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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 31 32 33 34 35 | )abbrev category IDPC IndexedDirectProductCategory
++ Author: James Davenport
++ Description:
++ This category represents the direct product of some set with
++ respect to an ordered indexing set.
IndexedDirectProductCategory(A,S) : Category == SIG where
A : SetCategory
S : OrderedSet
SIG ==> SetCategory with
map : (A -> A, %) -> %
++ map(f,z) returns the new element created by applying the
++ function f to each component of the direct product element z.
monomial : (A, S) -> %
++ monomial(a,s) constructs a direct product element with the s
++ component set to \spad{a}
leadingCoefficient : % -> A
++ leadingCoefficient(z) returns the coefficient of the leading
++ (with respect to the ordering on the indexing set)
++ monomial of z.
++ Error: if z has no support.
leadingSupport : % -> S
++ leadingSupport(z) returns the index of leading
++ (with respect to the ordering on the indexing set) monomial of z.
++ Error: if z has no support.
reductum : % -> %
++ reductum(z) returns a new element created by removing the
++ leading coefficient/support pair from the element z.
++ Error: if z has no support.
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