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#include "kernel/mod2.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/p_polys.h"
#include "polys/monomials/ring.h"
#include "polys/monomials/maps.h"
#include "polys/prCopy.h"
#include "polys/matpol.h"
#include "polys/shiftop.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) |
static idhdl | rSimpleFindHdl (const ring r, const idhdl root, const idhdl n) |
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) |
static void | rDecomposeRing_41 (leftv h, const coeffs C) |
void | rDecomposeRing (leftv h, const ring R) |
BOOLEAN | rDecompose_CF (leftv res, const coeffs C) |
static void | rDecompose_23456 (const ring r, lists L) |
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) |
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) |
BOOLEAN | jjPROC (leftv res, leftv u, leftv v) |
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... | |
void | iiSetReturn (const leftv source) |
Variables | |
VAR leftv | iiCurrArgs =NULL |
VAR idhdl | iiCurrProc =NULL |
const char * | lastreserved =NULL |
STATIC_VAR BOOLEAN | iiNoKeepRing =TRUE |
VAR BOOLEAN | iiDebugMarker =TRUE |
const short | MAX_SHORT = 32767 |
#define BREAK_LINE_LENGTH 80 |
Definition at line 1064 of file ipshell.cc.
enum semicState |
Definition at line 3434 of file ipshell.cc.
enum spectrumState |
Enumerator | |
---|---|
spectrumOK | |
spectrumZero | |
spectrumBadPoly | |
spectrumNoSingularity | |
spectrumNotIsolated | |
spectrumDegenerate | |
spectrumWrongRing | |
spectrumNoHC | |
spectrumUnspecErr |
Definition at line 3550 of file ipshell.cc.
Definition at line 3360 of file ipshell.cc.
int exprlist_length | ( | leftv | v | ) |
Definition at line 552 of file ipshell.cc.
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void iiCheckPack | ( | package & | p | ) |
Definition at line 1630 of file ipshell.cc.
BOOLEAN iiCheckRing | ( | int | i | ) |
Definition at line 1586 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 6572 of file ipshell.cc.
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Definition at line 936 of file ipshell.cc.
void iiDebug | ( | ) |
Definition at line 1065 of file ipshell.cc.
int iiDeclCommand | ( | leftv | sy, |
leftv | name, | ||
int | lev, | ||
int | t, | ||
idhdl * | root, | ||
BOOLEAN | isring, | ||
BOOLEAN | init_b | ||
) |
Definition at line 1198 of file ipshell.cc.
Definition at line 1260 of file ipshell.cc.
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Definition at line 1534 of file ipshell.cc.
poly iiHighCorner | ( | ideal | I, |
int | ak | ||
) |
Definition at line 1606 of file ipshell.cc.
Definition at line 1412 of file ipshell.cc.
Definition at line 1465 of file ipshell.cc.
void iiMakeResolv | ( | resolvente | r, |
int | length, | ||
int | rlen, | ||
char * | name, | ||
int | typ0, | ||
intvec ** | weights | ||
) |
Definition at line 847 of file ipshell.cc.
Definition at line 615 of file ipshell.cc.
int iiOpsTwoChar | ( | const char * | s | ) |
Definition at line 121 of file ipshell.cc.
Definition at line 1376 of file ipshell.cc.
int iiRegularity | ( | lists | L | ) |
Definition at line 1037 of file ipshell.cc.
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const char * iiTwoOps | ( | int | t | ) |
Definition at line 88 of file ipshell.cc.
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void killlocals | ( | int | v | ) |
Definition at line 386 of file ipshell.cc.
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void killlocals_rec | ( | idhdl * | root, |
int | v, | ||
ring | r | ||
) |
Definition at line 330 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 425 of file ipshell.cc.
void list_error | ( | semicState | state | ) |
Definition at line 3468 of file ipshell.cc.
semicState list_is_spectrum | ( | lists | l | ) |
Definition at line 4253 of file ipshell.cc.
lists listOfRoots | ( | rootArranger * | self, |
const unsigned int | oprec | ||
) |
Definition at line 5079 of file ipshell.cc.
compute Newton Polytopes of input polynomials
Definition at line 4563 of file ipshell.cc.
Implementation of the Simplex Algorithm.
For args, see class simplex.
Definition at line 4569 of file ipshell.cc.
Definition at line 3069 of file ipshell.cc.
Definition at line 3091 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 4678 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 4655 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 4922 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 4821 of file ipshell.cc.
Definition at line 6333 of file ipshell.cc.
ring rCompose | ( | const lists | L, |
const BOOLEAN | check_comp, | ||
const long | bitmask, | ||
const int | isLetterplace | ||
) |
Definition at line 2783 of file ipshell.cc.
void rComposeC | ( | lists | L, |
ring | R | ||
) |
Definition at line 2260 of file ipshell.cc.
Definition at line 2491 of file ipshell.cc.
void rComposeRing | ( | lists | L, |
ring | R | ||
) |
Definition at line 2312 of file ipshell.cc.
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void rKill | ( | idhdl | h | ) |
Definition at line 6226 of file ipshell.cc.
void rKill | ( | ring | r | ) |
Definition at line 6180 of file ipshell.cc.
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Definition at line 2405 of file ipshell.cc.
void rSetHdl | ( | idhdl | h | ) |
Definition at line 5126 of file ipshell.cc.
Definition at line 5305 of file ipshell.cc.
ring rSubring | ( | ring | org_ring, |
sleftv * | rv | ||
) |
Definition at line 6018 of file ipshell.cc.
Definition at line 1103 of file ipshell.cc.
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spectrumState spectrumCompute | ( | poly | h, |
lists * | L, | ||
int | fast | ||
) |
Definition at line 3810 of file ipshell.cc.
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Definition at line 3384 of file ipshell.cc.
void spectrumPrintError | ( | spectrumState | state | ) |
Definition at line 4102 of file ipshell.cc.
Definition at line 4133 of file ipshell.cc.
spectrumState spectrumStateFromList | ( | spectrumPolyList & | speclist, |
lists * | L, | ||
int | fast | ||
) |
Definition at line 3569 of file ipshell.cc.
Definition at line 4470 of file ipshell.cc.
Definition at line 3147 of file ipshell.cc.
syStrategy syConvList | ( | lists | li | ) |
Definition at line 3254 of file ipshell.cc.
lists syConvRes | ( | syStrategy | syzstr, |
BOOLEAN | toDel, | ||
int | add_row_shift | ||
) |
Definition at line 3182 of file ipshell.cc.
void test_cmd | ( | int | i | ) |
void type_cmd | ( | leftv | v | ) |
Definition at line 254 of file ipshell.cc.
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Definition at line 1063 of file ipshell.cc.
STATIC_VAR BOOLEAN iiNoKeepRing =TRUE |
Definition at line 84 of file ipshell.cc.
Definition at line 82 of file ipshell.cc.
const short MAX_SHORT = 32767 |
Definition at line 5613 of file ipshell.cc.