Illustrating permutations as braided group - TiKZ-PGF
3
I would like to illustrate the permutation group using the braid package in TikZ-PGF, such as this image (from Wikipedia):
In fact I would like to illustrate the permutation group for N = 3, which should have 6 total configurations. Having followed the example provided, I so far have:
documentclass[tikz]{standalone}
usepackage{pgfplots}
usepackage{braids}
pgfplotsset{compat=newest}
begin{document}
begin{tikzpicture}
braid[style strands={1}{red},style
strands={2}{blue},style strands={3}{green}] (TEST2) at (5,0) s_1
s_3^{-1} s_1 s_2^{−1} s_1 s_2^{−1};
end{tikzpicture}
end{document}
However, I am finding it difficult to understand how to change the ordering. Any help would be appreciated.
tikz-pgf braids
asked Oct 17 '18 at 1:55
SidSid
694314
add a comment |
3
I would like to illustrate the permutation group using the braid package in TikZ-PGF, such as this image (from Wikipedia):
In fact I would like to illustrate the permutation group for N = 3, which should have 6 total configurations. Having followed the example provided, I so far have:
documentclass[tikz]{standalone}
usepackage{pgfplots}
usepackage{braids}
pgfplotsset{compat=newest}
begin{document}
begin{tikzpicture}
braid[style strands={1}{red},style
strands={2}{blue},style strands={3}{green}] (TEST2) at (5,0) s_1
s_3^{-1} s_1 s_2^{−1} s_1 s_2^{−1};
end{tikzpicture}
end{document}
However, I am finding it difficult to understand how to change the ordering. Any help would be appreciated.
tikz-pgf braids
asked Oct 17 '18 at 1:55
SidSid
694314
1
@marmot, there is a documentation forknots(mirrors.ibiblio.org/CTAN/graphics/pgf/contrib/spath3/knots.pdf) written by the same author as the braids package (Andrew Stacey). The braids don't have any knots, but that's all I know. I'll update the MWE.
– Sid
Oct 17 '18 at 2:39
@marmot, alsopgfplotsis required
– Sid
Oct 17 '18 at 2:43
On my machine it runs withoutusepackage{pgfplots}.
– marmot
Oct 17 '18 at 2:49
@Sid, maybe the answer and package from this question: (tex.stackexchange.com/questions/32125/braid-diagrams-in-tikz) could be useful
– Luis Turcio
Oct 18 '18 at 17:26
add a comment |
3
3
3
1
I would like to illustrate the permutation group using the braid package in TikZ-PGF, such as this image (from Wikipedia):
In fact I would like to illustrate the permutation group for N = 3, which should have 6 total configurations. Having followed the example provided, I so far have:
documentclass[tikz]{standalone}
usepackage{pgfplots}
usepackage{braids}
pgfplotsset{compat=newest}
begin{document}
begin{tikzpicture}
braid[style strands={1}{red},style
strands={2}{blue},style strands={3}{green}] (TEST2) at (5,0) s_1
s_3^{-1} s_1 s_2^{−1} s_1 s_2^{−1};
end{tikzpicture}
end{document}
However, I am finding it difficult to understand how to change the ordering. Any help would be appreciated.
tikz-pgf braids
asked Oct 17 '18 at 1:55
SidSid
694314
I would like to illustrate the permutation group using the braid package in TikZ-PGF, such as this image (from Wikipedia):
In fact I would like to illustrate the permutation group for N = 3, which should have 6 total configurations. Having followed the example provided, I so far have:
documentclass[tikz]{standalone}
usepackage{pgfplots}
usepackage{braids}
pgfplotsset{compat=newest}
begin{document}
begin{tikzpicture}
braid[style strands={1}{red},style
strands={2}{blue},style strands={3}{green}] (TEST2) at (5,0) s_1
s_3^{-1} s_1 s_2^{−1} s_1 s_2^{−1};
end{tikzpicture}
end{document}
However, I am finding it difficult to understand how to change the ordering. Any help would be appreciated.
tikz-pgf braids
tikz-pgf braids
asked Oct 17 '18 at 1:55
SidSid
694314
asked Oct 17 '18 at 1:55
SidSid
694314
edited Oct 17 '18 at 2:43
Sid
asked Oct 17 '18 at 1:55
SidSid
694314
asked Oct 17 '18 at 1:55
SidSid
694314
asked Oct 17 '18 at 1:55
SidSid
694314
694314
1
@marmot, there is a documentation forknots(mirrors.ibiblio.org/CTAN/graphics/pgf/contrib/spath3/knots.pdf) written by the same author as the braids package (Andrew Stacey). The braids don't have any knots, but that's all I know. I'll update the MWE.
– Sid
Oct 17 '18 at 2:39
@marmot, alsopgfplotsis required
– Sid
Oct 17 '18 at 2:43
On my machine it runs withoutusepackage{pgfplots}.
– marmot
Oct 17 '18 at 2:49
@Sid, maybe the answer and package from this question: (tex.stackexchange.com/questions/32125/braid-diagrams-in-tikz) could be useful
– Luis Turcio
Oct 18 '18 at 17:26
add a comment |
1
@marmot, there is a documentation forknots(mirrors.ibiblio.org/CTAN/graphics/pgf/contrib/spath3/knots.pdf) written by the same author as the braids package (Andrew Stacey). The braids don't have any knots, but that's all I know. I'll update the MWE.
– Sid
Oct 17 '18 at 2:39
@marmot, alsopgfplotsis required
– Sid
Oct 17 '18 at 2:43
On my machine it runs withoutusepackage{pgfplots}.
– marmot
Oct 17 '18 at 2:49
@Sid, maybe the answer and package from this question: (tex.stackexchange.com/questions/32125/braid-diagrams-in-tikz) could be useful
– Luis Turcio
Oct 18 '18 at 17:26
1
1
@marmot, there is a documentation for
knots (mirrors.ibiblio.org/CTAN/graphics/pgf/contrib/spath3/knots.pdf) written by the same author as the braids package (Andrew Stacey). The braids don't have any knots, but that's all I know. I'll update the MWE.– Sid
Oct 17 '18 at 2:39
@marmot, there is a documentation for
knots (mirrors.ibiblio.org/CTAN/graphics/pgf/contrib/spath3/knots.pdf) written by the same author as the braids package (Andrew Stacey). The braids don't have any knots, but that's all I know. I'll update the MWE.– Sid
Oct 17 '18 at 2:39
@marmot, also
pgfplots is required– Sid
Oct 17 '18 at 2:43
@marmot, also
pgfplots is required– Sid
Oct 17 '18 at 2:43
On my machine it runs without
usepackage{pgfplots}.– marmot
Oct 17 '18 at 2:49
On my machine it runs without
usepackage{pgfplots}.– marmot
Oct 17 '18 at 2:49
@Sid, maybe the answer and package from this question: (tex.stackexchange.com/questions/32125/braid-diagrams-in-tikz) could be useful
– Luis Turcio
Oct 18 '18 at 17:26
@Sid, maybe the answer and package from this question: (tex.stackexchange.com/questions/32125/braid-diagrams-in-tikz) could be useful
– Luis Turcio
Oct 18 '18 at 17:26
add a comment |
1 Answer
1
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3
My apologies for being a bit late to the party, but here's the permutations of 3 objects represented as braids using the braids package.
documentclass[tikz,border=1cm]{standalone}
%url{https://tex.stackexchange.com/q/455488/86}
usepackage{tikz}
usepackage{braids}
begin{document}
begin{tikzpicture}[
/pgf/braid/.cd,
style strands={1}{red},
style strands={2}{blue},
style strands={3}{green},
number of strands=3
]
braid (identity) at (0,0) 1 1 1;
node at ([yshift=-1cm]identity-rev-2-e) {Identity};
braid (123) at ([xshift=2cm]identity-3-s) 1 s_2^{-1} s_1;
node at ([yshift=-1cm]123-rev-2-e) {((123))};
braid (321) at ([xshift=2cm]123-3-s) 1 s_1^{-1} s_2;
node at ([yshift=-1cm]321-rev-2-e) {((321))};
braid (12) at ([yshift=-2cm]identity-rev-1-e) 1 s_1^{-1} 1;
node at ([yshift=-1cm]12-rev-2-e) {((12))};
braid (23) at ([yshift=-2cm]123-rev-1-e) 1 s_2 1;
node at ([yshift=-1cm]23-rev-2-e) {((23))};
braid (31) at ([yshift=-2cm]321-rev-1-e) s_1^{-1} s_2 s_1^{-1};
node at ([yshift=-1cm]31-rev-2-e) {((31))};
end{tikzpicture}
end{document}
Obviously, I had free choice on the over-under crossings.
Result:
answered Mar 9 at 10:19
Loop SpaceLoop Space
113k29306609
I should note that this uses the more recent version of the braids package which isn't as yet available on CTAN (but is on github).
– Loop Space
Mar 9 at 10:27
Better late than never ;) Is there some user manual? I don't get the syntax for this but it's exactly what I wanted.
– Sid
Mar 14 at 3:06
add a comment |
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1 Answer
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1 Answer
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3
My apologies for being a bit late to the party, but here's the permutations of 3 objects represented as braids using the braids package.
documentclass[tikz,border=1cm]{standalone}
%url{https://tex.stackexchange.com/q/455488/86}
usepackage{tikz}
usepackage{braids}
begin{document}
begin{tikzpicture}[
/pgf/braid/.cd,
style strands={1}{red},
style strands={2}{blue},
style strands={3}{green},
number of strands=3
]
braid (identity) at (0,0) 1 1 1;
node at ([yshift=-1cm]identity-rev-2-e) {Identity};
braid (123) at ([xshift=2cm]identity-3-s) 1 s_2^{-1} s_1;
node at ([yshift=-1cm]123-rev-2-e) {((123))};
braid (321) at ([xshift=2cm]123-3-s) 1 s_1^{-1} s_2;
node at ([yshift=-1cm]321-rev-2-e) {((321))};
braid (12) at ([yshift=-2cm]identity-rev-1-e) 1 s_1^{-1} 1;
node at ([yshift=-1cm]12-rev-2-e) {((12))};
braid (23) at ([yshift=-2cm]123-rev-1-e) 1 s_2 1;
node at ([yshift=-1cm]23-rev-2-e) {((23))};
braid (31) at ([yshift=-2cm]321-rev-1-e) s_1^{-1} s_2 s_1^{-1};
node at ([yshift=-1cm]31-rev-2-e) {((31))};
end{tikzpicture}
end{document}
Obviously, I had free choice on the over-under crossings.
Result:
answered Mar 9 at 10:19
Loop SpaceLoop Space
113k29306609
I should note that this uses the more recent version of the braids package which isn't as yet available on CTAN (but is on github).
– Loop Space
Mar 9 at 10:27
Better late than never ;) Is there some user manual? I don't get the syntax for this but it's exactly what I wanted.
– Sid
Mar 14 at 3:06
add a comment |
3
My apologies for being a bit late to the party, but here's the permutations of 3 objects represented as braids using the braids package.
documentclass[tikz,border=1cm]{standalone}
%url{https://tex.stackexchange.com/q/455488/86}
usepackage{tikz}
usepackage{braids}
begin{document}
begin{tikzpicture}[
/pgf/braid/.cd,
style strands={1}{red},
style strands={2}{blue},
style strands={3}{green},
number of strands=3
]
braid (identity) at (0,0) 1 1 1;
node at ([yshift=-1cm]identity-rev-2-e) {Identity};
braid (123) at ([xshift=2cm]identity-3-s) 1 s_2^{-1} s_1;
node at ([yshift=-1cm]123-rev-2-e) {((123))};
braid (321) at ([xshift=2cm]123-3-s) 1 s_1^{-1} s_2;
node at ([yshift=-1cm]321-rev-2-e) {((321))};
braid (12) at ([yshift=-2cm]identity-rev-1-e) 1 s_1^{-1} 1;
node at ([yshift=-1cm]12-rev-2-e) {((12))};
braid (23) at ([yshift=-2cm]123-rev-1-e) 1 s_2 1;
node at ([yshift=-1cm]23-rev-2-e) {((23))};
braid (31) at ([yshift=-2cm]321-rev-1-e) s_1^{-1} s_2 s_1^{-1};
node at ([yshift=-1cm]31-rev-2-e) {((31))};
end{tikzpicture}
end{document}
Obviously, I had free choice on the over-under crossings.
Result:
answered Mar 9 at 10:19
Loop SpaceLoop Space
113k29306609
I should note that this uses the more recent version of the braids package which isn't as yet available on CTAN (but is on github).
– Loop Space
Mar 9 at 10:27
Better late than never ;) Is there some user manual? I don't get the syntax for this but it's exactly what I wanted.
– Sid
Mar 14 at 3:06
add a comment |
3
3
3
My apologies for being a bit late to the party, but here's the permutations of 3 objects represented as braids using the braids package.
documentclass[tikz,border=1cm]{standalone}
%url{https://tex.stackexchange.com/q/455488/86}
usepackage{tikz}
usepackage{braids}
begin{document}
begin{tikzpicture}[
/pgf/braid/.cd,
style strands={1}{red},
style strands={2}{blue},
style strands={3}{green},
number of strands=3
]
braid (identity) at (0,0) 1 1 1;
node at ([yshift=-1cm]identity-rev-2-e) {Identity};
braid (123) at ([xshift=2cm]identity-3-s) 1 s_2^{-1} s_1;
node at ([yshift=-1cm]123-rev-2-e) {((123))};
braid (321) at ([xshift=2cm]123-3-s) 1 s_1^{-1} s_2;
node at ([yshift=-1cm]321-rev-2-e) {((321))};
braid (12) at ([yshift=-2cm]identity-rev-1-e) 1 s_1^{-1} 1;
node at ([yshift=-1cm]12-rev-2-e) {((12))};
braid (23) at ([yshift=-2cm]123-rev-1-e) 1 s_2 1;
node at ([yshift=-1cm]23-rev-2-e) {((23))};
braid (31) at ([yshift=-2cm]321-rev-1-e) s_1^{-1} s_2 s_1^{-1};
node at ([yshift=-1cm]31-rev-2-e) {((31))};
end{tikzpicture}
end{document}
Obviously, I had free choice on the over-under crossings.
Result:
answered Mar 9 at 10:19
Loop SpaceLoop Space
113k29306609
My apologies for being a bit late to the party, but here's the permutations of 3 objects represented as braids using the braids package.
documentclass[tikz,border=1cm]{standalone}
%url{https://tex.stackexchange.com/q/455488/86}
usepackage{tikz}
usepackage{braids}
begin{document}
begin{tikzpicture}[
/pgf/braid/.cd,
style strands={1}{red},
style strands={2}{blue},
style strands={3}{green},
number of strands=3
]
braid (identity) at (0,0) 1 1 1;
node at ([yshift=-1cm]identity-rev-2-e) {Identity};
braid (123) at ([xshift=2cm]identity-3-s) 1 s_2^{-1} s_1;
node at ([yshift=-1cm]123-rev-2-e) {((123))};
braid (321) at ([xshift=2cm]123-3-s) 1 s_1^{-1} s_2;
node at ([yshift=-1cm]321-rev-2-e) {((321))};
braid (12) at ([yshift=-2cm]identity-rev-1-e) 1 s_1^{-1} 1;
node at ([yshift=-1cm]12-rev-2-e) {((12))};
braid (23) at ([yshift=-2cm]123-rev-1-e) 1 s_2 1;
node at ([yshift=-1cm]23-rev-2-e) {((23))};
braid (31) at ([yshift=-2cm]321-rev-1-e) s_1^{-1} s_2 s_1^{-1};
node at ([yshift=-1cm]31-rev-2-e) {((31))};
end{tikzpicture}
end{document}
Obviously, I had free choice on the over-under crossings.
Result:
answered Mar 9 at 10:19
Loop SpaceLoop Space
113k29306609
answered Mar 9 at 10:19
Loop SpaceLoop Space
113k29306609
answered Mar 9 at 10:19
Loop SpaceLoop Space
113k29306609
answered Mar 9 at 10:19
Loop SpaceLoop Space
113k29306609
113k29306609
I should note that this uses the more recent version of the braids package which isn't as yet available on CTAN (but is on github).
– Loop Space
Mar 9 at 10:27
Better late than never ;) Is there some user manual? I don't get the syntax for this but it's exactly what I wanted.
– Sid
Mar 14 at 3:06
add a comment |
I should note that this uses the more recent version of the braids package which isn't as yet available on CTAN (but is on github).
– Loop Space
Mar 9 at 10:27
Better late than never ;) Is there some user manual? I don't get the syntax for this but it's exactly what I wanted.
– Sid
Mar 14 at 3:06
I should note that this uses the more recent version of the braids package which isn't as yet available on CTAN (but is on github).
– Loop Space
Mar 9 at 10:27
I should note that this uses the more recent version of the braids package which isn't as yet available on CTAN (but is on github).
– Loop Space
Mar 9 at 10:27
Better late than never ;) Is there some user manual? I don't get the syntax for this but it's exactly what I wanted.
– Sid
Mar 14 at 3:06
Better late than never ;) Is there some user manual? I don't get the syntax for this but it's exactly what I wanted.
– Sid
Mar 14 at 3:06
add a comment |
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1
@marmot, there is a documentation for
knots(mirrors.ibiblio.org/CTAN/graphics/pgf/contrib/spath3/knots.pdf) written by the same author as the braids package (Andrew Stacey). The braids don't have any knots, but that's all I know. I'll update the MWE.– Sid
Oct 17 '18 at 2:39
@marmot, also
pgfplotsis required– Sid
Oct 17 '18 at 2:43
On my machine it runs without
usepackage{pgfplots}.– marmot
Oct 17 '18 at 2:49
@Sid, maybe the answer and package from this question: (tex.stackexchange.com/questions/32125/braid-diagrams-in-tikz) could be useful
– Luis Turcio
Oct 18 '18 at 17:26