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## Re: [Axiom-developer] Question concerning types...

**From**: |
Ralf Hemmecke |

**Subject**: |
Re: [Axiom-developer] Question concerning types... |

**Date**: |
Tue, 19 Sep 2006 17:20:59 +0200 |

**User-agent**: |
Thunderbird 1.5.0.5 (X11/20060719) |

http://wiki.axiom-developer.org/public/TheUnknownInComputerAlgebra.pdf

`Ah, by the way, I've read the paper and did not find it particularly
``useful. What they do is a bit too complicated in my eyes.
`
> \begin{spad}
> )abbrev domain PUNINT PureUnknownInteger
> PureUnknownInteger (D,BasicUnknown):Ring == Implementation where
> D:IntegerNumberSystem
> BasicUnknown:List Symbol
> Implementation ==> LocalAlgebra (Polynomial D,D,D) with
> "/" : ($,D) -> $
> ++ a/n computes the expression whose value is a/n if it
> ++ is actually an unknown integer
> \end{spad}

`It is certainly a wrong design to implement indefinite integers as
``polynomials.
`
Why?

`Suppose you have a nice algebra library and you want the system to
``understand indefinite objects, then you are certainly not going to add
``any function to existing domains or wrap one (and actually ALL) domains
``with a domain constructor "Indefinite". No. It should be completely
``transparent. The goal is to type
`
n: Integer;
and not
n: Indefinite(Integer);

`Either the interpreter or some layer between interpreter and library
``code should take care about indefinite objects.
`
I very much believe that this requires reflection from SPAD/Aldor.
Ralf

**Re: [Axiom-developer] Question concerning types...**, *(continued)*
**Re: [Axiom-developer] Question concerning types...**, *Bertfried Fauser*, `2006/09/18`
**Re: [Axiom-developer] Question concerning types...**, *Ralf Hemmecke*, `2006/09/18`
**RE: [Axiom-developer] Question concerning types...**, *Bill Page*, `2006/09/18`
**RE: [Axiom-developer] Question concerning types...**, *C Y*, `2006/09/18`
**RE: [Axiom-developer] Question concerning types...**, *Bill Page*, `2006/09/18`
**RE: [Axiom-developer] Question concerning types...**, *Bill Page*, `2006/09/18`
**Re: [Axiom-developer] Question concerning types...**, *Ralf Hemmecke*, `2006/09/18`
**Re: [Axiom-developer] Question concerning types...**, *C Y*, `2006/09/18`
**Re: [Axiom-developer] Question concerning types...**, *Ralf Hemmecke*, `2006/09/18`
**RE: [Axiom-developer] Question concerning types...**, *Bill Page*, `2006/09/18`
**Re: [Axiom-developer] Question concerning types...**,
*Ralf Hemmecke* **<=**
**RE: [Axiom-developer] Question concerning types...**, *Bill Page*, `2006/09/19`
**Re: [Axiom-developer] Question concerning types...**, *Ralf Hemmecke*, `2006/09/19`

**RE: [Axiom-developer] Question concerning types...**, *C Y*, `2006/09/17`