Bill Page writes:
[...]
| In contrast in OpenAxiom there is a default definition of 'before?' in
| SetCatagory.
|
| before?(x,y) == GGREATERP(y,x)$Foreign(Builtin)
|
| which is overridden in some domains.
In particular "before?" agrees with "<" for all domains that satisfy
OrderedSet.
On Wed, Sep 16, 2009 at 10:09 PM, Waldek Hebisch wrote:
>
> Bill Page wrote:
>
>> Note: In FriCAS
>> not all domains in OrderedSet are Comparable.
>
> Why do you think so? Definition of OrderedSet is supposed to
> insure that each OrderedSet is Comparable.
Sorry that was a typo. What I mean to wr
Bill Page writes:
[...]
| > It is an obscure binary relation, much of which not related to
| > the actual mathematics that OpenAxiom wants to deal with.
| > That is part of the reasons why it is not glorified into a category
| > of its own.
|
| In OpenAxiom 'before?' is exported by SetCategory
Bill Page wrote:
> Note: In FriCAS
> not all domains in OrderedSet are Comparable.
Why do you think so? Definition of OrderedSet is supposed to
insure that each OrderedSet is Comparable.
--
Waldek Hebisch
hebi...@math.uni.wroc.pl
Bill Page wrote:
>
> On Wed, Sep 16, 2009 at 6:20 PM, Waldek Hebisch wrote:
> >
> > Concerning having the same name as OpenAxiom: AFAICS 'smaller?'
> > and 'before?' are different and have different names. ?I doubt
> > we gain much by making name the same.
> >
>
> Although the implementation is d
On Wed, Sep 16, 2009 at 6:20 PM, Waldek Hebisch wrote:
>
> Concerning having the same name as OpenAxiom: AFAICS 'smaller?'
> and 'before?' are different and have different names. I doubt
> we gain much by making name the same.
>
Although the implementation is different as far as I can see the
pur
Bill Page writes:
| Gaby,
|
| On Wed, Sep 16, 2009 at 2:41 PM, you wrote:
| >...
| > This is just binary relation. It is an obscure binary relation, much
| > of which not related to the actual mathematics that OpenAxiom
| > wants to deal with. That is part of the reasons why it is not glorifie
Bill Page writes:
| Come to think of it, shouldn't "machine" or implementation-dependent
| *equality* be handled the same way? It has always seemed rather
| confusing to me that '=' is used in Axiom for this. (Both FriCAS and
| OpenAxiom still do this.)
I'm afraid I do not understand what you
Bill Page writes:
| On Wed, Sep 16, 2009 at 2:41 PM, Gabriel Dos Reis wrote:
| >
| > Bill Page writes:
| >
| > [...]
| >
| > | The problem is that FriCAS and OpenAxiom have choosen different
| > | names for the machine ordering. In FriCAS it is called "smaller?".
| > | smaller?(alpha,beta) evalua
Gaby,
On Wed, Sep 16, 2009 at 2:41 PM, you wrote:
>...
> This is just binary relation. It is an obscure binary relation, much
> of which not related to the actual mathematics that OpenAxiom
> wants to deal with. That is part of the reasons why it is not glorified
> into a category of its own.
>
Come to think of it, shouldn't "machine" or implementation-dependent
*equality* be handled the same way? It has always seemed rather
confusing to me that '=' is used in Axiom for this. (Both FriCAS and
OpenAxiom still do this.) Although there is the notion of "canonical"
which implies something ab
On Wed, Sep 16, 2009 at 2:41 PM, Gabriel Dos Reis wrote:
>
> Bill Page writes:
>
> [...]
>
> | The problem is that FriCAS and OpenAxiom have choosen different
> | names for the machine ordering. In FriCAS it is called "smaller?".
> | smaller?(alpha,beta) evaluates to true if the value of alpha come
Bill Page writes:
[...]
| The problem is that FriCAS and OpenAxiom have choosen different names
| for the machine ordering. In FriCAS it is called "smaller?".
| smaller?(alpha,beta) evaluates to true if the value of alpha comes
| before the value of beta in the machine ordering. OpenAxiom calls
I've been bugged a little lately by a minor issue of nomenclature.
Both FriCAS and OpenAxiom have implemented a distinction between some
"mathematical" or "natural" ordering and equality of the members of a
domain - which might not always be defined or may be defined in
different ways, versus the "
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