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http://page.axiom-developer.org/zope/mathaction/187TroubleWithTuples/diff
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??changed:
-From BillPage Fri Jul 1 14:47:12 -0500 2005
-From: Bill Page
-Date: Fri, 01 Jul 2005 14:47:12 -0500
-Subject: Cartesian products and tuples
-Message-ID: <[EMAIL PROTECTED]>
-
-I think the concept of a
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http://page.axiom-developer.org/zope/mathaction/187TroubleWithTuples/diff
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-> \begin{axiom}
-> f1:Record(a:INT,b:FLOAT)->FLOAT
-
-> f1(arg)==arg.b+arg.a
-> f1[1,1.1]
-> \end{axiom}
->
-> should be viewed as equivalent to
-> \begin{axiom}
-> f2:(INT,FLOAT)->FLOAT
-> f2(a,b)==
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http://page.axiom-developer.org/zope/mathaction/187TroubleWithTuples/diff
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-functionally superior but the tuple construct but it makes
functionally superior to the tuple construct but it makes
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http://page.axiom-developer.org/zope/mathaction/187TroubleWithTuples/diff
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William Sit wrote:
> I agree that the Cartesian product of A, B is implied in the notion
> of Mapping(T,A,B). But that is not the issue here.
??? But that *is* precisely the issue with which **I am** concerned.
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++added:
??changed:
-the same category. If $f:A \times B \rightarrow C$ is a mapping, where $A$, $B$
-are from the same category, we may sometimes let $D = A \times B$ and identify
-$f$ as $f:D \rightarrow C$ (
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http://page.axiom-developer.org/zope/mathaction/187TroubleWithTuples/diff
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??changed:
-let me rename this to: $$g:D \rightarrow C$$.
let me rename this to:
$$g:D \rightarrow C$$
??changed:
-If the target $C$ is more involved, say $C$ is D^2$ and $f$ is meant to be the
-diagonal map
If
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http://page.axiom-developer.org/zope/mathaction/187TroubleWithTuples/diff
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Bill Page wrote:
> From a mathematical point of view clearly the idea that
> Mapping(T, A, B) denotes the class of mappings from (A, B)
> into T implies that (A,B) denotes some kind of set, i.e.
> the Product(A,B
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http://page.axiom-developer.org/zope/mathaction/187TroubleWithTuples/diff
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Bill Page wrote:
> I think such tuples should be Products ...
>From page 246 of the Axiom book:
"The type of a function is always a mapping of the form
Source -> Target where Source and Target are types."
an
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http://page.axiom-developer.org/zope/mathaction/187TroubleWithTuples/diff
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-> (1,1.1)$(Product(Integer,Float)
> (1,1.1)$Product(Integer,Float)
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http://page.axiom-developer.org/zope/mathaction/187TroubleWithTuples/diff
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Bill Page wrote:
> William Sit wrote:
>
> > Tuple S is actually the infinite union of DirectProduct?(n,S) over all n.
>
> What you describe sounds more like InfiniteTuple - another interesting
> but undocumente
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Bill Page wrote:
> I think a domain such as Product deserves (much) more documentation
> then just to be listed in Appendix C! Of course that is also true of
> many other domains in Axiom. It worries me that a 1
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++added:
\begin{axiom}
(INT,INT)
\end{axiom}
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http://page.axiom-developer.org/zope/mathaction/187TroubleWithTuples/diff
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William Sit wrote:
> Tuple S is actually the infinite union of DirectProduct?(n,S) over all n.
What you describe sounds more like InfiniteTuple - another interesting
but undocumented domain.
--
forwarded from ht
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http://page.axiom-developer.org/zope/mathaction/187TroubleWithTuples/diff
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??changed:
-I prefer to read (2,3) or 2,3 for tuple, and [2,3] only for lists.
I prefer to read (2,3) or 2,3 for tuple, and ![2,3] only for lists.
??changed:
-(1,1.1)$(Product(Integer,Float)
makeprod(1,1.1)$Prod
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I think a domain such as Product deserves (much) more documentation
then just to be listed in Appendix C! Of course that is also true of
many other domains in Axiom. It worries me that a 1000+ page book is
not nea
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http://page.axiom-developer.org/zope/mathaction/187TroubleWithTuples/diff
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Product can be looked up in hyperdoc. It is listed in Appendix C (p. 613 of
Axiom (paper) Book; p. 1028 of eBook). Tuple is more like Direct Product since
the entries must come from the same domain. However, Pro
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-There error messages indicate some serious problems
These error messages indicate some serious problems
++added:
\end{axiom}
'Tuple Any' should work in a similar way to 'List Any' and
'DirectProduct
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http://page.axiom-developer.org/zope/mathaction/187TroubleWithTuples/diff
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I think the concept of a tuple and [Cartesian Product] should be related,
i.e. a tuple is an element of a Cartesian Product:
\begin{axiom}
)expose Product
makeprod(1,1.1)
f:(INT,Float)->Float
f:Product(INT,Float)
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http://page.axiom-developer.org/zope/mathaction/187TroubleWithTuples/diff
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??changed:
-This bug may be due to the Interpreter coercing 'Tuple INT' to 'PRIMARR INT'
and then to 'OutputForm', which perhaps uses the List output. Tim Daly may know
more.
This "bug" may be due to the Interp
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??changed:
-\par
??changed:
-\par
-Students and I make errors when the display is the same, even if there is a
type information.
Students and I make errors when the display is the same, even if there is a
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http://page.axiom-developer.org/zope/mathaction/187TroubleWithTuples/diff
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This page was renamed from #187 trouoble with tuples to #187 trouble with
tuples.
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http://page.axiom-developer.org/zope/mathaction/187TroubleWithTuples/diff
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Why tuples are displayed as list ?
\par
I prefer to read (2,3) or 2,3 for tuple, and [2,3] only for lists.
\par
Students and I make errors when the display is the same, even if there is a
type information.
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