Use more efficient multiplication of two Taylor models

[dpsanders]

That does not require duplicating the order of the Taylor series.

[dpsanders]

This is in TaylorN/arithmetic.jl

[dpsanders]

This is usually done by adding a new field order_bounds to each Taylor model.
This gives bounds for the homogeneous polynomial at each order.

[dpsanders]

How do you feel about that @lbenet ?

[lbenet]

I agree that this may avoid duplicating the order, which certainly improves memory allocations and speed.

I'll try to spend some time on this tonight or tomorrow (I have to give tomorrow a talk); I'll begin trying to upgrade what you had in TaylorN/arithmetic.jl.

This is usually done by adding a new field order_bounds to each Taylor model.
This gives bounds for the homogeneous polynomial at each order.

I'm not sure I understand the idea here; do you mean a function to compute the bounds of each HomogeneousPolynomial?

[dpsanders]

I mean that the bounds are computed when the TaylorModelN is defined. Alternatively they can just be computed in the moment, but this will be slower if the object is reused in other calculations.