"Bill Page" <[EMAIL PROTECTED]> writes:
> Hmmm... So what is the meaning of < in AN? Ok, I guess that it is just
> whatever is exported by Expression Integer. The fact that the positive
> roots appear < 0 while the negative roots appear > 0 must be just an
> accident of some strange lexical ordering rules for expressions. :-(
Well, it's not so strange, it's the order used for hashing.
Yes, it's high time to separate mathematical order and internal hashing order.
Waldek proposed a programme in the thread "RFC: Orders in algebra" some time
ago, as you know. There was a long discussion, but little result.
I believe that we wanted too much.
Here is the original programme:
> 1) create a new category, say Comparable which has functions
> like lessThen, lessOrEqual etc.
> 2) Change domains that use unnatural order to use comparisons from
> Comparable
> 3) Undefine unnatural orders (remove them from OrderedSet)
> 4) If possible define natural ones
>
> In particular for Expression w probably should _not_ define an
> order, but rather make '<' produce elements of new domain
> 'Inequality' (like Equation, but for ordered comparisons).
I guess it would be best to just go ahead and implement a simple version of
this at first. In fact, Bill, you did already implement a version of
Inequation and Inequality.
There was a lot of discussion about that, too. So I guess, there was *too
much* functionality. It's probably better to start with uncontroversial
things.
Sage also implements some functionality for equation, inequations and
inequalities, maybe this could serve as comparison.
Martin
sage: var('x y')
(x, y)
sage: sin(x) < 5
sin(x) < 5
sage: ieq = _
sage: ieq.
ieq.add_to_both_sides ieq.expand ieq.operator
ieq.solve
ieq.assume ieq.find_root ieq.rename
ieq.subs
ieq.category ieq.forget ieq.reset_name
ieq.substitute
ieq.db ieq.left ieq.rhs
ieq.subtract_from_both_sides
ieq.divide_both_sides ieq.left_hand_side ieq.right
ieq.variables
ieq.dump ieq.lhs ieq.right_hand_side
ieq.version
ieq.dumps ieq.multiply_both_sides ieq.save
sage: ieq2 = sin(x) <> 5
sage: ieq2.
ieq2.add_to_both_sides ieq2.expand ieq2.operator
ieq2.solve
ieq2.assume ieq2.find_root ieq2.rename
ieq2.subs
ieq2.category ieq2.forget ieq2.reset_name
ieq2.substitute
ieq2.db ieq2.left ieq2.rhs
ieq2.subtract_from_both_sides
ieq2.divide_both_sides ieq2.left_hand_side ieq2.right
ieq2.variables
ieq2.dump ieq2.lhs
ieq2.right_hand_side ieq2.version
ieq2.dumps ieq2.multiply_both_sides ieq2.save
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