expandGeomSeries -- Expand a geometric series to a specified degree.

Synopsis

Usage:

pSeries = expandGeomSeries(f,n)
Inputs:
- f, a ring element, Ratio of the geometric series to be expanded.
- n, an integer, Degree which to expand the geometric series.
Outputs:
- pSeries, a ring element, Power series representation of the geometric series.

Description

If the user supplies a list instead of a RingElement as the first argument, the return value is the product of all the each of the geometric series expanded to degree n obtained by calling expandGeomSeries on each element of the list.

i1 : A = ZZ[S,T_0,T_1]

o1 = A

o1 : PolynomialRing

i2 : f = expandGeomSeries(S^2*T_0^8,10)

      10 40    8 32    6 24    4 16    2 8
o2 = S  T   + S T   + S T   + S T   + S T  + 1
         0       0       0       0       0

o2 : A

i3 : g = expandGeomSeries(S^4*T_1^15,10)

      8 30    4 15
o3 = S T   + S T   + 1
        1       1

o3 : A

i4 : h = expandGeomSeries({S^2*T_0^8,S^4*T_1^15},10)

      10 40    10 24 15    10 8 30    8 32    8 16 15    8 30    6 24  
o4 = S  T   + S  T  T   + S  T T   + S T   + S T  T   + S T   + S T   +
         0        0  1        0 1       0       0  1       1       0   
     ------------------------------------------------------------------------
      6 8 15    4 16    4 15    2 8
     S T T   + S T   + S T   + S T  + 1
        0 1       0       1       0

o4 : A

i5 : B = A/(first gens A)^11

o5 = B

o5 : QuotientRing

i6 : substitute(f*g,B) == h

o6 = true

Ways to use expandGeomSeries :

expandGeomSeries(List,ZZ)
expandGeomSeries(RingElement,ZZ)

For the programmer

The object expandGeomSeries is a method function.