I want to find the coefficient of [a3b3c3] in the expansion of [1−(a+a21−(a+a2)+b+b21−(b+b2)+c+c21−(c+c2))](−1)
I have made research on internet about coefficient of this multivariable generating function, but could not find something valuable. Can you help me to calculate the coefficent using Sagemath ?
For example:
myprec = 10
def f(z):
t = (z + z^2).add_bigoh(myprec)
return t/(1-t)
R.<a,b,c> = PowerSeriesRing(QQ,default_prec=myprec)
g = (1-(f(a)+f(b)+f(c)))^(-1)
print( g.coefficients()[a^3*b^3*c^3] )For small degrees, default_prec= and .add_bigoh() are not really needed but they will speed up things / save memory when degrees of interest are large.
thanks a lot
@Max Alekseyev , i want to add something. Assume that i want to calculate g = (1-x(f(a)+f(b)+f(c)))^(-1) where print( g.coefficients()[x^9a^3b^3c^3] ). It did not work, how can i handle it ?
You need to define x first. E.g.:
K.<x> = QQ[]
R.<a,b,c> = PowerSeriesRing(K,default_prec=myprec)
g = (1-x*(f(a)+f(b)+f(c)))^(-1)Asked: 1 year ago
Seen: 222 times
Last updated: Aug 10 '23
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