# Example of a set with grading#

alias of NonNegativeIntegers

Non negative integers graded by themselves.

EXAMPLES:

sage: E = SetsWithGrading().example(); E
Non negative integers
sage: E in Sets().Infinite()
True
{0}
{100}

>>> from sage.all import *
Non negative integers
>>> E in Sets().Infinite()
True
{0}
{100}

an_element()[source]#

Return 0.

EXAMPLES:

sage: SetsWithGrading().example().an_element()
0

>>> from sage.all import *
0

generating_series(var='z')[source]#

Return $$1 / (1-z)$$.

EXAMPLES:

sage: N = SetsWithGrading().example(); N
Non negative integers
sage: f = N.generating_series(); f
1/(-z + 1)
sage: LaurentSeriesRing(ZZ,'z')(f)
1 + z + z^2 + z^3 + z^4 + z^5 + z^6 + z^7 + z^8 + z^9 + z^10 + z^11 + z^12 + z^13 + z^14 + z^15 + z^16 + z^17 + z^18 + z^19 + O(z^20)

>>> from sage.all import *
Non negative integers
>>> f = N.generating_series(); f
1/(-z + 1)
>>> LaurentSeriesRing(ZZ,'z')(f)
1 + z + z^2 + z^3 + z^4 + z^5 + z^6 + z^7 + z^8 + z^9 + z^10 + z^11 + z^12 + z^13 + z^14 + z^15 + z^16 + z^17 + z^18 + z^19 + O(z^20)


Return the component with grade grade.

EXAMPLES:

sage: N = SetsWithGrading().example()
{65}

>>> from sage.all import *
{65}


Return the grade of elt.

EXAMPLES:

sage: N = SetsWithGrading().example()

>>> from sage.all import *