I am trying to write a code that finds the multiplicative identity of a finite ring with addition modulo n and multiplication modulo n as the operations. Basically it should return that element e such that e*y%n=y for all y in R
What I have tried is the following:
U=[e for e in R for y in R if e*y%10==y]
Unity=[x for x in U if U.count(x)==len(R)]
if Unity:
print(“The given ring has multiplicative identity”,Unity[0])
else:
print(“The given ring has no multiplicative identity)
The problem with this is that the list U is not taking only that e which works for all y in R. That is the reason I’m creating another list that counts the number of times an e has occurred in U.
I was wondering if I could avoid having to create the second list by instead using some inbuilt function that works as “for all”? I checked online and found the .all() function but I am not sure how to use it here.
Python has an all function, which does most of what you want. Rather than having two nested for clauses in your list comprehension, you'll want a separate generator expression for the y loop, inside of all:
U = [e for e in R if all(e*y%10==y for y in R)]