q-analog-plots-on-unit-circle.sage

### The case of E_6
WCR = WeylCharacterRing("E6", style="coroots")
weylcovec = sum([rt.associated_coroot() for rt in WCR.positive_roots()])/2
R.<t> = QQ['t']
weyldenom = prod([t^rt.scalar(weylcovec)-1 for rt in WCR.positive_roots()])
weylnumertab = [None] + [prod([t^(rt.scalar(weylcovec)+(1 if WCR.fundamental_weights()[i].scalar(rt.associated_coroot())>0 else 0))-1 for rt in WCR.positive_roots()]) for i in range(1,6+1)]
counttab = [None] + [R(weylnumertab[i]/weyldenom) for i in range(1,6+1)]
def realize(pol):
    d = pol.degree()
    def v(x):
        q = N(exp(2*I*pi*x))
        return real(pol.subs(q)*N(exp(-d*I*pi*x)))
    return v
colortab = [None, "red", "green", "blue", "magenta", "brown", "yellow", "cyan", "gray"]
graphtab = [None] + [plot(realize(counttab[i]), (-0.5,0.5), ymin=-7, ymax=9, plot_points=500, color=colortab[i]) for i in range(1,4+1)]
sum(graphtab[1:]).show(dpi=192)