Add strands with different colors in BraidGroup plot

[mathzeta]

Currently, when plotting a braid, all the strands are in the same color. For plot3d(), even choosing a different color is unavailable.

The attached patch adds the ability to give each strand a different color. This is done for plot() and plot3d().

Few notes:

• I changed the default coloring scheme, so instead of blue strands, the braids are in different colors.
• The color option can be one of: single color, which is backwards-compatible; "rainbow", the default; A list or a tuple of colors.
• Some of the plot options are "global" for the entire plot (e.g. aspect ratio and axes), but some should be "local" for a specific strand (e.g. color, thickness or alpha). Maybe there should be another ticket for this, as I just needed different colored strands.
• When testing if the color is a list or a tuple I used the idiom isinstance(color, (list, tuple)) which is of prevalent use in Sage. Should we use isinstance(color, collections.Sequence) instead, with the downside that we need to check isinstance(color, types.StringTypes) first?

Two examples:

B6.<a,b,c,d,e> = BraidGroup(6)
z = a^-1*b*c^3*e^-2*a*b^2*a^-3*d^5*c*a*b*c*d*e^2*d^-1*c^-1*b^-1*a^-1
bp1 = z.plot(orientation="left-right")

from sage.plot import colors
B3.<f,g> = BraidGroup(3)
z2 = g^-1*f^2
bp2 = z2.plot(orientation="top-bottom",
            thickness=4,
            color=[colors.red.lighter(), colors.red, colors.red.darker()])

Apply:

• attachment: trac_14533_braid.patch
• attachment: trac_14533_braid-review-fc.patch
• attachment: trac_14533_braid2.patch

Component: group theory

Keywords: braid group, plot

Author: Tomer Bauer

Reviewer: Frédéric Chapoton

Merged: sage-5.10.beta3

Issue created by migration from https://trac.sagemath.org/ticket/14533

[mathzeta]

Attachment: trac_14533_braid.patch.gz

Attachment: colored_braid.png

A braid with different colored strands

[mathzeta]

Attachment: red_braid.png

A braid with different colored red strands

[fchapoton]

Reviewer: Frédéric Chapoton

[fchapoton]

comment:2

looks good to me. If you are happy with my review (add test and removes some unused imports) then you can set a positive review

[fchapoton]

comment:3

Attachment: trac_14533_braid-review-fc.patch.gz

[mathzeta]

Attachment: trac_14533_braid2.patch.gz

[mathzeta]

Author: Tomer Bauer

[mathzeta]

comment:6

Replying to @fchapoton:

looks good to me. If you are happy with my review (add test and removes some unused imports) then you can set a positive review

Thanks for your review. I had a trivial whitespace nitpick I added in attachment: trac_14533_braid2.patch. I think it's OK now.

This is new to me; Who should set the review status now?

[fchapoton]

comment:7

well, there is no rule, as far as I know, but maybe not the author of the "latest patch"..

Anyway, looks good to me, positive review !

[jdemeyer]

Merged: sage-5.10.beta3