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.
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
EXAMPLES:
sage: from sage.combinat.species.series_order import *
sage: o = InfiniteSeriesOrder()
sage: o > 2
True
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
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
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
EXAMPLES:
sage: from sage.combinat.species.series_order import *
sage: o = InfiniteSeriesOrder(); o
Infinite series order
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
EXAMPLES:
sage: from sage.combinat.species.series_order import *
sage: u = UnknownSeriesOrder()
sage: u + 2
Unknown series order
sage: u + u
Unknown series order
EXAMPLES:
sage: from sage.combinat.species.series_order import *
sage: u = UnknownSeriesOrder()
sage: u > 2
False
EXAMPLES:
sage: from sage.combinat.species.series_order import *
sage: u = UnknownSeriesOrder()
sage: u < 2
True
sage: o = InfiniteSeriesOrder()
sage: u < o
True
EXAMPLES:
sage: from sage.combinat.species.series_order import *
sage: u = UnknownSeriesOrder()
sage: u * 2
Unknown series order
sage: u * u
Unknown series order
EXAMPLES:
sage: from sage.combinat.species.series_order import *
sage: u = UnknownSeriesOrder()
sage: u + 2
Unknown series order
sage: u + u
Unknown series order
EXAMPLES:
sage: from sage.combinat.species.series_order import *
sage: u = UnknownSeriesOrder(); u
Unknown series order
EXAMPLES:
sage: from sage.combinat.species.series_order import *
sage: u = UnknownSeriesOrder()
sage: u * 2
Unknown series order
sage: u * u
Unknown series order
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
EXAMPLES:
sage: from sage.combinat.species.series_order import *
sage: u = UnknownSeriesOrder()
sage: increment(u)
Unknown series order
sage: increment(2)
3