Dear Waldek, thanks for your explanations.
Waldek Hebisch <[EMAIL PROTECTED]> writes: > Martin Rubey wrote: > > Waldek Hebisch <[EMAIL PROTECTED]> writes: > > I guess that the main problem with EXPR and friends is, that it is not > > clear what the variables are. Do you know the assumptions needed for > > RischNormalize? > I do not know what problems with variables you see here I meant that it is not clear what the coefficient field for rischNormalize is: rischNormalize works over F, which is a "FunctionSpace R". To fix things, suppose that F is EXPR INT and the expression we consider contains only one variable. I guess the field of constants is the field of "numeric" elements from EXPR INT, i.e., expressions that do not contain a variable. Of course, this is still not a computable coefficient field. However, in this case it is at least clear mathematically what sqrt(2)*sqrt(3)-sqrt(6) is supposed to be. Now, if we switch to a field of constants containing some variables, what about sqrt(x)*sqrt(y)-sqrt(x*y)? > But rischNormalize uses operations implemented by other domains to perform > actual computuations, so there are extra assumptions. One is that if an > expression does not depend on a kernel (which is checked using derivatives) > simplifier should eliminate this kernel from the expression. For example > representing 'y' as 'x - x + y' is legal for computable fields, There are some related axioms defined in attreg.spad (namely canonicalUnitNormal, unitsKnown and canonical). In any case, I think that there should be a way to check whether equality is "mathematical" or only heuristic. > but rischNormalize would not tolerate such representation. Of course, since > expressions are represented as rational functions of kernels such simple > problem can not happen in Axiom. But (sqrt(2)*sqrt(3)-sqrt(6))*exp(x) already > hints towards possible problems. By the way, are there any interesting computable coefficient fields for rischNormalize? > (I am aware of tread about Polynomial Expression Integer, but I think it is a > separate problem). Yes. In fact, I meanwhile think that it is not a problem, apart from the fact that axiom lacks domains UnivariateExpression and MultivariateExpression analogous to the polynomial domains. Martin _______________________________________________ Axiom-developer mailing list [email protected] http://lists.nongnu.org/mailman/listinfo/axiom-developer
