axiom F := MachineFloat
axiom a: F := -0.12345
axiom b: F := -1234567890.0
axiom c: F := 1234567890.12345
axiom (a+b)+c
axiom a+(b+c)
axiom F has Field
MachineFloat? clearly doesn't form a (mathematical) field as the above code demonstrates (and we all know). axiom )cl all
axiom digits()
axiom a: F := -0.12345
axiom b: F := -1234567890.0
axiom c: F := 1234567890.12345
axiom (a+b)+c
axiom a+(b+c)
axiom F has Field
- 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 , 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 Category: Axiom Mathematics => Axiom Library |

DoubleFloat? and Float too--greg, Thu, 22 Jun 2006 09:18:32 -0500 reply