Re: [boost] numeric: linear algebra concepts

From: Jeremy Siek (jsiek_at_[hidden])
Date: 2001-03-29 13:56:07

On Thu, 29 Mar 2001, Ullrich Koethe wrote:
koethe> Very nice. Here are a few remarks:
koethe> 
koethe> 1. All algebraic types must refine EqualityComparable. 

I'm not sure that is necessary. It seems to me there are lots of
algorithms on numeric quantities that do not need equality comparable.

koethe> 2. Would it be useful to also introduce (multiplicative) Semigroup and
koethe> Group?

I stopped at Additive Abelian Group because that was what I thought we
would need to use for linear algerba algorithms. There's a whole host of
more algebra concepts, but I'd like to leave those for the people
interested in algebra (vs. linear algebra).

koethe> 3. in Field, you dropped the requirement 
koethe> 
koethe>    a * b is equivalent to zero(a) if and only if a == zero(a) or b ==
koethe> zero(a)

I thought this property could be deduced from the others. Am I wrong?

koethe> 4. In an R-Module, is Commutativity also required ?

It's already there. The type G must be an Additive Abelian Group, which
includes Commutativity.

koethe> 5. The Norm type in a Banach space should be a Field (? not sure) and
koethe> StrictWeaklyOrdered

That sounds right, I'll add that it.

Cheers,
Jeremy

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 Jeremy Siek                        www: http://www.lsc.nd.edu/~jsiek/
 Ph.D. Candidate                  email: jsiek_at_[hidden]
 Univ. of Notre Dame         work phone: [phone]
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