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D.7.1.11 partial_molien
Procedure from library finvar.lib (see finvar_lib).
- Usage:
- partial_molien(M,n[,p]);
M: a 1x2 <matrix>, n: an <int> indicating number of terms in the
expansion, p: an optional <poly>
- Assume:
- M is the return value of molien or the second return value of
reynolds_molien, p ought to be the second return value of a previous
run of partial_molien and avoids recalculating known terms
- Return:
- n terms (type <poly>) of the partial expansion of the Molien series
(first n if there is no third parameter given, otherwise the next n
terms depending on a previous calculation) and an intermediate result
(type <poly>) of the calculation to be used as third parameter in a
next run of partial_molien
- Theory:
- The following calculation is implemented:
| (1+a1x+a2x^2+...+anx^n)/(1+b1x+b2x^2+...+bmx^m)=(1+(a1-b1)x+...
(1+b1x+b2x^2+...+bmx^m)
-----------------------
(a1-b1)x+(a2-b2)x^2+...
(a1-b1)x+b1(a1-b1)x^2+...
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Example:
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