Comparison

The comparison of two objects in Magma is generally performed with the following binary operators:

eq

equal to

ne

not equal to

gt

greater than

ge

greater than or equal to

lt

less than

le

less than or equal to

Each of them returns true or false .

Elements can be compared for equality/inequality only when they are of suitable types and Magma can find a common overstructure. Note that

• sometimes equal objects can be constructed in such a way that Magma lacks the information to realize that they are in fact equal
• for some magmas, it is possible to test isomorphism, a property weaker than equality

The tests such as `gt' only apply when there is an ordering defined on the parent magma of the elements. For such magmas, the maximum and minimum of a pair, set or sequence of elements may also be calculated, with the functions Maximum and Minimum (or Max and Min).

Example

> print 10*10 eq 100;
true

> G := SymmetricGroup(3);
> G!(1,2,3) gt G!(1,2);

>> G!(1,2,3) gt G!(1,2);
             ^
Runtime error in 'gt': Bad argument types
Argument types given: GrpPermElt, GrpPermElt
> Order(G!(1,2,3)) gt Order(G!(1,2));
true