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RE: [glas] Vector Spaces vs. "Objects called vectors"

From: Edwards, Harold C (hcedwar_at_[hidden])
Date: 2005-02-03 17:29:57

> > >> > I think it will not be uncommon to wish to forbid even
> > >> > between vectors of equal size, for example if one represents
> > >> > cell-based and the other one vertex-based quantities (speaking
> > >> > FEM). So one could introduce mechanisms to forbid assignment at
> > >> > compile time (i.e. making those vectors different types).
> > >> Or const?
> > >>
> > >
> > > No, because I still want to be able to assign vectors of the same
> > > (mathematical!) 'type'. Assignment is really just a special case:
> > > Think of operations like addition where we also will have to
> > > carefully decide which combinations are allowed and which are not.
> > > "Same c++ type" is not the only useful criterion here.
> >
> > It's usually the best one. Vectors et al. are "scalar" quantities
> > (like pi). You can always add type information later per
> >
> Heh, we enter the world of overlapping/conflicting
> definitions. But I
> agree completely. A vector is a simple abstraction for a
> function from
> a (finite, contiguous) set of integers to some type T.
> Anything beyond
> that belongs elsewhere.

Question regarding the definition of a "vector" in this discussion:
1) A value in a given finite-dimensional Vector Space (math)
2) A finite collection of elements (with contiguous storage) (cs).

If the math-definition then is the software-design concept for such a
vector to allow it to be reassigned to different vector spaces, or
locked into the vector space for which it is created? E.g., changing
the size of a vector, or the FEM example, reassigns the vector's
underlying vector space. It seems the policy is whether or not an
"object called a vector" can be locked into a vector space or reassigned
among vector spaces.

It may be useful to expand the software design notion of a vector space
beyond the element type and dimension to allow the above FEM example.
This opens the door to other considerations, such as including parallel
partitioning or other substructuring information in the software design
of a vector space.

--Carter Edwards