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#include <kernel/mod2.h>
#include <omalloc/omalloc.h>
#include <factory/factory.h>
#include <misc/auxiliary.h>
#include <misc/options.h>
#include <misc/mylimits.h>
#include <misc/intvec.h>
#include <misc/prime.h>
#include <coeffs/numbers.h>
#include <coeffs/coeffs.h>
#include <coeffs/rmodulon.h>
#include <coeffs/longrat.h>
#include <polys/monomials/ring.h>
#include <polys/monomials/maps.h>
#include <polys/prCopy.h>
#include <polys/matpol.h>
#include <polys/weight.h>
#include <polys/clapsing.h>
#include <polys/ext_fields/algext.h>
#include <polys/ext_fields/transext.h>
#include <kernel/polys.h>
#include <kernel/ideals.h>
#include <kernel/numeric/mpr_base.h>
#include <kernel/numeric/mpr_numeric.h>
#include <kernel/GBEngine/syz.h>
#include <kernel/GBEngine/kstd1.h>
#include <kernel/GBEngine/kutil.h>
#include <kernel/combinatorics/stairc.h>
#include <kernel/combinatorics/hutil.h>
#include <kernel/spectrum/semic.h>
#include <kernel/spectrum/splist.h>
#include <kernel/spectrum/spectrum.h>
#include <kernel/oswrapper/feread.h>
#include <Singular/lists.h>
#include <Singular/attrib.h>
#include <Singular/ipconv.h>
#include <Singular/links/silink.h>
#include <Singular/ipshell.h>
#include <Singular/maps_ip.h>
#include <Singular/tok.h>
#include <Singular/ipid.h>
#include <Singular/subexpr.h>
#include <Singular/fevoices.h>
#include <Singular/sdb.h>
#include <math.h>
#include <ctype.h>
#include <kernel/maps/fast_maps.h>
#include <Singular/number2.h>
#include <coeffs/bigintmat.h>
#include "libparse.h"
Go to the source code of this file.
Macros | |
#define | FAST_MAP |
#define | BREAK_LINE_LENGTH 80 |
Functions | |
const char * | iiTwoOps (int t) |
int | iiOpsTwoChar (const char *s) |
static void | list1 (const char *s, idhdl h, BOOLEAN c, BOOLEAN fullname) |
void | type_cmd (leftv v) |
static void | killlocals0 (int v, idhdl *localhdl, const ring r) |
void | killlocals_rec (idhdl *root, int v, ring r) |
BOOLEAN | killlocals_list (int v, lists L) |
void | killlocals (int v) |
void | list_cmd (int typ, const char *what, const char *prefix, BOOLEAN iterate, BOOLEAN fullname) |
void | test_cmd (int i) |
int | exprlist_length (leftv v) |
BOOLEAN | iiWRITE (leftv, leftv v) |
leftv | iiMap (map theMap, const char *what) |
void | iiMakeResolv (resolvente r, int length, int rlen, char *name, int typ0, intvec **weights) |
static resolvente | iiCopyRes (resolvente r, int l) |
BOOLEAN | jjMINRES (leftv res, leftv v) |
BOOLEAN | jjBETTI (leftv res, leftv u) |
BOOLEAN | jjBETTI2_ID (leftv res, leftv u, leftv v) |
BOOLEAN | jjBETTI2 (leftv res, leftv u, leftv v) |
int | iiRegularity (lists L) |
void | iiDebug () |
lists | scIndIndset (ideal S, BOOLEAN all, ideal Q) |
int | iiDeclCommand (leftv sy, leftv name, int lev, int t, idhdl *root, BOOLEAN isring, BOOLEAN init_b) |
BOOLEAN | iiDefaultParameter (leftv p) |
BOOLEAN | iiBranchTo (leftv r, leftv args) |
BOOLEAN | iiParameter (leftv p) |
static BOOLEAN | iiInternalExport (leftv v, int toLev) |
BOOLEAN | iiInternalExport (leftv v, int toLev, package rootpack) |
BOOLEAN | iiExport (leftv v, int toLev) |
BOOLEAN | iiExport (leftv v, int toLev, package pack) |
BOOLEAN | iiCheckRing (int i) |
poly | iiHighCorner (ideal I, int ak) |
void | iiCheckPack (package &p) |
idhdl | rDefault (const char *s) |
idhdl | rFindHdl (ring r, idhdl n) |
void | rDecomposeCF (leftv h, const ring r, const ring R) |
static void | rDecomposeC (leftv h, const coeffs C) |
void | rDecomposeRing (leftv h, const coeffs C) |
BOOLEAN | rDecompose_CF (leftv res, const coeffs C) |
lists | rDecompose (const ring r) |
void | rComposeC (lists L, ring R) |
void | rComposeRing (lists L, ring R) |
static void | rRenameVars (ring R) |
ring | rCompose (const lists L, const BOOLEAN check_comp) |
BOOLEAN | mpJacobi (leftv res, leftv a) |
BOOLEAN | mpKoszul (leftv res, leftv c, leftv b, leftv id) |
BOOLEAN | syBetti2 (leftv res, leftv u, leftv w) |
BOOLEAN | syBetti1 (leftv res, leftv u) |
lists | syConvRes (syStrategy syzstr, BOOLEAN toDel, int add_row_shift) |
syStrategy | syConvList (lists li, BOOLEAN toDel) |
syStrategy | syForceMin (lists li) |
BOOLEAN | kWeight (leftv res, leftv id) |
BOOLEAN | kQHWeight (leftv res, leftv v) |
BOOLEAN | jjRESULTANT (leftv res, leftv u, leftv v, leftv w) |
BOOLEAN | jjCHARSERIES (leftv res, leftv u) |
void | copy_deep (spectrum &spec, lists l) |
spectrum | spectrumFromList (lists l) |
lists | getList (spectrum &spec) |
void | list_error (semicState state) |
spectrumState | spectrumStateFromList (spectrumPolyList &speclist, lists *L, int fast) |
spectrumState | spectrumCompute (poly h, lists *L, int fast) |
void | spectrumPrintError (spectrumState state) |
BOOLEAN | spectrumProc (leftv result, leftv first) |
BOOLEAN | spectrumfProc (leftv result, leftv first) |
semicState | list_is_spectrum (lists l) |
BOOLEAN | spaddProc (leftv result, leftv first, leftv second) |
BOOLEAN | spmulProc (leftv result, leftv first, leftv second) |
BOOLEAN | semicProc3 (leftv res, leftv u, leftv v, leftv w) |
BOOLEAN | semicProc (leftv res, leftv u, leftv v) |
BOOLEAN | loNewtonP (leftv res, leftv arg1) |
compute Newton Polytopes of input polynomials More... | |
BOOLEAN | loSimplex (leftv res, leftv args) |
Implementation of the Simplex Algorithm. More... | |
BOOLEAN | nuMPResMat (leftv res, leftv arg1, leftv arg2) |
returns module representing the multipolynomial resultant matrix Arguments 2: ideal i, int k k=0: use sparse resultant matrix of Gelfand, Kapranov and Zelevinsky k=1: use resultant matrix of Macaulay (k=0 is default) More... | |
BOOLEAN | nuLagSolve (leftv res, leftv arg1, leftv arg2, leftv arg3) |
find the (complex) roots an univariate polynomial Determines the roots of an univariate polynomial using Laguerres' root-solver. More... | |
BOOLEAN | nuVanderSys (leftv res, leftv arg1, leftv arg2, leftv arg3) |
COMPUTE: polynomial p with values given by v at points p1,..,pN derived from p; more precisely: consider p as point in K^n and v as N elements in K, let p1,..,pN be the points in K^n obtained by evaluating all monomials of degree 0,1,...,N at p in lexicographical order, then the procedure computes the polynomial f satisfying f(pi) = v[i] RETURN: polynomial f of degree d. More... | |
BOOLEAN | nuUResSolve (leftv res, leftv args) |
solve a multipolynomial system using the u-resultant Input ideal must be 0-dimensional and (currRing->N) == IDELEMS(ideal). More... | |
lists | listOfRoots (rootArranger *self, const unsigned int oprec) |
void | rSetHdl (idhdl h) |
static leftv | rOptimizeOrdAsSleftv (leftv ord) |
BOOLEAN | rSleftvOrdering2Ordering (sleftv *ord, ring R) |
BOOLEAN | rSleftvList2StringArray (sleftv *sl, char **p) |
ring | rInit (sleftv *pn, sleftv *rv, sleftv *ord) |
ring | rSubring (ring org_ring, sleftv *rv) |
void | rKill (ring r) |
void | rKill (idhdl h) |
idhdl | rSimpleFindHdl (ring r, idhdl root, idhdl n) |
BOOLEAN | jjPROC (leftv res, leftv u, leftv v) |
ideal | kGroebner (ideal F, ideal Q) |
static void | jjINT_S_TO_ID (int n, int *e, leftv res) |
BOOLEAN | jjVARIABLES_P (leftv res, leftv u) |
BOOLEAN | jjVARIABLES_ID (leftv res, leftv u) |
void | paPrint (const char *n, package p) |
BOOLEAN | iiApplyINTVEC (leftv res, leftv a, int op, leftv proc) |
BOOLEAN | iiApplyBIGINTMAT (leftv res, leftv a, int op, leftv proc) |
BOOLEAN | iiApplyIDEAL (leftv res, leftv a, int op, leftv proc) |
BOOLEAN | iiApplyLIST (leftv res, leftv a, int op, leftv proc) |
BOOLEAN | iiApply (leftv res, leftv a, int op, leftv proc) |
BOOLEAN | iiTestAssume (leftv a, leftv b) |
BOOLEAN | iiARROW (leftv r, char *a, char *s) |
BOOLEAN | iiAssignCR (leftv r, leftv arg) |
static void | iiReportTypes (int nr, int t, const short *T) |
BOOLEAN | iiCheckTypes (leftv args, const short *type_list, int report) |
check a list of arguemys against a given field of types return TRUE if the types match return FALSE (and, if report) report an error via Werror otherwise More... | |
Variables | |
leftv | iiCurrArgs =NULL |
idhdl | iiCurrProc =NULL |
const char * | lastreserved =NULL |
static BOOLEAN | iiNoKeepRing =TRUE |
BOOLEAN | iiDebugMarker =TRUE |
const short | MAX_SHORT = 32767 |
#define BREAK_LINE_LENGTH 80 |
Definition at line 980 of file ipshell.cc.
#define FAST_MAP |
Definition at line 74 of file ipshell.cc.
enum semicState |
Definition at line 3298 of file ipshell.cc.
enum spectrumState |
Enumerator | |
---|---|
spectrumOK | |
spectrumZero | |
spectrumBadPoly | |
spectrumNoSingularity | |
spectrumNotIsolated | |
spectrumDegenerate | |
spectrumWrongRing | |
spectrumNoHC | |
spectrumUnspecErr |
Definition at line 3414 of file ipshell.cc.
Definition at line 3224 of file ipshell.cc.
int exprlist_length | ( | leftv | v | ) |
Definition at line 559 of file ipshell.cc.
Definition at line 3260 of file ipshell.cc.
Definition at line 6293 of file ipshell.cc.
Definition at line 6251 of file ipshell.cc.
Definition at line 6256 of file ipshell.cc.
Definition at line 6219 of file ipshell.cc.
Definition at line 6261 of file ipshell.cc.
Definition at line 6342 of file ipshell.cc.
Definition at line 6376 of file ipshell.cc.
Definition at line 1174 of file ipshell.cc.
void iiCheckPack | ( | package & | p | ) |
Definition at line 1512 of file ipshell.cc.
BOOLEAN iiCheckRing | ( | int | i | ) |
Definition at line 1468 of file ipshell.cc.
check a list of arguemys against a given field of types return TRUE if the types match return FALSE (and, if report) report an error via Werror otherwise
type_list | < [in] argument list (may be NULL) [in] field of types len, t1,t2,... |
report | ;in] report error? |
Definition at line 6434 of file ipshell.cc.
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static |
Definition at line 861 of file ipshell.cc.
void iiDebug | ( | ) |
Definition at line 981 of file ipshell.cc.
int iiDeclCommand | ( | leftv | sy, |
leftv | name, | ||
int | lev, | ||
int | t, | ||
idhdl * | root, | ||
BOOLEAN | isring, | ||
BOOLEAN | init_b | ||
) |
Definition at line 1119 of file ipshell.cc.
Definition at line 1161 of file ipshell.cc.
Definition at line 1388 of file ipshell.cc.
Definition at line 1414 of file ipshell.cc.
poly iiHighCorner | ( | ideal | I, |
int | ak | ||
) |
Definition at line 1488 of file ipshell.cc.
Definition at line 1280 of file ipshell.cc.
Definition at line 1342 of file ipshell.cc.
void iiMakeResolv | ( | resolvente | r, |
int | length, | ||
int | rlen, | ||
char * | name, | ||
int | typ0, | ||
intvec ** | weights | ||
) |
Definition at line 772 of file ipshell.cc.
Definition at line 622 of file ipshell.cc.
int iiOpsTwoChar | ( | const char * | s | ) |
Definition at line 125 of file ipshell.cc.
Definition at line 1244 of file ipshell.cc.
int iiRegularity | ( | lists | L | ) |
Definition at line 953 of file ipshell.cc.
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Definition at line 6416 of file ipshell.cc.
Definition at line 6315 of file ipshell.cc.
const char* iiTwoOps | ( | int | t | ) |
Definition at line 92 of file ipshell.cc.
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Definition at line 6158 of file ipshell.cc.
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Definition at line 1607 of file iparith.cc.
Definition at line 3204 of file ipshell.cc.
Definition at line 6188 of file ipshell.cc.
Definition at line 6180 of file ipshell.cc.
ideal kGroebner | ( | ideal | F, |
ideal | Q | ||
) |
Definition at line 6113 of file ipshell.cc.
void killlocals | ( | int | v | ) |
Definition at line 385 of file ipshell.cc.
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void killlocals_rec | ( | idhdl * | root, |
int | v, | ||
ring | r | ||
) |
Definition at line 328 of file ipshell.cc.
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Definition at line 153 of file ipshell.cc.
void list_cmd | ( | int | typ, |
const char * | what, | ||
const char * | prefix, | ||
BOOLEAN | iterate, | ||
BOOLEAN | fullname | ||
) |
Definition at line 425 of file ipshell.cc.
void list_error | ( | semicState | state | ) |
Definition at line 3332 of file ipshell.cc.
semicState list_is_spectrum | ( | lists | l | ) |
Definition at line 4117 of file ipshell.cc.
lists listOfRoots | ( | rootArranger * | self, |
const unsigned int | oprec | ||
) |
Definition at line 4932 of file ipshell.cc.
Implementation of the Simplex Algorithm.
For args, see class simplex.
Definition at line 4433 of file ipshell.cc.
Definition at line 2934 of file ipshell.cc.
Definition at line 2956 of file ipshell.cc.
find the (complex) roots an univariate polynomial Determines the roots of an univariate polynomial using Laguerres' root-solver.
Good for polynomials with low and middle degree (<40). Arguments 3: poly arg1 , int arg2 , int arg3 arg2>0: defines precision of fractional part if ground field is Q arg3: number of iterations for approximation of roots (default=2) Returns a list of all (complex) roots of the polynomial arg1
Definition at line 4542 of file ipshell.cc.
returns module representing the multipolynomial resultant matrix Arguments 2: ideal i, int k k=0: use sparse resultant matrix of Gelfand, Kapranov and Zelevinsky k=1: use resultant matrix of Macaulay (k=0 is default)
Definition at line 4519 of file ipshell.cc.
solve a multipolynomial system using the u-resultant Input ideal must be 0-dimensional and (currRing->N) == IDELEMS(ideal).
Resultant method can be MPR_DENSE, which uses Macaulay Resultant (good for dense homogeneous polynoms) or MPR_SPARSE, which uses Sparse Resultant (Gelfand, Kapranov, Zelevinsky). Arguments 4: ideal i, int k, int l, int m k=0: use sparse resultant matrix of Gelfand, Kapranov and Zelevinsky k=1: use resultant matrix of Macaulay (k=0 is default) l>0: defines precision of fractional part if ground field is Q m=0,1,2: number of iterations for approximation of roots (default=2) Returns a list containing the roots of the system.
Definition at line 4775 of file ipshell.cc.
COMPUTE: polynomial p with values given by v at points p1,..,pN derived from p; more precisely: consider p as point in K^n and v as N elements in K, let p1,..,pN be the points in K^n obtained by evaluating all monomials of degree 0,1,...,N at p in lexicographical order, then the procedure computes the polynomial f satisfying f(pi) = v[i] RETURN: polynomial f of degree d.
Definition at line 4674 of file ipshell.cc.
Definition at line 6203 of file ipshell.cc.
Definition at line 2409 of file ipshell.cc.
void rComposeC | ( | lists | L, |
ring | R | ||
) |
Definition at line 2216 of file ipshell.cc.
void rComposeRing | ( | lists | L, |
ring | R | ||
) |
Definition at line 2275 of file ipshell.cc.
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Definition at line 5461 of file ipshell.cc.
void rKill | ( | ring | r | ) |
Definition at line 5999 of file ipshell.cc.
void rKill | ( | idhdl | h | ) |
Definition at line 6068 of file ipshell.cc.
Definition at line 5033 of file ipshell.cc.
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void rSetHdl | ( | idhdl | h | ) |
Definition at line 4979 of file ipshell.cc.
Definition at line 6087 of file ipshell.cc.
Definition at line 5417 of file ipshell.cc.
Definition at line 5145 of file ipshell.cc.
ring rSubring | ( | ring | org_ring, |
sleftv * | rv | ||
) |
Definition at line 5837 of file ipshell.cc.
Definition at line 1019 of file ipshell.cc.
Definition at line 4415 of file ipshell.cc.
Definition at line 4375 of file ipshell.cc.
Definition at line 4292 of file ipshell.cc.
spectrumState spectrumCompute | ( | poly | h, |
lists * | L, | ||
int | fast | ||
) |
Definition at line 3674 of file ipshell.cc.
Definition at line 4048 of file ipshell.cc.
Definition at line 3248 of file ipshell.cc.
void spectrumPrintError | ( | spectrumState | state | ) |
Definition at line 3966 of file ipshell.cc.
Definition at line 3997 of file ipshell.cc.
spectrumState spectrumStateFromList | ( | spectrumPolyList & | speclist, |
lists * | L, | ||
int | fast | ||
) |
Definition at line 3433 of file ipshell.cc.
Definition at line 4334 of file ipshell.cc.
Definition at line 3034 of file ipshell.cc.
Definition at line 3011 of file ipshell.cc.
syStrategy syConvList | ( | lists | li, |
BOOLEAN | toDel | ||
) |
Definition at line 3119 of file ipshell.cc.
lists syConvRes | ( | syStrategy | syzstr, |
BOOLEAN | toDel, | ||
int | add_row_shift | ||
) |
Definition at line 3046 of file ipshell.cc.
syStrategy syForceMin | ( | lists | li | ) |
Definition at line 3149 of file ipshell.cc.
void test_cmd | ( | int | i | ) |
Definition at line 521 of file ipshell.cc.
void type_cmd | ( | leftv | v | ) |
Definition at line 251 of file ipshell.cc.
Definition at line 84 of file ipshell.cc.
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Definition at line 979 of file ipshell.cc.
Definition at line 88 of file ipshell.cc.
Definition at line 86 of file ipshell.cc.
const short MAX_SHORT = 32767 |
Definition at line 5448 of file ipshell.cc.