/usr/lib/open-axiom/src/algebra/modmonom.spad is in open-axiom-source 1.4.1+svn~2626-2ubuntu2.
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)abbrev domain MODMONOM ModuleMonomial
++ Description:
++ This package \undocumented
ModuleMonomial(IS: OrderedSet,
E: SetCategory,
ff:(MM, MM) -> Boolean): T == C where
MM ==> Record(index:IS, exponent:E)
T == Join(OrderedSet, HomotopicTo MM) with
exponent: $ -> E
++ exponent(x) \undocumented
index: $ -> IS
++ index(x) \undocumented
construct: (IS, E) -> $
++ construct(i,e) \undocumented
C == MM add
Rep:= MM
x:$ < y:$ == ff(x::Rep, y::Rep)
exponent(x:$):E == x.exponent
index(x:$): IS == x.index
coerce(x:$):MM == x::Rep::MM
coerce(x:MM):$ == x::Rep::$
construct(i:IS, e:E):$ == [i, e]$MM::Rep::$
)abbrev domain GMODPOL GeneralModulePolynomial
++ Description:
++ This package \undocumented
GeneralModulePolynomial(vl, R, IS, E, ff, P): public == private where
vl: List(Symbol)
R: CommutativeRing
IS: OrderedSet
NNI ==> NonNegativeInteger
E: DirectProductCategory(#vl, NNI)
MM ==> Record(index:IS, exponent:E)
ff: (MM, MM) -> Boolean
OV ==> OrderedVariableList(vl)
P: PolynomialCategory(R, E, OV)
ModMonom ==> ModuleMonomial(IS, E, ff)
public == Join(Module(P), Module(R)) with
leadingCoefficient: $ -> R
++ leadingCoefficient(x) \undocumented
leadingMonomial: $ -> ModMonom
++ leadingMonomial(x) \undocumented
leadingExponent: $ -> E
++ leadingExponent(x) \undocumented
leadingIndex: $ -> IS
++ leadingIndex(x) \undocumented
reductum: $ -> $
++ reductum(x) \undocumented
monomial: (R, ModMonom) -> $
++ monomial(r,x) \undocumented
unitVector: IS -> $
++ unitVector(x) \undocumented
build: (R, IS, E) -> $
++ build(r,i,e) \undocumented
multMonom: (R, E, $) -> $
++ multMonom(r,e,x) \undocumented
*: (P,$) -> $
++ p*x \undocumented
private == FreeModule(R, ModMonom) add
Rep:= FreeModule(R, ModMonom)
leadingMonomial(p:$):ModMonom == leadingSupport(p)$Rep
leadingExponent(p:$):E == exponent(leadingMonomial p)
leadingIndex(p:$):IS == index(leadingMonomial p)
unitVector(i:IS):$ == monomial(1,[i, 0$E]$ModMonom)
-----------------------------------------------------------------------------
build(c:R, i:IS, e:E):$ == monomial(c, construct(i, e))
-----------------------------------------------------------------------------
---- WARNING: assumes c ~= 0
multMonom(c:R, e:E, mp:$):$ ==
zero? mp => mp
monomial(c * leadingCoefficient mp, [leadingIndex mp,
e + leadingExponent mp]) + multMonom(c, e, reductum mp)
-----------------------------------------------------------------------------
((p:P) * (mp:$)):$ ==
zero? p => 0
multMonom(leadingCoefficient p, degree p, mp) +
reductum(p) * mp
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