On Tue, Nov 21, 2023 at 06:35:57PM +0800, Qian Yun wrote:
>
> If so, I want to confirm that is 'nthRoot already a kind of
> algebraic number?
I am not sure what you want to say here: 'nthRoot is in
AlgebraicNumber which under right conditions models
algebraic numbers and in Expression, where we have
things more general than numbers.
> 'nthRoot constructs radicals, a subset of algebraic numbers.
> And clearly code in different places treats 'nthRoot by
> using its real valued branch, different than 'rootOf.
Well, part of original motivation for domains and packages
was that each domain and package can have its own assumptions.
For example one place may assume that square root has nonnegative
argument and nonnegative value and different place can make
different assumbption. There was hope that modularity
(that is domains and packages) will prevent contradictions.
This does not work as well as originally hoped for.
In integrator we deal with rather general roots and we should
not depend on "reality" of expressions for correctness (this
is the reason for removing calls to 'real'). We can use
"reality" arguments in advisory way, so that result is correct
independent of "reality", but if determination of "reality"
is correct then we get nicer looking result. AFAICS this
applies to basic Rioboo algorithm: result is always a valid
antiderivative, but it removes poles and imaginaries only when
determination of real parts was correct.
--
Waldek Hebisch
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