|
#############################################################################
##
#W utilsfrgrp.gd automgrp package Yevgen Muntyan
#W Dmytro Savchuk
##
#Y Copyright (C) 2003 - 2018 Yevgen Muntyan, Dmytro Savchuk
##
## Here are utility functions dealing with free groups, words, etc.
##
#############################################################################
##
## AG_ReducedListOfWordsByNielsen(<words_list>[, <any_string>])
## AG_ReducedListOfWordsByNielsenBack(<words_list>[, <any_string>])
##
## It applies Nielsen transformations to <words_list>;
## input is a list of associative words from the same family.
##
## Returned value is either fail in case of some error or
## triple [<result>, <transform>, <did_something>] :
## <result> is the list of words obtained from <list> using Nielsen
## transformations;
## <transform> is the list of words for obtaining <result> from
## <list> by substituting: <transform> = [w_1, ..., w_n],
## where w_i are words on alphabet of Length(<list>) letters such that
## w_i(<words_list>[1], ..., <words_list>[n]) = <result>[i];
## <did_something> is true if <result> differs from <list> and is
## false otherwise
##
## ReduceListOfWordsByNielsenBack is almost identical to
## ReduceListOfWordsByNielsen: the difference is in the order of
## comparisons performed inside of main loop;
## it makes Mihaylov feel better?
##
## The variants with the second string argument do the same
## except that the lexicographic ordering on set of words is generated
## by the following ordering: x_1 < x_1^{-1} < x_2 < x_2^{-1} < ...
## It's intended for nice output - like "a^2, b^2" instead of "a^-2, b^-2"
##
DeclareOperation("AG_ReducedListOfWordsByNielsen", [IsAssocWordCollection]);
DeclareOperation("AG_ReducedListOfWordsByNielsenBack", [IsAssocWordCollection]);
DeclareOperation("AG_ReducedListOfWordsByNielsen", [IsAssocWordCollection, IsString]);
DeclareOperation("AG_ReducedListOfWordsByNielsenBack", [IsAssocWordCollection, IsString]);
DeclareOperation("AG_ReducedListOfWordsByNielsen", [IsAssocWordCollection, IsFunction]);
DeclareOperation("AG_ReducedListOfWordsByNielsenBack", [IsAssocWordCollection, IsFunction]);
#############################################################################
##
## AG_ReducedByNielsen(<obj>)
## AG_ApplyNielsen(<obj>)
##
## It applies Nielsen transformations to <obj> or to generators of <obj> if
## <obj> is a group etc.
## AG_ReducedByNielsen is nondestructive variant; AG_ApplyNielsen changes object.
## They are not necessarily implemented both in the same for given type.
##
DeclareOperation("AG_ReducedByNielsen", [IsObject]);
DeclareOperation("AG_ApplyNielsen", [IsObject]);
#############################################################################
##
## AG_ComputeMihailovaSystemPairs(<pairs_list>)
##
## For given list of pairs of free group words, it tries to compute the
## Mihaylov normal form.
##
## Returned value is either fail in case of some error or
## triple [<result>, <transform>, <did_something>] :
## <result> is the list of pairs representing Mihaylov normal form;
## <transform> is the list of words for obtaining <result> from
## <list> by substituting: <transform> = [w_1, ..., w_n],
## where w_i are words on alphabet of Length(<pairs_list>) letters
## such that w_i(<pairs_list>[1], ..., <pairs_list>[n]) = <result>[i];
## <did_something> is true if <result> differs from <pairs_list> and is
## false otherwise
##
DeclareGlobalFunction("AG_ComputeMihailovaSystemPairs");
#E
[ Dauer der Verarbeitung: 0.16 Sekunden
(vorverarbeitet)
]
|
