The MultivariatePowerSeries package is new. It provides functionality for doing lazy computations with multivariate power series at high speed and high precision. The word 'lazy' here means that terms are computed only when necessary; further terms can always be computed at relatively little cost.
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The package also has functionality for univariate polynomials over such power series, including Hensel factorization. Mathematically, these objects are just power series where one of the variables occurs only up to a given finite degree, but implementation-wise, they allow for more and more efficient functionality.
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Let us examine the coefficients of the quadratic factor further.
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