy(ideal h1, const ring r)
copy an ideal
STATIC_VAR jList * Q
Definition: janet.cc:30
#define assume(x)
Definition: mod2.h:387
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
#define omFreeSize(addr, size)
Definition: omAllocDecl.h:260
#define omAlloc(size)
Definition: omAllocDecl.h:210
int p_IsPurePower(const poly p, const ring r)
return i, if head depends only on var(i)
Definition: p_polys.cc:1221
static void p_Delete(poly *p, const ring r)
Definition: p_polys.h:861
#define pSetComp(p, v)
Definition: polys.h:38
static void pLmFree(poly p)
frees the space of the monomial m, assumes m != NULL coef is not freed, m is not advanced
Definition: polys.h:70
void pWrite(poly p)
Definition: polys.h:308
#define pInit()
allocates a new monomial and initializes everything to 0
Definition: polys.h:61
int idElem(const ideal F)
count non-zero elements
#define id_TestTail(A, lR, tR)
Definition: simpleideals.h:77

◆ scDegree()

void scDegree ( ideal  s,
intvec modulweight,
ideal  Q = NULL 
)

Definition at line 895 of file hdegree.cc.

896 {
897  id_Test(S, currRing);
898  if( Q!=NULL ) id_Test(Q, currRing);
899 
900  int co, mu, l;
901  intvec *hseries2;
902  intvec *hseries1 = hFirstSeries(S, modulweight, Q);
903  l = hseries1->length()-1;
904  if (l > 1)
905  hseries2 = hSecondSeries(hseries1);
906  else
907  hseries2 = hseries1;
908  hDegreeSeries(hseries1, hseries2, &co, &mu);
909  if ((l == 1) &&(mu == 0))
910  scPrintDegree((currRing->N)+1, 0);
911  else
912  scPrintDegree(co, mu);
913  if (l>1)
914  delete hseries1;
915  delete hseries2;
916 }
void mu(int **points, int sizePoints)
int length() const
Definition: intvec.h:94
void scPrintDegree(int co, int mu)
Definition: hdegree.cc:881
void hDegreeSeries(intvec *s1, intvec *s2, int *co, int *mu)
Definition: hilb.cc:1380
intvec * hSecondSeries(intvec *hseries1)
Definition: hilb.cc:1345
intvec * hFirstSeries(ideal S, intvec *modulweight, ideal Q, intvec *wdegree, ring tailRing)
Definition: hilb.cc:1335

◆ scDimInt()

int scDimInt ( ideal  s,
ideal  Q = NULL 
)

ideal dimension

Definition at line 77 of file hdegree.cc.

78 {
79  id_Test(S, currRing);
80  if( Q!=NULL ) id_Test(Q, currRing);
81 
82  int mc;
83  hexist = hInit(S, Q, &hNexist, currRing);
84  if (!hNexist)
85  return (currRing->N);
86  hwork = (scfmon)omAlloc(hNexist * sizeof(scmon));
87  hvar = (varset)omAlloc(((currRing->N) + 1) * sizeof(int));
88  hpure = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int));
89  mc = hisModule;
90  if (!mc)
91  {
92  hrad = hexist;
93  hNrad = hNexist;
94  }
95  else
96  hrad = (scfmon)omAlloc(hNexist * sizeof(scmon));
97  radmem = hCreate((currRing->N) - 1);
98  hCo = (currRing->N) + 1;
99  loop
100  {
101  if (mc)
102  hComp(hexist, hNexist, mc, hrad, &hNrad);
103  if (hNrad)
104  {
105  hNvar = (currRing->N);
106  hRadical(hrad, &hNrad, hNvar);
107  hSupp(hrad, hNrad, hvar, &hNvar);
108  if (hNvar)
109  {
110  memset(hpure, 0, ((currRing->N) + 1) * sizeof(int));
111  hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure);
112  hLexR(hrad, hNrad, hvar, hNvar);
114  }
115  }
116  else
117  {
118  hCo = 0;
119  break;
120  }
121  mc--;
122  if (mc <= 0)
123  break;
124  }
125  hKill(radmem, (currRing->N) - 1);
126  omFreeSize((ADDRESS)hpure, (1 + ((currRing->N) * (currRing->N))) * sizeof(int));
127  omFreeSize((ADDRESS)hvar, ((currRing->N) + 1) * sizeof(int));
128  omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon));
130  if (hisModule)
131  omFreeSize((ADDRESS)hrad, hNexist * sizeof(scmon));
132  return (currRing->N) - hCo;
133 }
VAR int hCo
Definition: hdegree.cc:27
void hDimSolve(scmon pure, int Npure, scfmon rad, int Nrad, varset var, int Nvar)
Definition: hdegree.cc:34
void hSupp(scfmon stc, int Nstc, varset var, int *Nvar)
Definition: hutil.cc:177
void hLexR(scfmon rad, int Nrad, varset var, int Nvar)
Definition: hutil.cc:568
VAR scfmon hrad
Definition: hutil.cc:16
VAR int hisModule
Definition: hutil.cc:20
VAR monf radmem
Definition: hutil.cc:21
VAR int hNrad
Definition: hutil.cc:19
void hRadical(scfmon rad, int *Nrad, int Nvar)
Definition: hutil.cc:414
#define loop
Definition: structs.h:80

◆ scDimIntRing()

int scDimIntRing ( ideal  s,
ideal  Q = NULL 
)

scDimInt for ring-coefficients

Definition at line 135 of file hdegree.cc.

136 {
137 #ifdef HAVE_RINGS
139  {
140  int i = idPosConstant(vid);
141  if ((i != -1) && (n_IsUnit(pGetCoeff(vid->m[i]),currRing->cf)))
142  { /* ideal v contains unit; dim = -1 */
143  return(-1);
144  }
145  ideal vv = id_Head(vid,currRing);
146  idSkipZeroes(vv);
147  i = idPosConstant(vid);
148  int d;
149  if(i == -1)
150  {
151  d = scDimInt(vv, Q);
152  if(rField_is_Z(currRing))
153  d++;
154  }
155  else
156  {
157  if(n_IsUnit(pGetCoeff(vv->m[i]),currRing->cf))
158  d = -1;
159  else
160  d = scDimInt(vv, Q);
161  }
162  //Anne's Idea for std(4,2x) = 0 bug
163  int dcurr = d;
164  for(unsigned ii=0;ii<(unsigned)IDELEMS(vv);ii++)
165  {
166  if(vv->m[ii] != NULL && !n_IsUnit(pGetCoeff(vv->m[ii]),currRing->cf))
167  {
168  ideal vc = idCopy(vv);
169  poly c = pInit();
170  pSetCoeff0(c,nCopy(pGetCoeff(vv->m[ii])));
171  idInsertPoly(vc,c);
172  idSkipZeroes(vc);
173  for(unsigned jj = 0;jj<(unsigned)IDELEMS(vc)-1;jj++)
174  {
175  if((vc->m[jj]!=NULL)
176  && (n_DivBy(pGetCoeff(vc->m[jj]),pGetCoeff(c),currRing->cf)))
177  {
178  pDelete(&vc->m[jj]);
179  }
180  }
181  idSkipZeroes(vc);
182  i = idPosConstant(vc);
183  if (i != -1) pDelete(&vc->m[i]);
184  dcurr = scDimInt(vc, Q);
185  // the following assumes the ground rings to be either zero- or one-dimensional
186  if((i==-1) && rField_is_Z(currRing))
187  {
188  // should also be activated for other euclidean domains as groundfield
189  dcurr++;
190  }
191  idDelete(&vc);
192  }
193  if(dcurr > d)
194  d = dcurr;
195  }
196  idDelete(&vv);
197  return d;
198  }
199 #endif
200  return scDimInt(vid,Q);
201 }
static FORCE_INLINE BOOLEAN n_DivBy(number a, number b, const coeffs r)
test whether 'a' is divisible 'b'; for r encoding a field: TRUE iff 'b' does not represent zero in Z:...
Definition: coeffs.h:777
int scDimInt(ideal S, ideal Q)
ideal dimension
Definition: hdegree.cc:77
BOOLEAN idInsertPoly(ideal h1, poly h2)
insert h2 into h1 (if h2 is not the zero polynomial) return TRUE iff h2 was indeed inserted
ideal idCopy(ideal A)
Definition: ideals.h:60
#define idPosConstant(I)
index of generator with leading term in ground ring (if any); otherwise -1
Definition: ideals.h:37
#define pSetCoeff0(p, n)
Definition: monomials.h:59
#define nCopy(n)
Definition: numbers.h:15
#define pDelete(p_ptr)
Definition: polys.h:186
static BOOLEAN rField_is_Z(const ring r)
Definition: ring.h:514

◆ scIndIntvec()

intvec* scIndIntvec ( ideal  S,
ideal  Q = NULL 
)

Definition at line 285 of file hdegree.cc.

286 {
287  id_Test(S, currRing);
288  if( Q!=NULL ) id_Test(Q, currRing);
289 
290  intvec *Set=new intvec((currRing->N));
291  int mc,i;
292  hexist = hInit(S, Q, &hNexist, currRing);
293  if (hNexist==0)
294  {
295  for(i=0; i<(currRing->N); i++)
296  (*Set)[i]=1;
297  return Set;
298  }
299  hwork = (scfmon)omAlloc(hNexist * sizeof(scmon));
300  hvar = (varset)omAlloc(((currRing->N) + 1) * sizeof(int));
301  hpure = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int));
302  hInd = (scmon)omAlloc0((1 + (currRing->N)) * sizeof(int));
303  mc = hisModule;
304  if (mc==0)
305  {
306  hrad = hexist;
307  hNrad = hNexist;
308  }
309  else
310  hrad = (scfmon)omAlloc(hNexist * sizeof(scmon));
311  radmem = hCreate((currRing->N) - 1);
312  hCo = (currRing->N) + 1;
313  loop
314  {
315  if (mc!=0)
316  hComp(hexist, hNexist, mc, hrad, &hNrad);
317  if (hNrad!=0)
318  {
319  hNvar = (currRing->N);
320  hRadical(hrad, &hNrad, hNvar);
321  hSupp(hrad, hNrad, hvar, &hNvar);
322  if (hNvar!=0)
323  {
324  memset(hpure, 0, ((currRing->N) + 1) * sizeof(int));
325  hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure);
326  hLexR(hrad, hNrad, hvar, hNvar);
328  }
329  }
330  else
331  {
332  hCo = 0;
333  break;
334  }
335  mc--;
336  if (mc <= 0)
337  break;
338  }
339  for(i=0; i<(currRing->N); i++)
340  (*Set)[i] = hInd[i+1];
341  hKill(radmem, (currRing->N) - 1);
342  omFreeSize((ADDRESS)hpure, (1 + ((currRing->N) * (currRing->N))) * sizeof(int));
343  omFreeSize((ADDRESS)hInd, (1 + (currRing->N)) * sizeof(int));
344  omFreeSize((ADDRESS)hvar, ((currRing->N) + 1) * sizeof(int));
345  omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon));
347  if (hisModule)
348  omFreeSize((ADDRESS)hrad, hNexist * sizeof(scmon));
349  return Set;
350 }
STATIC_VAR scmon hInd
Definition: hdegree.cc:204
static void hIndSolve(scmon pure, int Npure, scfmon rad, int Nrad, varset var, int Nvar)
Definition: hdegree.cc:206
#define omAlloc0(size)
Definition: omAllocDecl.h:211

◆ scKBase()

ideal scKBase ( int  deg,
ideal  s,
ideal  Q = NULL,
intvec mv = NULL 
)

Definition at line 1426 of file hdegree.cc.

1427 {
1428  if( Q!=NULL) id_Test(Q, currRing);
1429 
1430  int i, di;
1431  poly p;
1432 
1433  if (deg < 0)
1434  {
1435  di = scDimInt(s, Q);
1436  if (di != 0)
1437  {
1438  //Werror("KBase not finite");
1439  return idInit(1,s->rank);
1440  }
1441  }
1442  stcmem = hCreate((currRing->N) - 1);
1443  hexist = hInit(s, Q, &hNexist, currRing);
1444  p = last = pInit();
1445  /*pNext(p) = NULL;*/
1446  act = (scmon)omAlloc(((currRing->N) + 1) * sizeof(int));
1447  *act = 0;
1448  if (!hNexist)
1449  {
1450  scAll((currRing->N), deg);
1451  goto ende;
1452  }
1453  if (!hisModule)
1454  {
1455  if (deg < 0) scInKbase(hexist, hNexist, (currRing->N));
1456  else scDegKbase(hexist, hNexist, (currRing->N), deg);
1457  }
1458  else
1459  {
1460  hstc = (scfmon)omAlloc(hNexist * sizeof(scmon));
1461  for (i = 1; i <= hisModule; i++)
1462  {
1463  *act = i;
1464  hComp(hexist, hNexist, i, hstc, &hNstc);
1465  int deg_ei=deg;
1466  if (mv!=NULL) deg_ei -= (*mv)[i-1];
1467  if ((deg < 0) || (deg_ei>=0))
1468  {
1469  if (hNstc)
1470  {
1471  if (deg < 0) scInKbase(hstc, hNstc, (currRing->N));
1472  else scDegKbase(hstc, hNstc, (currRing->N), deg_ei);
1473  }
1474  else
1475  scAll((currRing->N), deg_ei);
1476  }
1477  }
1478  omFreeSize((ADDRESS)hstc, hNexist * sizeof(scmon));
1479  }
1480 ende:
1482  omFreeSize((ADDRESS)act, ((currRing->N) + 1) * sizeof(int));
1483  hKill(stcmem, (currRing->N) - 1);
1484  pLmFree(&p);
1485  if (p == NULL)
1486  return idInit(1,s->rank);
1487 
1488  last = p;
1489  return scIdKbase(p, s->rank);
1490 }
const CanonicalForm int s
Definition: facAbsFact.cc:51
STATIC_VAR poly last
Definition: hdegree.cc:1150
static void scAll(int Nvar, int deg)
Definition: hdegree.cc:1237
static void scDegKbase(scfmon stc, int Nstc, int Nvar, int deg)
Definition: hdegree.cc:1271
STATIC_VAR scmon act
Definition: hdegree.cc:1151
static ideal scIdKbase(poly q, const int rank)
Definition: hdegree.cc:1408
static void scInKbase(scfmon stc, int Nstc, int Nvar)
Definition: hdegree.cc:1352
VAR scfmon hstc
Definition: hutil.cc:16
ideal idInit(int idsize, int rank)
initialise an ideal / module
Definition: simpleideals.cc:35

◆ scMult0Int()

int scMult0Int ( ideal  s,
ideal  Q = NULL,
const ring  tailRing = currRing 
)

Definition at line 992 of file hdegree.cc.

993 {
994  id_TestTail(S, currRing, tailRing);
995  if (Q!=NULL) id_TestTail(Q, currRing, tailRing);
996 
997  hDegree0(S, Q, tailRing);
998  return hMu;
999 }
VAR int hMu
Definition: hdegree.cc:27
static void hDegree0(ideal S, ideal Q, const ring tailRing)
Definition: hdegree.cc:918

◆ scMultInt()

int scMultInt ( ideal  s,
ideal  Q = NULL 
)

Definition at line 872 of file hdegree.cc.

873 {
874  id_Test(S, currRing);
875  if( Q!=NULL ) id_Test(Q, currRing);
876 
877  hDegree(S, Q);
878  return hMu;
879 }
static void hDegree(ideal S, ideal Q)
Definition: hdegree.cc:771

◆ scPrintDegree()

void scPrintDegree ( int  co,
int  mu 
)

Definition at line 881 of file hdegree.cc.

882 {
883  int di = (currRing->N)-co;
884  if (currRing->OrdSgn == 1)
885  {
886  if (di>0)
887  Print("// dimension (proj.) = %d\n// degree (proj.) = %d\n", di-1, mu);
888  else
889  Print("// dimension (affine) = 0\n// degree (affine) = %d\n", mu);
890  }
891  else
892  Print("// dimension (local) = %d\n// multiplicity = %d\n", di, mu);
893 }