I wonder if the current work on figuring out simplified roots
of degree 4 polynomial is somewhat related to the recent
"radicalSolve" post on sci.math.symbolic?
(aka: will this also improve radicalSolve?)
- Qian
On 12/5/23 00:27, Waldek Hebisch wrote:
On Mon, Dec 04, 2023 at 01:52:39AM +0100, Waldek Hebisch wrote:
Third version in the attachemtnt, this time handling rather
general quartics where we can find real parts of roots. It
uses precomputed resolvent. After normalizing so that sum
of roots is zero resolvent is an even polynomial, so we
get equation of degree 3 for square of real part. If
this has one posivite real root which can be obtained via
factoring, then we are in business, otherwise this fails.
The routine fails on integrals like
integrate((z^2+z)^(1/2)/(1+z^2)^2, z)
where the poly is a^4 - (1/64)*a^2 + 1/8192 and
resolvent is 64*u^3 + (1/2)*u^2 - (1/1024)*u which
factors as 64* u*(u^2 + (1/128)*u - 1/65536. Here linear
factor must be discarded and quadratic factor has one
positive root. We should use this positive root, but
currently the routine gives up.
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