AUTHOR: David Kohel, 09-2005.
SAGE supports free abelian monoids on any prescribed finite number
of generators. Use the
FreeAbelianMonoid
function to
create a free abelian monoid, and the gen
and gens
functions to obtain the corresponding generators. You can print the
generators as arbitrary strings using the optional names
argument to
the FreeAbelianMonoid
function.
The module monoids.free_abelian_monoid defines the following methods:
n, [names=None]) |
Create the free abelian monoid in
generators.
INPUT: n -- integer names -- (optional) names of generators OUTPUT: free abelian monoid
sage: FreeAbelianMonoid(0) Free abelian monoid on 0 generators () sage: F = FreeAbelianMonoid(5,names = list("abcde")) sage: F Free abelian monoid on 5 generators (a, b, c, d, e) sage: F(1) 1 sage: (a, b, c, d, e) = F.gens() sage: mul([ a, b, a, c, b, d, c, d ]) a^2*b^2*c^2*d^2 sage: a**2 * b**3 * a**2 * b**4 a^4*b^7
x) |
Return True if
is a free abelian monoid.
sage: is_FreeAbelianMonoid(5) False sage: is_FreeAbelianMonoid(FreeAbelianMonoid(7)) True sage: is_FreeAbelianMonoid(FreeMonoid(7)) False sage: is_FreeAbelianMonoid(FreeMonoid(0)) False
The module monoids.free_abelian_monoid defines the following classes: