PuiseuxSeries

structured expression for Puiseux series

Calling sequence:

$\operatorname{PuiseuxSeries}(q, s)$

Parameters:

• $q$, a positive rational number
  
• $s$, an object of type series or $0$

Description:

• $\operatorname{PuiseuxSeries}$ is an essentially inert function. It codes a Puiseux series as a ramification order and a Laurent series, except when the ramification order $q = 1$ and then the returned object is a Laurent series.
  
• The name PuiseuxSeries is a `undocumented protected name', (it is used by RegularChains[AlgebraicGeometryTools][RegularChainBranches] with a different use to describe a Puiseux series). As a consequence, we first unprotect it and next we protect it as name in the package dcfun.

Example:

libname := libname, FileTools:-JoinPath(["maple","lib","dcfun.mla"],base=homedir):

 with(dcfun):

We define two Puiseux series. When the ramification order is $1$, we obtain a Laurent series.

 s := PuiseuxSeries(2, series(1/(1 - 3*x)/x, x));

$$\frac{1}{\sqrt{x}}+3+9 \sqrt{x}+27 x +81 x^{\frac{3}{2}}+243 x^{2}+O\! \left(x^{\frac{5}{2}}\right)$$

 s := PuiseuxSeries(1, series(1/(1 - 3*x)/x, x));

$$x^{-1}+3+9 x +27 x^{2}+81 x^{3}+243 x^{4}+\mathrm{O}\! \left(x^{5}\right)$$