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 Submitted by : (unknown) at: 2007-11-17T22:23:08-08:00 (12 years ago) Name : Axiom Version : default friCAS-20090114 Axiom-20050901 OpenAxiom-20091012 OpenAxiom-20110220 OpenAxiom-Release-141 Category : Axiom Aldor Interface Axiom Compiler Axiom Library Axiom Interpreter Axiom Documentation Axiom User Interface building Axiom from source lisp system MathAction Doyen CD Reduce Axiom on Windows Axiom on Linux Severity : critical serious normal minor wishlist Status : open closed rejected not reproducible fix proposed fixed somewhere duplicate need more info Optional subject :   Optional comment :

axiom
F := MachineFloat (1)
Type: Domain
axiom
a: F := -0.12345 (2)
Type: MachineFloat
axiom
b: F := -1234567890.0 (3)
Type: MachineFloat
axiom
c: F := 1234567890.12345 (4)
Type: MachineFloat
axiom
(a+b)+c (5)
Type: MachineFloat
axiom
a+(b+c) (6)
Type: MachineFloat
axiom
F has Field (7)
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
All user variables and function definitions have been cleared.
F := Float (8)
Type: Domain
axiom
digits() (9)
Type: PositiveInteger
axiom
a: F := -0.12345 (10)
Type: Float
axiom
b: F := -1234567890.0 (11)
Type: Float
axiom
c: F := 1234567890.12345 (12)
Type: Float
axiom
(a+b)+c (13)
Type: Float
axiom
a+(b+c) (14)
Type: Float
axiom
F has Field (15)
Type: Boolean

Axiom is not very strict... --kratt6, Thu, 22 Jun 2006 09:39:26 -0500 reply
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.

  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


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

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