type/laurentseries¶

formal Laurent series type¶

Calling sequence:¶

$\operatorname{type}(f, {\mathit laurentseries})$ $\operatorname{type}(f, {\mathit laurentseries}(K))$ $\operatorname{type}(f, {\mathit laurentseries}(K, v))$

Parameters:¶

  • $f$, a Maple expression
  • $K$, type name for coefficient domain
  • $v$, a variable, given as a name, a list or set of one name

Description:¶

  • $\operatorname{type}(f, {\mathit laurentseries}(K, v))$ answers $\mathit true$ iff $f$ is a formal Laurent series in the variable $v$ with coefficients in $K$.
  • A Laurent series is an object of type series, possibly with some negative exponents, whose coefficients does not depend on the variable.

Example:¶

In [1]:
libname := libname, FileTools:-JoinPath(["maple","lib","dcfun.mla"],base=homedir):
In [2]:
 with(dcfun):
Out[2]:

Let us give a very simple example.

In [3]:
 f := series(sin(x*y)/x^5, x);
Out[3]:

$$y \,x^{-4}-\frac{1}{6} y^{3} x^{-2}+\frac{y^{5}}{120}+\mathrm{O}\! \left(x^{2}\right)$$

In [4]:
 type(f, laurentseries);
Out[4]:

$$\mathit{true}$$

In [5]:
 type(f, laurentseries(anything,x));
Out[5]:

$$\mathit{true}$$

In [6]:
 type(f, laurentseries(rational, x));
Out[6]:

$$\mathit{false}$$

In [7]:
 type(f, laurentseries(polynom(anything, y), x));
Out[7]:

$$\mathit{true}$$