WeierstrassPreparation RΒΆ

weier.spad line 1

This package implements the Weierstrass preparation theorem f for multivariate power series. weierstrass(v, p) where v is a variable, and p is a TaylorSeries(R) in which there is term of form c*v^s where c is a constant. Let s be minimal as above. The result is a list of TaylorSeries coefficients A[i] of the equivalent polynomial A = A[0] + A[1]*v + A[2]*v^2 + ... + A[s-1]*v^(s-1) + v^s such that p=A*B , B being a TaylorSeries of minimum degree 0

weierstrass: (Symbol, TaylorSeries R) -> List TaylorSeries R
weierstrass(v, ts) where v is a variable and ts is a TaylorSeries, implements the Weierstrass Preparation Theorem. The result is a list of TaylorSeries that are the coefficients of the equivalent series.