Series Order

This file provides some utility classes which are useful when working with unknown, known, and infinite series orders for univariate power series.

This code is based on the work of Ralf Hemmecke and Martin Rubey’s Aldor-Combinat, which can be found at http://www.risc.uni-linz.ac.at/people/hemmecke/aldor/combinat/index.html. In particular, the relevant section for this file can be found at http://www.risc.uni-linz.ac.at/people/hemmecke/AldorCombinat/combinatsu30.html.

class sage.combinat.species.series_order.InfiniteSeriesOrder
__add__(x)

EXAMPLES:

sage: from sage.combinat.species.series_order import *
sage: o = InfiniteSeriesOrder()
sage: o + 2
Infinite series order
sage: o + o
Infinite series order
sage: u = UnknownSeriesOrder()
sage: o + u
Unknown series order

TESTS:

sage: o + -1
...
ValueError: x must be a positive integer
__gt__(x)

EXAMPLES:

sage: from sage.combinat.species.series_order import *
sage: o = InfiniteSeriesOrder()
sage: o > 2
True
__lt__(x)

EXAMPLES:

sage: from sage.combinat.species.series_order import *
sage: o = InfiniteSeriesOrder()
sage: o < 2
False
sage: o < o
False
sage: u = UnknownSeriesOrder()
sage: o < u
False
__mul__(x)

EXAMPLES:

sage: from sage.combinat.species.series_order import *
sage: o = InfiniteSeriesOrder()
sage: o * 2
Infinite series order
sage: o * o
Infinite series order
sage: u = UnknownSeriesOrder()
sage: o * u
Unknown series order

TESTS:

sage: o * -1
...
ValueError: x must be a positive integer
__radd__(x)

EXAMPLES:

sage: from sage.combinat.species.series_order import *
sage: o = InfiniteSeriesOrder()
sage: o + 2
Infinite series order
sage: o + o
Infinite series order
sage: u = UnknownSeriesOrder()
sage: o + u
Unknown series order

TESTS:

sage: o + -1
...
ValueError: x must be a positive integer
__repr__()

EXAMPLES:

sage: from sage.combinat.species.series_order import *
sage: o = InfiniteSeriesOrder(); o
Infinite series order
__rmul__(x)

EXAMPLES:

sage: from sage.combinat.species.series_order import *
sage: o = InfiniteSeriesOrder()
sage: o * 2
Infinite series order
sage: o * o
Infinite series order
sage: u = UnknownSeriesOrder()
sage: o * u
Unknown series order

TESTS:

sage: o * -1
...
ValueError: x must be a positive integer
class sage.combinat.species.series_order.SeriesOrderElement
class sage.combinat.species.series_order.UnknownSeriesOrder
__add__(x)

EXAMPLES:

sage: from sage.combinat.species.series_order import *
sage: u = UnknownSeriesOrder()
sage: u + 2
Unknown series order
sage: u + u
Unknown series order
__gt__(x)

EXAMPLES:

sage: from sage.combinat.species.series_order import *
sage: u = UnknownSeriesOrder()
sage: u > 2
False
__lt__(x)

EXAMPLES:

sage: from sage.combinat.species.series_order import *
sage: u = UnknownSeriesOrder()
sage: u < 2
True
sage: o = InfiniteSeriesOrder()
sage: u < o
True
__mul__(x)

EXAMPLES:

sage: from sage.combinat.species.series_order import *
sage: u = UnknownSeriesOrder()
sage: u * 2
Unknown series order
sage: u * u
Unknown series order
__radd__(x)

EXAMPLES:

sage: from sage.combinat.species.series_order import *
sage: u = UnknownSeriesOrder()
sage: u + 2
Unknown series order
sage: u + u
Unknown series order
__repr__()

EXAMPLES:

sage: from sage.combinat.species.series_order import *
sage: u = UnknownSeriesOrder(); u
Unknown series order
__rmul__(x)

EXAMPLES:

sage: from sage.combinat.species.series_order import *
sage: u = UnknownSeriesOrder()
sage: u * 2
Unknown series order
sage: u * u
Unknown series order
sage.combinat.species.series_order.bounded_decrement(x)

EXAMPLES:

sage: from sage.combinat.species.series_order import *
sage: u = UnknownSeriesOrder()
sage: bounded_decrement(u)
Unknown series order
sage: bounded_decrement(4)
3
sage: bounded_decrement(0)
0
sage.combinat.species.series_order.increment(x)

EXAMPLES:

sage: from sage.combinat.species.series_order import *
sage: u = UnknownSeriesOrder()
sage: increment(u)
Unknown series order
sage: increment(2)
3

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