FunctionalLaurentInverse K

newtonpuiseux.spad line 549 [edit on github]

• K: Join(Algebra Fraction Integer, PolynomialFactorizationExplicit)

For a Laurent series f(q) = q^(-n)(1 + a1*q + a2*q^2 + …) find all n Puiseux series q1(v), …, qn(v) such that f(qi(v))=v for all v in a close neighborhood of v_0. Algorithm follows cite{PauleRadu_ProofWeierstrassGapTheorem_2019} Section 6.

functionalInverse: QEtaLaurentSeries K -> QEtaLaurentSeries K

functionalInverse(t) where t is non-zero and d = order(t) ~= 0 returns a Laurent series w of order 1 such that t(w(q))=q^d Note that this is the same as doing the following: functionalInverse(t) == revert nthRoot(t, n)