Edit detail for FreeModuleCategory revision 1 of 2

A domain of this category implements formal linear combinations of elements from a domain S with coefficients in a domain R. The coefficient ring may be non-commutative.

See the XDistributedPolynomial? constructor for examples of domains built with the FreeModuleCategory? category constructor.

Author: Michel Petitot (petitot@lifl.fr)

Modified by: Franz Lehner, June 2009

)sh FreeModuleCategory

 FreeModuleCategory(R: Join(SemiRng,AbelianMonoid),S: Comparable)  is a category constructor
 Abbreviation for FreeModuleCategory is FMCAT 
 This constructor is exposed in this frame.
------------------------------- Operations --------------------------------
 ?*? : (S,R) -> %                      ?*? : (R,S) -> %
 ?*? : (%,R) -> %                      ?*? : (R,%) -> %
 ?*? : (PositiveInteger,%) -> %        ?+? : (%,%) -> %
 ?=? : (%,%) -> Boolean                coefficient : (%,S) -> R
 coefficients : % -> List(R)           coerce : % -> OutputForm
 hash : % -> SingleInteger             latex : % -> String
 leadingCoefficient : % -> R           leadingMonomial : % -> S
 leadingSupport : % -> S               map : ((R -> R),%) -> %
 monom : (S,R) -> %                    monomial : (R,S) -> %
 monomial? : % -> Boolean              monomials : % -> List(%)
 reductum : % -> %                     support : % -> List(S)
 ?~=? : (%,%) -> Boolean              
 ?*? : (NonNegativeInteger,%) -> % if and(OR(has(R,AbelianMonoid),has(R,AbelianMonoid)),has(R,CommutativeRing)) or R has OAMON and S has ORDSET or R has OAMONS and S has ORDSET or R has ABELMON
 ?*? : (Integer,%) -> % if and(OR(has(R,AbelianGroup),has(R,AbelianGroup)),has(R,CommutativeRing)) or R has ABELGRP or R has ABELGRP
 -? : % -> % if and(OR(has(R,AbelianGroup),has(R,AbelianGroup)),has(R,CommutativeRing)) or R has ABELGRP or R has ABELGRP
 ?-? : (%,%) -> % if and(OR(has(R,AbelianGroup),has(R,AbelianGroup)),has(R,CommutativeRing)) or R has ABELGRP or R has ABELGRP
 ?<? : (%,%) -> Boolean if R has OAMON and S has ORDSET or R has OAMONS and S has ORDSET
 ?<=? : (%,%) -> Boolean if R has OAMON and S has ORDSET or R has OAMONS and S has ORDSET
 ?>? : (%,%) -> Boolean if R has OAMON and S has ORDSET or R has OAMONS and S has ORDSET
 ?>=? : (%,%) -> Boolean if R has OAMON and S has ORDSET or R has OAMONS and S has ORDSET
 0 : () -> % if and(OR(has(R,AbelianMonoid),has(R,AbelianMonoid)),has(R,CommutativeRing)) or R has OAMON and S has ORDSET or R has OAMONS and S has ORDSET or R has ABELMON
 coerce : S -> % if R has SRING
 construct : List(Record(k: S,c: R)) -> %
 constructOrdered : List(Record(k: S,c: R)) -> %
 hashUpdate! : (HashState,%) -> HashState
 leadingTerm : % -> Record(k: S,c: R)
 linearExtend : ((S -> R),%) -> R if R has COMRING
 listOfTerms : % -> List(Record(k: S,c: R))
 max : (%,%) -> % if R has OAMON and S has ORDSET or R has OAMONS and S has ORDSET
 min : (%,%) -> % if R has OAMON and S has ORDSET or R has OAMONS and S has ORDSET
 numberOfMonomials : % -> NonNegativeInteger
 retract : % -> S if R has SRING
 retractIfCan : % -> Union(S,"failed") if R has SRING
 sample : () -> % if and(OR(has(R,AbelianMonoid),has(R,AbelianMonoid)),has(R,CommutativeRing)) or R has OAMON and S has ORDSET or R has OAMONS and S has ORDSET or R has ABELMON
 smaller? : (%,%) -> Boolean if R has COMPAR or R has OAMON and S has ORDSET or R has OAMONS and S has ORDSET
 subtractIfCan : (%,%) -> Union(%,"failed") if and(OR(has(R,AbelianGroup),has(R,AbelianGroup)),has(R,CommutativeRing)) or R has OAMONS and S has ORDSET or R has CABMON or R has ABELGRP
 sup : (%,%) -> % if R has OAMONS and S has ORDSET
 zero? : % -> Boolean if and(OR(has(R,AbelianMonoid),has(R,AbelianMonoid)),has(R,CommutativeRing)) or R has OAMON and S has ORDSET or R has OAMONS and S has ORDSET or R has ABELMON