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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 <cmath>
#include <ctype.h>
#include "kernel/maps/gen_maps.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, const long bitmask, const int isLetterplace) |
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 988 of file ipshell.cc.
enum semicState |
Definition at line 3403 of file ipshell.cc.
enum spectrumState |
Enumerator | |
---|---|
spectrumOK | |
spectrumZero | |
spectrumBadPoly | |
spectrumNoSingularity | |
spectrumNotIsolated | |
spectrumDegenerate | |
spectrumWrongRing | |
spectrumNoHC | |
spectrumUnspecErr |
Definition at line 3519 of file ipshell.cc.
Definition at line 3329 of file ipshell.cc.
int exprlist_length | ( | leftv | v | ) |
Definition at line 549 of file ipshell.cc.
Definition at line 3365 of file ipshell.cc.
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Definition at line 1184 of file ipshell.cc.
void iiCheckPack | ( | package & | p | ) |
Definition at line 1541 of file ipshell.cc.
BOOLEAN iiCheckRing | ( | int | i | ) |
Definition at line 1497 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 6546 of file ipshell.cc.
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static |
Definition at line 860 of file ipshell.cc.
void iiDebug | ( | ) |
Definition at line 989 of file ipshell.cc.
int iiDeclCommand | ( | leftv | sy, |
leftv | name, | ||
int | lev, | ||
int | t, | ||
idhdl * | root, | ||
BOOLEAN | isring, | ||
BOOLEAN | init_b | ||
) |
Definition at line 1127 of file ipshell.cc.
Definition at line 1171 of file ipshell.cc.
Definition at line 1419 of file ipshell.cc.
Definition at line 1445 of file ipshell.cc.
poly iiHighCorner | ( | ideal | I, |
int | ak | ||
) |
Definition at line 1517 of file ipshell.cc.
Definition at line 1321 of file ipshell.cc.
Definition at line 1373 of file ipshell.cc.
void iiMakeResolv | ( | resolvente | r, |
int | length, | ||
int | rlen, | ||
char * | name, | ||
int | typ0, | ||
intvec ** | weights | ||
) |
Definition at line 771 of file ipshell.cc.
Definition at line 612 of file ipshell.cc.
int iiOpsTwoChar | ( | const char * | s | ) |
Definition at line 119 of file ipshell.cc.
Definition at line 1285 of file ipshell.cc.
int iiRegularity | ( | lists | L | ) |
Definition at line 961 of file ipshell.cc.
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static |
Definition at line 6528 of file ipshell.cc.
Definition at line 6429 of file ipshell.cc.
const char* iiTwoOps | ( | int | t | ) |
Definition at line 86 of file ipshell.cc.
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static |
Definition at line 6271 of file ipshell.cc.
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Definition at line 1618 of file iparith.cc.
Definition at line 3309 of file ipshell.cc.
Definition at line 6301 of file ipshell.cc.
Definition at line 6293 of file ipshell.cc.
ideal kGroebner | ( | ideal | F, |
ideal | Q | ||
) |
Definition at line 6226 of file ipshell.cc.
void killlocals | ( | int | v | ) |
Definition at line 383 of file ipshell.cc.
Definition at line 292 of file ipshell.cc.
Definition at line 363 of file ipshell.cc.
void killlocals_rec | ( | idhdl * | root, |
int | v, | ||
ring | r | ||
) |
Definition at line 327 of file ipshell.cc.
Definition at line 3292 of file ipshell.cc.
Definition at line 3270 of file ipshell.cc.
Definition at line 147 of file ipshell.cc.
void list_cmd | ( | int | typ, |
const char * | what, | ||
const char * | prefix, | ||
BOOLEAN | iterate, | ||
BOOLEAN | fullname | ||
) |
Definition at line 422 of file ipshell.cc.
void list_error | ( | semicState | state | ) |
Definition at line 3437 of file ipshell.cc.
semicState list_is_spectrum | ( | lists | l | ) |
Definition at line 4222 of file ipshell.cc.
lists listOfRoots | ( | rootArranger * | self, |
const unsigned int | oprec | ||
) |
Definition at line 5034 of file ipshell.cc.
Implementation of the Simplex Algorithm.
For args, see class simplex.
Definition at line 4538 of file ipshell.cc.
Definition at line 3040 of file ipshell.cc.
Definition at line 3062 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 4647 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 4624 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 4877 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 4776 of file ipshell.cc.
Definition at line 6316 of file ipshell.cc.
ring rCompose | ( | const lists | L, |
const BOOLEAN | check_comp, | ||
const long | bitmask, | ||
const int | isLetterplace | ||
) |
Definition at line 2760 of file ipshell.cc.
void rComposeC | ( | lists | L, |
ring | R | ||
) |
Definition at line 2244 of file ipshell.cc.
Definition at line 2494 of file ipshell.cc.
void rComposeRing | ( | lists | L, |
ring | R | ||
) |
Definition at line 2315 of file ipshell.cc.
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Definition at line 5574 of file ipshell.cc.
void rKill | ( | ring | r | ) |
Definition at line 6119 of file ipshell.cc.
void rKill | ( | idhdl | h | ) |
Definition at line 6165 of file ipshell.cc.
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static |
void rSetHdl | ( | idhdl | h | ) |
Definition at line 5081 of file ipshell.cc.
Definition at line 6208 of file ipshell.cc.
Definition at line 5526 of file ipshell.cc.
Definition at line 5254 of file ipshell.cc.
ring rSubring | ( | ring | org_ring, |
sleftv * | rv | ||
) |
Definition at line 5957 of file ipshell.cc.
Definition at line 1027 of file ipshell.cc.
Definition at line 4520 of file ipshell.cc.
Definition at line 4480 of file ipshell.cc.
Definition at line 4397 of file ipshell.cc.
spectrumState spectrumCompute | ( | poly | h, |
lists * | L, | ||
int | fast | ||
) |
Definition at line 3779 of file ipshell.cc.
Definition at line 4153 of file ipshell.cc.
Definition at line 3353 of file ipshell.cc.
void spectrumPrintError | ( | spectrumState | state | ) |
Definition at line 4071 of file ipshell.cc.
Definition at line 4102 of file ipshell.cc.
spectrumState spectrumStateFromList | ( | spectrumPolyList & | speclist, |
lists * | L, | ||
int | fast | ||
) |
Definition at line 3538 of file ipshell.cc.
Definition at line 4439 of file ipshell.cc.
Definition at line 3141 of file ipshell.cc.
Definition at line 3118 of file ipshell.cc.
syStrategy syConvList | ( | lists | li | ) |
Definition at line 3225 of file ipshell.cc.
lists syConvRes | ( | syStrategy | syzstr, |
BOOLEAN | toDel, | ||
int | add_row_shift | ||
) |
Definition at line 3153 of file ipshell.cc.
syStrategy syForceMin | ( | lists | li | ) |
Definition at line 3254 of file ipshell.cc.
void test_cmd | ( | int | i | ) |
Definition at line 511 of file ipshell.cc.
void type_cmd | ( | leftv | v | ) |
Definition at line 251 of file ipshell.cc.
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Definition at line 987 of file ipshell.cc.
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Definition at line 80 of file ipshell.cc.
const short MAX_SHORT = 32767 |
Definition at line 5562 of file ipshell.cc.