http://math.stackexchange.com/questions/1308395

s="(0,0,2),(0,0,-2),(2^*,1,1^*),(2^*,-1,-1^*),(0^*,1,-1^*),(0^*,-1,1^*),(0^*,-1,-1^*),(1,2^*,0^*),(-1,2^*,0^*),(1,0^*,-2^*),(-1,0^*,2^*),(1,0^*,0^*),(-1,0^*,0^*)"
def dmul(x,y):
    _x,_y=map(lambda x:int(x.rstrip("*")),[x,y])
    if not x.endswith('*'):
        if not y.endswith('*'):
            return str(_x+_y)
        else:
            return str(_x+_y)+'*'
    else:
        if not y.endswith('*'):
            return str(_x-_y)+'*'
        else:
            return str(_x-_y)
l=[]
even=[0,2,-2,4,-4]
odd=[1,-1,3,-3]
l+=[(str(a),str(b),str(c))
    for a in even
    for b in even
    for c in even]
l+=[(str(a)+'*',str(b),str(c)+'*')
    for a in even
    for b in odd
    for c in even]
l+=[(str(a),str(b)+'*',str(c)+'*')
    for a in odd
    for b in even
    for c in even]
l+=[(str(a)+'*',str(b)+'*',str(c))
    for a in odd
    for b in odd
    for c in odd]
d={}
for x in l:
    for y in l:
        xy=tuple(map(dmul,x,y))
        if not xy in d:
            d[xy]=[x,y]
s=map(lambda x:tuple(x.split(',')),s.replace('^*','*')[1:-1].split('),('))
for x in s:
    for y in s:
        xy=tuple(map(dmul,x,y))
        if xy in d:
            print "(%s)(%s)\t=(%s)(%s)"%tuple(map(lambda s:','.join(s),[x,y,d[xy][0],d[xy][1]]))
        else:
            print "(%s)(%s)\t=(%s) is not EnEm"%tuple(map(lambda s:','.join(s),[x,y,xy]))

(0,0,2)(0,0,2)  =(0,0,0)(0,0,4)
(0,0,2)(0,0,-2) =(0,0,0)(0,0,0)
(0,0,2)(2*,1,1*)    =(1,0*,0*)(1*,-1*,-3)
(0,0,2)(2*,-1,-1*)  =(1,0*,0*)(1*,1*,-1)
(0,0,2)(0*,1,-1*)   =(1,0*,0*)(-1*,-1*,-1)
(0,0,2)(0*,-1,1*)   =(1,0*,0*)(-1*,1*,-3)
(0,0,2)(0*,-1,-1*)  =(1,0*,0*)(-1*,1*,-1)
(0,0,2)(1,2*,0*)    =(0,0,0)(1,2*,2*)
(0,0,2)(-1,2*,0*)   =(0,0,0)(-1,2*,2*)
(0,0,2)(1,0*,-2*)   =(0,0,0)(1,0*,0*)
(0,0,2)(-1,0*,2*)   =(0,0,0)(-1,0*,4*)
(0,0,2)(1,0*,0*)    =(0,0,0)(1,0*,2*)
(0,0,2)(-1,0*,0*)   =(0,0,0)(-1,0*,2*)
(0,0,-2)(0,0,2) =(0,0,0)(0,0,0)
(0,0,-2)(0,0,-2)    =(0,0,0)(0,0,-4)
(0,0,-2)(2*,1,1*)   =(1,0*,0*)(1*,-1*,1)
(0,0,-2)(2*,-1,-1*) =(1,0*,0*)(1*,1*,3)
(0,0,-2)(0*,1,-1*)  =(1,0*,0*)(-1*,-1*,3)
(0,0,-2)(0*,-1,1*)  =(1,0*,0*)(-1*,1*,1)
(0,0,-2)(0*,-1,-1*) =(1,0*,0*)(-1*,1*,3)
(0,0,-2)(1,2*,0*)   =(0,0,0)(1,2*,-2*)
(0,0,-2)(-1,2*,0*)  =(0,0,0)(-1,2*,-2*)
(0,0,-2)(1,0*,-2*)  =(0,0,0)(1,0*,-4*)
(0,0,-2)(-1,0*,2*)  =(0,0,0)(-1,0*,0*)
(0,0,-2)(1,0*,0*)   =(0,0,0)(1,0*,-2*)
(0,0,-2)(-1,0*,0*)  =(0,0,0)(-1,0*,-2*)
(2*,1,1*)(0,0,2)    =(1,0*,0*)(1*,-1*,1)
(2*,1,1*)(0,0,-2)   =(1,0*,0*)(1*,-1*,-3)
(2*,1,1*)(2*,1,1*)  =(0,0,0)(0,2,0)
(2*,1,1*)(2*,-1,-1*)    =(0,0,0)(0,0,2)
(2*,1,1*)(0*,1,-1*) =(0,0,0)(2,2,2)
(2*,1,1*)(0*,-1,1*) =(0,0,0)(2,0,0)
(2*,1,1*)(0*,-1,-1*)    =(0,0,0)(2,0,2)
(2*,1,1*)(1,2*,0*)  =(0,0,0)(1*,3*,1)
(2*,1,1*)(-1,2*,0*) =(0,0,0)(3*,3*,1)
(2*,1,1*)(1,0*,-2*) =(0,0,0)(1*,1*,3)
(2*,1,1*)(-1,0*,2*) =(0,0,0)(3*,1*,-1)
(2*,1,1*)(1,0*,0*)  =(0,0,0)(1*,1*,1)
(2*,1,1*)(-1,0*,0*) =(0,0,0)(3*,1*,1)
(2*,-1,-1*)(0,0,2)  =(1,0*,0*)(1*,1*,3)
(2*,-1,-1*)(0,0,-2) =(1,0*,0*)(1*,1*,-1)
(2*,-1,-1*)(2*,1,1*)    =(0,0,0)(0,0,-2)
(2*,-1,-1*)(2*,-1,-1*)  =(0,0,0)(0,-2,0)
(2*,-1,-1*)(0*,1,-1*)   =(0,0,0)(2,0,0)
(2*,-1,-1*)(0*,-1,1*)   =(0,0,0)(2,-2,-2)
(2*,-1,-1*)(0*,-1,-1*)  =(0,0,0)(2,-2,0)
(2*,-1,-1*)(1,2*,0*)    =(0,0,0)(1*,1*,-1)
(2*,-1,-1*)(-1,2*,0*)   =(0,0,0)(3*,1*,-1)
(2*,-1,-1*)(1,0*,-2*)   =(0,0,0)(1*,-1*,1)
(2*,-1,-1*)(-1,0*,2*)   =(0,0,0)(3*,-1*,-3)
(2*,-1,-1*)(1,0*,0*)    =(0,0,0)(1*,-1*,-1)
(2*,-1,-1*)(-1,0*,0*)   =(0,0,0)(3*,-1*,-1)
(0*,1,-1*)(0,0,2)   =(1,0*,0*)(-1*,-1*,3)
(0*,1,-1*)(0,0,-2)  =(1,0*,0*)(-1*,-1*,-1)
(0*,1,-1*)(2*,1,1*) =(0,0,0)(-2,2,-2)
(0*,1,-1*)(2*,-1,-1*)   =(0,0,0)(-2,0,0)
(0*,1,-1*)(0*,1,-1*)    =(0,0,0)(0,2,0)
(0*,1,-1*)(0*,-1,1*)    =(0,0,0)(0,0,-2)
(0*,1,-1*)(0*,-1,-1*)   =(0,0,0)(0,0,0)
(0*,1,-1*)(1,2*,0*) =(0,0,0)(-1*,3*,-1)
(0*,1,-1*)(-1,2*,0*)    =(0,0,0)(1*,3*,-1)
(0*,1,-1*)(1,0*,-2*)    =(0,0,0)(-1*,1*,1)
(0*,1,-1*)(-1,0*,2*)    =(0,0,0)(1*,1*,-3)
(0*,1,-1*)(1,0*,0*) =(0,0,0)(-1*,1*,-1)
(0*,1,-1*)(-1,0*,0*)    =(0,0,0)(1*,1*,-1)
(0*,-1,1*)(0,0,2)   =(1,0*,0*)(-1*,1*,1)
(0*,-1,1*)(0,0,-2)  =(1,0*,0*)(-1*,1*,-3)
(0*,-1,1*)(2*,1,1*) =(0,0,0)(-2,0,0)
(0*,-1,1*)(2*,-1,-1*)   =(0,0,0)(-2,-2,2)
(0*,-1,1*)(0*,1,-1*)    =(0,0,0)(0,0,2)
(0*,-1,1*)(0*,-1,1*)    =(0,0,0)(0,-2,0)
(0*,-1,1*)(0*,-1,-1*)   =(0,0,0)(0,-2,2)
(0*,-1,1*)(1,2*,0*) =(0,0,0)(-1*,1*,1)
(0*,-1,1*)(-1,2*,0*)    =(0,0,0)(1*,1*,1)
(0*,-1,1*)(1,0*,-2*)    =(0,0,0)(-1*,-1*,3)
(0*,-1,1*)(-1,0*,2*)    =(0,0,0)(1*,-1*,-1)
(0*,-1,1*)(1,0*,0*) =(0,0,0)(-1*,-1*,1)
(0*,-1,1*)(-1,0*,0*)    =(0,0,0)(1*,-1*,1)
(0*,-1,-1*)(0,0,2)  =(1,0*,0*)(-1*,1*,3)
(0*,-1,-1*)(0,0,-2) =(1,0*,0*)(-1*,1*,-1)
(0*,-1,-1*)(2*,1,1*)    =(0,0,0)(-2,0,-2)
(0*,-1,-1*)(2*,-1,-1*)  =(0,0,0)(-2,-2,0)
(0*,-1,-1*)(0*,1,-1*)   =(0,0,0)(0,0,0)
(0*,-1,-1*)(0*,-1,1*)   =(0,0,0)(0,-2,-2)
(0*,-1,-1*)(0*,-1,-1*)  =(0,0,0)(0,-2,0)
(0*,-1,-1*)(1,2*,0*)    =(0,0,0)(-1*,1*,-1)
(0*,-1,-1*)(-1,2*,0*)   =(0,0,0)(1*,1*,-1)
(0*,-1,-1*)(1,0*,-2*)   =(0,0,0)(-1*,-1*,1)
(0*,-1,-1*)(-1,0*,2*)   =(0,0,0)(1*,-1*,-3)
(0*,-1,-1*)(1,0*,0*)    =(0,0,0)(-1*,-1*,-1)
(0*,-1,-1*)(-1,0*,0*)   =(0,0,0)(1*,-1*,-1)
(1,2*,0*)(0,0,2)    =(0,0,0)(1,2*,-2*)
(1,2*,0*)(0,0,-2)   =(0,0,0)(1,2*,2*)
(1,2*,0*)(2*,1,1*)  =(0,0,0)(3*,1*,-1)
(1,2*,0*)(2*,-1,-1*)    =(0,0,0)(3*,3*,1)
(1,2*,0*)(0*,1,-1*) =(0,0,0)(1*,1*,1)
(1,2*,0*)(0*,-1,1*) =(0,0,0)(1*,3*,-1)
(1,2*,0*)(0*,-1,-1*)    =(0,0,0)(1*,3*,1)
(1,2*,0*)(1,2*,0*)  =(0,0,0)(2,0,0)
(1,2*,0*)(-1,2*,0*) =(0,0,0)(0,0,0)
(1,2*,0*)(1,0*,-2*) =(0,0,0)(2,2,2)
(1,2*,0*)(-1,0*,2*) =(0,0,0)(0,2,-2)
(1,2*,0*)(1,0*,0*)  =(0,0,0)(2,2,0)
(1,2*,0*)(-1,0*,0*) =(0,0,0)(0,2,0)
(-1,2*,0*)(0,0,2)   =(0,0,0)(-1,2*,-2*)
(-1,2*,0*)(0,0,-2)  =(0,0,0)(-1,2*,2*)
(-1,2*,0*)(2*,1,1*) =(0,0,0)(1*,1*,-1)
(-1,2*,0*)(2*,-1,-1*)   =(0,0,0)(1*,3*,1)
(-1,2*,0*)(0*,1,-1*)    =(0,0,0)(-1*,1*,1)
(-1,2*,0*)(0*,-1,1*)    =(0,0,0)(-1*,3*,-1)
(-1,2*,0*)(0*,-1,-1*)   =(0,0,0)(-1*,3*,1)
(-1,2*,0*)(1,2*,0*) =(0,0,0)(0,0,0)
(-1,2*,0*)(-1,2*,0*)    =(0,0,0)(-2,0,0)
(-1,2*,0*)(1,0*,-2*)    =(0,0,0)(0,2,2)
(-1,2*,0*)(-1,0*,2*)    =(0,0,0)(-2,2,-2)
(-1,2*,0*)(1,0*,0*) =(0,0,0)(0,2,0)
(-1,2*,0*)(-1,0*,0*)    =(0,0,0)(-2,2,0)
(1,0*,-2*)(0,0,2)   =(0,0,0)(1,0*,-4*)
(1,0*,-2*)(0,0,-2)  =(0,0,0)(1,0*,0*)
(1,0*,-2*)(2*,1,1*) =(0,0,0)(3*,-1*,-3)
(1,0*,-2*)(2*,-1,-1*)   =(0,0,0)(3*,1*,-1)
(1,0*,-2*)(0*,1,-1*)    =(0,0,0)(1*,-1*,-1)
(1,0*,-2*)(0*,-1,1*)    =(0,0,0)(1*,1*,-3)
(1,0*,-2*)(0*,-1,-1*)   =(0,0,0)(1*,1*,-1)
(1,0*,-2*)(1,2*,0*) =(0,0,0)(2,-2,-2)
(1,0*,-2*)(-1,2*,0*)    =(0,0,0)(0,-2,-2)
(1,0*,-2*)(1,0*,-2*)    =(0,0,0)(2,0,0)
(1,0*,-2*)(-1,0*,2*)    =(0,0,0)(0,0,-4)
(1,0*,-2*)(1,0*,0*) =(0,0,0)(2,0,-2)
(1,0*,-2*)(-1,0*,0*)    =(0,0,0)(0,0,-2)
(-1,0*,2*)(0,0,2)   =(0,0,0)(-1,0*,0*)
(-1,0*,2*)(0,0,-2)  =(0,0,0)(-1,0*,4*)
(-1,0*,2*)(2*,1,1*) =(0,0,0)(1*,-1*,1)
(-1,0*,2*)(2*,-1,-1*)   =(0,0,0)(1*,1*,3)
(-1,0*,2*)(0*,1,-1*)    =(0,0,0)(-1*,-1*,3)
(-1,0*,2*)(0*,-1,1*)    =(0,0,0)(-1*,1*,1)
(-1,0*,2*)(0*,-1,-1*)   =(0,0,0)(-1*,1*,3)
(-1,0*,2*)(1,2*,0*) =(0,0,0)(0,-2,2)
(-1,0*,2*)(-1,2*,0*)    =(0,0,0)(-2,-2,2)
(-1,0*,2*)(1,0*,-2*)    =(0,0,0)(0,0,4)
(-1,0*,2*)(-1,0*,2*)    =(0,0,0)(-2,0,0)
(-1,0*,2*)(1,0*,0*) =(0,0,0)(0,0,2)
(-1,0*,2*)(-1,0*,0*)    =(0,0,0)(-2,0,2)
(1,0*,0*)(0,0,2)    =(0,0,0)(1,0*,-2*)
(1,0*,0*)(0,0,-2)   =(0,0,0)(1,0*,2*)
(1,0*,0*)(2*,1,1*)  =(0,0,0)(3*,-1*,-1)
(1,0*,0*)(2*,-1,-1*)    =(0,0,0)(3*,1*,1)
(1,0*,0*)(0*,1,-1*) =(0,0,0)(1*,-1*,1)
(1,0*,0*)(0*,-1,1*) =(0,0,0)(1*,1*,-1)
(1,0*,0*)(0*,-1,-1*)    =(0,0,0)(1*,1*,1)
(1,0*,0*)(1,2*,0*)  =(0,0,0)(2,-2,0)
(1,0*,0*)(-1,2*,0*) =(0,0,0)(0,-2,0)
(1,0*,0*)(1,0*,-2*) =(0,0,0)(2,0,2)
(1,0*,0*)(-1,0*,2*) =(0,0,0)(0,0,-2)
(1,0*,0*)(1,0*,0*)  =(0,0,0)(2,0,0)
(1,0*,0*)(-1,0*,0*) =(0,0,0)(0,0,0)
(-1,0*,0*)(0,0,2)   =(0,0,0)(-1,0*,-2*)
(-1,0*,0*)(0,0,-2)  =(0,0,0)(-1,0*,2*)
(-1,0*,0*)(2*,1,1*) =(0,0,0)(1*,-1*,-1)
(-1,0*,0*)(2*,-1,-1*)   =(0,0,0)(1*,1*,1)
(-1,0*,0*)(0*,1,-1*)    =(0,0,0)(-1*,-1*,1)
(-1,0*,0*)(0*,-1,1*)    =(0,0,0)(-1*,1*,-1)
(-1,0*,0*)(0*,-1,-1*)   =(0,0,0)(-1*,1*,1)
(-1,0*,0*)(1,2*,0*) =(0,0,0)(0,-2,0)
(-1,0*,0*)(-1,2*,0*)    =(0,0,0)(-2,-2,0)
(-1,0*,0*)(1,0*,-2*)    =(0,0,0)(0,0,2)
(-1,0*,0*)(-1,0*,2*)    =(0,0,0)(-2,0,-2)
(-1,0*,0*)(1,0*,0*) =(0,0,0)(0,0,0)
(-1,0*,0*)(-1,0*,0*)    =(0,0,0)(-2,0,0)