Implementing Additional Features for Lazy Formal Laurent Series

[tejasvicsr1]

This ticket deals with implementing composition for a formal Laurent Series.

Conditions:

Given two formal Laurent series - f and g

f o g exists, if and only if:

• g = 0 and val(f) >= 0
• g is non-zero and f has only finitely many nonzero coefficients
• g is non-zero and val(g) > 0.

This ticket is part of the meta ticket #31651

CC: @mantepse

Component: combinatorics

Keywords: LazyPowerSeries, FormalSeries, gsoc2021

Branch/Commit: u/gh-tejasvicsr1/implementing_additional_features_for_lazy_formal_laurent_series @ f304cb7

Issue created by migration from https://trac.sagemath.org/ticket/31899

[mantepse]

Changed keywords from LazyPowerSeries, FormalSeries, GSoC to LazyPowerSeries, FormalSeries, GSoC21

[mantepse]

comment:2

Let me note that the second case works already:

sage: L.<z> = LaurentPolynomialRing(QQ)
sage: LS.<y> = LazyLaurentSeriesRing(QQ)
sage: f = z^-2 + 1 + z
sage: g = 1/(y*(1-y)); g
y^-1 + 1 + y + y^2 + y^3 + y^4 + y^5 + ...
sage: f(g)
y^-1 + 2 + y + 2*y^2 - y^3 + 2*y^4 + y^5 + ...

Here is, why this works: the relevant line in __call__ in LaurentPolynomial_univariate is

    return self.__u(x) * (x[0]**self.__n)

• x is a singleton tuple with the Laurent series as its only element, that is, g from above.
• self.__n is the valuation of the Laurent polynomial, that is -2 in our case
• x[0]**self.__n therefore is the n-th power of the Laurent series
• self.__u is the polynomial obtained by multiplying the Laurent polynomial with z^-n
• self.__u(x) is therefore calling the __call__ method of the polynomial ring, and this works for similar reasons.

It might be a good idea to briefly doctest this in the future __call__ of LazyLaurentSeries.

I am not sure whether this is an efficient way to obtain the composition. But that's certainly not important now.

[tejasvicsr1]

Branch: t/31899/implementing_additional_features_for_lazy_formal_laurent_series

[tejasvicsr1]

Changed branch from t/31899/implementing_additional_features_for_lazy_formal_laurent_series to u/gh-tejasvicsr1/implementing_additional_features_for_lazy_formal_laurent_series

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

350f2f9

Cleaned code.

[sagetrac-git]

Commit: 350f2f9

[sagetrac-git]

Changed commit from 350f2f9 to 7b231ec

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

7b231ec

Added integration for the Lazy Laurent Series Code.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

974b361	Fixed change ring to ensure that the original implementation remains.
3f7b07b	Fixed integration.

[sagetrac-git]

Changed commit from 7b231ec to 3f7b07b

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

f304cb7

Formatting push.

[sagetrac-git]

Changed commit from 3f7b07b to f304cb7

[tscrim]

Changed keywords from LazyPowerSeries, FormalSeries, GSoC21 to LazyPowerSeries, FormalSeries, gsoc2021

[mantepse]

comment:13

superseded