23 int dim(ideal I, ring r)
39 if (i != -1)
pDelete(&vv->m[i]);
67 gfan::ZVector allOnes(n);
68 for (
int i=0;
i<n;
i++)
70 ring rShortcut =
rCopy0(r);
73 int* block0 = rShortcut->block0;
74 int* block1 = rShortcut->block1;
75 int** wvhdl = rShortcut->wvhdl;
79 rShortcut->block0 = (
int*)
omAlloc0((h+2)*
sizeof(int));
80 rShortcut->block1 = (
int*)
omAlloc0((h+2)*
sizeof(int));
81 rShortcut->wvhdl = (
int**)
omAlloc0((h+2)*
sizeof(
int*));
83 rShortcut->block0[0] = 1;
84 rShortcut->block1[0] = n;
87 for (
int i=1;
i<=
h;
i++)
89 rShortcut->order[
i] = order[
i-1];
90 rShortcut->block0[
i] = block0[
i-1];
91 rShortcut->block1[
i] = block1[
i-1];
92 rShortcut->wvhdl[
i] = wvhdl[
i-1];
108 ideal IShortcut =
idInit(k);
110 for (
int i=0;
i<
k;
i++)
122 for (
int i=0;
i<
k;
i++)
139 const bool completelyHomogeneous,
140 const bool completeSpace):
141 originalRing(
rCopy(r)),
143 expectedDimension(
dim(originalIdeal,originalRing)),
145 startingRing(
rCopy(originalRing)),
146 startingIdeal(
id_Copy(originalIdeal,originalRing)),
147 uniformizingParameter(
NULL),
149 onlyLowerHalfSpace(
false),
155 if (!completelyHomogeneous)
178 char** oldNames = s->names;
179 s->names = (
char**)
omAlloc((n+1)*
sizeof(
char**));
181 for (
int i=1;
i<n;
i++)
182 s->names[
i] = oldNames[
i-1];
186 s->block0 = (
int*)
omAlloc0(3*
sizeof(
int));
187 s->block1 = (
int*)
omAlloc0(3*
sizeof(
int));
188 s->wvhdl = (
int**)
omAlloc0(3*
sizeof(
int**));
192 s->wvhdl[0] = (
int*)
omAlloc(n*
sizeof(
int));
204 for (
int i=1;
i<n;
i++)
209 for (
int i=1;
i<n;
i++)
214 for (
int i=1;
i<n;
i++)
215 s->wvhdl[0][
i] = r->wvhdl[0][
i-1];
219 for (
int i=1;
i<n;
i++)
220 s->wvhdl[0][
i] = -r->wvhdl[0][
i-1];
232 poly
g =
p_One(startingRing);
233 p_SetCoeff(g,uniformizingParameter,startingRing);
245 int n =
rVar(originalRing);
246 int* shiftByOne = (
int*)
omAlloc((n+1)*
sizeof(int));
247 for (
int i=1;
i<=n;
i++)
249 for (
int i=0;
i<
k;
i++)
251 if(originalIdeal->m[
i]!=
NULL)
253 J->m[
i] =
p_PermPoly(originalIdeal->m[
i],shiftByOne,originalRing,startingRing,nMap,
NULL,0);
264 startingIdeal->m[
k] = pt->m[0];
382 if (shortcutRing)
rTest(shortcutRing);
408 for (
int i=l;
i>0;
i--)
452 int* block0 = rShortcut->block0;
453 int* block1 = rShortcut->block1;
454 int** wvhdl = rShortcut->wvhdl;
460 rShortcut->block0 = (
int*)
omAlloc0((h+2)*
sizeof(int));
461 rShortcut->block1 = (
int*)
omAlloc0((h+2)*
sizeof(int));
462 rShortcut->wvhdl = (
int**)
omAlloc0((h+2)*
sizeof(
int*));
464 rShortcut->block0[0] = 1;
465 rShortcut->block1[0] = n;
468 for (
int i=1;
i<=
h;
i++)
470 rShortcut->order[
i] = order[
i-1];
471 rShortcut->block0[
i] = block0[
i-1];
472 rShortcut->block1[
i] = block1[
i-1];
473 rShortcut->wvhdl[
i] = wvhdl[
i-1];
498 for (
int i=0;
i<
k;
i++)
504 return std::pair<poly,int>(
g,
i);
520 for (
int i=0;
i<
k;
i++)
533 gfan::ZCone pos = gfan::ZCone::positiveOrthant(C0.ambientDimension());
534 gfan::ZCone C0pos = intersection(C0,pos);
535 C0pos.canonicalize();
536 gfan::ZVector wpos = C0pos.getRelativeInteriorPoint();
542 poly monomial =
NULL;
559 return std::pair<poly,int>(monomial,-1);
594 ideal inJShortcut =
idInit(k);
595 ideal inIShortcut =
idInit(l);
597 for (
int i=0;
i<
k;
i++)
599 for (
int j=0;
j<
l;
j++)
601 id_Test(inJShortcut,rShortcut);
602 id_Test(inIShortcut,rShortcut);
611 for (
int ij=k*l-1; ij>=0; ij--)
621 for (
int j=0;
j<
k;
j++)
624 for (
int i=0;
i<
l;
i++)
627 poly inIi =
p_Copy(inI->m[
i],r);
634 for (
int i=0;
i<
l;
i++)
665 ideal inIShortcut =
idInit(k);
666 for (
int i=0;
i<
k;
i++)
674 inJ->m[0] =
p_One(r);
677 for (
int i=0;
i<
k;
i++)
691 for (
int i=0;
i<
k;
i++)
697 for (
int i=0;
i<
k;
i++)
711 s->block0 = (
int*)
omAlloc0(5*
sizeof(
int));
712 s->block1 = (
int*)
omAlloc0(5*
sizeof(
int));
713 s->wvhdl = (
int**)
omAlloc0(5*
sizeof(
int**));
739 s->block0 = (
int*)
omAlloc0(5*
sizeof(
int));
740 s->block1 = (
int*)
omAlloc0(5*
sizeof(
int));
741 s->wvhdl = (
int**)
omAlloc0(5*
sizeof(
int**));
761 const gfan::ZVector &interiorPoint,
762 const gfan::ZVector &facetNormal)
const 770 ideal inIr =
initial(Ir,r,interiorPoint);
774 ideal inIsAdjusted =
idInit(k);
775 for (
int i=0;
i<
k;
i++)
783 identity =
n_SetMap(sAdjusted->cf,r->cf);
784 for (
int i=0;
i<
k;
i++)
791 for (
int i=0;
i<
k;
i++)
808 return std::make_pair(Js,s);
#define idPosConstant(I)
index of generator with leading term in ground ring (if any); otherwise -1
void putUniformizingBinomialInFront(ideal I, const ring r, const number q) const
bool checkForNonPositiveEntries(const gfan::ZVector &w)
implementation of the class tropicalStrategy
ring getShortcutRing() const
const CanonicalForm int s
ring getShortcutRingPrependingWeight(const ring r, const gfan::ZVector &w) const
If valuation trivial, returns a copy of r with a positive weight prepended, such that any ideal homog...
matrix divisionDiscardingRemainder(const poly f, const ideal G, const ring r)
Computes a division discarding remainder of f with respect to G.
poly kNF(ideal F, ideal Q, poly p, int syzComp, int lazyReduce)
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.
gfan::ZCone homogeneitySpace(ideal I, ring r)
gfan::ZVector nonvalued_adjustWeightUnderHomogeneity(const gfan::ZVector &e, const gfan::ZVector &)
int findPositionOfUniformizingBinomial(const ideal I, const ring r) const
ring copyAndChangeCoefficientRing(const ring r) const
#define idDelete(H)
delete an ideal
ring getOriginalRing() const
returns the polynomial ring over the field with valuation
bool isOrderingLocalInT(const ring r)
ideal id_Copy(ideal h1, const ring r)
copy an ideal
static FORCE_INLINE BOOLEAN n_IsOne(number n, const coeffs r)
TRUE iff 'n' represents the one element.
ideal computeWitness(const ideal inJ, const ideal inI, const ideal I, const ring r) const
suppose w a weight in maximal groebner cone of > suppose I (initially) reduced standard basis w...
bool ppreduceInitially(poly *hStar, const poly g, const ring r)
reduces h initially with respect to g, returns false if h was initially reduced in the first place...
static FORCE_INLINE number n_Init(long i, const coeffs r)
a number representing i in the given coeff field/ring r
#define omFreeSize(addr, size)
static short rVar(const ring r)
#define rVar(r) (r->N)
void id_Delete(ideal *h, ring r)
deletes an ideal/module/matrix
ring getStartingRing() const
returns the polynomial ring over the valuation ring
poly p_Div_nn(poly p, const number n, const ring r)
static ideal constructStartingIdeal(ideal originalIdeal, ring originalRing, number uniformizingParameter, ring startingRing)
bool onlyLowerHalfSpace
true if valuation non-trivial, false otherwise
int * ZVectorToIntStar(const gfan::ZVector &v, bool &overflow)
number getUniformizingParameter() const
returns the uniformizing parameter in the valuation ring
static number p_SetCoeff(poly p, number n, ring r)
static void swapElements(ideal I, ideal J)
static ring constructStartingRing(ring r)
Given a polynomial ring r over the rational numbers and a weighted ordering, returns a polynomial rin...
static poly p_Copy(poly p, const ring r)
returns a copy of p
std::pair< ideal, ring > computeFlip(const ideal Ir, const ring r, const gfan::ZVector &interiorPoint, const gfan::ZVector &facetNormal) const
given an interior point of a groebner cone computes the groebner cone adjacent to it ...
ideal startingIdeal
preimage of the input ideal under the map that sends t to the uniformizing parameter ...
~tropicalStrategy()
destructor
poly initial(const poly p, const ring r, const gfan::ZVector &w)
Returns the initial form of p with respect to w.
static int rBlocks(ring r)
poly p_PermPoly(poly p, const int *perm, const ring oldRing, const ring dst, nMapFunc nMap, const int *par_perm, int OldPar, BOOLEAN use_mult)
BOOLEAN linealitySpace(leftv res, leftv args)
ideal originalIdeal
input ideal, assumed to be a homogeneous prime ideal
static bool noExtraReduction(ideal I, ring r, number)
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 ...
bool isValuationTrivial() const
BOOLEAN rComplete(ring r, int force)
this needs to be called whenever a new ring is created: new fields in ring are created (like VarOffse...
ring shortcutRing
polynomial ring over the residue field
static long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset)
get a single variable exponent : the integer VarOffset encodes:
ideal gfanlib_kStd_wrapper(ideal I, ring r, tHomog h=testHomog)
gfan::ZCone getHomogeneitySpace() const
returns the homogeneity space of the preimage ideal
ring rCopy0(const ring r, BOOLEAN copy_qideal, BOOLEAN copy_ordering)
ideal getStartingIdeal() const
returns the input ideal
int scDimInt(ideal S, ideal Q)
number(* nMapFunc)(number a, const coeffs src, const coeffs dst)
maps "a", which lives in src, into dst
ring copyAndChangeOrderingLS(const ring r, const gfan::ZVector &w, const gfan::ZVector &v) const
bool areIdealsEqual(ideal I, ring r, ideal J, ring s)
#define n_Test(a, r)
BOOLEAN n_Test(number a, const coeffs r)
void pReduce(ideal I, const ring r) const
bool checkForUniformizingParameter(const ideal inI, const ring r) const
if valuation non-trivial, checks whether the genearting system contains p otherwise returns true ...
only used if HAVE_RINGS is defined
poly searchForMonomialViaStepwiseSaturation(const ideal I, const ring r, const gfan::ZVector w0)
gfan::ZVector adjustWeightForHomogeneity(gfan::ZVector w) const
Given weight w, returns a strictly positive weight u such that an ideal satisfying the valuation-sepc...
bool restrictToLowerHalfSpace() const
returns true, if valuation non-trivial, false otherwise
static BOOLEAN rField_is_Q(const ring r)
gfan::ZVector(* weightAdjustingAlgorithm2)(const gfan::ZVector &v, const gfan::ZVector &w)
A function such that: Given strictly positive weight w and weight v, returns a strictly positive weig...
void mp_Delete(matrix *a, const ring r)
static FORCE_INLINE nMapFunc n_SetMap(const coeffs src, const coeffs dst)
set the mapping function pointers for translating numbers from src to dst
void idSkipZeroes(ideal ide)
gives an ideal/module the minimal possible size
ideal computeLift(const ideal inJs, const ring s, const ideal inIr, const ideal Ir, const ring r) const
BOOLEAN p_EqualPolys(poly p1, poly p2, const ring r)
gfan::ZVector valued_adjustWeightUnderHomogeneity(const gfan::ZVector &e, const gfan::ZVector &w)
void rChangeCurrRing(ring r)
static BOOLEAN rField_is_Zp(const ring r)
ring copyAndChangeOrderingWP(const ring r, const gfan::ZVector &w, const gfan::ZVector &v) const
bool checkForUniformizingBinomial(const ideal I, const ring r) const
if valuation non-trivial, checks whether the generating system contains p-t otherwise returns true ...
matrix mpNew(int r, int c)
create a r x c zero-matrix
static FORCE_INLINE coeffs nCopyCoeff(const coeffs r)
"copy" coeffs, i.e. increment ref
static void p_Delete(poly *p, const ring r)
ideal idInit(int idsize, int rank)
initialise an ideal / module
const Variable & v
< [in] a sqrfree bivariate poly
number uniformizingParameter
uniformizing parameter in the valuation ring
static unsigned long p_SetExp(poly p, const unsigned long e, const unsigned long iBitmask, const int VarOffset)
set a single variable exponent : VarOffset encodes the position in p->exp
ring startingRing
polynomial ring over the valuation ring extended by one extra variable t
bool isValuationNonTrivial() const
bool reduce(ideal I, const ring r) const
reduces the generators of an ideal I so that the inequalities and equations of the Groebner cone can ...
static BOOLEAN rField_is_Ring(const ring r)
poly witness(const poly m, const ideal I, const ideal inI, const ring r)
Let w be the uppermost weight vector in the matrix defining the ordering on r.
bool(* extraReductionAlgorithm)(ideal I, ring r, number p)
A function that reduces the generators of an ideal I so that the inequalities and equations of the Gr...
ideal getOriginalIdeal() const
returns the input ideal over the field with valuation
static FORCE_INLINE number n_Copy(number n, const coeffs r)
return a copy of 'n'
void rDelete(ring r)
unconditionally deletes fields in r
static BOOLEAN rField_is_Ring_Z(const ring r)
gfan::ZVector nonvalued_adjustWeightForHomogeneity(const gfan::ZVector &w)
gfan::ZVector valued_adjustWeightForHomogeneity(const gfan::ZVector &w)
ideal id_Head(ideal h, const ring r)
returns the ideals of initial terms
int getExpectedDimension() const
returns the expected Dimension of the polyhedral output
ring currRing
Widely used global variable which specifies the current polynomial ring for Singular interpreter and ...
std::pair< poly, int > checkInitialIdealForMonomial(const ideal I, const ring r, const gfan::ZVector &w=0) const
If given w, assuming w is in the Groebner cone of the ordering on r and I is a standard basis with re...
static void p_Setm(poly p, const ring r)
gfan::ZVector adjustWeightUnderHomogeneity(gfan::ZVector v, gfan::ZVector w) const
Given strictly positive weight w and weight v, returns a strictly positive weight u such that on an i...
bool checkWeightVector(const ideal I, const ring r, const gfan::ZVector &weightVector, bool checkBorder)
tropicalStrategy(const ideal I, const ring r, const bool completelyHomogeneous=true, const bool completeSpace=true)
Constructor for the trivial valuation case.
static poly p_Neg(poly p, const ring r)
static FORCE_INLINE void n_Delete(number *p, const coeffs r)
delete 'p'
ring originalRing
polynomial ring over a field with valuation
static poly p_Add_q(poly p, poly q, const ring r)
tropicalStrategy & operator=(const tropicalStrategy ¤tStrategy)
assignment operator
gfan::ZCone linealitySpace
the homogeneity space of the Grobner fan
void nKillChar(coeffs r)
undo all initialisations
static poly p_Mult_q(poly p, poly q, const ring r)
int expectedDimension
the expected Dimension of the polyhedral output, i.e.
gfan::ZVector(* weightAdjustingAlgorithm1)(const gfan::ZVector &w)
A function such that: Given weight w, returns a strictly positive weight u such that an ideal satisfy...
#define MATELEM(mat, i, j)
coeffs nInitChar(n_coeffType t, void *parameter)
one-time initialisations for new coeffs in case of an error return NULL
ideal computeStdOfInitialIdeal(const ideal inI, const ring r) const
given generators of the initial ideal, computes its standard basis