Evariste provides a simple way to look at groups, their elements, and their basic properties. It beats doing so by hand!
There are three groups we will look at in the initial version. The first is multiplicative groups modulo n, with elements coprime with n; or, U(n). The second are the additive integers modulo n; or, Z_n. Finally, we'll look at p-groups. My generating a group, you will be able to see its elements printed immediately. Next, you can obtain some basic properties: Their order, the order of each element, and whether the group is cyclic.
The starting point is:
Hello there! What group or property would you like to look at?
To find see the group of units mod n under multiplication, enter U(n).
U(10)
(1 3 7 9)
The following are a list of operations you can run. These include the definition of a group, order of the group, listing of generators, cyclic check, and element orders.
###Define Group
There are two supported groups at the moment. The multiplicative group of integers modulo n, "U(n)". The additive group of integers modulo n, "Z_n".
> U(10)
> (1 3 7 9)
> Z_4
> (0 1 2 3)
###Order
To find order of a group,
> order Z_4
> The order of Z_4 is 4
###Generating Elements
Find the generators of a group
> generators U(22)
> (7, 13, 17, 19)
###Nongenerating Elements
Find the non-generating elements
> non-generators U(22)
> (1, 3, 5, 9, 15, 21)
Copyright © 2013 Thomas Meier
Distributed under the Eclipse Public License, the same as Clojure.