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#include <kernel/mod2.h>
#include <omalloc/omalloc.h>
#include <factory/factory.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/gen_maps.h>
#include <Singular/number2.h>
#include <coeffs/bigintmat.h>
#include "libparse.h"
Go to the source code of this file.
Macros | |
#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, 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_41 (leftv h, const coeffs C) |
static void | rDecomposeC (leftv h, const ring R) |
void | rDecomposeRing_41 (leftv h, const coeffs C) |
void | rDecomposeRing (leftv h, const ring R) |
BOOLEAN | rDecompose_CF (leftv res, const coeffs C) |
lists | rDecompose_list_cf (const ring r) |
lists | rDecompose (const ring r) |
void | rComposeC (lists L, ring R) |
void | rComposeRing (lists L, ring R) |
static void | rRenameVars (ring R) |
static BOOLEAN | rComposeVar (const lists L, ring R) |
static BOOLEAN | rComposeOrder (const lists L, const BOOLEAN check_comp, 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) |
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) |
static BOOLEAN | rSleftvList2StringArray (leftv sl, char **p) |
ring | rInit (leftv pn, leftv rv, leftv 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, leftv, int, leftv) |
BOOLEAN | iiApplyIDEAL (leftv, leftv, int, leftv) |
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 985 of file ipshell.cc.
enum semicState |
Definition at line 3339 of file ipshell.cc.
enum spectrumState |
Enumerator | |
---|---|
spectrumOK | |
spectrumZero | |
spectrumBadPoly | |
spectrumNoSingularity | |
spectrumNotIsolated | |
spectrumDegenerate | |
spectrumWrongRing | |
spectrumNoHC | |
spectrumUnspecErr |
Definition at line 3455 of file ipshell.cc.
Definition at line 3265 of file ipshell.cc.
int exprlist_length | ( | leftv | v | ) |
Definition at line 546 of file ipshell.cc.
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void iiCheckPack | ( | package & | p | ) |
Definition at line 1509 of file ipshell.cc.
BOOLEAN iiCheckRing | ( | int | i | ) |
Definition at line 1465 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 6460 of file ipshell.cc.
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static |
Definition at line 857 of file ipshell.cc.
void iiDebug | ( | ) |
Definition at line 986 of file ipshell.cc.
int iiDeclCommand | ( | leftv | sy, |
leftv | name, | ||
int | lev, | ||
int | t, | ||
idhdl * | root, | ||
BOOLEAN | isring, | ||
BOOLEAN | init_b | ||
) |
Definition at line 1124 of file ipshell.cc.
Definition at line 1168 of file ipshell.cc.
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poly iiHighCorner | ( | ideal | I, |
int | ak | ||
) |
Definition at line 1485 of file ipshell.cc.
Definition at line 1287 of file ipshell.cc.
Definition at line 1339 of file ipshell.cc.
void iiMakeResolv | ( | resolvente | r, |
int | length, | ||
int | rlen, | ||
char * | name, | ||
int | typ0, | ||
intvec ** | weights | ||
) |
Definition at line 768 of file ipshell.cc.
Definition at line 609 of file ipshell.cc.
int iiOpsTwoChar | ( | const char * | s | ) |
Definition at line 119 of file ipshell.cc.
Definition at line 1251 of file ipshell.cc.
int iiRegularity | ( | lists | L | ) |
Definition at line 958 of file ipshell.cc.
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static |
Definition at line 6442 of file ipshell.cc.
Definition at line 6341 of file ipshell.cc.
const char* iiTwoOps | ( | int | t | ) |
Definition at line 86 of file ipshell.cc.
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static |
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Definition at line 1602 of file iparith.cc.
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ideal kGroebner | ( | ideal | F, |
ideal | Q | ||
) |
Definition at line 6139 of file ipshell.cc.
void killlocals | ( | int | v | ) |
Definition at line 376 of file ipshell.cc.
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void killlocals_rec | ( | idhdl * | root, |
int | v, | ||
ring | r | ||
) |
Definition at line 320 of file ipshell.cc.
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void list_cmd | ( | int | typ, |
const char * | what, | ||
const char * | prefix, | ||
BOOLEAN | iterate, | ||
BOOLEAN | fullname | ||
) |
Definition at line 415 of file ipshell.cc.
void list_error | ( | semicState | state | ) |
Definition at line 3373 of file ipshell.cc.
semicState list_is_spectrum | ( | lists | l | ) |
Definition at line 4158 of file ipshell.cc.
lists listOfRoots | ( | rootArranger * | self, |
const unsigned int | oprec | ||
) |
Definition at line 4970 of file ipshell.cc.
Implementation of the Simplex Algorithm.
For args, see class simplex.
Definition at line 4474 of file ipshell.cc.
Definition at line 2976 of file ipshell.cc.
Definition at line 2998 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 4583 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 4560 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 4813 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 4712 of file ipshell.cc.
Definition at line 6229 of file ipshell.cc.
Definition at line 2708 of file ipshell.cc.
void rComposeC | ( | lists | L, |
ring | R | ||
) |
Definition at line 2208 of file ipshell.cc.
Definition at line 2458 of file ipshell.cc.
void rComposeRing | ( | lists | L, |
ring | R | ||
) |
Definition at line 2279 of file ipshell.cc.
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void rKill | ( | ring | r | ) |
Definition at line 6044 of file ipshell.cc.
void rKill | ( | idhdl | h | ) |
Definition at line 6095 of file ipshell.cc.
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static |
void rSetHdl | ( | idhdl | h | ) |
Definition at line 5017 of file ipshell.cc.
Definition at line 6121 of file ipshell.cc.
Definition at line 5455 of file ipshell.cc.
Definition at line 5183 of file ipshell.cc.
ring rSubring | ( | ring | org_ring, |
sleftv * | rv | ||
) |
Definition at line 5882 of file ipshell.cc.
Definition at line 1024 of file ipshell.cc.
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Definition at line 4416 of file ipshell.cc.
Definition at line 4333 of file ipshell.cc.
spectrumState spectrumCompute | ( | poly | h, |
lists * | L, | ||
int | fast | ||
) |
Definition at line 3715 of file ipshell.cc.
Definition at line 4089 of file ipshell.cc.
Definition at line 3289 of file ipshell.cc.
void spectrumPrintError | ( | spectrumState | state | ) |
Definition at line 4007 of file ipshell.cc.
Definition at line 4038 of file ipshell.cc.
spectrumState spectrumStateFromList | ( | spectrumPolyList & | speclist, |
lists * | L, | ||
int | fast | ||
) |
Definition at line 3474 of file ipshell.cc.
Definition at line 4375 of file ipshell.cc.
Definition at line 3076 of file ipshell.cc.
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syStrategy syConvList | ( | lists | li | ) |
Definition at line 3161 of file ipshell.cc.
lists syConvRes | ( | syStrategy | syzstr, |
BOOLEAN | toDel, | ||
int | add_row_shift | ||
) |
Definition at line 3088 of file ipshell.cc.
syStrategy syForceMin | ( | lists | li | ) |
Definition at line 3190 of file ipshell.cc.
void test_cmd | ( | int | i | ) |
Definition at line 508 of file ipshell.cc.
void type_cmd | ( | leftv | v | ) |
Definition at line 244 of file ipshell.cc.
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Definition at line 984 of file ipshell.cc.
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const short MAX_SHORT = 32767 |
Definition at line 5491 of file ipshell.cc.