Add function to return the nth s-gonal number

[sheareralexj]

This ticket adds a function to return elements of the s-gonal sequences. For example, this enables:

sage: tri = [polygonal_number(3, n) for n in [0..9]]
sage: tri
[0, 1, 3, 6, 10, 15, 21, 28, 36, 45]

sage: square = [polygonal_number(4, n) for n in [0..9]]
sage: square
[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]

Component: combinatorics

Author: Alex Shearer

Branch/Commit: e10fd35

Reviewer: Jonathan Kliem

Issue created by migration from https://trac.sagemath.org/ticket/27986

[embray]

comment:2

As the Sage-8.8 release milestone is pending, we should delete the sage-8.8 milestone for tickets that are not actively being worked on or that still require significant work to move forward. If you feel that this ticket should be included in the next Sage release at the soonest please set its milestone to the next release milestone (sage-8.9).

[embray]

comment:3

As the Sage-8.8 release milestone is pending, we should delete the sage-8.8 milestone for tickets that are not actively being worked on or that still require significant work to move forward. If you feel that this ticket should be included in the next Sage release at the soonest please set its milestone to the next release milestone (sage-8.9).

[sheareralexj]

Author: gh-sheareralexj

[sheareralexj]

Changed author from gh-sheareralexj to sheareralexj

[sheareralexj]

Branch: u/gh-sheareralexj/27986

[sheareralexj]

Changed branch from u/gh-sheareralexj/27986 to u/sheareralexj/27986

[sheareralexj]

Changed branch from u/sheareralexj/27986 to t/27986/add_function_to_return_the_nth_s_gonal_number

[sheareralexj]

Changed branch from t/27986/add_function_to_return_the_nth_s_gonal_number to none

[sheareralexj]

Changed author from sheareralexj to none

[sheareralexj]

Branch: u/gh-sheareralexj/add_function_to_return_the_nth_s_gonal_number

[sheareralexj]

Author: Alex Shearer

[sheareralexj]

New commits:

b829a43

27986: Added function to return polygonal numbers

[sheareralexj]

Commit: b829a43

[sagetrac-git]

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

c325028

27986: Removed restriction on n - can now find polygonal numbers for negative indices

[sagetrac-git]

Changed commit from b829a43 to c325028

[embray]

comment:15

Ticket retargeted after milestone closed

[sagetrac-git]

Changed commit from c325028 to a616782

[sagetrac-git]

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

3ef7663	Merge branch 'u/gh-sheareralexj/add_function_to_return_the_nth_s_gonal_number' of git://trac.sagemath.org/sage into test_27986
a616782	27986: Updated documentation

[sheareralexj]

comment:19

Made the changes above and updated the documentation

[kliem]

comment:21

Some more minor things I missed before.

• The arguments in the INPUT block are usually not sentences and end not with a period. See https://doc.sagemath.org/html/en/developer/coding_basics.html#input

• I would propose the following:

-    - ``s`` -- integer; the size of the polygon. For example, `s = 3`
-      returns a 3-gonal (triangular) number. `s` must be greater than 1.
+    - ``s`` -- integer greater than 1; the number of sides of the polygon

• The details from the input block about s are probably easier to read for a user on the example block as in:

EXAMPLES:

The triangular numbers::

    sage: [polygonal_number(3, n) for n in range(10)]
    [0, 1, 3, 6, 10, 15, 21, 28, 36, 45]

The square numbers::

    sage: [polygonal_number(4, n) for n in range(10)]
    [0, 1, 4, 9, 16, 25, 36, 49, 64, 81]

The pentagonal numbers::

    sage: [polygonal_number(5, n) for n in range(10)]
    [0, 1, 5, 12, 22, 35, 51, 70, 92, 117]

The hexagonal numbers::

    sage: [polygonal_number(6, n) for n in range(10)]
    [0, 1, 6, 15, 28, 45, 66, 91, 120, 153]

• It would be great if the other examples could be shortly illustrated by half a sentence or so. (Maybe something as The input is converted to an integer).

[sagetrac-git]

Changed commit from a616782 to 856d669

[sagetrac-git]

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

856d669

27986: Updated input block and example documentation

[sheareralexj]

comment:23

Thank you Jonathan, I made your suggested edits

[sagetrac-git]

Changed commit from 856d669 to cccb629

[sagetrac-git]

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

cccb629

27986: updated documentation

[kliem]

comment:25

One last thing I noticed by the the bots:

-    EXAMPLES::
+    EXAMPLES:

    The triangular numbers::

[sagetrac-git]

Changed commit from cccb629 to 1cbb3ac

[sagetrac-git]

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

1cbb3ac

27986: Updated examples block

[sheareralexj]

comment:27

Fixed

[tscrim]

comment:28

One other trivial thing:

     REFERENCES:
 
-        :wikipedia:`Polygonal_number`
+    :wikipedia:`Polygonal_number`

(or possibly with a bullet point - :wikipedia:...).

[sagetrac-git]

Changed commit from 1cbb3ac to e10fd35

[sagetrac-git]

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

e10fd35

27986: updated references block

[kliem]

comment:30

Sorry, forgot about this. It has been fine for a while now.

[vbraun]

Changed branch from u/gh-sheareralexj/add_function_to_return_the_nth_s_gonal_number to e10fd35