#### 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+...

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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