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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) |
void | rDecomposeC (leftv h, const ring R) |
void | rDecomposeRing (leftv h, 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) |
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 973 of file ipshell.cc.
#define FAST_MAP |
Definition at line 74 of file ipshell.cc.
enum semicState |
Definition at line 3015 of file ipshell.cc.
enum spectrumState |
Enumerator | |
---|---|
spectrumOK | |
spectrumZero | |
spectrumBadPoly | |
spectrumNoSingularity | |
spectrumNotIsolated | |
spectrumDegenerate | |
spectrumWrongRing | |
spectrumNoHC | |
spectrumUnspecErr |
Definition at line 3131 of file ipshell.cc.
Definition at line 2941 of file ipshell.cc.
int exprlist_length | ( | leftv | v | ) |
Definition at line 552 of file ipshell.cc.
Definition at line 2977 of file ipshell.cc.
Definition at line 5984 of file ipshell.cc.
Definition at line 5942 of file ipshell.cc.
Definition at line 5947 of file ipshell.cc.
Definition at line 5910 of file ipshell.cc.
Definition at line 5952 of file ipshell.cc.
Definition at line 6033 of file ipshell.cc.
Definition at line 6067 of file ipshell.cc.
Definition at line 1167 of file ipshell.cc.
void iiCheckPack | ( | package & | p | ) |
Definition at line 1504 of file ipshell.cc.
BOOLEAN iiCheckRing | ( | int | i | ) |
Definition at line 1460 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 6122 of file ipshell.cc.
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static |
Definition at line 854 of file ipshell.cc.
void iiDebug | ( | ) |
Definition at line 974 of file ipshell.cc.
int iiDeclCommand | ( | leftv | sy, |
leftv | name, | ||
int | lev, | ||
int | t, | ||
idhdl * | root, | ||
BOOLEAN | isring, | ||
BOOLEAN | init_b | ||
) |
Definition at line 1112 of file ipshell.cc.
Definition at line 1154 of file ipshell.cc.
Definition at line 1380 of file ipshell.cc.
Definition at line 1406 of file ipshell.cc.
poly iiHighCorner | ( | ideal | I, |
int | ak | ||
) |
Definition at line 1480 of file ipshell.cc.
Definition at line 1272 of file ipshell.cc.
Definition at line 1334 of file ipshell.cc.
void iiMakeResolv | ( | resolvente | r, |
int | length, | ||
int | rlen, | ||
char * | name, | ||
int | typ0, | ||
intvec ** | weights | ||
) |
Definition at line 765 of file ipshell.cc.
Definition at line 615 of file ipshell.cc.
int iiOpsTwoChar | ( | const char * | s | ) |
Definition at line 125 of file ipshell.cc.
Definition at line 1237 of file ipshell.cc.
int iiRegularity | ( | lists | L | ) |
Definition at line 946 of file ipshell.cc.
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static |
Definition at line 6104 of file ipshell.cc.
Definition at line 6006 of file ipshell.cc.
const char* iiTwoOps | ( | int | t | ) |
Definition at line 92 of file ipshell.cc.
Definition at line 588 of file ipshell.cc.
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Definition at line 5849 of file ipshell.cc.
Definition at line 864 of file ipshell.cc.
Definition at line 1606 of file iparith.cc.
Definition at line 2921 of file ipshell.cc.
Definition at line 5879 of file ipshell.cc.
Definition at line 5871 of file ipshell.cc.
ideal kGroebner | ( | ideal | F, |
ideal | Q | ||
) |
Definition at line 5804 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 3049 of file ipshell.cc.
semicState list_is_spectrum | ( | lists | l | ) |
Definition at line 3834 of file ipshell.cc.
lists listOfRoots | ( | rootArranger * | self, |
const unsigned int | oprec | ||
) |
Definition at line 4649 of file ipshell.cc.
Implementation of the Simplex Algorithm.
For args, see class simplex.
Definition at line 4150 of file ipshell.cc.
Definition at line 2648 of file ipshell.cc.
Definition at line 2670 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 4259 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 4236 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 4492 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 4391 of file ipshell.cc.
Definition at line 5894 of file ipshell.cc.
Definition at line 2130 of file ipshell.cc.
void rComposeC | ( | lists | L, |
ring | R | ||
) |
Definition at line 1937 of file ipshell.cc.
void rComposeRing | ( | lists | L, |
ring | R | ||
) |
Definition at line 1996 of file ipshell.cc.
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void rKill | ( | ring | r | ) |
Definition at line 5690 of file ipshell.cc.
void rKill | ( | idhdl | h | ) |
Definition at line 5759 of file ipshell.cc.
Definition at line 4750 of file ipshell.cc.
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static |
void rSetHdl | ( | idhdl | h | ) |
Definition at line 4696 of file ipshell.cc.
Definition at line 5778 of file ipshell.cc.
Definition at line 5135 of file ipshell.cc.
Definition at line 4862 of file ipshell.cc.
ring rSubring | ( | ring | org_ring, |
sleftv * | rv | ||
) |
Definition at line 5528 of file ipshell.cc.
Definition at line 1012 of file ipshell.cc.
Definition at line 4132 of file ipshell.cc.
Definition at line 4092 of file ipshell.cc.
Definition at line 4009 of file ipshell.cc.
spectrumState spectrumCompute | ( | poly | h, |
lists * | L, | ||
int | fast | ||
) |
Definition at line 3391 of file ipshell.cc.
Definition at line 3765 of file ipshell.cc.
Definition at line 2965 of file ipshell.cc.
void spectrumPrintError | ( | spectrumState | state | ) |
Definition at line 3683 of file ipshell.cc.
Definition at line 3714 of file ipshell.cc.
spectrumState spectrumStateFromList | ( | spectrumPolyList & | speclist, |
lists * | L, | ||
int | fast | ||
) |
Definition at line 3150 of file ipshell.cc.
Definition at line 4051 of file ipshell.cc.
Definition at line 2748 of file ipshell.cc.
Definition at line 2725 of file ipshell.cc.
syStrategy syConvList | ( | lists | li, |
BOOLEAN | toDel | ||
) |
Definition at line 2836 of file ipshell.cc.
lists syConvRes | ( | syStrategy | syzstr, |
BOOLEAN | toDel, | ||
int | add_row_shift | ||
) |
Definition at line 2760 of file ipshell.cc.
syStrategy syForceMin | ( | lists | li | ) |
Definition at line 2866 of file ipshell.cc.
void test_cmd | ( | int | i | ) |
Definition at line 514 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 972 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 5166 of file ipshell.cc.