My Project  debian-1:4.1.2-p1+ds-2
ringgb.cc
Go to the documentation of this file.
1 /****************************************
2 * Computer Algebra System SINGULAR *
3 ****************************************/
4 /*
5 * ABSTRACT: ringgb interface
6 */
7 //#define HAVE_TAIL_RING
8 #define NO_BUCKETS
9 
10 #include "kernel/mod2.h"
11 #include "kernel/GBEngine/kutil.h"
12 #include "kernel/structs.h"
13 #include "kernel/polys.h"
15 #include "kernel/ideals.h"
16 #include "kernel/GBEngine/kstd1.h"
17 #include "kernel/GBEngine/khstd.h"
18 #include "polys/kbuckets.h"
19 #include "polys/weight.h"
20 #include "misc/intvec.h"
21 #include "kernel/polys.h"
22 #ifdef HAVE_PLURAL
23 #include "polys/nc/nc.h"
24 #endif
25 
26 #include "kernel/GBEngine/ringgb.h"
27 
28 #ifdef HAVE_RINGS
29 poly reduce_poly_fct(poly p, ring r)
30 {
31  return kFindZeroPoly(p, r, r);
32 }
33 
34 /*
35  * Returns maximal k, such that
36  * 2^k | n
37  */
38 int indexOf2(number n)
39 {
40  long test = (long) n;
41  int i = 0;
42  while (test%2 == 0)
43  {
44  i++;
45  test = test / 2;
46  }
47  return i;
48 }
49 
50 /***************************************************************
51  *
52  * Lcm business
53  *
54  ***************************************************************/
55 // get m1 = LCM(LM(p1), LM(p2))/LM(p1)
56 // m2 = LCM(LM(p1), LM(p2))/LM(p2)
57 BOOLEAN ring2toM_GetLeadTerms(const poly p1, const poly p2, const ring p_r,
58  poly &m1, poly &m2, const ring m_r)
59 {
60  int i;
61  int x;
62  m1 = p_Init(m_r);
63  m2 = p_Init(m_r);
64 
65  for (i = p_r->N; i; i--)
66  {
67  x = p_GetExpDiff(p1, p2, i, p_r);
68  if (x > 0)
69  {
70  p_SetExp(m2,i,x, m_r);
71  p_SetExp(m1,i,0, m_r);
72  }
73  else
74  {
75  p_SetExp(m1,i,-x, m_r);
76  p_SetExp(m2,i,0, m_r);
77  }
78  }
79  p_Setm(m1, m_r);
80  p_Setm(m2, m_r);
81  long cp1 = (long) pGetCoeff(p1);
82  long cp2 = (long) pGetCoeff(p2);
83  if (cp1 != 0 && cp2 != 0)
84  {
85  while (cp1%2 == 0 && cp2%2 == 0)
86  {
87  cp1 = cp1 / 2;
88  cp2 = cp2 / 2;
89  }
90  }
91  p_SetCoeff(m1, (number) cp2, m_r);
92  p_SetCoeff(m2, (number) cp1, m_r);
93  return TRUE;
94 }
95 
96 void printPolyMsg(const char * start, poly f, const char * end)
97 {
98  PrintS(start);
99  wrp(f);
100  PrintS(end);
101 }
102 
103 poly spolyRing2toM(poly f, poly g, ring r)
104 {
105  poly m1 = NULL;
106  poly m2 = NULL;
107  ring2toM_GetLeadTerms(f, g, r, m1, m2, r);
108  // printPolyMsg("spoly: m1=", m1, " | ");
109  // printPolyMsg("m2=", m2, "");
110  // PrintLn();
111  poly sp = pSub(p_Mult_mm(f, m1, r), pp_Mult_mm(g, m2, r));
112  pDelete(&m1);
113  pDelete(&m2);
114  return(sp);
115 }
116 
117 poly ringRedNF (poly f, ideal G, ring r)
118 {
119  // If f = 0, then normal form is also 0
120  if (f == NULL) { return NULL; }
121  poly h = NULL;
122  poly g = pCopy(f);
123  int c = 0;
124  while (g != NULL)
125  {
126  Print("%d-step RedNF - g=", c);
127  wrp(g);
128  PrintS(" | h=");
129  wrp(h);
130  PrintLn();
131  g = ringNF(g, G, r);
132  if (g != NULL) {
133  h = pAdd(h, pHead(g));
134  pLmDelete(&g);
135  }
136  c++;
137  }
138  return h;
139 }
140 
141 #endif
142 
143 #ifdef HAVE_RINGS
144 
145 /*
146  * Find an index i from G, such that
147  * LT(rside) = x * LT(G[i]) has a solution
148  * or -1 if rside is not in the
149  * ideal of the leading coefficients
150  * of the suitable g from G.
151  */
152 int findRingSolver(poly rside, ideal G, ring r)
153 {
154  if (rside == NULL) return -1;
155  int i;
156 // int iO2rside = indexOf2(pGetCoeff(rside));
157  for (i = 0; i < IDELEMS(G); i++)
158  {
159  if // (indexOf2(pGetCoeff(G->m[i])) <= iO2rside && / should not be necessary any more
160  (p_LmDivisibleBy(G->m[i], rside, r))
161  {
162  return i;
163  }
164  }
165  return -1;
166 }
167 
168 poly plain_spoly(poly f, poly g)
169 {
170  number cf = nCopy(pGetCoeff(f)), cg = nCopy(pGetCoeff(g));
171  (void)ksCheckCoeff(&cf, &cg, currRing->cf); // gcd and zero divisors
172  poly fm, gm;
173  k_GetLeadTerms(f, g, currRing, fm, gm, currRing);
174  pSetCoeff0(fm, cg);
175  pSetCoeff0(gm, cf); // and now, m1 * LT(p1) == m2 * LT(p2)
176  poly sp = pSub(ppMult_mm(f, fm), ppMult_mm(g, gm));
177  pDelete(&fm);
178  pDelete(&gm);
179  return(sp);
180 }
181 
182 /*2
183 * Generates spoly(0, h) if applicable. Assumes ring in Z/2^n.
184 */
185 poly plain_zero_spoly(poly h)
186 {
187  poly p = NULL;
188  number gcd = n_Gcd((number) 0, pGetCoeff(h), currRing->cf);
189  if (!n_IsOne( gcd, currRing->cf ))
190  {
191  number tmp=n_Ann(gcd,currRing->cf);
192  p = p_Copy(h->next, currRing);
193  p = __p_Mult_nn(p, tmp, currRing);
194  n_Delete(&tmp,currRing->cf);
195  }
196  return p;
197 }
198 
199 poly ringNF(poly f, ideal G, ring r)
200 {
201  // If f = 0, then normal form is also 0
202  if (f == NULL) { return NULL; }
203  poly tmp = NULL;
204  poly h = pCopy(f);
205  int i = findRingSolver(h, G, r);
206  int c = 1;
207  while (h != NULL && i >= 0) {
208 // Print("%d-step NF - h:", c);
209 // wrp(h);
210 // PrintS(" ");
211 // PrintS("G->m[i]:");
212 // wrp(G->m[i]);
213 // PrintLn();
214  tmp = h;
215  h = plain_spoly(h, G->m[i]);
216  pDelete(&tmp);
217 // PrintS("=> h=");
218 // wrp(h);
219 // PrintLn();
220  i = findRingSolver(h, G, r);
221  c++;
222  }
223  return h;
224 }
225 
226 int testGB(ideal I, ideal GI) {
227  poly f, g, h, nf;
228  int i = 0;
229  int j = 0;
230  PrintS("I included?");
231  for (i = 0; i < IDELEMS(I); i++) {
232  if (ringNF(I->m[i], GI, currRing) != NULL) {
233  PrintS("Not reduced to zero from I: ");
234  wrp(I->m[i]);
235  PrintS(" --> ");
236  wrp(ringNF(I->m[i], GI, currRing));
237  PrintLn();
238  return(0);
239  }
240  PrintS("-");
241  }
242  PrintS(" Yes!\nspoly --> 0?");
243  for (i = 0; i < IDELEMS(GI); i++)
244  {
245  for (j = i + 1; j < IDELEMS(GI); j++)
246  {
247  f = pCopy(GI->m[i]);
248  g = pCopy(GI->m[j]);
249  h = plain_spoly(f, g);
250  nf = ringNF(h, GI, currRing);
251  if (nf != NULL)
252  {
253  PrintS("spoly(");
254  wrp(GI->m[i]);
255  PrintS(", ");
256  wrp(GI->m[j]);
257  PrintS(") = ");
258  wrp(h);
259  PrintS(" --> ");
260  wrp(nf);
261  PrintLn();
262  return(0);
263  }
264  pDelete(&f);
265  pDelete(&g);
266  pDelete(&h);
267  pDelete(&nf);
268  PrintS("-");
269  }
270  }
271  if (!(rField_is_Domain(currRing)))
272  {
273  PrintS(" Yes!\nzero-spoly --> 0?");
274  for (i = 0; i < IDELEMS(GI); i++)
275  {
276  f = plain_zero_spoly(GI->m[i]);
277  nf = ringNF(f, GI, currRing);
278  if (nf != NULL) {
279  PrintS("spoly(");
280  wrp(GI->m[i]);
281  PrintS(", ");
282  wrp(0);
283  PrintS(") = ");
284  wrp(h);
285  PrintS(" --> ");
286  wrp(nf);
287  PrintLn();
288  return(0);
289  }
290  pDelete(&f);
291  pDelete(&nf);
292  PrintS("-");
293  }
294  }
295  PrintS(" Yes!");
296  PrintLn();
297  return(1);
298 }
299 
300 #endif
test
CanonicalForm test
Definition: cfModGcd.cc:4037
ksCheckCoeff
int ksCheckCoeff(number *a, number *b)
kFindZeroPoly
poly kFindZeroPoly(poly input_p, ring leadRing, ring tailRing)
Definition: kstd2.cc:454
kutil.h
j
int j
Definition: facHensel.cc:105
f
FILE * f
Definition: checklibs.c:9
x
Variable x
Definition: cfModGcd.cc:4023
ppMult_mm
#define ppMult_mm(p, m)
Definition: polys.h:189
rField_is_Domain
static BOOLEAN rField_is_Domain(const ring r)
Definition: ring.h:481
h
STATIC_VAR Poly * h
Definition: janet.cc:971
p_Mult_mm
static poly p_Mult_mm(poly p, poly m, const ring r)
Definition: p_polys.h:985
weight.h
cf
CanonicalForm cf
Definition: cfModGcd.cc:4024
polys.h
g
g
Definition: cfModGcd.cc:4031
n_Delete
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete 'p'
Definition: coeffs.h:454
findRingSolver
int findRingSolver(poly rside, ideal G, ring r)
Definition: ringgb.cc:151
pp_Mult_mm
static poly pp_Mult_mm(poly p, poly m, const ring r)
Definition: p_polys.h:975
reduce_poly_fct
poly reduce_poly_fct(poly p, ring r)
Definition: ringgb.cc:29
pDelete
#define pDelete(p_ptr)
Definition: polys.h:175
n_IsOne
static FORCE_INLINE BOOLEAN n_IsOne(number n, const coeffs r)
TRUE iff 'n' represents the one element.
Definition: coeffs.h:467
testGB
int testGB(ideal I, ideal GI)
Definition: ringgb.cc:225
__p_Mult_nn
#define __p_Mult_nn(p, n, r)
Definition: p_polys.h:915
p_LmDivisibleBy
static BOOLEAN p_LmDivisibleBy(poly a, poly b, const ring r)
Definition: p_polys.h:1802
nf
Definition: gnumpfl.cc:25
p_SetExp
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:475
p_Copy
static poly p_Copy(poly p, const ring r)
returns a copy of p
Definition: p_polys.h:796
TRUE
#define TRUE
Definition: auxiliary.h:100
i
int i
Definition: cfEzgcd.cc:125
spolyRing2toM
poly spolyRing2toM(poly f, poly g, ring r)
Definition: ringgb.cc:102
n_Ann
static FORCE_INLINE number n_Ann(number a, const coeffs r)
if r is a ring with zero divisors, return an annihilator!=0 of b otherwise return NULL
Definition: coeffs.h:700
ring2toM_GetLeadTerms
BOOLEAN ring2toM_GetLeadTerms(const poly p1, const poly p2, const ring p_r, poly &m1, poly &m2, const ring m_r)
Definition: ringgb.cc:56
PrintS
void PrintS(const char *s)
Definition: reporter.cc:283
ringgb.h
BOOLEAN
int BOOLEAN
Definition: auxiliary.h:87
structs.h
mod2.h
G
STATIC_VAR TreeM * G
Definition: janet.cc:31
k_GetLeadTerms
KINLINE BOOLEAN k_GetLeadTerms(const poly p1, const poly p2, const ring p_r, poly &m1, poly &m2, const ring m_r)
Definition: kInline.h:960
cg
CanonicalForm cg
Definition: cfModGcd.cc:4024
p_polys.h
p_Init
static poly p_Init(const ring r, omBin bin)
Definition: p_polys.h:1242
printPolyMsg
void printPolyMsg(const char *start, poly f, const char *end)
Definition: ringgb.cc:95
intvec.h
indexOf2
int indexOf2(number n)
Definition: ringgb.cc:38
pAdd
#define pAdd(p, q)
Definition: polys.h:191
plain_spoly
poly plain_spoly(poly f, poly g)
Definition: ringgb.cc:167
kbuckets.h
ringRedNF
poly ringRedNF(poly f, ideal G, ring r)
Definition: ringgb.cc:116
kstd1.h
nc.h
Print
#define Print
Definition: emacs.cc:79
khstd.h
p_SetCoeff
static number p_SetCoeff(poly p, number n, ring r)
Definition: p_polys.h:399
pSetCoeff0
#define pSetCoeff0(p, n)
Definition: monomials.h:56
n_Gcd
static FORCE_INLINE number n_Gcd(number a, number b, const coeffs r)
in Z: return the gcd of 'a' and 'b' in Z/nZ, Z/2^kZ: computed as in the case Z in Z/pZ,...
Definition: coeffs.h:685
p_GetExpDiff
static long p_GetExpDiff(poly p1, poly p2, int i, ring r)
Definition: p_polys.h:622
NULL
#define NULL
Definition: omList.c:11
pLmDelete
#define pLmDelete(p)
assume p != NULL, deletes Lm(p)->coef and Lm(p)
Definition: polys.h:74
ideals.h
p_Setm
static void p_Setm(poly p, const ring r)
Definition: p_polys.h:223
gcd
int gcd(int a, int b)
Definition: walkSupport.cc:836
p
int p
Definition: cfModGcd.cc:4019
currRing
VAR ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
Definition: polys.cc:13
pCopy
#define pCopy(p)
return a copy of the poly
Definition: polys.h:174
ringNF
poly ringNF(poly f, ideal G, ring r)
Definition: ringgb.cc:198
IDELEMS
#define IDELEMS(i)
Definition: simpleideals.h:23
plain_zero_spoly
poly plain_zero_spoly(poly h)
Definition: ringgb.cc:184
pHead
#define pHead(p)
returns newly allocated copy of Lm(p), coef is copied, next=NULL, p might be NULL
Definition: polys.h:65
pGetCoeff
static number & pGetCoeff(poly p)
return an alias to the leading coefficient of p assumes that p != NULL NOTE: not copy
Definition: monomials.h:41
PrintLn
void PrintLn()
Definition: reporter.cc:309
pSub
#define pSub(a, b)
Definition: polys.h:271
nCopy
#define nCopy(n)
Definition: numbers.h:14
wrp
void wrp(poly p)
Definition: polys.h:294