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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 | )abbrev domain IDPOAM IndexedDirectProductOrderedAbelianMonoid
++ Author: Mark Botch
++ Description:
++ Indexed direct products of ordered abelian monoids \spad{A} of
++ generators indexed by the ordered set S.
++ The inherited order is lexicographical.
++ All items have finite support: only non-zero terms are stored.
IndexedDirectProductOrderedAbelianMonoid(A,S) : SIG == CODE where
A : OrderedAbelianMonoid
S : OrderedSet
SIG ==> Join(OrderedAbelianMonoid,IndexedDirectProductCategory(A,S))
CODE ==> IndexedDirectProductAbelianMonoid(A,S) add
--representations
Term:= Record(k:S,c:A)
Rep:= List Term
x,y: %
x<y ==
empty? y => false
empty? x => true -- note careful order of these two lines
y.first.k > x.first.k => true
y.first.k < x.first.k => false
y.first.c > x.first.c => true
y.first.c < x.first.c => false
x.rest < y.rest
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