Re: what's it worth to write a short program for polynomial multiplication?

rjf wrote:

Why should not the object-oriented choice of operator use
the types of all the operands?

Good question. Most OO programming languages work that way. CLOS, the
Common Lisp Object System
is the one exception I am aware of, but perhaps there are more.

In C++, you can overload functions (including operators) on all
arguments, sure:

template <typename coeffT>
SparsePoly<coeffT> operator*(SparsePoly<coeffT> &a const,
SparsePoly<coeffT> &b const);

template <typename coeffT>
SparsePoly<coeffT> operator*(DensePoly<coeffT> &a const,
SparsePoly<coeffT> &b const);

template <typename coeffT>
SparsePoly<coeffT> operator*(SparsePoly<coeffT> &a const,
DensePoly<coeffT> &b const);

template <typename coeffT>
DensePoly<coeffT> operator*(DensePoly<coeffT> &a const,
DensePoly<coeffT> &b const);

This is also possible for types only determined at runtime, but
requires more code. The idiom is called a double dispatch pattern. Oh,
and I should point out that the choice of return types above is of
course not a good idea in general. Using the double dispatch pattern and
determining whether to return a sparse or dense polynomial based on the
actual data found is likely to be much better. But I haven't done any
tests on this yet.

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