Studies of Euler diagrams/dukeli NP/keyneg

dummy

In each row the same places are negated. I.e. circles with spikes on the outside are in the same position.
E.g. in row 3 the negator is always in the first two positions. I.e. the two circles on the left have spikes on the outside.


(0, 1, 2, 3)	(1, 0, 2, 3)	(0, 2, 1, 3)	(2, 0, 1, 3)	(1, 2, 0, 3)	(2, 1, 0, 3)	(0, 1, 3, 2)	(1, 0, 3, 2)	(0, 3, 1, 2)	(3, 0, 1, 2)	(1, 3, 0, 2)	(3, 1, 0, 2)	(0, 2, 3, 1)	(2, 0, 3, 1)	(0, 3, 2, 1)	(3, 0, 2, 1)	(2, 3, 0, 1)	(3, 2, 0, 1)	(1, 2, 3, 0)	(2, 1, 3, 0)	(1, 3, 2, 0)	(3, 1, 2, 0)	(2, 3, 1, 0)	(3, 2, 1, 0)
(~0, 1, 2, 3)	(~1, 0, 2, 3)	(~0, 2, 1, 3)	(~2, 0, 1, 3)	(~1, 2, 0, 3)	(~2, 1, 0, 3)	(~0, 1, 3, 2)	(~1, 0, 3, 2)	(~0, 3, 1, 2)	(~3, 0, 1, 2)	(~1, 3, 0, 2)	(~3, 1, 0, 2)	(~0, 2, 3, 1)	(~2, 0, 3, 1)	(~0, 3, 2, 1)	(~3, 0, 2, 1)	(~2, 3, 0, 1)	(~3, 2, 0, 1)	(~1, 2, 3, 0)	(~2, 1, 3, 0)	(~1, 3, 2, 0)	(~3, 1, 2, 0)	(~2, 3, 1, 0)	(~3, 2, 1, 0)
(0, ~1, 2, 3)	(1, ~0, 2, 3)	(0, ~2, 1, 3)	(2, ~0, 1, 3)	(1, ~2, 0, 3)	(2, ~1, 0, 3)	(0, ~1, 3, 2)	(1, ~0, 3, 2)	(0, ~3, 1, 2)	(3, ~0, 1, 2)	(1, ~3, 0, 2)	(3, ~1, 0, 2)	(0, ~2, 3, 1)	(2, ~0, 3, 1)	(0, ~3, 2, 1)	(3, ~0, 2, 1)	(2, ~3, 0, 1)	(3, ~2, 0, 1)	(1, ~2, 3, 0)	(2, ~1, 3, 0)	(1, ~3, 2, 0)	(3, ~1, 2, 0)	(2, ~3, 1, 0)	(3, ~2, 1, 0)
(~0, ~1, 2, 3)	(~1, ~0, 2, 3)	(~0, ~2, 1, 3)	(~2, ~0, 1, 3)	(~1, ~2, 0, 3)	(~2, ~1, 0, 3)	(~0, ~1, 3, 2)	(~1, ~0, 3, 2)	(~0, ~3, 1, 2)	(~3, ~0, 1, 2)	(~1, ~3, 0, 2)	(~3, ~1, 0, 2)	(~0, ~2, 3, 1)	(~2, ~0, 3, 1)	(~0, ~3, 2, 1)	(~3, ~0, 2, 1)	(~2, ~3, 0, 1)	(~3, ~2, 0, 1)	(~1, ~2, 3, 0)	(~2, ~1, 3, 0)	(~1, ~3, 2, 0)	(~3, ~1, 2, 0)	(~2, ~3, 1, 0)	(~3, ~2, 1, 0)
(0, 1, ~2, 3)	(1, 0, ~2, 3)	(0, 2, ~1, 3)	(2, 0, ~1, 3)	(1, 2, ~0, 3)	(2, 1, ~0, 3)	(0, 1, ~3, 2)	(1, 0, ~3, 2)	(0, 3, ~1, 2)	(3, 0, ~1, 2)	(1, 3, ~0, 2)	(3, 1, ~0, 2)	(0, 2, ~3, 1)	(2, 0, ~3, 1)	(0, 3, ~2, 1)	(3, 0, ~2, 1)	(2, 3, ~0, 1)	(3, 2, ~0, 1)	(1, 2, ~3, 0)	(2, 1, ~3, 0)	(1, 3, ~2, 0)	(3, 1, ~2, 0)	(2, 3, ~1, 0)	(3, 2, ~1, 0)
(~0, 1, ~2, 3)	(~1, 0, ~2, 3)	(~0, 2, ~1, 3)	(~2, 0, ~1, 3)	(~1, 2, ~0, 3)	(~2, 1, ~0, 3)	(~0, 1, ~3, 2)	(~1, 0, ~3, 2)	(~0, 3, ~1, 2)	(~3, 0, ~1, 2)	(~1, 3, ~0, 2)	(~3, 1, ~0, 2)	(~0, 2, ~3, 1)	(~2, 0, ~3, 1)	(~0, 3, ~2, 1)	(~3, 0, ~2, 1)	(~2, 3, ~0, 1)	(~3, 2, ~0, 1)	(~1, 2, ~3, 0)	(~2, 1, ~3, 0)	(~1, 3, ~2, 0)	(~3, 1, ~2, 0)	(~2, 3, ~1, 0)	(~3, 2, ~1, 0)
(0, ~1, ~2, 3)	(1, ~0, ~2, 3)	(0, ~2, ~1, 3)	(2, ~0, ~1, 3)	(1, ~2, ~0, 3)	(2, ~1, ~0, 3)	(0, ~1, ~3, 2)	(1, ~0, ~3, 2)	(0, ~3, ~1, 2)	(3, ~0, ~1, 2)	(1, ~3, ~0, 2)	(3, ~1, ~0, 2)	(0, ~2, ~3, 1)	(2, ~0, ~3, 1)	(0, ~3, ~2, 1)	(3, ~0, ~2, 1)	(2, ~3, ~0, 1)	(3, ~2, ~0, 1)	(1, ~2, ~3, 0)	(2, ~1, ~3, 0)	(1, ~3, ~2, 0)	(3, ~1, ~2, 0)	(2, ~3, ~1, 0)	(3, ~2, ~1, 0)
(~0, ~1, ~2, 3)	(~1, ~0, ~2, 3)	(~0, ~2, ~1, 3)	(~2, ~0, ~1, 3)	(~1, ~2, ~0, 3)	(~2, ~1, ~0, 3)	(~0, ~1, ~3, 2)	(~1, ~0, ~3, 2)	(~0, ~3, ~1, 2)	(~3, ~0, ~1, 2)	(~1, ~3, ~0, 2)	(~3, ~1, ~0, 2)	(~0, ~2, ~3, 1)	(~2, ~0, ~3, 1)	(~0, ~3, ~2, 1)	(~3, ~0, ~2, 1)	(~2, ~3, ~0, 1)	(~3, ~2, ~0, 1)	(~1, ~2, ~3, 0)	(~2, ~1, ~3, 0)	(~1, ~3, ~2, 0)	(~3, ~1, ~2, 0)	(~2, ~3, ~1, 0)	(~3, ~2, ~1, 0)
(0, 1, 2, ~3)	(1, 0, 2, ~3)	(0, 2, 1, ~3)	(2, 0, 1, ~3)	(1, 2, 0, ~3)	(2, 1, 0, ~3)	(0, 1, 3, ~2)	(1, 0, 3, ~2)	(0, 3, 1, ~2)	(3, 0, 1, ~2)	(1, 3, 0, ~2)	(3, 1, 0, ~2)	(0, 2, 3, ~1)	(2, 0, 3, ~1)	(0, 3, 2, ~1)	(3, 0, 2, ~1)	(2, 3, 0, ~1)	(3, 2, 0, ~1)	(1, 2, 3, ~0)	(2, 1, 3, ~0)	(1, 3, 2, ~0)	(3, 1, 2, ~0)	(2, 3, 1, ~0)	(3, 2, 1, ~0)
(~0, 1, 2, ~3)	(~1, 0, 2, ~3)	(~0, 2, 1, ~3)	(~2, 0, 1, ~3)	(~1, 2, 0, ~3)	(~2, 1, 0, ~3)	(~0, 1, 3, ~2)	(~1, 0, 3, ~2)	(~0, 3, 1, ~2)	(~3, 0, 1, ~2)	(~1, 3, 0, ~2)	(~3, 1, 0, ~2)	(~0, 2, 3, ~1)	(~2, 0, 3, ~1)	(~0, 3, 2, ~1)	(~3, 0, 2, ~1)	(~2, 3, 0, ~1)	(~3, 2, 0, ~1)	(~1, 2, 3, ~0)	(~2, 1, 3, ~0)	(~1, 3, 2, ~0)	(~3, 1, 2, ~0)	(~2, 3, 1, ~0)	(~3, 2, 1, ~0)
(0, ~1, 2, ~3)	(1, ~0, 2, ~3)	(0, ~2, 1, ~3)	(2, ~0, 1, ~3)	(1, ~2, 0, ~3)	(2, ~1, 0, ~3)	(0, ~1, 3, ~2)	(1, ~0, 3, ~2)	(0, ~3, 1, ~2)	(3, ~0, 1, ~2)	(1, ~3, 0, ~2)	(3, ~1, 0, ~2)	(0, ~2, 3, ~1)	(2, ~0, 3, ~1)	(0, ~3, 2, ~1)	(3, ~0, 2, ~1)	(2, ~3, 0, ~1)	(3, ~2, 0, ~1)	(1, ~2, 3, ~0)	(2, ~1, 3, ~0)	(1, ~3, 2, ~0)	(3, ~1, 2, ~0)	(2, ~3, 1, ~0)	(3, ~2, 1, ~0)
(~0, ~1, 2, ~3)	(~1, ~0, 2, ~3)	(~0, ~2, 1, ~3)	(~2, ~0, 1, ~3)	(~1, ~2, 0, ~3)	(~2, ~1, 0, ~3)	(~0, ~1, 3, ~2)	(~1, ~0, 3, ~2)	(~0, ~3, 1, ~2)	(~3, ~0, 1, ~2)	(~1, ~3, 0, ~2)	(~3, ~1, 0, ~2)	(~0, ~2, 3, ~1)	(~2, ~0, 3, ~1)	(~0, ~3, 2, ~1)	(~3, ~0, 2, ~1)	(~2, ~3, 0, ~1)	(~3, ~2, 0, ~1)	(~1, ~2, 3, ~0)	(~2, ~1, 3, ~0)	(~1, ~3, 2, ~0)	(~3, ~1, 2, ~0)	(~2, ~3, 1, ~0)	(~3, ~2, 1, ~0)
(0, 1, ~2, ~3)	(1, 0, ~2, ~3)	(0, 2, ~1, ~3)	(2, 0, ~1, ~3)	(1, 2, ~0, ~3)	(2, 1, ~0, ~3)	(0, 1, ~3, ~2)	(1, 0, ~3, ~2)	(0, 3, ~1, ~2)	(3, 0, ~1, ~2)	(1, 3, ~0, ~2)	(3, 1, ~0, ~2)	(0, 2, ~3, ~1)	(2, 0, ~3, ~1)	(0, 3, ~2, ~1)	(3, 0, ~2, ~1)	(2, 3, ~0, ~1)	(3, 2, ~0, ~1)	(1, 2, ~3, ~0)	(2, 1, ~3, ~0)	(1, 3, ~2, ~0)	(3, 1, ~2, ~0)	(2, 3, ~1, ~0)	(3, 2, ~1, ~0)
(~0, 1, ~2, ~3)	(~1, 0, ~2, ~3)	(~0, 2, ~1, ~3)	(~2, 0, ~1, ~3)	(~1, 2, ~0, ~3)	(~2, 1, ~0, ~3)	(~0, 1, ~3, ~2)	(~1, 0, ~3, ~2)	(~0, 3, ~1, ~2)	(~3, 0, ~1, ~2)	(~1, 3, ~0, ~2)	(~3, 1, ~0, ~2)	(~0, 2, ~3, ~1)	(~2, 0, ~3, ~1)	(~0, 3, ~2, ~1)	(~3, 0, ~2, ~1)	(~2, 3, ~0, ~1)	(~3, 2, ~0, ~1)	(~1, 2, ~3, ~0)	(~2, 1, ~3, ~0)	(~1, 3, ~2, ~0)	(~3, 1, ~2, ~0)	(~2, 3, ~1, ~0)	(~3, 2, ~1, ~0)
(0, ~1, ~2, ~3)	(1, ~0, ~2, ~3)	(0, ~2, ~1, ~3)	(2, ~0, ~1, ~3)	(1, ~2, ~0, ~3)	(2, ~1, ~0, ~3)	(0, ~1, ~3, ~2)	(1, ~0, ~3, ~2)	(0, ~3, ~1, ~2)	(3, ~0, ~1, ~2)	(1, ~3, ~0, ~2)	(3, ~1, ~0, ~2)	(0, ~2, ~3, ~1)	(2, ~0, ~3, ~1)	(0, ~3, ~2, ~1)	(3, ~0, ~2, ~1)	(2, ~3, ~0, ~1)	(3, ~2, ~0, ~1)	(1, ~2, ~3, ~0)	(2, ~1, ~3, ~0)	(1, ~3, ~2, ~0)	(3, ~1, ~2, ~0)	(2, ~3, ~1, ~0)	(3, ~2, ~1, ~0)
(~0, ~1, ~2, ~3)	(~1, ~0, ~2, ~3)	(~0, ~2, ~1, ~3)	(~2, ~0, ~1, ~3)	(~1, ~2, ~0, ~3)	(~2, ~1, ~0, ~3)	(~0, ~1, ~3, ~2)	(~1, ~0, ~3, ~2)	(~0, ~3, ~1, ~2)	(~3, ~0, ~1, ~2)	(~1, ~3, ~0, ~2)	(~3, ~1, ~0, ~2)	(~0, ~2, ~3, ~1)	(~2, ~0, ~3, ~1)	(~0, ~3, ~2, ~1)	(~3, ~0, ~2, ~1)	(~2, ~3, ~0, ~1)	(~3, ~2, ~0, ~1)	(~1, ~2, ~3, ~0)	(~2, ~1, ~3, ~0)	(~1, ~3, ~2, ~0)	(~3, ~1, ~2, ~0)	(~2, ~3, ~1, ~0)	(~3, ~2, ~1, ~0)

Python fragment

from discretehelpers.boolf.examples import dukeli
from discretehelpers.sig_perm import SigPerm


for n in range(24):
    style = 'style="border-left: 3px solid #a2a9b1;"|' if n in [6, 12, 18] else ''
    print(f'!{style} [[File:Finite permutation number {n}.svg|30px]]')

for i in range(16):
    style = ' style="border-top: 3px solid #a2a9b1;"' if i in [4, 8, 12] else ''
    print(f'|-{style}')
    print(f'! [[File:Cube vertex number {i} in square.svg|30px]]')
    for n in range(24):
        sigperm = SigPerm(keyneg_index=i, perm_index=n)
        m = sigperm.binv.intval
        sequence_str = sigperm.sequence_string(4)
        mn_str = str(m).zfill(2) + ' ' + str(n).zfill(2)
        file_euler = f'[[File:EuDi; dukeli NP {mn_str} {sequence_str}.svg|175px]]'
        file_i = f'[[File:Cube vertex number {i} in square.svg|18px]]'
        file_m = f'[[File:Cube vertex number {m}.svg|18px]]'
        file_n = f'[[File:Finite permutation number {n}.svg|18px]]'
        style = 'style="border-left: 3px solid #a2a9b1;"|' if n in [6, 12, 18] else ''
        print(f'|{style}{file_euler}<br><span class="keyneg">{file_i}</span> <span class="valneg_perm">{file_m}{file_n}</span> <small class="sequence">{sequence_str}</small>')