Hi,

I have two questions regarding the implementation of multivariate power 
series is Sage.

I was wondering if Weierstrass Preparation Theorem and Hensel Lemma ( which 
use multivariate power series) have been implemented in Sage.

About the implementation of multivariate power series (which use the lazy 
algorithm): suppose that we want to compute the inverse of a power series, 
from the documentation I know that Sage has a default precision for 
computation and in order to get more term we need to set the default_prec 
option of the power series ring to our desired value. I am wondering when 
we increase the accuracy does Sage remember the terms which have been  
computed so far?

Thank you very much

Mahsa

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