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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 | )abbrev domain LA LocalAlgebra
++ Author: Dave Barton, Barry Trager
++ Description:
++ LocalAlgebra produces the localization of an algebra,
++ fractions whose numerators come from some R algebra.
LocalAlgebra(A,R,S) : SIG == CODE where
A : Algebra R
R : CommutativeRing
S : SubsetCategory(Monoid, R)
SIG ==> Algebra R with
if A has OrderedRing then OrderedRing
_/ : (%,S) -> %
++ x / d divides the element x by d.
_/ : (A,S) -> %
++ a / d divides the element \spad{a} by d.
numer : % -> A
++ numer x returns the numerator of x.
denom : % -> S
++ denom x returns the denominator of x.
CODE ==> Localize(A, R, S) add
1 == 1$A / 1$S
x:% * y:% == (numer(x) * numer(y)) / (denom(x) * denom(y))
characteristic() == characteristic()$A
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