MolienSeries-A_n

2695 days ago by J.Wisniewski

# the aim of this exercise is to compute the Molien series of the action of the cyclic group # of m elements with weights (1,-1) # the calculation is done in the ring of power series R.<t>=PowerSeriesRing(QQ,30) f3 = (3*((1-t^6)/((1-t^2)*(1-t^3)^2)-1/(3*(1-t)^2)))*(1+t+t^2) f3 
       
2 + O(t^30)
f4 = ((4*((1-t^8)/((1-t^2)*(1-t^4)^2)-1/(4*(1-t)^2)))*(1+t+t^2+t^3)*(1+t)) f4 
       
3 + 4*t + 3*t^2 + O(t^30)
f5 = (5*((1-t^(10))/((1-t^2)*(1-t^5)^2)-1/(5*(1-t)^2)))*(1+t+t^2+t^3+t^4) f5 
       
4 + 2*t + 4*t^2 + O(t^30)
f6 = ((6*((1-t^(12))/((1-t^2)*(1-t^6)^2)-1/(6*(1-t)^2)))*(1+t+t^2+t^3+t^4+t^5)*(1+t)) f6 
       
5 + 8*t + 9*t^2 + 8*t^3 + 5*t^4 + O(t^30)