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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:
| | LIB "finvar.lib";
ring R=0,(x,y,z),dp;
matrix A[3][3]=0,1,0,-1,0,0,0,0,-1;
matrix REY,M=reynolds_molien(A);
poly p(1..2);
p(1..2)=partial_molien(M,5);
p(1);
==> 4x5+5x4+2x3+2x2+1
p(1..2)=partial_molien(M,5,p(2));
p(1);
==> 18x10+12x9+13x8+8x7+8x6
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