@comment -*-texinfo-*-
@comment $Id: pluconventions.doc,v 1.7 2004-08-12 16:58:19 levandov Exp $
@comment this file contains the type definitions

@c The following directives are necessary for proper compilation
@c with emacs (C-c C-e C-r).  Please keep it as it is.  Since it
@c is wrapped in `@ignore' and `@end ignore' it does not harm `tex' or
@c `makeinfo' but is a great help in editing this file (emacs
@c ignores the conditionals).

@ignore
%**start
\input texinfo.tex
@setfilename plureference.info
@settitel PLURAL
@node Top, PLURAL conventions, (dir), (dir)
@menu
* PLURAL conventions ::
@end menu
@node PLURAL conventions,  , Top, Top
@chapter PLURAL conventions
%**end
@end ignore


@c @c -----------------------------
@c @menu
@c * *-multiplication@value{PSUFFIX}::
@c * factor@value{PSUFFIX}::
@c * ideals@value{PSUFFIX}::
@c * modules@value{PSUFFIX}::
@c * ordering@value{PSUFFIX}::
@c * qring@value{PSUFFIX}::
@c @end menu

@c ----------------------------------------------- 
@table @strong

@item relations on algebra
@itemize 
@sc{Plural} @strong{can not} compute in free algebra or in its
general factor algebras. One can only input and work with 
G-algebras (see @ref{G-algebras}), which relations are of the special form
but still general enough to handle many important algebras. See
@ref{PLURAL libraries} for pre-defined definitions for many of them.
@end itemize

@item *-multiplication  @value{PSUFFIX}
@itemize 

in the non-commutative case,
one should use @code{y*x} for the multiplication while @code{yx} is interpreted as
commutative expression. See example in  @ref{poly expressions @value{PSUFFIX}}. 

@end itemize



@item   @code{ideal} @value{PSUFFIX}
@itemize
                        
Under an @code{ideal} @sc{Plural} understands a @strong{left} ideal.
For more information see @ref{ideal @value{PSUFFIX}}. For the operations
with two-sided ideals see @ref{twostd}. 
@end itemize

@item @code{module} @value{PSUFFIX}
@itemize
Under a @code{module} @sc{Plural} understands a @strong{left} submodule of a free module of a finite rank.
For more information see @ref{module @value{PSUFFIX}}. 
@end itemize

@item ordering @value{PSUFFIX}
@itemize
@sc{Plural} works with @strong{global} orderings  only.  
@ifset singularmanual
See @ref{ General definitions for orderings }
@end ifset
@ifclear singularmanual 
See @sc{Singular} manual section General definitions for orderings. 
@end ifclear

@end itemize

@item @code{qring} @value{PSUFFIX}

@itemize
In @sc{Plural} it is only possible to build factor-algebras modulo @strong{two-sided} ideals. 
@end itemize 


@end table