Changes
http://wiki.axiom-developer.org/358VariableIsApparentlyAlwaysAssumedToBePositive/diff
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In the example below, the domain 'dom' is linearly ordered by lexicographical
order. Thus it should be possible to increment by any element (or equivalently
in any rational direction, including the vertical) in the domain. Axiom
currently only allows incrementing by 'Integer' which is coerced into the
domain via the diagonal. Certainly this is not expansion by counting along the
segment.
\begin{axiom}
dom:=DirectProduct(2,INT)
a:dom:=directProduct([2,1])
b:dom:=directProduct([10,8])
s:SEG dom:=a..b by 3
expand s
\end{axiom}
Note that the lexicographic order is not particular kind to segments, which can
have infinitely many elements and hence if allowed to increment by arbitrary
elements of the domain. Axiom has 'UNISEG' which allows expansion into 'Stream
S' but even theret, the increment is limited to an "integer".
Billpage wrote::
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.
I think it is more like a summer project!
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