python and abstract algebra help

1. Execute the statement R = Integers(40) to create the set [0,1,2,...,3 , ...,39] This is a group under addition mod 40, which we will ignore. Instead we are interested in the subset of elements which have an inverse under multiplication mod 40. Determine how big this subgroup is by executing the command R.unit_group_order(), and then obtain a list of these elements with R.list_of_elements_of_multiplicative_group() . 2. You can create elements of this group by coercing regular integers into U, such as with the statement a = U(7) . (Don't confuse this with our mathematical notation U(40).) This will tell Sage that you want to view 7 as an element of U, subject to the corresponding operations. Determine the elements of the cyclic subgroup of U generated by 7 with a list comprehension as follows: 1 2 R = Integers (40) a = R(7) [a^i for i in srange(16)] 3 What is the order of 7 in U(40)? 1. Execute the statement R = Integers(40) to create the set [0,1,2,...,3 , ...,39] This is a group under addition mod 40, which we will ignore. Instead we are interested in the subset of elements which have an inverse under multiplication mod 40. Determine how big this subgroup is by executing the command R.unit_group_order(), and then obtain a list of these elements with R.list_of_elements_of_multiplicative_group() . 2. You can create elements of this group by coercing regular integers into U, such as with the statement a = U(7) . (Don't confuse this with our mathematical notation U(40).) This will tell Sage that you want to view 7 as an element of U, subject to the corresponding operations. Determine the elements of the cyclic subgroup of U generated by 7 with a list comprehension as follows: 1 2 R = Integers (40) a = R(7) [a^i for i in srange(16)] 3 What is the order of 7 in U(40)