Edit detail for #299 MachineFloat is not a FIeld revision 1 of 2

changed:
-
\begin{axiom}
F := MachineFloat
a: F := -0.12345
b: F := -1234567890.0
c: F := 1234567890.12345
(a+b)+c
a+(b+c)
F has Field
\end{axiom}
MachineFloat clearly doesn't form a (mathematical) field as the above code demonstrates (and we all know).

From greg Thu Jun 22 09:18:32 -0500 2006
From: greg
Date: Thu, 22 Jun 2006 09:18:32 -0500
Subject: DoubleFloat and Float too
Message-ID: <20060622091832-0500@wiki.axiom-developer.org>

\begin{axiom}
)cl all
F := Float
digits()
a: F := -0.12345
b: F := -1234567890.0
c: F := 1234567890.12345
(a+b)+c
a+(b+c)
F has Field
\end{axiom}

From kratt6 Thu Jun 22 09:39:26 -0500 2006
From: kratt6
Date: Thu, 22 Jun 2006 09:39:26 -0500
Subject: Axiom is not very strict...
Message-ID: <20060622093926-0500@wiki.axiom-developer.org>

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

Submitted by : (unknown) at: 2007-11-17T22:23:08-08:00 (16 years ago) Name : Axiom Version : default friCAS-20090114 Axiom-20050901 OpenAxiom-20091012 OpenAxiom-20110220 OpenAxiom-Release-141 Category : general Severity : critical serious normal minor wishlist Status : open pending closed 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.

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