Ooops. In OrderedRing I find
positive? x == x>0
negative? x == x<0
sign x ==
positive? x => 1
negative? x => -1
zero? x => 0
error "x satisfies neither positive?, negative? or zero?"
abs x ==
positive? x => x
negative? x => -x
zero? x => 0
error "x satisfies neither positive?, negative? or zero?"
If a ring is equipped with a total order, how can this error case ever
occur? It would mean there are elements that are neither 0 nor smaller
nor bigger than 0. What kind of total order is this?
Or is it taking care of the Float domain? But Float is only a fake ring
for convenience. In the long run I would like to take away the Ring
property from Float.
Anyway, if I now provide a patch in moving the above functions to
OrderedAbelianGroup, I would like to remove this error case. But I fear
that this might change something in other places of FriCAS.
Suggestions?
Ralf
On 6/21/25 13:14, Waldek Hebisch wrote:
On Sat, Jun 21, 2025 at 01:11:12PM +0200, 'Ralf Hemmecke' via FriCAS - computer
algebra system wrote:
While looking into the generalization of AInterval, I realized that abs is
defined in OrderedRing.
https://fricas.github.io/api/OrderedRing.html#index-1
Technically, it would be OK to define it already in OrderedAbelianGroup.
Basically the definition is
abs(x) == if x>0 then x else -x
so why is there need to have a multiplication in the structure?
Right, current location of abs is a historical artifact.
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