Ralf Hemmecke wrote:
>
> > One remark: if we want just preserve existing functionality,
> > then the simplest way is probably to remove the third argument to
> > Localize and LocalAlgebra. Namely, currentlty there is probably
> > no way to create nontrivial domain of SubsetCategory, so the
> > in working code third argument will be the same as the second
> > one.
>
> Oh, good that you yourself say this. I was exactly thinking in this
> direction and wanted to create a two parameter Localize and LocalAlgebra
> (*in addition*, in order not to break other people's code that relies on
> 3-parameter version).
>
In Spad there is no overloading of constructors, so we can only
have one version of Localize and LocalAlgebra.
> But yes, I am very much in favour of removing the third parameter. Or
> rather to replace it with a boolean function in the following sense
> (It's similar to SubDomain.):
>
> Instead of
>
> Localize(M:Module R,
> R:CommutativeRing,
> S:SubsetCategory(Monoid, R)): Module R with
>
> we would have
>
> Localize(M:Module R,
> R:CommutativeRing,
> denominator?: R -> Boolean): Module R with
>
> where denominator is the characteristic function for the subset S of R
> that can be used for denominators.
>
> Of course, there is a big problem: It cannot be ensured that the set of
> all r for which denominator?(r) returns true is indeed a sub-monoid of
> R.
<snip>
> > So it seems that the only current
> > use of Localize and LocalAlgebra is via Fraction.
>
> In this case, I would even go to the extreme and remove LocalAlgebra and
> Localize completely. If somebody later sees some need for their
> reimplementation then we have someone who is familiar with all the
> issues and who knows probably some use cases that should work.
>
I am tempted to apply the patch below which just removes the
third argument. Why:
1) Adding extra function for membership test _may_ be a good idea.
However, I am reluctant to add untested and unused code, while
proper developement (including creating test domain which actually
uses new functionlity) would take a bit more time that
I want to spent on this.
2) I think that Localize and LocalAlgebra represent important
concept and that current domain may be good start for future
developement. So I am not eager to remove them.
BTW: the patch passes all tests and AFAICS should cause no
performance difference.
diff -ru trunk.bb/src/algebra/fraction.spad.pamphlet
trunk/src/algebra/fraction.spad.pamphlet
--- trunk.bb/src/algebra/fraction.spad.pamphlet 2008-12-13 19:28:26.000000000
+0100
+++ trunk/src/algebra/fraction.spad.pamphlet 2008-12-13 19:47:37.000000000
+0100
@@ -24,28 +24,27 @@
++ Description: Localize(M,R,S) produces fractions with numerators
++ from an R module M and denominators from some multiplicative subset
++ D of R.
-Localize(M:Module R,
- R:CommutativeRing,
- S:SubsetCategory(Monoid, R)): Module R with
+Localize(M : Module R,
+ R : CommutativeRing): Module R with
if M has OrderedAbelianGroup then OrderedAbelianGroup
- _/ :(%,S) -> %
+ _/ : (%, R) -> %
++ x / d divides the element x by d.
- _/ :(M,S) -> %
+ _/ : (M, R) -> %
++ m / d divides the element m by d.
numer: % -> M
++ numer x returns the numerator of x.
- denom: % -> S
+ denom: % -> R
++ denom x returns the denominator of x.
==
add
--representation
- Rep:= Record(num:M,den:S)
+ Rep:= Record(num : M, den : R)
--declarations
- x,y: %
+ x, y: %
n: Integer
m: M
r: R
- d: S
+ d: R
--definitions
0 == [0,1]
zero? x == zero? (x.num)
@@ -62,7 +61,7 @@
n*x == [n*x.num,x.den]
r*x == if r=x.den then [x.num,1] else [r*x.num,x.den]
x/d ==
- zero?(u:S:=d*x.den) => error "division by zero"
+ zero?(u:R:=d*x.den) => error "division by zero"
[x.num,u]
m/d == if zero? d then error "division by zero" else [m,d]
coerce(x:%):OutputForm ==
@@ -92,19 +91,18 @@
++ Description: LocalAlgebra produces the localization of an algebra, i.e.
++ fractions whose numerators come from some R algebra.
LocalAlgebra(A: Algebra R,
- R: CommutativeRing,
- S: SubsetCategory(Monoid, R)): Algebra R with
+ R: CommutativeRing): Algebra R with
if A has OrderedRing then OrderedRing
- _/ : (%,S) -> %
+ _/ : (%,R) -> %
++ x / d divides the element x by d.
- _/ : (A,S) -> %
+ _/ : (A,R) -> %
++ a / d divides the element \spad{a} by d.
numer: % -> A
++ numer x returns the numerator of x.
- denom: % -> S
+ denom: % -> R
++ denom x returns the denominator of x.
- == Localize(A, R, S) add
- 1 == 1$A / 1$S
+ == Localize(A, R) add
+ 1 == 1$A / 1$R
x:% * y:% == (numer(x) * numer(y)) / (denom(x) * denom(y))
characteristic() == characteristic()$A
@@ -315,7 +313,7 @@
if S has Canonical and S has GcdDomain and S has canonicalUnitNormal
then Canonical
++ \spad{Canonical} means that equal elements are in fact
identical.
- == LocalAlgebra(S, S, S) add
+ == LocalAlgebra(S, S) add
Rep:= Record(num:S, den:S)
coerce(d:S):% == [d,1]
zero?(x:%) == zero? x.num
diff -ru trunk.bb/src/algebra/solverad.spad.pamphlet
trunk/src/algebra/solverad.spad.pamphlet
--- trunk.bb/src/algebra/solverad.spad.pamphlet 2008-12-13 19:28:26.000000000
+0100
+++ trunk/src/algebra/solverad.spad.pamphlet 2008-12-13 19:49:19.000000000
+0100
@@ -35,7 +35,6 @@
ST ==> String
PR ==> Polynomial R
UP ==> SparseUnivariatePolynomial PR
- LA ==> LocalAlgebra(PR, Z, Z)
RF ==> Fraction PR
RE ==> Expression R
EQ ==> Equation
--
Waldek Hebisch
[email protected]
--~--~---------~--~----~------------~-------~--~----~
You received this message because you are subscribed to the Google Groups
"FriCAS - computer algebra system" group.
To post to this group, send email to [email protected]
To unsubscribe from this group, send email to
[email protected]
For more options, visit this group at
http://groups.google.com/group/fricas-devel?hl=en
-~----------~----~----~----~------~----~------~--~---
