<!-- HAPPRIME - functions.xml.in Function documentation template file for HAPprime Paul Smith Copyright (C) 2007 Paul Smith National University of Ireland Galway $Id: functions.xml.in 200 2008-02-05 14:29:47Z pas $ --> <!-- ********************************************************** --> <Chapter> <Heading>Function Reference</Heading> <Section> <Heading>Matrices as generators of a row space</Heading> <Package>HAPprime</Package> represents <M>\mathbb{F}G</M>-modules as vector spaces and makes use of standard &GAP; operations and datatypes to store and manipulate them. There are a few particular variants of functions that are not provided as part &GAP;, and they are described here. <!-- GAPDocSourceSuffix="_manBaseMat" --> </Section> <Section Label="FG modules"> <Heading><M>\mathbb{F}G</M>-modules</Heading> <!-- GAPDocSourceSuffix="_manFpGModule" --> </Section> <Section Label="FG module homomorphisms"> <Heading><M>\mathbb{F}G</M>-module homomorphisms</Heading> <!-- GAPDocSourceSuffix="_manFpGModuleHom" --> </Section> <Section> <Heading>Resolutions</Heading> <!-- GAPDocSourceSuffix="_manResolution" --> </Section> <Section> <Heading>Poincaré Series</Heading> <!-- GAPDocSourceSuffix="_manPoincare" --> </Section> <Section> <Heading>Ring structure</Heading> <!-- GAPDocSourceSuffix="_manRings" --> </Section> <Section> <Heading>Polynomials</Heading> <!-- GAPDocSourceSuffix="_manPolynomial" --> </Section> <Section> <Heading>Derivations</Heading> <!-- GAPDocSourceSuffix="_manDerivation" --> </Section> <Section> <Heading>Interface with <Package>singular</Package></Heading> <!-- GAPDocSourceSuffix="_manSingular" --> </Section> <Section> <Heading>Test functions</Heading> <!-- GAPDocSourceSuffix="_manTest" --> </Section> <Section> <Heading>Miscellaneous functions</Heading> <!-- GAPDocSourceSuffix="_manMisc" --> </Section> </Chapter> <!-- ********************************************************** --> <Chapter> <Heading>Internal Function Reference</Heading> These are functions that are used internally in <Package>HAPprime</Package>. They should not be needed by users of the package, but may be useful to developers and are provided for completeness <Section> <Heading>Matrices as <M>g</M>-generators of a row space</Heading> Both <K>FpGModuleGF</K> and <K>FpGModuleHomomorphismGF</K> store a matrix whose rows are <M>g</M>-generators for a module vector space (the module and the homomorphism's image respectively). The internal functions listed here provide common operations for dealing with these matrices. <!-- GAPDocSourceSuffix="_manGenMatInt" --> </Section> <Section> <Heading><M>\mathbb{F}G</M>-modules</Heading> Internal helper functions for <K>FpGModuleGFs</K>s. <!-- GAPDocSourceSuffix="_manFpGModuleInt" --> </Section> <Section> <Heading>Resolutions</Heading> Internal helper functions for building resolutions. <!-- GAPDocSourceSuffix="_manResolutionInt" --> </Section> <Section> <Heading>Miscellaneous</Heading> Miscellaneous internal helper functions. <!-- GAPDocSourceSuffix="_manMiscInt" --> </Section> </Chapter>