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The Maxima on-line user's manual

Algebra Calculator

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Divisors Calculator

Divisors

Function: divisors (<n>) Represents the set of divisors of <n>.

divisors(<n>) simplifies to a set of integers when <n> is a nonzero integer. The set of divisors includes the members 1 and <n>. The divisors of a negative integer are the divisors of its absolute value.

divisors distributes over equations, lists, matrices, and sets.

Examples:

We can verify that 28 is a perfect number: the sum of its divisors (except for itself) is 28.

          (%i1) s: divisors(28);
          (%o1)                 {1, 2, 4, 7, 14, 28}
          (%i2) lreduce ("+", args(s)) - 28;
          (%o2)                          28

divisors is a simplifying function. Substituting 8 for a in divisors(a) yields the divisors without reevaluating divisors(8).

          (%i1) divisors (a);
          (%o1)                      divisors(a)
          (%i2) subst (8, a, %);
          (%o2)                     {1, 2, 4, 8}

divisors distributes over equations, lists, matrices, and sets.

          (%i1) divisors (a = b);
          (%o1)               divisors(a) = divisors(b)
          (%i2) divisors ([a, b, c]);
          (%o2)        [divisors(a), divisors(b), divisors(c)]
          (%i3) divisors (matrix ([a, b], [c, d]));
                            [ divisors(a)  divisors(b) ]
          (%o3)             [                          ]
                            [ divisors(c)  divisors(d) ]
          (%i4) divisors ({a, b, c});
          (%o4)        {divisors(a), divisors(b), divisors(c)}

(%o1)                                true
(%i2) 

Divisors Example

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