update the precision to which a power series or univariate polynomial over power series is known
power series generated by this package
univariate polynomial over power series generated by this package
The command UpdatePrecision(p,d) increases the precision of p so that this precision equals at least d. This is achieved by repeated calls to the generator of p.
The command UpdatePrecision(u,d) increases the precision of each power series coefficient of u so that this precision equals at least d.
When using the MultivariatePowerSeries package, do not assign anything to the variables occurring in the power series, Puiseux series, and univariate polynomials over these series. If you do, you may see invalid results.
We create a new power series object. Initially, it is known only to low precision.
p ≔ 1PowerSeries⁡1+x
p≔PowⅇrSⅇrⅈⅇs of 11+x : 1+…
If we update the precision, more terms are known.
PowⅇrSⅇrⅈⅇs of 11+x : 1−x+x2−x3+x4−x5+x6−x7+x8−x9+x10+…
We create a new polynomial over power series involving the power series defined above, p, and a new power series, q.
q ≔ GeometricSeries⁡x,y
q≔PowⅇrSⅇrⅈⅇs of 11−x−y : 1+x+y+…
f ≔ UnivariatePolynomialOverPowerSeries⁡q,p,z
Because q is new, it is again known only to low precision.
Updating the precision of f updates the precision of each of its coefficients, p and q, if necessary. In this case, p was already known to higher precision, but q's precision is updated.
The MultivariatePowerSeries[UpdatePrecision] command was introduced in Maple 2021.
For more information on Maple 2021 changes, see Updates in Maple 2021.
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