diff options
Diffstat (limited to 'src/algebra')
| -rw-r--r-- | src/algebra/indexedp.spad.pamphlet | 81 |
1 files changed, 45 insertions, 36 deletions
diff --git a/src/algebra/indexedp.spad.pamphlet b/src/algebra/indexedp.spad.pamphlet index 2caf4e10..1e1a569f 100644 --- a/src/algebra/indexedp.spad.pamphlet +++ b/src/algebra/indexedp.spad.pamphlet @@ -52,50 +52,59 @@ IndexedDirectProductCategory(A:SetCategory,S:OrderedSet): Category == ++ and the corresponding value (the second component). @ + \section{domain IDPO IndexedDirectProductObject} <<domain IDPO IndexedDirectProductObject>>= )abbrev domain IDPO IndexedDirectProductObject -++ Data Last Updated: June 28, 2010 -++ Indexed direct products of objects over a set \spad{A} -++ of generators indexed by an ordered set S. All items have finite support. -IndexedDirectProductObject(A:SetCategory,S:OrderedSet): IndexedDirectProductCategory(A,S) - == add - --representations - Term:= Record(k:S,c:A) - Rep:= List Term - --declarations - x,y: % - f: A -> A - s: S - --define - x = y == - while not null x and not null y repeat - x.first.k ~= y.first.k => return false - x.first.c ~= y.first.c => return false - x:=x.rest - y:=y.rest - null x and null y +++ Author: James Davenport, Gabriel Dos Reis +++ Date Created: +++ Date Last Updated: June 28, 2010 +++ Description: +++ Indexed direct products of objects over a set \spad{A} +++ of generators indexed by an ordered set S. All items have finite support. +IndexedDirectProductObject(A,S): Public == Private where + A: SetCategory + S: OrderedSet + Public == IndexedDirectProductCategory(A,S) + Private == add + Term == Pair(S,A) + Rep == List Term + -- Return the index of a term + termIndex(t: Term): S == first t + -- Return the value of a term + termValue(t: Term): A == second t + + x = y == + x' := rep x + y' := rep y + while not null x' and not null y' repeat + termIndex first x' ~= termIndex first y' => return false + termValue first x' ~= termValue first y' => return false + x' := rest x' + y' := rest y' + null x' and null y' - coerce(x:%):OutputForm == - bracket [rarrow(t.k :: OutputForm, t.c :: OutputForm) for t in x] + coerce(x:%):OutputForm == + bracket [rarrow(termIndex(t)::OutputForm, termValue(t)::OutputForm) + for t in rep x] - -- sample():% == [[sample()$S,sample()$A]$Term]$Rep + -- sample():% == [[sample()$S,sample()$A]$Term]$Rep - monomial(r,s) == [[s,r]] - map(f,x) == [[tm.k,f(tm.c)] for tm in x] + monomial(r,s) == per [[s,r]] + map(f,x) == per [[termIndex tm,f termValue tm] for tm in rep x] - reductum x == - rest x - leadingCoefficient x == - null x => error "Can't take leadingCoefficient of empty product element" - x.first.c - leadingSupport x == - null x => error "Can't take leadingCoefficient of empty product element" - x.first.k + reductum x == + per rest rep x + leadingCoefficient x == + null rep x => + error "Can't take leadingCoefficient of empty product element" + termValue first rep x + leadingSupport x == + null rep x => + error "Can't take leadingCoefficient of empty product element" + termIndex first rep x - -- FIXME: We should define Rep directly as List Pair(S,R) - -- so that this gross pretend can go away. - support x == x pretend List Pair(S,A) + support x == rep x @ \section{domain IDPAM IndexedDirectProductAbelianMonoid} |