I'd like to see improvements on expression, but I have
no ideas on where to start...
One thing to to have "per expression" kernels. More
precisely, currently Expression serves as a kind of
universal differential field inside which we embed
other fields. This is good as user interface, because
user are spared burden of creating each needed
differential field. But integration, limits and
solvers really should work with differenatial
fields.
Wouldn't it make sense to use Expression just as user interface and when
it comes to "integrate", take the input expression and construct a
proper differential field out of if. As far as I understand the
transcendental part of the Risch algorithm, one works with differential
field s of the form K(t1)(t2)...(tn) where tk is an indeterminate such
that D(tk) = rational function in t{k-1}, ..., t1. So at each time
there is a concrete differential field and it is clear which tk are
involve and what these tk model. Isn´t it done this way in FriCAS so
that the tk are represented by the kernels? Or is internally always
Expression(...) employed and the actual differential field must be read
from the expression that is involved?
Ralf
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