%run -i FPENAG.py

G = gap.AlternatingGroup(4) 
[mg,ng] = G.Generators() # [(1,2,3),(2,3,4)]
kG = gap.GroupRing(GF(2), G)
f = gap.Embedding(G, kG)

m = gap.Image(f, mg)
n = gap.Image(f, ng)
id = gap.Image(f, mg^0)

# The action of C_3 = <c> on C_2^2 = <a, b> satisfies:
#
# a |---> cac^(-1) = ab
# b |---> cbc^(-1) = a

c = m       # (1,2,3)
a = m*n     # (1,3)(2,4)
b = c^2*a*c # (1,2)(3,4)

x = id + a + c + a*c # 1 + (1,3)(2,4) + (1,2,3) + (2,4,3)
y = id + b + c + b*c # 1 + (1,2)(3,4) + (1,2,3) + (1,3,4)

Igens = [x, y]
I = gap.Ideal(kG, [x,y])
kGmodI = kG/I

analyzekGmodI(G, f, id, I, kGmodI, Igens)