Changes
http://wiki.axiom-developer.org/358VariableIsApparentlyAlwaysAssumedToBePositive/diff
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Anonymous wrote::
Axiom is "stupid" to even think that in the definition
of h, the x is symbolic
In Axiom x, 1, and 1.0 are all equally symbolic. The distinction
between "symbolic" and "numeric" is not relevant. All of these
things are members of some domain or other and the Axiom
interpreter will make some assumptions unless you specify
explicitly which domains (e.g. in this case the assumed domains
are Variable(x), PositiveInteger, and Float, respectively).
Anonymous wrote::
definition [ h(x | x<=0) == -x^2 ]is complete as shown
No it is not. This is just a function prototype, not a
function. The Axiom intetpreter automatically fills in the
missing information based on the context where you use this
prototype so what you get is the evaluation of a function
that was partly created by assumptions made by the Axiom
interpreter. These assumptions do not work when you call
h with something of type Variable(x).
Anonymous asked::
Why is the signature of BY ... (%, Integer)->% and not
(%, S)->%
I think that's a good question!
The definition of BY is::
BY: (%, Integer) -> %
++ \spad{s by n} creates a new segment in which only every n-th
++ element is used.
and the representation for Segment is::
Segment(S:Type): SegmentCategory(S) with
...
Rep := Record(low: S, high: S, incr: Integer)
( See
"seg.spad.pamphlet":http://wiki.axiom-developer.org/axiom--test--1/src/algebra/SegSpad
)
So this is how it works by design, but I think it would
be quite easy to define a new type of segment that has
the properties that you expect.
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