def sum(ii=10, d=10):
for i in range(ii):
a = randrange(0, d)
b = randrange(0, d)
gg = R().permgroup(a)
hh = R().permgroup(b)
print(gg.sum(hh))
def intersection(ii = 10, a = 5, b = 5):
for i in range(ii):
print("=====================")
c1 = R().permcoset(a)
c2 = R().permcoset(b)
print(c1)
print(c2)
print(c1.intersection(c2))
def gridFromseqinv(ii = 10, d = 10):
for i in range(ii):
g = R().perm(randrange(0, d))
h = R().perm(randrange(0, d))
m = g.seq().gridFromseq(h.seq())
n = m.gridFromseqinv()
print(g)
print(h)
print(m)
print(n)
def prodinv(ii = 10, d = 10):
for i in range(ii):
g = R().perm(randrange(0, d))
h = R().perm(randrange(0, d))
print("---")
print(g)
print(h)
print(g.prod(h))
print(g.prod(h).prodinv())
assert(g.prod(h).prodinv() == g)
def prod(ii=10, d=10):
for i in range(ii):
a = randrange(0, d)
b = randrange(0, d)
gg = R().permgroup(a)
hh = R().permgroup(b)
print("---")
print(gg)
print(hh)
print(gg.prod(hh))
def gridFromseq(ii = 10, d = 10):
for i in range(ii):
g = R().perm(randrange(0, d))
h = R().perm(randrange(0, d))
print("---")
print(g)
print(h)
print(g.seq())
print(h.seq())
print(g.seq().gridFromseq(h.seq()))
def mul(ii = 10, d = 10):
for i in range(ii):
a = randrange(0, d)
b = randrange(0, d)
g = R().perm(a)
print("g is {}".format(g))
h = R().perm(b)
print("h is {}".format(h))
m = g * h
print("g * h is {}".format(m))
def eq(ii = 10, d = 10):
for i in range(ii):
g1 = R().perm(randrange(0, d))
g2 = R().perm(randrange(0, d))
g3 = R().perm(randrange(0, d))
m1 = g1 * g2
m2 = g2 * g3
print("----")
print(m1 * g3)
print(g1 * m2)
assert(m1 * g3 == g1 * m2), "Associativity"
def grid(ii = 10, d = 10):
for i in range(ii):
g = R().perm(randrange(0, d))
h = R().perm(randrange(0, d))
m = g.grid(h)
n = m.gridinv_0()
print("----")
print(g)
print(h)
print(m)
print(n)
def gridFromseq(ii=10, d=10):
for i in range(ii):
a = randrange(0, d)
b = randrange(0, d)
gg = R().permgroup(a)
hh = R().permgroup(b)
print("---")
print(gg)
print(gg.seq())
print(hh)
print(hh.seq())
print(gg.seq().gridFromseq(hh.seq()))
def prod(ii = 10, d = 10):
for i in range(ii):
g = R().perm(randrange(0, d))
h = R().perm(randrange(0, d))
print("---")
print(g)
g2 = g * g
h2 = h * h
print(h)
print(g.prod(h))
print(g.prod(h) * g.prod(h))
print(g2.prod(h2))
assert(g.prod(h) * g.prod(h) == g2.prod(h2))
def seq(ii=10, d=10):
for i in range(ii):
a = randrange(0, d)
gg = R().permgroup(a)
print("---")
print(gg)
print(gg.seq())
def movedpt(ii = 10, d = 10):
for i in range(ii):
g = R().perm(randrange(0, d))
p = randrange(0, d)
print("---")
print(g)
print(g.movedpt())
def inv(ii = 10, d = 10):
for i in range(ii):
g = R().perm(randrange(0, d))
print("---")
print(g)
print(g.inv())
print(g * g.inv())
assert(g * g.inv() == g.id() and g.inv() * g == g.id()), "Inverses"
def id(ii = 10, d = 10):
for i in range(ii):
g = R().perm(randrange(0, d))
print("---")
print(g)
print(g.id())
print(g * g.id())
assert(g * g.id() == g and g.id() * g == g), "Identity"
def orbitstab(ii=10, d=10):
for i in range(ii):
a = randrange(1, d)
b = randrange(0, a)
gg = R().permgroup(a)
print("----")
print(gg)
print(b)
print(gg.orbitstab(b))
def SchStr(ii=10, d=10):
for i in range(ii):
a = randrange(1, d)
b = randrange(0, a)
gg = R().permgroup(a)
print("----")
print(gg)
print(b)
print(gg.SchStr(b))
def seqinv(ii = 10, d = 10):
for i in range(ii):
g = R().perm(randrange(0, d))
print("---")
print(g)
h = g.seq()
print(h)
print(h.seqinv())
assert(g.seq().seqinv() == g)
def seq(ii = 10, d = 10):
for i in range(ii):
g = R().perm(randrange(0, d))
print("---")
print(g)
print(g.seq())