Sponsored links: Algebra eBooks
 

Help Index

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

The Maxima on-line user's manual

Algebra Calculator

Search:

Moebius Calculator

Moebius

Function: moebius (<n>) Represents the Moebius function.

moebius (1);
 moebius (2 * 3 * 5);
 moebius (11 * 17 * 29 * 31);
 moebius (2^32);
 moebius (n);
 moebius (n = 12);
 moebius ([11, 11 * 13, 11 * 13 * 15]);
 moebius (matrix ([11, 12], [13, 14]));
 moebius ({21, 22, 23, 24});

When <n> is product of k distinct primes, moebius(<n>) simplifies to (-1)^k; when <n> = 1, it simplifies to 1; and it simplifies to 0 for all other positive integers.

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

Examples:

          (%i1) moebius (1);
          (%o1)                           1
          (%i2) moebius (2 * 3 * 5);
          (%o2)                          - 1
          (%i3) moebius (11 * 17 * 29 * 31);
          (%o3)                           1
          (%i4) moebius (2^32);
          (%o4)                           0
          (%i5) moebius (n);
          (%o5)                      moebius(n)
          (%i6) moebius (n = 12);
          (%o6)                    moebius(n) = 0
          (%i7) moebius ([11, 11 * 13, 11 * 13 * 15]);
          (%o7)                      [- 1, 1, 1]
          (%i8) moebius (matrix ([11, 12], [13, 14]));
                                     [ - 1  0 ]
          (%o8)                      [        ]
                                     [ - 1  1 ]
          (%i9) moebius ({21, 22, 23, 24});
          (%o9)                      {- 1, 0, 1}

(%o1)                                true
(%i2) 

Moebius Example

Related Examples

moebius-nusum-true

nusum(moebius(i),i,1,...

Calculate

moebius-nusum

nusum(moebius(i),i,1,...

Calculate

moebius

moebius (-2);

Calculate

moebius

moebius (2216);

Calculate

moebius

moebius (37);

Calculate

moebius

moebius (5);

Calculate

moebius

moebius (2216);

Calculate

moebius

moebius (2221);

Calculate

moebius

moebius (55);

Calculate

moebius

moebius (1);

Calculate