# Changeset 7a051de in git

Ignore:
Timestamp:
Jul 23, 2010, 7:28:28 PM (13 years ago)
Branches:
(u'jengelh-datetime', 'ceac47cbc86fe4a15902392bdbb9bd2ae0ea02c6')(u'spielwiese', 'a800fe4b3e9d37a38c5a10cc0ae9dfa0c15a4ee6')
Children:
6ffcdfa261c4242fc6d748ecd4529fc5920ab7c3
Parents:
77e09dc401b1e40ae64c4756637d51f60281cd65
Message:
```syntax fix in doc

Location:
Singular/LIB
Files:
5 edited

Unmodified
Removed
• ## Singular/LIB/bfun.lib

 r77e09d MAIN PROCEDURES: PROCEDURES: bfct(f[,s,t,v]);            compute the BS polynomial of f with linear reductions bfctSyz(f[,r,s,t,u,v]);  compute the BS polynomial of f with syzygy-solver linSyzSolve(I[,s]);         compute a linear dependency of elements of ideal I AUXILIARY PROCEDURES: allPositive(v);  checks whether all entries of an intvec are positive scalarProd(v,w); computes the standard scalar product of two intvecs vec2poly(v[,i]); constructs an univariate polynomial with given coefficients SEE ALSO: dmod_lib, dmodapp_lib, dmodvar_lib, gmssing_lib KEYWORDS: D-module; global Bernstein-Sato polynomial; Bernstein-Sato polynomial; b-function; graded Weyl algebra; initial ideal; initial form; principal intersection; linear interreduction; initial ideal approach; initial ideal approach "; //AUXILIARY PROCEDURES: // //allPositive(v);  checks whether all entries of an intvec are positive //scalarProd(v,w); computes the standard scalar product of two intvecs //vec2poly(v[,i]); constructs an univariate polynomial with given coefficients
• ## Singular/LIB/dmod.lib

 r77e09d KEYWORDS: D-module; D-module structure; left annihilator ideal; Bernstein-Sato polynomial; global Bernstein-Sato polynomial; Weyl algebra; Bernstein operator; logarithmic annihilator ideal; parametric annihilator; root of Bernstein-Sato polynomial; hyperplane arrangement; Oaku-Takayama algorithm; Briancon-Maisonobe algorithm; LOT algorithm; hyperplane arrangement; Oaku-Takayama algorithm; Briancon-Maisonobe algorithm; LOT algorithm ";
• ## Singular/LIB/dmodapp.lib

 r77e09d @* (ONW) Oaku, Takayama, Walther 'A Localization Algorithm for D-modules', 2000 MAIN PROCEDURES: PROCEDURES: annPoly(f);   annihilator of a polynomial f in the corr. Weyl algebra isFsat(I, F);       check whether the ideal I is F-saturated AUXILIARY PROCEDURES: bFactor(F);  computes the roots of irreducible factors of an univariate poly appelF1();      create an ideal annihilating Appel F1 function appelF2();      create an ideal annihilating Appel F2 function appelF4();      create an ideal annihilating Appel F4 function engine(I,i);     computes a Groebner basis with the algorithm given by i poly2list(f);   decompose a polynomial into a list of terms and exponents fl2poly(L,s);  reconstruct a monic univariate polynomial from its factorization insertGenerator(id,p[,k]); insert an element into an ideal/module deleteGenerator(id,k); delete the k-th element from an ideal/module SEE ALSO: bfun_lib, dmod_lib, dmodvar_lib, gmssing_lib KEYWORDS: D-module; annihilator of polynomial; annihilator of rational function; D-localization; localization of D-module; Appel function; Appel hypergeometric function; localization of D-module; Appel function; Appel hypergeometric function "; //AUXILIARY PROCEDURES: // //bFactor(F);  computes the roots of irreducible factors of an univariate poly //appelF1();      create an ideal annihilating Appel F1 function //appelF2();      create an ideal annihilating Appel F2 function //appelF4();      create an ideal annihilating Appel F4 function //engine(I,i);     computes a Groebner basis with the algorithm given by i //poly2list(f);   decompose a polynomial into a list of terms and exponents //fl2poly(L,s);  reconstruct a monic univariate polynomial from its factorization //insertGenerator(id,p[,k]); insert an element into an ideal/module //deleteGenerator(id,k); delete the k-th element from an ideal/module LIB "poly.lib";
• ## Singular/LIB/dmodvar.lib

 r77e09d (ALM09) Andres, Levandovskyy, Martin-Morales : Principal Intersection and Bernstein-Sato Polynomial of an Affine Variety (2009). MAIN PROCEDURES: PROCEDURES: bfctVarIn(F[,L]);     compute the roots of the Bernstein-Sato polynomial b(s) of the variety V(F) using initial ideal approach bfctVarAnn(F[,L]);  compute the roots of the Bernstein-Sato polynomial b(s) of the variety V(F) using Sannfs approach SannfsVar(F[,O,e]); compute the annihilator of F^s in the ring D AUXILIARY PROCEDURES: makeIF(F[,ORD]);    create the Malgrange ideal, associated with F = F[1],..,F[P] SEE ALSO: bfun_lib, dmod_lib, dmodapp_lib, gmssing_lib KEYWORDS: D-module; D-module structure; Bernstein-Sato polynomial for variety; global Bernstein-Sato polynomial for variety; Weyl algebra; parametric annihilator for variety; Budur-Mustata-Saito approach; initial ideal approach; Weyl algebra; parametric annihilator for variety; Budur-Mustata-Saito approach; initial ideal approach "; //AUXILIARY PROCEDURES: //makeIF(F[,ORD]);    create the Malgrange ideal, associated with F = F[1],..,F[P] // Static procs:
• ## Singular/LIB/jacobson.lib

 r77e09d SEE ALSO: control_lib KEYWORDS: Jacobson form; Jacobson normal form; Smith form; Smith normal form; matrix diagonalization; KEYWORDS: Jacobson form; Jacobson normal form; Smith form; Smith normal form; matrix diagonalization "; LIB "poly.lib"; LIB "involut.lib"; // involution LIB "dmodapp.lib"; // engine LIB "qhmoduli.lib"; // Min LIB "poly.lib"; LIB "involut.lib"; // involution LIB "dmodapp.lib"; // engine LIB "qhmoduli.lib"; // Min proc tstjacobson()
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