axiom F := MachineFloat
Type: Domain axiom a: F := -0.12345
Type: MachineFloat axiom b: F := -1234567890.0
Type: MachineFloat axiom c: F := 1234567890.12345
Type: MachineFloat axiom (a+b)+c
Type: MachineFloat axiom a+(b+c)
Type: MachineFloat axiom F has Field
Type: Boolean MachineFloat? clearly doesn't form a (mathematical) field as the above code demonstrates (and we all know). DoubleFloat? and Float too --greg, Thu, 22 Jun 2006 09:18:32 -0500 reply axiom )cl all
Type: Domain axiom digits()
Type: PositiveInteger axiom a: F := -0.12345
Type: Float axiom b: F := -1234567890.0
Type: Float axiom c: F := 1234567890.12345
Type: Float axiom (a+b)+c
Type: Float axiom a+(b+c)
Type: Float axiom F has Field
Type: Boolean
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.
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 |