\input texinfo @c -*-texinfo-*-
@comment $Id: singular.doc,v 1.127 2005-05-02 13:18:58 Singular Exp $
@comment this file contains the main structure of the manual
@c ------------------------
@c %**start of header
@c ------------------------
@setfilename singular.hlp
@settitle Singular Manual
@c @setchapternewpage odd
@paragraphindent 0
@c ------------------------
@c %**end of header
@c ------------------------
@c --------------------- general settings --------------------
@iftex
@afourpaper
@finalout
@pagesizes 23cm, 16.5cm
@end iftex
@set singularmanual 1
@set withplural 1
@set PSUFFIX (plural)
@set namespaces 1
@include version.texi
@include uname.texi
@c --------------------- end general setting --------------------
@c --------------------- invisible Info header ------------------------
@ifinfo
This is the texinfo file describing Singular (version @value{VERSION})
@end ifinfo
@c --------------------- end Info invisible header --------------------
@c --------------------- tex titlepage --------------------
@titlepage
@sp 2
@center @titlefont{Singular}
@sp 2
@center A Computer Algebra System for Polynomial Computations
@sp 5
@center @titlefont{Manual}
@center Version @value{VERSION}
@sp 2
@center Singular is created and its development is directed and coordinated by
@center G.-M. Greuel, G. Pfister, and H. Sch@"onemann
@sp 2
@center with contributions by
@center O. Bachmann, W. Decker, S. Endra@ss{}, I. Farran, A. Fr@"uhbis-Kr@"uger, C. Gorzel,
@center H. Grassmann, A. Heydtmann, D. Hillebrand, T. Keilen, U. Klein, K. Kr@"uger, M. Lamm, V. Levandovskyy
@center C. Lossen, B. Martin, M. Me@ss{}ollen, W. Neumann, T. N@"u@ss{}ler, W. Pohl, T. Siebert,
@center J. Schmidt, M. Schulze, R. Stobbe, M. Wenk, T. Wichmann, D. Yanovich
@sp 2
@author Fachbereich Mathematik
@author Zentrum f@"ur Computeralgebra
@author Universit@"at Kaiserslautern
@author D-67653 Kaiserslautern
@end titlepage
@c print short table of contents in tex right after titlepage
@c Detailed ToC is printed at the end of the manual
@shortcontents
@c -----------------------Top node-----------------------------------
@node Top, Preface, (dir), (dir)
@ifnothtml
@ifinfo
@center @strong{SINGULAR}
@center A Computer Algebra System for Polynomial Computations
@center User Manual for @sc{Singular} Version @value{VERSION}
@center @uref{http://www.singular.uni-kl.de}
@end ifinfo
@end ifnothtml
@ifhtml
@html
A Computer Algebra System for Polynomial Computations
HTML User Manual for Singular Version
@end html
@value{VERSION}, @value{VERSION_DATE}
@html
University of Kaiserslautern
Department of Mathematics
Centre for Computer Algebra
@end html
@end ifhtml
@menu
* Preface::
* Introduction::
* General concepts::
* Data types::
* Functions and system variables::
* Tricks and pitfalls::
@ifset withplural
* PLURAL::
@end ifset
* Examples::
* Polynomial data::
* Mathematical background::
* SINGULAR libraries::
* Release Notes::
* Index::
@end menu
@c ----------------------------------------------------------------------------
@node Preface, Introduction, Top, Top
@chapter Preface
@cindex Preface
@include COPYING.texi
@c ----------------------------------------------------------------------------
@node Introduction, General concepts, Preface, Top
@chapter Introduction
@cindex Introduction
@include start.tex
@c ----------------------------------------------------------------------------
@node General concepts, Data types, Introduction, Top
@chapter General concepts
@cindex General concepts
@include general.tex
@c ----------------------------------------------------------------------------
@node Data types, Functions and system variables, General concepts, Top
@chapter Data types
@cindex Data types
@include types.tex
@c ----------------------------------------------------------------------------
@node Functions and system variables, Tricks and pitfalls, Data types, Top
@chapter Functions and system variables
@cindex Commands
@include reference.tex
@c ----------------------------------------------------------------------------
@ifset withplural
@node Tricks and pitfalls, PLURAL, Functions and system variables, Top
@end ifset
@ifclear withplural
@node Tricks and pitfalls, Examples, Functions and system variables, Top
@end ifclear
@chapter Tricks and pitfalls
@cindex Tricks and pitfalls
@include tricks.tex
@c ----------------------------------------------------------------------------
@ifset withplural
@node PLURAL, Examples, Tricks and pitfalls, Top
@chapter PLURAL
@cindex PLURAL
@include s-plural.tex
@end ifset
@c ----------------------------------------------------------------------------
@ifset withplural
@node Examples, Polynomial data, PLURAL, Top
@end ifset
@ifclear withplural
@node Examples, Polynomial data, Tricks and pitfalls, Top
@end ifclear
@appendix Examples
@cindex Examples
@include examples.tex
@c ----------------------------------------------------------------------------
@node Polynomial data, Mathematical background, Examples, Top
@appendix Polynomial data
@cindex Polynomial data
@include pdata.tex
@c ----------------------------------------------------------------------------
@node Mathematical background, SINGULAR libraries, Polynomial data, Top
@appendix Mathematical background
@cindex Mathematical background
@include math.tex
@c @ifset withplural
@c @include s-plumath.tex
@c @end ifset
@c ----------------------------------------------------------------------------
@node SINGULAR libraries, Release Notes, Mathematical background, Top
@appendix SINGULAR libraries
@cindex SINGULAR libraries
@cindex LIBs
@sc{Singular} comes with a set of standard libraries. Their content is
described in the following subsections.
Use the @ref{LIB} command for loading of single libraries, and the
command @code{LIB "all.lib";} for loading all libraries.
@menu
* standard_lib:: extensions of Singular kernel
* General purpose::
* Linear algebra::
* Commutative algebra::
* Singularities::
* Invariant theory::
* Symbolic-numerical solving::
* Visualization::
* Coding theory::
* System and Control theory::
@end menu
@c ----------------------------------------------------------
@node standard_lib, General purpose, SINGULAR libraries, SINGULAR libraries
@section standard_lib
The library @code{standard.lib} provides extensions to the
set of built-in commands and is automatically loaded
during the start of @sc{Singular}, unless @sc{Singular} is started up
with the @code{--no-stdlib} command line option (see
@ref{Command line options}).
@c lib standard.lib:LibInfo lib_fun lib_ex section
@c ----------------------------------------------------------------------------
@node General purpose, Linear algebra, standard_lib, SINGULAR libraries
@section General purpose
@cindex General purpose
@menu
* all_lib:: load all other libraries
* general_lib:: procedures of general type
* inout_lib:: procedures for manipulating in- and output
* poly_lib:: procedures for manipulating polynomials and ideals
* random_lib:: procedures of random/sparse matrix and poly operations
* ring_lib:: procedures for manipulating rings and maps
@end menu
@c ----------------------------------------------------------
@node all_lib, general_lib, General purpose, General purpose
@subsection all_lib
@cindex all_lib
@cindex all.lib
The library @code{all.lib} provides a convenient way to load all
libraries of the @sc{Singular} distribution.
@strong{Example:}
@smallexample
@c example
option(loadLib);
LIB "all.lib";
@c example
@end smallexample
@c ----------------------------------------------------------
@node general_lib, inout_lib, all_lib, General purpose
@subsection general_lib
@c lib general.lib no_ex
@c ----------------------------------------------------------
@node inout_lib, poly_lib, general_lib, General purpose
@subsection inout_lib
@c lib inout.lib
@c ----------------------------------------------------------
@node poly_lib, random_lib, inout_lib, General purpose
@subsection poly_lib
@c lib poly.lib
@c ----------------------------------------------------------
@node random_lib, ring_lib, poly_lib, General purpose
@subsection random_lib
@c lib random.lib
@c ----------------------------------------------------------
@node ring_lib, , random_lib, General purpose
@subsection ring_lib
@c lib ring.lib
@c ----------------------------------------------------------------------------
@node Linear algebra, Commutative algebra, General purpose, SINGULAR libraries
@section Linear algebra
@cindex Linear algebra
@menu
* matrix_lib:: procedures for matrix operations
* linalg_lib:: procedures for algorithmic linear algebra
@end menu
@c ----------------------------------------------------------
@node matrix_lib, linalg_lib, Linear algebra, Linear algebra
@subsection matrix_lib
@c lib matrix.lib
@c ---------------------------------------------------------
@node linalg_lib, , matrix_lib, Linear algebra
@subsection linalg_lib
@c lib linalg.lib no_ex
@c ----------------------------------------------------------------------------
@node Commutative algebra, Singularities, Linear algebra, SINGULAR libraries
@section Commutative algebra
@cindex Commutative algebra
@menu
* algebra_lib:: procedures for computing with algebras and maps
* elim_lib:: procedures for elimination, saturation and blowing up
* homolog_lib:: procedures for homological algebra
* mprimdec_lib:: procedures for primary decomposition of modules
* mregular_lib:: procedures for Castelnuovo-Mumford regularity
* normal_lib:: procedure for normalization
* primdec_lib:: procedures for primary decomposition
* primitiv_lib:: procedures for finding a primitive element
* reesclos_lib:: Rees Algebra and integral closure of an ideal
* intprog_lib:: Integer Programming
* toric_lib:: toric ideals
@end menu
@c ---------------------------------------------------------
@node algebra_lib, elim_lib, Commutative algebra, Commutative algebra
@subsection algebra_lib
@c lib algebra.lib
@c ----------------------------------------------------------
@node elim_lib, homolog_lib, algebra_lib, Commutative algebra
@subsection elim_lib
@c lib elim.lib
@c ----------------------------------------------------------
@node homolog_lib, mprimdec_lib, elim_lib, Commutative algebra
@subsection homolog_lib
@c lib homolog.lib
@c ----------------------------------------------------------
@node mprimdec_lib, mregular_lib, homolog_lib, Commutative algebra
@subsection mprimdec_lib
@c lib mprimdec.lib
@c ----------------------------------------------------------
@node mregular_lib, normal_lib, mprimdec_lib, Commutative algebra
@subsection mregular_lib
@c lib mregular.lib
@c ---------------------------------------------------------
@node normal_lib, primdec_lib, mregular_lib, Commutative algebra
@subsection normal_lib
@c lib normal.lib
@c ----------------------------------------------------------
@node primdec_lib, primitiv_lib, normal_lib, Commutative algebra
@subsection primdec_lib
@c lib primdec.lib
@c ---------------------------------------------------------
@node primitiv_lib, reesclos_lib, primdec_lib, Commutative algebra
@subsection primitiv_lib
@c lib primitiv.lib
@c ---------------------------------------------------------
@node reesclos_lib, intprog_lib, primitiv_lib, Commutative algebra
@subsection reesclos_lib
@c lib reesclos.lib
@c ---------------------------------------------------------
@node intprog_lib, toric_lib, reesclos_lib, Commutative algebra
@subsection intprog_lib
@c lib intprog.lib
@c ---------------------------------------------------------
@node toric_lib, ,intprog_lib, Commutative algebra
@subsection toric_lib
@c lib toric.lib
@c ----------------------------------------------------------------------------
@node Singularities, Invariant theory, Commutative algebra, SINGULAR libraries
@section Singularities
@cindex Singularities
@menu
* classify_lib:: procedures for the Arnold-classifier of singularities
* deform_lib:: procedures for computing miniversal deformation
* equising_lib:: procedures for equisingularity strata
* gmssing_lib:: procedures for gauss-manin system of a singularity
* gmspoly_lib:: procedures for gauss-manin system of cohomologically tame polynomials
* hnoether_lib:: procedures for the Hamburger-Noether (Puiseux) development
* mondromy_lib:: procedures to compute the monodromy of a singularity
* qhmoduli_lib:: procedures for moduli spaces of sqh-singularities
* sing_lib:: procedures for computing invariants of singularities
* spcurve_lib:: procedures for cm codimension 2 singularities
* spectrum_lib:: procedures for computing singularity spectra
@end menu
@c ---------------------------------------------------------
@node classify_lib, deform_lib, Singularities, Singularities
@subsection classify_lib
@c lib classify.lib unix_only
@c ----------------------------------------------------------
@node deform_lib, equising_lib, classify_lib, Singularities
@subsection deform_lib
@c lib deform.lib
@c ----------------------------------------------------------
@node equising_lib, gmssing_lib, deform_lib, Singularities
@subsection equising_lib
@c lib equising.lib
@c ----------------------------------------------------------
@node gmssing_lib, gmspoly_lib, equising_lib, Singularities
@subsection gmssing_lib
@c lib gmssing.lib no_ex
@c ----------------------------------------------------------
@node gmspoly_lib, hnoether_lib, gmssing_lib, Singularities
@subsection gmspoly_lib
@c lib gmspoly.lib no_ex
@c ---------------------------------------------------------
@node hnoether_lib, mondromy_lib, gmspoly_lib, Singularities
@subsection hnoether_lib
@c lib hnoether.lib
@c ---------------------------------------------------------
@node mondromy_lib, qhmoduli_lib, hnoether_lib, Singularities
@subsection mondromy_lib
@c lib mondromy.lib no_ex
@c ---------------------------------------------------------
@node qhmoduli_lib, sing_lib, mondromy_lib, Singularities
@subsection qhmoduli_lib
@c lib qhmoduli.lib no_ex
@c ----------------------------------------------------------
@node sing_lib, spcurve_lib, qhmoduli_lib, Singularities
@subsection sing_lib
@c lib sing.lib
@c ---------------------------------------------------------
@node spcurve_lib, spectrum_lib, sing_lib, Singularities
@subsection spcurve_lib
@c lib spcurve.lib
@c ---------------------------------------------------------
@node spectrum_lib, , spcurve_lib, Singularities
@subsection spectrum_lib
@c lib spectrum.lib
@c ----------------------------------------------------------------------------
@node Invariant theory, Symbolic-numerical solving, Singularities, SINGULAR libraries
@section Invariant theory
@cindex Invariant theory
@menu
* finvar_lib:: procedures to compute invariant rings of finite groups
* ainvar_lib:: procedures to compute invariants rings of the additive group
* rinvar_lib:: procedures to compute invariants ring of reductive groups
* stratify_lib:: algorithmic stratification by the Greuel-Pfister algorithm
@end menu
@c ----------------------------------------------------------
@node finvar_lib, ainvar_lib, Invariant theory, Invariant theory
@subsection finvar_lib
@c lib finvar.lib no_ex
@c ----------------------------------------------------------
@node ainvar_lib, rinvar_lib, finvar_lib, Invariant theory
@subsection ainvar_lib
@c lib ainvar.lib
@c ----------------------------------------------------------
@node rinvar_lib, stratify_lib, ainvar_lib, Invariant theory
@subsection rinvar_lib
@c lib rinvar.lib
@c ----------------------------------------------------------
@node stratify_lib, ,rinvar_lib, Invariant theory
@subsection stratify_lib
@c lib stratify.lib no_ex
@c ----------------------------------------------------------------------------
@node Symbolic-numerical solving, Visualization, Invariant theory, SINGULAR libraries
@section Symbolic-numerical solving
@cindex Symbolic-numerical solving
@menu
* presolve_lib:: procedures for pre-solving polynomial equations
* solve_lib:: procedures to solve polynomial systems
* triang_lib:: procedures for decomposing zero-dimensional ideals
* ntsolve_lib:: one real solution of polynomial systems (Newton iteration)
* zeroset_lib:: procedures for roots and factorization
* mrrcount_lib:: counting the number of real roots
* signcond_lib:: computing realizable sign conditions
* urrcount_lib:: counting number of real roots of univariate polynomial
@end menu
@c ---------------------------------------------------------
@node presolve_lib, solve_lib, Symbolic-numerical solving, Symbolic-numerical solving
@subsection presolve_lib
@c lib presolve.lib
@c ---------------------------------------------------------
@node solve_lib, triang_lib, presolve_lib, Symbolic-numerical solving
@subsection solve_lib
@c lib solve.lib
@c ---------------------------------------------------------
@node triang_lib, ntsolve_lib, solve_lib, Symbolic-numerical solving
@subsection triang_lib
@c lib triang.lib no_ex
@c ---------------------------------------------------------
@node ntsolve_lib, zeroset_lib, triang_lib, Symbolic-numerical solving
@subsection ntsolve_lib
@c lib ntsolve.lib
@c ---------------------------------------------------------
@node zeroset_lib,mrrcount_lib , ntsolve_lib, Symbolic-numerical solving
@subsection zeroset_lib
@c lib zeroset.lib
@c ---------------------------------------------------------
@node mrrcount_lib, signcond_lib ,zeroset_lib, Symbolic-numerical solving
@subsection mrrcount_lib
@c lib mrrcount.lib
@c ---------------------------------------------------------
@node signcond_lib, urrcount_lib, mrrcount_lib, Symbolic-numerical solving
@subsection signcond_lib
@c lib signcond.lib
@c ---------------------------------------------------------
@node urrcount_lib, , signcond_lib, Symbolic-numerical solving
@subsection urrcount_lib
@c lib urrcount.lib
@c ----------------------------------------------------------------------------
@node Visualization, Coding theory, Symbolic-numerical solving, SINGULAR libraries
@section Visualization
@cindex Visualization
@menu
* graphics_lib:: procedures to draw with Mathematica
* latex_lib:: procedures for typesetting in TeX
* surf_lib:: interface to the surf programm::
@end menu
@c ---------------------------------------------------------
@node graphics_lib, latex_lib, Visualization, Visualization
@subsection graphics_lib
@c lib graphics.lib no_ex
@c ---------------------------------------------------------
@node latex_lib, surf_lib, graphics_lib, Visualization
@subsection latex_lib
@c lib latex.lib
@c ---------------------------------------------------------
@node surf_lib,, latex_lib, Visualization
@subsection surf_lib
@c lib surf.lib no_ex
@c ----------------------------------------------------------------------------
@node Coding theory, System and Control theory, Visualization, SINGULAR libraries
@section Coding theory
@cindex Coding theory
@menu
* brnoeth_lib:: Brill-Noether algorithm, Weierstrass semigroups and AG codes
@end menu
@c ---------------------------------------------------------
@node brnoeth_lib, , , Coding theory
@subsection brnoeth_lib
@c lib brnoeth.lib
@c ----------------------------------------------------------------------------
@node System and Control theory, , Coding theory, SINGULAR libraries
@section System and Control theory
@cindex System and Control theory
@cindex Control theory
@menu
* control_lib:: Algebraic analysis tools for System and Control Theory
@end menu
@c ---------------------------------------------------------
@node control_lib, , , System and Control theory
@subsection control_lib
@c lib control.lib
@c ----------------------------------------------------------
@node Release Notes, Index, SINGULAR libraries, Top
@chapter Release Notes
@cindex Release Notes
@include platform.tex
@c ----------------------------------------------------------
@node Index, , Release Notes, Top
@chapter Index
@cindex Index
@printindex cp
@c ---------------------------------------------------------
@c generate table of content and short table of content
@contents
@bye