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Diff for /OpenXM/src/asir-doc/papers/risa-asir.tex between version 1.1 and 1.4

version 1.1, 2005/06/22 07:22:07

version 1.4, 2005/07/01 04:24:54

Line 7

\usepackage{makeidx} % allows index generation

\usepackage{graphicx} % standard LaTeX graphics tool

% for including eps-figure files

\usepackage{subeqnar} % subnumbers individual equations

%\usepackage{subeqnar} % subnumbers individual equations

% within an array

\usepackage{multicol} % used for the two-column index

%\usepackage{multicol} % used for the two-column index

\usepackage{cropmark} % cropmarks for pages without

%\usepackage{cropmark} % cropmarks for pages without

% pagenumbers

\usepackage{math} % placeholder for figures

%\usepackage{math} % placeholder for figures

\makeindex % used for the subject index

% please use the style sprmidx.sty with

% your makeindex program

Line 293 the precomputed inverse of a divisor),

\item Polynomial Factorization

{\tt fctr } (factorization over the rationals),

{\tt fctr\_ff } (univariate factorization over finite fields),

{\tt modfctr}, {\tt fctr\_ff } (univariate factorization over finite fields),

{\tt af } (univariate factorization over algebraic number fields),

{\tt sp} (splitting field computation).

Line 329 quadratic first-order formula),

{\tt det} (determinant),

{\tt qsort} (sorting of an array by the quick sort algorithm),

{\tt eval} (evaluation of a formula containing transcendental functions

{\tt eval}, {\tt deval} (evaluation of a formula containing transcendental functions

such as

{\tt sin}, {\tt cos}, {\tt tan}, {\tt exp},

{\tt log})

{\tt roots} (finding all roots of a univariate polynomial),

{\tt pari(roots)} (finding all roots of a univariate polynomial),

{\tt lll} (computation of an LLL-reduced basis of a lattice).

{\tt pari(lll)} (computation of an LLL-reduced basis of a lattice).

\item $D$-modules ($D$ is the Weyl algebra)

{\tt gb } (Gr\"obner basis),

{\tt sm1.gb } (Gr\"obner basis),

{\tt syz} (syzygy),

{\tt sm1.syz} (syzygy),

{\tt annfs} (Annhilating ideal of $f^s$),

{\tt sm1.bfunction},{\tt bfunction} (the global $b$-function of a polynomial)

{\tt bfunction},\\

{\tt sm1.restriction} in the derived category of $D$-modules,

{\tt schreyer} (free resolution by the Schreyer method),

{\tt sm1.slope},

{\tt vMinRes} (V-minimal free resolution),\\

{\tt sm1.sm1(annfs)} (Annhilating ideal of $f^s$),

{\tt characteristic} (Characteristic variety),

{\tt sm1.sm1(schreyer)} (free resolution by the Schreyer method),

{\tt restriction} in the derived category of $D$-modules,

%{\tt sm1.sm1(vMinRes)} (V-minimal free resolution),\\

{\tt integration} in the derived category,

{\tt sm1.sm1(characteristic)} (Characteristic variety),

{\tt tensor} in the derived category,

{\tt sm1.sm1(integration)} in the derived category,

{\tt dual} (Dual as a D-module),

%{\tt sm1.sm1(tensor)} in the derived category,

{\tt slope}.

{\tt sm1.sm1(res-dual)} (Dual as a D-module).

\item Cohomology groups

Line 362 and the ring of formal power series).

Helping to derive and prove {\tt combinatorial} and

{special function identities},

{\tt gkz} (GKZ hypergeometric differential equations),

{\tt sm1.gkz} (GKZ hypergeometric differential equations),

{\tt appell} (Appell's hypergeometric differential equations),

{\tt sm1.appell1}, {\tt sm1.appell4} (Appell's hypergeometric differential equations),

{\tt indicial} (indicial equations),

%{\tt indicial} (indicial equations),

{\tt rank} (Holonomic rank),

{\tt sm1.generalized\_bfunction} (indicial equations),

{\tt rrank} (Holonomic rank of regular holonomic systems),

{\tt sm1.rank} (Holonomic rank),

{\tt dsolv} (series solutions of holonomic systems).

{\tt sm1.rrank} (Holonomic rank of regular holonomic systems),

%{\tt dsolv} (series solutions of holonomic systems).

{\tt dsolv\_dual}, {\tt dsolv\_starting\_terms} (series solutions of holonomic systems).

\item OpenMATH support

Line 376 Helping to derive and prove {\tt combinatorial} and

Line 378 Helping to derive and prove {\tt combinatorial} and

\item Homotopy Method

{\tt phc} (Solving systems of algebraic equations by

{\tt phc.phc} (Solving systems of algebraic equations by

numerical and polyhedral homotopy methods).

\item Toric ideal

{\tt tigers} (Enumerate all Gr\"obner basis of a toric ideal.

{\tt tigers.tigers} (Enumerate all Gr\"obner basis of a toric ideal.

Finding test sets for integer program),

{\tt arithDeg} (Arithmetic degree of a monomial ideal),

%{\tt arithDeg} (Arithmetic degree of a monomial ideal),

{\tt stdPair} (Standard pair decomposition of a monomial ideal).

%{\tt stdPair} (Standard pair decomposition of a monomial ideal).

\item Communications

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