Skip to content
This repository has been archived by the owner on Jan 30, 2023. It is now read-only.

Commit

Permalink
Adding documentation to the user-facing class level documentation.
Browse files Browse the repository at this point in the history
  • Loading branch information
Travis Scrimshaw committed Aug 10, 2021
1 parent 51357a0 commit 7501204
Show file tree
Hide file tree
Showing 2 changed files with 109 additions and 18 deletions.
68 changes: 56 additions & 12 deletions src/sage/rings/lazy_laurent_series.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -1158,25 +1158,69 @@ class LazyLaurentSeries(LazySequencesModuleElement, LazyCauchyProductSeries):
EXAMPLES::
sage: L.<z> = LazyLaurentSeriesRing(ZZ)
sage: L(lambda i: i, valuation=-3, constant=(-1,3))
-3*z^-3 - 2*z^-2 - z^-1 + z + 2*z^2 - z^3 - z^4 - z^5 + O(z^6)
sage: L(lambda i: i, valuation=-3, constant=-1, degree=3)
-3*z^-3 - 2*z^-2 - z^-1 + z + 2*z^2 - z^3 - z^4 - z^5 + O(z^6)
::
We can build a series from a function and specify if the series
eventually takes a constant value::
sage: f = 1 / (1 - z - z^2); f
sage: f = L(lambda i: i, valuation=-3, constant=-1, degree=3)
sage: f
-3*z^-3 - 2*z^-2 - z^-1 + z + 2*z^2 - z^3 - z^4 - z^5 + O(z^6)
sage: f[-2]
-2
sage: f[10]
-1
sage: f[-5]
0
sage: f = L(lambda i: i, valuation=-3)
sage: f
-3*z^-3 - 2*z^-2 - z^-1 + z + 2*z^2 + 3*z^3 + O(z^4)
sage: f[20]
20
Anything that converts into a polynomial can be input, where
we can also specify the valuation or if the series eventually
takes a constant value::
sage: L([-5,2,0,5])
-5 + 2*z + 5*z^3
sage: L([-5,2,0,5], constant=6)
-5 + 2*z + 5*z^3 + 6*z^4 + 6*z^5 + 6*z^6 + O(z^7)
sage: L([-5,2,0,5], degree=6, constant=6)
-5 + 2*z + 5*z^3 + 6*z^6 + 6*z^7 + 6*z^8 + O(z^9)
sage: L([-5,2,0,5], valuation=-2, degree=3, constant=6)
-5*z^-2 + 2*z^-1 + 5*z + 6*z^3 + 6*z^4 + 6*z^5 + O(z^6)
sage: L([-5,2,0,5], valuation=5)
-5*z^5 + 2*z^6 + 5*z^8
sage: L({-2:9, 3:4}, constant=2, degree=5)
9*z^-2 + 4*z^3 + 2*z^5 + 2*z^6 + 2*z^7 + O(z^8)
We can also perform arithmetic::
sage: f = 1 / (1 - z - z^2)
sage: f
1 + z + 2*z^2 + 3*z^3 + 5*z^4 + 8*z^5 + 13*z^6 + O(z^7)
sage: f.coefficient(100)
573147844013817084101
sage: f = (z^-2 - 1 + 2*z) / (z^-1 - z + 3*z^2)
sage: f
z^-1 - z^2 - z^4 + 3*z^5 + O(z^6)
Lazy Laurent series is picklable::
However, we may not always be able to know when a result is
exactly a polynomial::
sage: g = loads(dumps(f))
sage: g
1 + z + 2*z^2 + 3*z^3 + 5*z^4 + 8*z^5 + 13*z^6 + O(z^7)
sage: g == f
True
sage: f * (z^-1 - z + 3*z^2)
z^-2 - 1 + 2*z + O(z^5)
TESTS::
sage: L.<z> = LazyLaurentSeriesRing(ZZ, sparse=True)
sage: f = 1 / (1 - z - z^2)
sage: TestSuite(f).run()
sage: L.<z> = LazyLaurentSeriesRing(ZZ, sparse=False)
sage: f = 1 / (1 - z - z^2)
sage: TestSuite(f).run()
"""

def change_ring(self, ring):
Expand Down
59 changes: 53 additions & 6 deletions src/sage/rings/lazy_laurent_series_ring.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -58,9 +58,9 @@ class LazyLaurentSeriesRing(UniqueRepresentation, Parent):
EXAMPLES::
sage: L.<z> = LazyLaurentSeriesRing(QQ)
sage: 1/(1 - z)
sage: 1 / (1 - z)
1 + z + z^2 + z^3 + z^4 + z^5 + z^6 + O(z^7)
sage: 1/(1 - z) == 1/(1 - z)
sage: 1 / (1 - z) == 1 / (1 - z)
True
sage: L in Fields
True
Expand All @@ -75,17 +75,57 @@ class LazyLaurentSeriesRing(UniqueRepresentation, Parent):
sage: e.coefficient(100).parent()
Finite Field of size 3
Generating functions of integer sequences are Laurent series over the
integer ring::
Series can be defined by specifying a coefficient function
along with a valuation or a degree where after the series
is evenutally constant::
sage: R.<x,y> = QQ[]
sage: L.<z> = LazyLaurentSeriesRing(R)
sage: def coeff(n):
....: if n < 0:
....: return -2 + n
....: if n == 0:
....: return 6
....: return x + y^n
sage: f = L(coeff, valuation=-5)
sage: f
-7*z^-5 - 6*z^-4 - 5*z^-3 - 4*z^-2 - 3*z^-1 + 6 + (x + y)*z + O(z^2)
sage: 1 / (1 - f)
1/7*z^5 - 6/49*z^6 + 1/343*z^7 + 8/2401*z^8 + 64/16807*z^9
+ 17319/117649*z^10 + (1/49*x + 1/49*y - 180781/823543)*z^11 + O(z^12)
sage: L(coeff, valuation=-3, degree=3, constant=x)
-5*z^-3 - 4*z^-2 - 3*z^-1 + 6 + (x + y)*z + (y^2 + x)*z^2
+ x*z^3 + x*z^4 + x*z^5 + O(z^6)
Similarly, we can specify a polynomial or the initial
coefficients with anything that converts into the
corresponding Laurent polynomial ring::
sage: L([1, x, y, 0, x+y])
1 + x*z + y*z^2 + (x + y)*z^4
sage: L([1, x, y, 0, x+y], constant=2)
1 + x*z + y*z^2 + (x + y)*z^4 + 2*z^5 + 2*z^6 + 2*z^7 + O(z^8)
sage: L([1, x, y, 0, x+y], degree=7, constant=2)
1 + x*z + y*z^2 + (x + y)*z^4 + 2*z^7 + 2*z^8 + 2*z^9 + O(z^10)
sage: L([1, x, y, 0, x+y], valuation=-2)
z^-2 + x*z^-1 + y + (x + y)*z^2
sage: L([1, x, y, 0, x+y], valuation=-2, constant=3)
z^-2 + x*z^-1 + y + (x + y)*z^2 + 3*z^3 + 3*z^4 + 3*z^5 + O(z^6)
sage: L([1, x, y, 0, x+y], valuation=-2, degree=4, constant=3)
z^-2 + x*z^-1 + y + (x + y)*z^2 + 3*z^4 + 3*z^5 + 3*z^6 + O(z^7)
Generating functions of integer sequences are Laurent series
over the integer ring::
sage: L.<z> = LazyLaurentSeriesRing(ZZ); L
Lazy Laurent Series Ring in z over Integer Ring
sage: L in Fields
False
sage: 1/(1 - 2*z)^3
sage: 1 / (1 - 2*z)^3
1 + 6*z + 24*z^2 + 80*z^3 + 240*z^4 + 672*z^5 + 1792*z^6 + O(z^7)
Power series can be defined recursively::
Power series can be defined recursively (see :meth:`define()` for
more examples)::
sage: L.<z> = LazyLaurentSeriesRing(ZZ)
sage: s = L(None)
Expand Down Expand Up @@ -370,6 +410,13 @@ def _element_constructor_(self, x=None, valuation=None, constant=None, degree=No
...
ValueError: constant may only be specified if the degree is specified
We support the old input format for ``constant``::
sage: f = L(lambda i: i, valuation=-3, constant=-1, degree=3)
sage: g = L(lambda i: i, valuation=-3, constant=(-1,3))
sage: f == g
True
.. TODO::
Add a method to change the sparse/dense implementation.
Expand Down

0 comments on commit 7501204

Please sign in to comment.