Changes http://wiki.axiom-developer.org/299MachineFloatIsNotAFIeld/diff
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Unfortunately, Axiom is not very strict with these things, although it should
be, I believe. Some examples:
* in Axiom, every field has the attribute 'canonicalUnitNormal'.
In ATTREG.SPAD, we find::
canonicalUnitNormal
++ \spad{canonicalUnitNormal} is true if we can choose a canonical
++ representative for each class of associate elements, that is
++ \spad{associates?(a,b)} returns true if and only if
++ \spad{unitCanonical(a) = unitCanonical(b)}.
However, I suspect, this cannot be done in every field.
* the domain 'EXPR' is a field, although it is (I think) meant to allow
arbitrary functions to be expressed, for example $\chi(x<0)$, which does not
have an inverse, I'd say.
In the documentation of MuPAD, they say that (their) expression domain is a
field for "convenience". Maybe this is related to the above.
In any case, we certainly cannot decide whether an element is zero or not.
Martin
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