\input texinfo    @c -*-texinfo-*-
x@comment this file contains the main structure of the manual


@c ------------------------
@c %**start of header
@c ------------------------
@setfilename singular.info
@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 withpython 1
@set PSUFFIX  (plural)
@set namespaces 1
@include version.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}, @value{VERSION_DATE}
@sp 2
@center @sc{Singular} is created and its development is directed and coordinated by
@center W. Decker, G.-M. Greuel, G. Pfister, and H. Sch@"onemann
@sp 2
@c @center with contributions by
@center Principal developers:
@center O. Bachmann, M. Brickenstein, W. Decker, A. Fr@"uhbis-Kr@"uger, K. Kr@"uger,
@center V. Levandovskyy, C. Lossen, W. Neumann, W. Pohl, J. Schmidt, M. Schulze,
@center T. Siebert, R. Stobbe, E. Westenberger, T. Wichmann, O. Wienand
@c @center O. Bachmann, W. Decker, A. Fr@"uhbis-Kr@"uger, C. Gorzel,
@c @center H. Grassmann, A. Heydtmann, D. Hillebrand, T. Keilen, U. Klein, K. Kr@"uger, M. Lamm, V. Levandovskyy
@c @center C. Lossen, B. Martin, M. Me@ss{}ollen, W. Neumann, T. N@"u@ss{}ler, W. Pohl, T. Siebert,
@c @center J. Schmidt, M. Schulze, R. Stobbe, M. Wenk, T. Wichmann, D. Yanovich
@sp 2
@author Department of Mathematics
@author Centre of computer algebra
@author University Kaiserslautern-Landau
@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{https://www.singular.uni-kl.de}
@end ifinfo
@end ifnothtml

@ifhtml
@html
<CENTER>
<A HREF="https://www.singular.uni-kl.de">
<IMG SRC="singular.jpg"></A><br>
<h3> A Computer Algebra System for Polynomial Computations </h3>
<p></p>
<h4>HTML User Manual for Singular Version
@end html
@value{VERSION}, @value{VERSION_DATE}
@html
</h4>
</center>
<CENTER><A HREF="https://rptu.de/"><I>University of Kaiserslautern-Landau</I></A></CENTER>
<CENTER><A HREF="https://math.rptu.de/"><I>Department of Mathematics</I></A></CENTER>
<CENTER><I>Centre for Computer Algebra</I></CENTER><p></p>
@end html
@end ifhtml

@menu
* Preface::
* Introduction::
* General concepts::
* Data types::
* Functions and system variables::
* Tricks and pitfalls::
@ifset withplural
* Non-commutative subsystem::
@end ifset
* Examples::
* Polynomial data::
* Mathematical background::
* SINGULAR libraries::
* Release Notes::
* Index::
@end menu

@c ----------------------------------------------------------------------------
@node Preface
@chapter Preface
@cindex Preface
@include COPYING.texi

@c ----------------------------------------------------------------------------
@node Introduction
@chapter Introduction
@cindex Introduction

@include start.tex
@c ----------------------------------------------------------------------------
@node General concepts
@chapter General concepts
@cindex General concepts
@include general.tex

@c ----------------------------------------------------------------------------
@node Data types
@chapter Data types
@cindex Data types
@include types.tex

@c ----------------------------------------------------------------------------
@node Functions and system variables
@chapter Functions and system variables
@cindex Commands
@include reference.tex

@c ----------------------------------------------------------------------------
@node Tricks and pitfalls
@chapter Tricks and pitfalls
@cindex Tricks and pitfalls
@include tricks.tex

@c ----------------------------------------------------------------------------
@ifset withplural
@node Non-commutative subsystem,Examples,Tricks and pitfalls,Top
@chapter Non-commutative subsystem
@cindex Non-commutative subsystem

@sc{Singular} has three non-commutative subsystems, handling various classes of associative
non-commutative rings: @sc{Plural}, @sc{Sca} and @sc{Letterplace}.

@menu
* PLURAL::
* Data types (plural)::
* Functions  (plural)::
* Mathematical background (plural)::
* PLURAL libraries::
* Graded commutative algebras (SCA)::
* LETTERPLACE::
* Functions  (letterplace)::
* Mathematical background (letterplace)::
* LETTERPLACE libraries::
* Release Notes (letterplace)::
@end menu
@include s-plural.tex
@include s-plulibs.tex
@include sca.tex
@include s-letterplace.tex
@end ifset

@c ----------------------------------------------------------------------------
@ifset withplural
@node Examples,Polynomial data,Non-commutative subsystem,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 ----------------------------------------------------------------------------
@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 @code{LIB} command (see @ref{LIB}) for loading of single libraries,
and the command @code{LIB "all.lib";} for loading all libraries.

@c levandov: moved to below
@c @ifset withplural
@c See also @ref{PLURAL libraries} and .
@c @end ifset

@strong{Interpreter libraries:}

@menu
* standard_lib:: extensions of Singular kernel
* General purpose::
* Linear algebra::
* Commutative algebra::
* Algebraic geometry::
* Singularities::
* Invariant theory::
* Symbolic-numerical solving::
* Visualization::
* Coding theory::
* System and Control theory::
* Teaching::
* Tropical Geometry::
* Miscellaneous libraries::
* Experimental libraries::
@end menu
@ifset withplural
@c @xref{PLURAL libraries}, @xref{LETTERPLACE libraries}.
See also @ref{PLURAL libraries} and @ref{LETTERPLACE libraries}.
@end ifset

@c ----------------------------------------------------------
@node standard_lib
@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 ----------------------------------------------------------------------
@c and now some routines from standard.lib:
@c ---------------------------------------------------------
@node qslimgb,par2varRing,standard_lib, standard_lib
@subsection qslimgb
@cindex qslimgb
@c lib standard.lib:qslimgb Fun subsection
@c ---------------------------------------------------------
@node par2varRing,,qslimgb, standard_lib
@subsection par2varRing
@cindex par2varRing
@c lib standard.lib:par2varRing Fun subsection

@c ----------------------------------------------------------------------------
@node General purpose
@section General purpose
@cindex General purpose

@menu
* all_lib:: load all other libraries
* compregb_lib:: comprehensive Groebner base system
* general_lib:: procedures of general type
* grobcov_lib:: Groebner Cover for parametric ideals
* inout_lib:: procedures for manipulating in- and output
* modular_lib::abstraction layer for modular techniques
* parallel_lib:: Tools for parallelization
* polylib_lib:: procedures for manipulating polynomials and ideals
* random_lib:: procedures of random/sparse  matrix and polynomial operations
* redcgs_lib:: Reduced Comprehensive Groebner Systems
* resources_lib:: Tools to manage the computational resources
* ring_lib:: procedures for manipulating rings and maps
* tasks_lib:: A parallel framework based on tasks
@end menu

@c ----------------------------------------------------------
@node all_lib
@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 compregb_lib
@subsection compregb_lib
@c lib compregb.lib
@c ----------------------------------------------------------
@node general_lib
@subsection general_lib
@c lib general.lib
@c ----------------------------------------------------------
@node grobcov_lib
@subsection grobcov_lib
@cindex Comprehensive Groebner Systems
@c lib grobcov.lib
@c ----------------------------------------------------------
@node inout_lib
@subsection inout_lib
@c lib inout.lib
@c ----------------------------------------------------------
@node modular_lib
@subsection modular_lib
@c lib modular.lib
@c ----------------------------------------------------------
@node parallel_lib
@subsection parallel_lib
@c lib parallel.lib
@c ----------------------------------------------------------
@node polylib_lib
@subsection polylib_lib
@c lib polylib.lib
@c ----------------------------------------------------------
@node redcgs_lib
@subsection redcgs_lib
@cindex Reduced Comprehensive Groebner Systems
@cindex Comprehensive Groebner Systems
@c lib redcgs.lib
@c ----------------------------------------------------------
@node random_lib
@subsection random_lib
@c lib random.lib
@c ----------------------------------------------------------
@node resources_lib
@subsection resources_lib
@c lib resources.lib
@c ----------------------------------------------------------
@node ring_lib
@subsection ring_lib
@c lib ring.lib
@c ----------------------------------------------------------
@node tasks_lib
@subsection tasks_lib
@c lib tasks.lib
@c ----------------------------------------------------------------------------
@node Linear algebra
@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
@subsection matrix_lib
@c lib matrix.lib
@c ---------------------------------------------------------
@node linalg_lib
@subsection linalg_lib
@c lib linalg.lib
@c ----------------------------------------------------------------------------
@node Commutative algebra
@section Commutative algebra
@cindex Commutative algebra

@menu
* absfact_lib:: absolute factorization for characteristic 0
* algebra_lib:: procedures for computing with algebras and maps
* assprimeszerodim_lib:: associated primes of a zero-dimensional ideal
* cisimplicial_lib:: is the toric ideal of a simplicial toric variety a complete intersection?
* curveInv_lib:: invariants of curves
* decomp_lib:: Functional decomposition of polynomials
* elim_lib:: procedures for elimination, saturation and blowing up
* ellipticcovers_lib::  Gromov Witten numbers of elliptic curves
* ffmodstd_lib::  Groebner bases in polynomial rings over rational function fields
* grwalk_lib:: Groebner walk and Fraktal walk
* homolog_lib:: procedures for homological algebra
* integralbasis_lib:: Integral basis in algebraic function fields
* intprog_lib:: Integer Programming
* modprimdec_lib:: primary decomposition using modular methods
* modquotient_lib:: ideal quotient and saturation using modular methods
* modstd_lib:: Groebner basis of ideals via modular computations
* modules_lib:: Representations of Modules
* monomialideal_lib:: Primary and irreducible decompositions of monomial ideals
* mprimdec_lib:: procedures for primary decomposition of modules
* mregular_lib:: procedures for Castelnuovo-Mumford regularity
* nfmodstd_lib:: Groebner bases of ideals in rings over algebraic number fields
* nfmodsyz_lib:: Syzygy modules of submodules of free modules over algebraic number fields
* noether_lib:: Noether normalization of an ideal
* normal_lib:: procedure for normalization
* normaliz_lib:: integral closure, normalization for monomial ideals, toric ideals
* pointid_lib:: factorized lex GB of the vanishing ideal of a set of points
* primdec_lib:: procedures for primary decomposition
* primdecint_lib:: primary decomposition over the integers
* primitiv_lib:: procedures for finding a primitive element
* realrad_lib:: procedures for finding the real radical
* reesclos_lib:: Rees Algebra and integral closure of an ideal
* rstandard_lib:: Janet bases and border bases for ideals
* sagbi_lib:: Subalgebras bases Analogous to Groebner bases for ideals
* sing4ti2_lib:: interface to program 4ti2
* symodstd_lib:: Groebner bases for symmetric ideals
* toric_lib:: toric ideals
@end menu

@c ---------------------------------------------------------
@node absfact_lib
@subsection absfact_lib
@c lib absfact.lib
@c ---------------------------------------------------------
@node algebra_lib
@subsection algebra_lib
@c lib algebra.lib
@c ---------------------------------------------------------
@node assprimeszerodim_lib
@subsection assprimeszerodim_lib
@c lib assprimeszerodim.lib
@c ---------------------------------------------------------
@node cisimplicial_lib
@subsection cisimplicial_lib
@c lib cisimplicial.lib
@c ----------------------------------------------------------
@node curveInv_lib
@subsection curveInv_lib
@c lib curveInv.lib
@c ----------------------------------------------------------
@node decomp_lib
@subsection decomp_lib
@c lib decomp.lib
@c ----------------------------------------------------------
@node elim_lib
@subsection elim_lib
@c lib elim.lib
@c ----------------------------------------------------------
@node ellipticcovers_lib
@subsection ellipticcovers_lib
@c lib ellipticcovers.lib
@c ----------------------------------------------------------
@node ffmodstd_lib
@subsection ffmodstd_lib
@c lib ffmodstd.lib
@c ----------------------------------------------------------
@node grwalk_lib
@subsection grwalk_lib
@c lib grwalk.lib
@c ----------------------------------------------------------
@node homolog_lib
@subsection homolog_lib
@c lib homolog.lib
@c ----------------------------------------------------------
@node integralbasis_lib
@subsection integralbasis_lib
@c lib integralbasis.lib
@c ----------------------------------------------------------
@node intprog_lib
@subsection intprog_lib
@c lib intprog.lib
@c ----------------------------------------------------------
@node modprimdec_lib
@subsection modprimdec_lib
@c lib modprimdec.lib
@c ----------------------------------------------------------
@node modquotient_lib
@subsection modquotient_lib
@c lib modquotient.lib
@c ---------------------------------------------------------
@node modules_lib
@subsection modules_lib
@c lib modules.lib
@c ----------------------------------------------------------
@node modstd_lib
@subsection modstd_lib
@c lib modstd.lib
@c ---------------------------------------------------------
@node monomialideal_lib
@subsection monomialideal_lib
@c lib monomialideal.lib
@c ---------------------------------------------------------
@node mprimdec_lib
@subsection mprimdec_lib
@c lib mprimdec.lib
@c ----------------------------------------------------------
@node mregular_lib
@subsection mregular_lib
@c lib mregular.lib
@c ----------------------------------------------------------
@node nfmodstd_lib
@subsection nfmodstd_lib
@c lib nfmodstd.lib
@c ----------------------------------------------------------
@node nfmodsyz_lib
@subsection nfmodsyz_lib
@c lib nfmodsyz.lib
@c ----------------------------------------------------------
@node noether_lib
@subsection noether_lib
@c lib noether.lib
@c ---------------------------------------------------------
@node normal_lib
@subsection normal_lib
@c lib normal.lib
@c ---------------------------------------------------------
@node normaliz_lib
@subsection normaliz_lib
@c lib normaliz.lib tag:normaliz
@c ----------------------------------------------------------
@node pointid_lib
@subsection pointid_lib
@c lib pointid.lib
@c ----------------------------------------------------------
@node primdec_lib
@subsection primdec_lib
@c lib primdec.lib
@c ---------------------------------------------------------
@node primdecint_lib
@subsection primdecint_lib
@c lib primdecint.lib
@c ---------------------------------------------------------
@node primitiv_lib
@subsection primitiv_lib
@c lib primitiv.lib
@c ---------------------------------------------------------
@node realrad_lib
@subsection realrad_lib
@c lib realrad.lib
@c ---------------------------------------------------------
@node reesclos_lib
@subsection reesclos_lib
@c lib reesclos.lib
@c ----------------------------------------------------------
@node rstandard_lib
@subsection rstandard_lib
@c lib rstandard.lib
@c ---------------------------------------------------------
@node sagbi_lib
@subsection sagbi_lib
@c lib sagbi.lib
@c ---------------------------------------------------------
@node sing4ti2_lib
@subsection sing4ti2_lib
@c lib sing4ti2.lib tag:sing4ti2
@c ----------------------------------------------------------
@node symodstd_lib
@subsection symodstd_lib
@c lib symodstd.lib
@c ---------------------------------------------------------
@node toric_lib
@subsection toric_lib
@c lib toric.lib
@c ---------------------------------------------------------
@node Algebraic geometry
@section Algebraic geometry
@cindex Algebraic geometry

@menu
* brillnoether_lib:: Riemann-Roch spaces of divisors on curves
* chern_lib:: Symbolic Computations with Chern classes
* deRham_lib:: Computation of deRham cohomology
* divisors_lib:: Divisors and P-Divisors
* goettsche_lib:: Goettsche's formula for the Betti numbers of the Hilbert scheme
* graal_lib:: localization at prime ideals and their associated graded rings
* hess_lib:: Riemann-Roch space of divisors on function fields and curves
* numerAlg_lib:: Numerical Algebraic Algorithms
* numerDecom_lib:: Bertini interface
* orbitparam_lib:: Parametrizing unipotent orbits
* paraplanecurves_lib:: Rational parametrization of rational plane curves
* resbinomial_lib:: Resolution of singularities of binomial ideals
* resgraph_lib:: Visualization of Resolution data
* resjung_lib:: Resolution of Surface Singularities by Jung's Algorithm
* resolve_lib:: Resolution of Singularities
* reszeta_lib:: Applications of Resolution of Singularities
* schubert_lib:: Intersection Theory
* sheafcoh_lib:: Procedures for Computing Sheaf Cohomology
* JMBTest_lib:: performs J-Marked basis test
* JMSConst_lib::  constructing J-Marked Schemes
@end menu

@c ----------------------------------------------------------
@node brillnoether_lib
@subsection brillnoether_lib
@c lib brillnoether.lib
@c ----------------------------------------------------------
@node chern_lib
@subsection chern_lib
@c lib chern.lib tag:lrcalc
@c ----------------------------------------------------------
@node deRham_lib
@subsection deRham_lib
@c lib deRham.lib
@c ----------------------------------------------------------
@node divisors_lib
@subsection divisors_lib
@c lib divisors.lib
@c ----------------------------------------------------------
@node goettsche_lib
@subsection goettsche_lib
@c lib goettsche.lib
@c ----------------------------------------------------------
@node graal_lib
@subsection graal_lib
@c lib graal.lib
@c ----------------------------------------------------------
@node hess_lib
@subsection hess_lib
@c lib hess.lib
@c ----------------------------------------------------------
@node numerAlg_lib
@subsection numerAlg_lib

Todos/Issues:
@itemize
@item does not follow the naming convention
@item syntax errors in examples
@item no test suite
@end itemize

@c lib numerAlg.lib no_ex
@c ----------------------------------------------------------
@node numerDecom_lib
@subsection numerDecom_lib

Todos/Issues:
@itemize
@item does not follow the naming convention
@item syntax errors in examples
@item no test suite
@end itemize

@c lib numerDecom.lib no_ex
@c ----------------------------------------------------------
@node orbitparam_lib
@subsection orbitparam_lib
@c lib orbitparam.lib
@c ---------------------------------------------------------
@node paraplanecurves_lib
@subsection paraplanecurves_lib
@c lib paraplanecurves.lib
@c ---------------------------------------------------------
@node resbinomial_lib
@subsection resbinomial_lib

Todos/Issues:
@itemize
@item formatting is inappropriate
@item avoid export
@item bad names(or should be static):
identifyvars, elimrep, convertdata, lcmofall, genoutput, salida,
iniD, reslist, sumlist, dividelist, createlist
@end itemize

@c lib resbinomial.lib
@c ---------------------------------------------------------
@node resgraph_lib
@subsection resgraph_lib
@c lib resgraph.lib
@c ---------------------------------------------------------
@node resjung_lib
@subsection resjung_lib
@c lib resjung.lib
@c ---------------------------------------------------------
@node resolve_lib
@subsection resolve_lib
@c lib resolve.lib
@c ---------------------------------------------------------
@node reszeta_lib
@subsection reszeta_lib
@c lib reszeta.lib
@c ----------------------------------------------------------
@node schubert_lib
@subsection schubert_lib
@c lib schubert.lib
@c ---------------------------------------------------------
@node sheafcoh_lib
@subsection sheafcoh_lib
@c lib sheafcoh.lib tag:memory
@c ----------------------------------------------------------
@node JMBTest_lib
@subsection JMBTest_lib
@c lib JMBTest.lib
@c ----------------------------------------------------------
@node JMSConst_lib
@subsection JMSConst_lib
@c lib JMSConst.lib
@c ----------------------------------------------------------------------------
@node Singularities
@section Singularities
@cindex Singularities

@menu
* alexpoly_lib:: resolution graph and Alexander polynomial
* arcpoint_lib:: truncations of arcs at a singular point
* arnoldclassify_lib:: Arnol'd Classifier of Singularities
* classify_lib:: procedures for the Arnold-classifier of singularities
* classify2_lib:: Classification of isolated singularties
* classify_aeq_lib:: Simple Space Curve singularities in characteristic 0
* classifyceq_lib:: simple hypersurface singularities in characteristic p > 0
* classifyci_lib:: isolated complete intersection singularities in char 0
* classifyMapGerms_lib:: standard basis of the tangent space at the orbit of an algebraic group action
* curvepar_lib:: procedures for space curves
* 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
* kskernel_lib:: procedures for kernel  of the kodaira-spencer map
* mondromy_lib:: procedures to compute the monodromy of a singularity
* qhmoduli_lib:: procedures for moduli spaces of sqh-singularities
* realclassify_lib:: Classification of real singularities
* sing_lib:: procedures for computing invariants of singularities
* spcurve_lib:: procedures for cm codimension 2 singularities
* spectrum_lib:: procedures for computing singularity spectra
* surfacesignature_lib:: signature of surface singularities
@end menu

@c ---------------------------------------------------------
@node alexpoly_lib
@subsection alexpoly_lib
@c lib alexpoly.lib
@c ---------------------------------------------------------
@node arcpoint_lib
@subsection arcpoint_lib
@c lib arcpoint.lib
@c ----------------------------------------------------------
@node arnoldclassify_lib
@subsection arnoldclassify_lib
@cindex SingularityDBM.lib
@cindex SingularityDBM_lib
@c lib arnoldclassify.lib
@c ---------------------------------------------------------
@node classify_lib
@subsection classify_lib
@c lib classify.lib unix_only
@c ----------------------------------------------------------
@node classify2_lib
@subsection classify2_lib
@c lib classify2.lib
@c ----------------------------------------------------------
@node classify_aeq_lib
@subsection classify_aeq_lib
@c lib classify_aeq.lib
@c ----------------------------------------------------------
@node classifyceq_lib
@subsection classifyceq_lib
@c lib classifyceq.lib
@c ----------------------------------------------------------
@node classifyci_lib
@subsection classifyci_lib
@c lib classifyci.lib
@c ----------------------------------------------------------
@node classifyMapGerms_lib
@subsection classifyMapGerms_lib
@c lib classifyMapGerms.lib
@c ---------------------------------------------------------
@node curvepar_lib
@subsection curvepar_lib
@c lib curvepar.lib
@c ----------------------------------------------------------
@node deform_lib
@subsection deform_lib
@c lib deform.lib
@c ----------------------------------------------------------
@node equising_lib
@subsection equising_lib
@c lib equising.lib
@c ----------------------------------------------------------
@node gmssing_lib
@subsection gmssing_lib
@c lib gmssing.lib
@c ----------------------------------------------------------
@node gmspoly_lib
@subsection gmspoly_lib
@c lib gmspoly.lib
@c ---------------------------------------------------------
@node hnoether_lib
@subsection hnoether_lib
@c lib hnoether.lib
@c ---------------------------------------------------------
@node kskernel_lib
@subsection kskernel_lib
@c lib kskernel.lib
@c ---------------------------------------------------------
@node mondromy_lib
@subsection mondromy_lib
@c lib mondromy.lib
@c ---------------------------------------------------------
@node qhmoduli_lib
@subsection qhmoduli_lib
@c lib qhmoduli.lib
@c ----------------------------------------------------------
@node realclassify_lib
@subsection realclassify_lib
@c lib realclassify.lib
@c ----------------------------------------------------------
@node sing_lib
@subsection sing_lib
@c lib sing.lib
@c ---------------------------------------------------------
@node spcurve_lib
@subsection spcurve_lib
@c lib spcurve.lib
@c ---------------------------------------------------------
@node spectrum_lib
@subsection spectrum_lib
@c lib spectrum.lib
@c ---------------------------------------------------------
@node surfacesignature_lib
@subsection surfacesignature_lib
@c lib surfacesignature.lib
@c ----------------------------------------------------------------------------
@node Invariant theory
@section Invariant theory
@cindex Invariant theory

@menu
* finvar_lib:: procedures to compute invariant rings of finite groups
* ainvar_lib:: procedures to compute invariant rings of the additive group
* rinvar_lib:: procedures to compute invariant rings of reductive groups
* invar_lib:: procedures to compute invariant rings of SL(n) and torus groups
* stratify_lib:: algorithmic stratification by the Greuel-Pfister algorithm
@end menu

@c ----------------------------------------------------------
@node finvar_lib
@subsection finvar_lib
@c lib finvar.lib
@c ----------------------------------------------------------
@node ainvar_lib
@subsection ainvar_lib
@c lib ainvar.lib
@c ----------------------------------------------------------
@node rinvar_lib
@subsection rinvar_lib
@c lib rinvar.lib
@c ----------------------------------------------------------
@node invar_lib
@subsection invar_lib
@c lib invar.lib
@c ----------------------------------------------------------
@node stratify_lib
@subsection stratify_lib
@c lib stratify.lib
@c ----------------------------------------------------------------------------
@node Symbolic-numerical solving
@section Symbolic-numerical solving
@cindex Symbolic-numerical solving

@menu
* ffsolve_lib:: multivariate equation solving over finite fields
* interval_lib:: interval arithmetic on polynomials
* 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)
* recover_lib:: Hybrid numerical/symbolical algorithms
* rootisolation_lib:: real root isolation with intervals
* signcond_lib:: computing realizable sign conditions
* zeroset_lib:: procedures for roots and factorization
@end menu

@c ---------------------------------------------------------
@node ffsolve_lib
@subsection ffsolve_lib
@c lib ffsolve.lib
@c ---------------------------------------------------------
@node interval_lib
@subsection interval_lib
@c lib interval.lib
@c ---------------------------------------------------------
@node presolve_lib
@subsection presolve_lib
@c lib presolve.lib
@c ---------------------------------------------------------
@node solve_lib
@subsection solve_lib
@c lib solve.lib
@c ---------------------------------------------------------
@node triang_lib
@subsection triang_lib
@c lib triang.lib
@c ---------------------------------------------------------
@node ntsolve_lib
@subsection ntsolve_lib
@c lib ntsolve.lib
@c ---------------------------------------------------------
@node recover_lib
@subsection recover_lib
@c lib recover.lib tag:bertini
@c ----------------------------------------------------------
@node rootisolation_lib
@subsection rootisolation_lib
@c lib rootisolation.lib
@c ---------------------------------------------------------
@node signcond_lib
@subsection signcond_lib
@c lib signcond.lib
@c ---------------------------------------------------------
@node zeroset_lib
@subsection zeroset_lib
@c lib zeroset.lib
@c ---------------------------------------------------------
@node Visualization
@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
* surfex_lib:: Procedures for Visualizing Surfaces
@end menu

@c ---------------------------------------------------------
@node graphics_lib
@subsection graphics_lib
@c lib graphics.lib
@c ---------------------------------------------------------
@node latex_lib
@subsection latex_lib
@c lib latex.lib
@c ---------------------------------------------------------
@node surf_lib
@subsection surf_lib
@c lib surf.lib no_ex
@c ---------------------------------------------------------
@node surfex_lib
@subsection surfex_lib
@c lib surfex.lib no_ex
@c ----------------------------------------------------------------------------
@node Coding theory
@section Coding theory
@cindex Coding theory

@menu
* brnoeth_lib:: Brill-Noether algorithm, Weierstrass semigroups and AG codes
* decodegb_lib:: Generating and solving systems of polynomial equations for decoding and finding the minimum distance of linear codes
@end menu

@c ---------------------------------------------------------
@node brnoeth_lib
@subsection brnoeth_lib
@c lib brnoeth.lib
@c ---------------------------------------------------------
@node decodegb_lib
@subsection decodegb_lib
@c lib decodegb.lib


@c ----------------------------------------------------------------------------
@node System and Control theory
@section System and Control theory
@cindex System and Control theory
@cindex Control theory

@menu
* Control theory background:: An overview of the theory
* control_lib:: Algebraic analysis tools for System and Control Theory
* jacobson_lib:: Algorithms for Smith and Jacobson Normal Form
* findifs_lib:: Tools for the finite difference schemes
@end menu

@c ---------------------------------------------------------
@node Control theory background
@subsection Control theory background

Control systems are usually described by differential (or
difference) equations, but their properties of interest are
most naturally expressed in terms of the system trajectories
(the set of all solutions to the equations). This is formalized
by the notion of the system @emph{behavior}. On the other hand,
the manipulation of linear system equations can be formalized
using algebra, more precisely module theory. The relationship
between modules and behaviors is very rich and leads to deep
results on system structure.


The key to the module-behavior correspondence
is a property of some signal spaces that are modules
over the ring of differential (or difference) operators,
namely, @emph{the injective cogenerator property}.
This property makes it possible to translate any statement on the
solution spaces that can be expressed in terms of images and kernels,
to an equivalent statement on the modules. Thus analytic properties
can be identified with algebraic properties, and conversely, the
results of manipulating the modules using computer algebra can
be re-translated and interpreted using the language of systems theory.
This duality (@emph{algebraic analysis}) is widely used in behavioral
systems and control theory today.


For instance, a system is @strong{controllable} (a fundamental property
for any control system) if and only if the associated module
is torsion-free. This concept can be refined by the so-called
controllability degrees. The strongest form of controllability
(@emph{flatness}) corresponds to a projective (or even free) module.

Controllability means that one can switch from one system trajectory
to another without violating the system law (concatenation of
trajectories). For one-dimensional systems (ODE) that evolve in time,
this is usually interpreted as switching from a given past trajectory
to a desired future trajectory. Thus the system can be forced to
behave in an arbitrarily prescribed way.


The extreme case opposed to controllability is @strong{autonomy}: autonomous systems evolve independently according to their law, without being influenceable
from the outside. Again, the property can be refined in terms
of autonomy degrees.

@c ---------------------------------------------------------
@node control_lib
@subsection control_lib
@c lib control.lib

@c ---------------------------------------------------------
@node jacobson_lib
@subsection jacobson_lib
@c lib jacobson.lib

@c ----------------------------------------------------------
@node findifs_lib
@subsection findifs_lib
@c lib findifs.lib
@c ----------------------------------------------------------------------------
@node Teaching
@section Teaching
@cindex Teaching

The libraries in this section are intended to be used for teaching purposes
but not for serious computations.

@menu
* aksaka_lib:: Algorithms for primality testing in polynomial time
* crypto_lib:: Procedures for teaching cryptography
* hyperel_lib:: Divisors in the jacobian of hyperelliptic curves
* teachstd_lib:: Procedures for teaching standard bases
* weierstr_lib:: Procedures for the Weierstrass Theorems
* rootsmr_lib:: counting the number of real roots
* rootsur_lib:: counting number of real roots of univariate polynomial
@end menu
@c ---------------------------------------------------------
@node aksaka_lib
@subsection aksaka_lib
@c lib aksaka.lib

@c ---------------------------------------------------------
@node crypto_lib
@subsection crypto_lib
@c lib crypto.lib

@c ---------------------------------------------------------
@node hyperel_lib
@subsection hyperel_lib
@c lib hyperel.lib

@c ---------------------------------------------------------
@node teachstd_lib
@subsection teachstd_lib
@c lib teachstd.lib

@c ---------------------------------------------------------
@node weierstr_lib
@subsection weierstr_lib
@c lib weierstr.lib

@c ---------------------------------------------------------
@node rootsmr_lib
@subsection rootsmr_lib
@c lib rootsmr.lib

@c ---------------------------------------------------------
@node rootsur_lib
@subsection rootsur_lib
@c lib rootsur.lib

@c ----------------------------------------------------------------------------
@node Tropical Geometry
@section Tropical Geometry
@cindex Tropical Geometry

@menu
* cimonom_lib:: complete intersection for toric ideals
* gfan_lib:: A gfanlib interface for Singular
* gitfan_lib:: Compute GIT-fans
* polymake_lib:: interface to TOPCOM
* realizationMatroids_lib:: Realizability for Tropical Fan Curves
* tropical_lib:: interface to gfan
* tropicalNewton_lib:: Newton polygons in tropical geometry
@end menu
@c ----------------------------------------------------------
@node cimonom_lib
@subsection cimonom_lib
@c lib cimonom.lib
@c ----------------------------------------------------------
@node gfan_lib
@subsection gfan_lib
@c lib gfan.lib
@c ----------------------------------------------------------
@node gitfan_lib
@subsection gitfan_lib
@c lib gitfan.lib
@c ----------------------------------------------------------
@node polymake_lib
@subsection polymake_lib
@c lib polymake.lib tag:topcom
@c ----------------------------------------------------------
@node realizationMatroids_lib
@subsection realizationMatroids_lib
@c lib realizationMatroids.lib
@c ----------------------------------------------------------
@node tropical_lib
@subsection tropical_lib
@c lib tropical.lib tag:gfan
@c ----------------------------------------------------------
@node tropicalNewton_lib
@subsection tropicalNewton_lib
@c lib tropicalNewton.lib
@c ----------------------------------------------------------------------------
@node  Miscellaneous libraries
@section  Miscellaneous libraries
@cindex  Miscellaneous libraries

@menu
* arr_lib:: algorithms for arrangements of hyperplanes
* combinat_lib:: Some useful functions from combinatoric
* customstd_lib:: additional variants of std
* methods_lib:: construction procedures
* nets_lib:: Pretty printing
* phindex_lib:: index of real analytic vector fields
* polybori_lib:: interface for PolyBoRi
* sets_lib:: Sets
@end menu
@c ----------------------------------------------------------
@node arr_lib
@subsection arr_lib
@c lib arr.lib
@c ---------------------------------------------------------
@node combinat_lib
@subsection combinat_lib
@c lib combinat.lib
@c ----------------------------------------------------------
@node customstd_lib
@subsection customstd_lib
@c lib customstd.lib
@c ----------------------------------------------------------
@node methods_lib
@subsection methods_lib
@c lib methods.lib
@c ----------------------------------------------------------
@node nets_lib
@subsection nets_lib
@c lib nets.lib
@c ----------------------------------------------------------
@node phindex_lib
@subsection phindex_lib
@c lib phindex.lib
@c ----------------------------------------------------------
@node polybori_lib
@subsection polybori_lib
@c lib polybori.lib tag:pyobject no_ex
@c ----------------------------------------------------------
@node sets_lib
@subsection sets_lib
@c lib sets.lib
@c ----------------------------------------------------------------------------
@node Experimental libraries
@section Experimental libraries
@cindex Experimental libraries

This sections collect libraries in the beta test phase.
Everything in these libraries may change.

For the minimal requirements and guidelines
see @ref{Libraries}.

Comments should be send to the author of the library directly.

@menu
* arnold_lib:: Classification of isolated singularities with a nondegenerate Newton Boundary
* autgradalg_lib:: automorphism groups of pointedly graded algebras and of Mori dream spaces
* difform_lib:: Procedures for differential forms
* enumpoints_lib:: enumerating rational points
* finitediff_lib:: finite difference schemes for linear differential equations
* GND_lib:: General Neron Desingularization
* gradedModules_lib::Operations with graded modules/matrices/resolutions
* hodge_lib:: Algorithms for Hodge ideals
* lrcalc_lib:: interface to the Littlewood-Richardson Calculator by Anders Buch
* maxlike_lib:: maximum likelihood estimates
* modfinduni_lib:: parallel computation of finduni
* modwalk_lib:: Groebner basis conversion
* multigrading_lib:: Multigradings and related computations
* pfd_lib:: Multivartiate partial fraction decomposition
* polyclass_lib:: class of polynomials
* puiseuxexpansions_lib:: Puiseux expansions over algebraic extensions
* ringgb_lib:: Functions for coefficient rings
* rwalk_lib:: Groebner Walk Conversion
* sagbigrob_lib:: Sagbi-Groebner basis of an ideal of a subalgebra
* sagbiNormaliz_lib:: computation of Sagbi bases via normaliz
* ssi_lib:: Wrapper for handling SSI files
* stanleyreisner_lib:: T1 and T2 for a general Stanley-Reiser ring
* stdmodule_lib:: Compute Standard Bases of submodule of free module over polynomial subalgebra
* swalk_lib:: Sagbi Walk Conversion Algorithm
* systhreads_lib:: multi-threaded objects
* tateProdCplxNegGrad_lib:: sheaf cohomology on product of projective spaces
* transformation_lib:: image of a transformation given up to a specified degree
* tropicalEllipticCovers_lib:: Gromov-Witten numbers of tropical elliptic curves and their covers
* VecField_lib:: vector fields
@end menu
@c ----------------------------------------------------------
@node arnold_lib
@subsection arnold_lib
@c lib arnold.lib
@c ----------------------------------------------------------
@node autgradalg_lib
@subsection autgradalg_lib
@c lib autgradalg.lib
@c ----------------------------------------------------------
@node difform_lib
@subsection difform_lib
@c lib difform.lib
@c ----------------------------------------------------------
@node enumpoints_lib
@subsection enumpoints_lib
@c lib enumpoints.lib
@c ----------------------------------------------------------
@node finitediff_lib
@subsection finitediff_lib

Issues:
@itemize
@item installation of qepcadfilter.pl needs to be solved
@item tests for (nearly) all procedures are missing
@item global variables needs to be cleaned
@item temporary files needs to be cleaned
@item temporary file names need to be unique (think about multiple instances)
@item pollution of global Top namespace must be solved
@item u is not a good name for a procedure
@end itemize

@c lib finitediff.lib

@c ----------------------------------------------------------
@node GND_lib
@subsection GND_lib
@c lib GND.lib
@c ----------------------------------------------------------
@node gradedModules_lib
@subsection gradedModules_lib
@c lib gradedModules.lib
@c ----------------------------------------------------------
@node hodge_lib
@subsection hodge_lib
@c lib hodge.lib
@c ----------------------------------------------------------
@node lrcalc_lib
@subsection lrcalc_lib
@c lib lrcalc.lib tag:lrcalc
@c ----------------------------------------------------------
@node maxlike_lib
@subsection maxlike_lib
@c lib maxlike.lib
@c ----------------------------------------------------------
@node modfinduni_lib
@subsection modfinduni_lib
@c lib modfinduni.lib
@c ----------------------------------------------------------
@node modwalk_lib
@subsection modwalk_lib
@c lib modwalk.lib
@c ----------------------------------------------------------
@node multigrading_lib
@subsection multigrading_lib

Todos/Issues:
@itemize
@item See @url{http://code.google.com/p/convex-singular/wiki/Multigrading}
@end itemize

@c lib multigrading.lib
@c ----------------------------------------------------------
@node pfd_lib
@subsection pfd_lib
@c lib pfd.lib
@c ----------------------------------------------------------
@node polyclass_lib
@subsection polyclass_lib
@c lib polyclass.lib
@c ----------------------------------------------------------
@node puiseuxexpansions_lib
@subsection puiseuxexpansions_lib
@c lib puiseuxexpansions.lib
@c ----------------------------------------------------------
@node ringgb_lib
@subsection ringgb_lib
@c lib ringgb.lib
@c ----------------------------------------------------------
@node rwalk_lib
@subsection rwalk_lib
@c lib rwalk.lib
@c ----------------------------------------------------------
@node sagbigrob_lib
@subsection sagbigrob_lib
@c lib sagbigrob.lib
@c ----------------------------------------------------------
@node sagbiNormaliz_lib
@subsection sagbiNormaliz_lib
@c lib sagbiNormaliz.lib tag:normaliz
@c ----------------------------------------------------------
@node ssi_lib
@subsection ssi_lib
@c lib ssi.lib
@c ----------------------------------------------------------
@node stanleyreisner_lib
@subsection stanleyreisner_lib
@c lib stanleyreisner.lib
@c ---------------------------------------------------------
@node stdmodule_lib
@subsection stdmodule_lib
@c lib stdmodule.lib
@c ---------------------------------------------------------
@node swalk_lib
@subsection swalk_lib
@c lib swalk.lib
@c ---------------------------------------------------------
@node systhreads_lib
@subsection systhreads_lib
@c lib systhreads.lib
@c ---------------------------------------------------------
@node tateProdCplxNegGrad_lib
@subsection tateProdCplxNegGrad_lib
@c lib tateProdCplxNegGrad.lib tag:sing4ti2
@c ---------------------------------------------------------
@node transformation_lib
@subsection transformation_lib
@c lib transformation.lib
@c ---------------------------------------------------------
@node tropicalEllipticCovers_lib
@subsection tropicalEllipticCovers_lib
@c lib tropicalEllipticCovers.lib no_ex
@c ---------------------------------------------------------
@node VecField_lib
@subsection VecField_lib
@c lib VecField.lib
@c ---------------------------------------------------------

@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