substitute(FormalSeries,BasicList) -- compose formal series

Synopsis

Function: substitute
Usage:

substitute(s,l)
Inputs:
- s, an instance of the type FormalSeries,
- l, a basic list,
Outputs:
- an instance of the type FormalSeries,

Description

All the FormalSeries involved should have the same coefficient ring. The function substitutes the variables in s with the series in the BasicList l. Also note that this also works when s is a FormalGroupLaw which is a subclass of FormalSeries.

i1 : R=ZZ[x,y]

o1 = R

o1 : PolynomialRing

i2 : s = series(x^2+x+y,2)

                   2
o2 = FormalSeries{x  + x + y, 2}

o2 : FormalSeries

i3 : substitute(s,{s,s})

                    2           2
o3 = FormalSeries{3x  + 2x*y + y  + 2x + 2y, 2}

o3 : FormalSeries

Ways to use this method: