Maxima Function
equiv_classes (s, F)
Returns a set of the equivalence classes of the set s with respect to the equivalence relation F.
F is a function of two variables defined on the Cartesian product of s with s.
The return value of F is either true
or false
,
or an expression expr such that is(expr)
is either true
or false
.
When F is not an equivalence relation,
equiv_classes
accepts it without complaint,
but the result is generally incorrect in that case.
Examples:
The equivalence relation is a lambda expression which returns true
or false
.
(%i1) equiv_classes ({1, 1.0, 2, 2.0, 3, 3.0}, lambda ([x, y], is (equal (x, y)))); (%o1) {{1, 1.0}, {2, 2.0}, {3, 3.0}}
The equivalence relation is the name of a relational function
which is
evaluates to true
or false
.
(%i1) equiv_classes ({1, 1.0, 2, 2.0, 3, 3.0}, equal); (%o1) {{1, 1.0}, {2, 2.0}, {3, 3.0}}
The equivalence classes are numbers which differ by a multiple of 3.
(%i1) equiv_classes ({1, 2, 3, 4, 5, 6, 7}, lambda ([x, y], remainder (x - y, 3) = 0)); (%o1) {{1, 4, 7}, {2, 5}, {3, 6}}