Python generator for free group variable names

[sagetrac-dshurbert]

When creating free and finitely presented groups, default variable names are often ugly.

sage: F = FreeGroup(12)
sage: F
Free Group on generators {x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11}
sage: F/[F([1,2,2,1,1,4,7,-8]),F([10,10,4,-5,4,-8]) ] 
Finitely presented group < x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11 | x0*x1^2*x0^2*x3*x6*x7^-1, x9^2*x3*x4^-1*x3*x7^-1 >

Created by a utility function, the simple generator in this patch provides an easy way to consistently generate better variable names, and will be useful in creating free groups algorithmically.

Apply

• attachment: trac_14790_fpg_names.patch

CC: @rbeezer

Component: group theory

Author: Davis Shurbert

Reviewer: Rob Beezer

Merged: sage-5.12.beta0

Issue created by migration from https://trac.sagemath.org/ticket/14790

[sagetrac-dshurbert]

comment:3

Added option to specify whether or not initial iteration through alphabet appends '0' to
output string

[rbeezer]

comment:4

To test this function, first run

from sage.groups.free_group import _lexi_gen

then

lex = _lexi_gen()

then repeated use of

lex.next()

[rbeezer]

comment:5

Utility method to create generator for free group variable names,
for use when creating free groups of dynamic size.

"generator" has two meanings here (and I confused the two). Better:

Return a generator object that produces names suitable for the
generators of a free group.

2. And, flag as a keyword name is totally uninformative. Use something with some meaning. Help the reader. I'd suggest zeros=False.

3. seed is not a seed. It is a counter. Call it count or i or something else.

4. Do you really need to import "string" and use the lowercase array? The usual idiom is:

chr(ord('a') + ind)

I guess this one is a toss-up.

5. while (True): does not need parentheses.

6. Include an EXAMPLE doctest that shows a higher iteration through the alphabet, maybe show

ls = [test.next() for i in range(3*26)]
ls[2*26:3*26]

You can break the long list of output in the middle at whitespace and the test will succeed.

7. The doctest in the TESTS section is great as is, though you could put both outputs on one line:

ls[234], ls[260]

and get a pair as the output. Just more concise.

8. Changing flag inside your if/else on flag is very confusing. How about

if mwrap == 0 and not(zeros):
    name=''
else:
    name = str(mwrap)

and you can drop the line initializing name.

[sagetrac-dshurbert]

comment:6

Made changes suggested above.

[rbeezer]

comment:7

Looks good! Passes tests on 5.11.beta3. Positive review.

[rbeezer]

Reviewer: Rob Beezer

[sagetrac-dshurbert]

comment:8

Just moved count increment to top of code for ease of reader.

[rbeezer]

comment:11

Change looks good, and passes all necessary testing. So back to "positive review".

[jdemeyer]

comment:13

The patch needs a proper commit message (use hg qrefresh -e for that).

[sagetrac-dshurbert]

Replacement patch, requested changes made, added commit message

[sagetrac-dshurbert]

comment:15

Attachment: trac_14790_fpg_names.patch.gz

Just added commit message, ready for re-review.

[jdemeyer]

Merged: sage-5.12.beta0