[boost] Re: [ublas-dev] Re: Boost Mathematicians

From: Jeremy Graham Siek (jsiek_at_[hidden])
Date: 2004-07-09 11:28:30

Hi Paul,

Yes, you've got the idea.

The following document shows one such attempt to construct a
system of traits for algebraic concepts:

http://www.cs.rpi.edu/~schupp/entries/SOFTWARE/simpl/doc/AlgCpp.pdf

also, more information is available starting at:

http://www.cs.rpi.edu/~schupp/entries/SOFTWARE/simpl/

Cheers,
Jeremy

On Jul 7, 2004, at 7:32 PM, Paul C. Leopardi wrote:

> Jeremy, Dave,
>  I think I get it. See below.
>  Best regards
>  On Thursday 08 July 2004 02:25, David Abrahams wrote:
>  >  Jeremy Graham Siek <jsiek_at_[hidden]> writes:
>  >  > group_traits<T>::is_commutative
>  >      is_commutative_group<T>::type
>  >      is_commutative_group<T>::type::value
>
>  OK, for a type where you have one operation (a group).
>  For a two operation type, I suppose you would then want
>
>  is_ring<T>::type
>  is_ring<T>::type::value
>
>  is_commutative_ring<T>::type
>  is_commutative_ring<T>::type::value
>
>  Along these lines, you could build a header file called 
> arithmetic_traits.hpp
>  or something similar. The object of this file would be to describe 
> some of
>  the semantics of operator+, operator* and possibly other operators 
> when used
>  with various types. Eg. you could have say
>
>  is_algebra< framed_multi<T,L,H>, T>::type
>  is_algebra< framed_multi<T,L,H>, T>::scalar_type
>
>  This header would also be used to define the zero element of addition 
> and the
>  identity element of multiplication, if it exists.
>
>  Once this header is established, you could build template libraries 
> which
>  perform arithmetic according to the axioms embodied in the traits. 
> Such a
>  library would not eg. assume that multiplication is commutative, it 
> would
>  check this at compile time.
>
>  Note that there would also need to be a distinction between 
> approximate and
>  exact arithmetic. This especially affects associativity, where eg. 
> addition
>  of real numbers behaves differently from addition of floating point 
> numbers
>  due to loss of precision. eg.
> http://h18009.www1.hp.com/fortran/docs/vf-html/pg/pg1round.htm
> http://www.ibiblio.org/pub/languages/fortran/ch4-6.html
>
>
>
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_______________________________________________
Jeremy Siek <jsiek_at_[hidden]>
http://www.osl.iu.edu/~jsiek
Ph.D. Candidate, Indiana University Bloomington
C++ Booster (http://www.boost.org)
_______________________________________________