1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
|
#!/usr/bin/perl -w
# Copyright 2020 Kevin Ryde
# This file is part of Math-PlanePath.
#
# Math-PlanePath is free software; you can redistribute it and/or modify it
# under the terms of the GNU General Public License as published by the Free
# Software Foundation; either version 3, or (at your option) any later
# version.
#
# Math-PlanePath is distributed in the hope that it will be useful, but
# WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
# or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
# for more details.
#
# You should have received a copy of the GNU General Public License along
# with Math-PlanePath. If not, see <http://www.gnu.org/licenses/>.
use 5.004;
use strict;
use List::Util 'max';
use Test;
plan tests => 8;
use lib 't','xt';
use MyTestHelpers;
BEGIN { MyTestHelpers::nowarnings(); }
use MyOEIS;
use Math::PlanePath::WunderlichSerpentine;
use Math::PlanePath::Base::Digits
'digit_split_lowtohigh', 'digit_join_lowtohigh';
use Math::PlanePath;
*_divrem_mutate = \&Math::PlanePath::_divrem_mutate;
use Math::NumSeq::PlanePathTurn;
# GP-DEFINE read("my-oeis.gp");
#------------------------------------------------------------------------------
# A163343 - X=Y diagonal in all serpentine types
foreach my $type ('alternating',
'coil',
'Peano',
'100 000 001',
'000 111 000',
'000 111 111',
) {
MyOEIS::compare_values
(anum => 'A163343',
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::WunderlichSerpentine->new
(serpentine_type => $type);
my @got;
for (my $i = 0; @got < $count; $i++) {
push @got, $path->xy_to_n($i,$i);
}
return \@got;
});
}
#------------------------------------------------------------------------------
# A332380 alternating type, diagonals across, so segment replacement
# A332381
# GP-DEFINE A332380 = OEIS_bfile_func("A332380");
# GP-DEFINE A332381 = OEIS_bfile_func("A332381");
# plothraw(vector(3^6,n,n--; A332380(n)), \
# vector(3^6,n,n--; A332381(n)), 1+8+16+32)
# poldegree(OEIS_bfile_gf("A332380"))
# poldegree(OEIS_bfile_gf("A332381"))
# midpoints
# GP-DEFINE A332380mid(n) = (A332380(n+1) + A332380(n))/2;
# GP-DEFINE A332381mid(n) = (A332381(n+1) + A332381(n))/2;
# plothraw(vector(3^6,n,n--; A332380mid(n)), \
# vector(3^6,n,n--; A332381mid(n)), 1+8+16+32)
#
# rotated
# plothraw(vector(3^6,n,n--; A332380mid(n) - A332381mid(n)), \
# vector(3^6,n,n--; A332380mid(n) + A332381mid(n)), 1+8+16+32)
#
# by func
# GP-DEFINE A332380z(n) = A332380(n) + I*A332381(n);
# vector(18,n,n--; A332380z(n))
# GP-DEFINE A332380zmid(n) = (A332380z(n+1) + A332380z(n))/2;
# my(v=vector(9^3,n,n--; (1+I)*A332380z(n))); \
# plothraw(real(v),imag(v),1+32);
# chamfered corners
# GP-DEFINE A332380_dz(n) = A332380z(n+1) - A332380z(n);
# GP-DEFINE A332380_midfrac(n,f) = A332380z(n) + A332380_dz(n)*f;
# my(l=List([])); \
# for(n=0,9^2-1, \
# listput(l,A332380_midfrac(n,.1)); \
# listput(l,A332380_midfrac(n,.9))); \
# l=Vec(l);\
# plothraw(real(l),imag(l),1+8+16+32);
# Remy Sigrist's directions code in A332380
# [R, U, L, D]=[0..3];
# p = [R, U, R, D, L, D, R, U, R];
# l=List([]); z=0; \
# for(n=0, 9^3, \
# listput(l,z); z += I^vecsum(apply(d -> p[1+d], digits(n, #p))));
# l=Vec(l);
# l=vector(#l-1,n, (1+I) * (l[n+1]+l[n])/2);
# plothraw(real(l),imag(l),1+32);
# GP-DEFINE alt_dir_table = [0,1,0,-1,-2,-1,0,1,0];
# GP-DEFINE alt_dir(n) = {
# GP-DEFINE my(v=digits(n,9));
# GP-DEFINE sum(i=1,#v, alt_dir_table[v[i]+1]);
# GP-DEFINE }
# vector(50,n,n--; alt_dir(n))
# A159195 abs values
# S_0 = [1]; morphism t -> |t-1|,t,t+1; sequence gives limiting value of S_{2n+1}
#
# vector(20,n,n--; alt_dir(n) % 4)
# not in OEIS: 0, 1, 0, 3, 2, 3, 0, 1, 0, 1, 2, 1, 0, 3, 0, 1, 2, 1, 0, 1
# GP-DEFINE \\ triplets 010 323 232 101
# GP-DEFINE \\ 121 030 303 212
# GP-DEFINE { my(table=[[0,1,0, 3,2,3, 0,1,0],
# GP-DEFINE [1,2,1, 0,3,0, 1,2,1],
# GP-DEFINE [2,3,2, 1,0,1, 2,3,2],
# GP-DEFINE [3,0,3, 2,1,2, 3,0,3]]);
# GP-DEFINE alt_dir_morphism(k) =
# GP-DEFINE my(v=[0]);
# GP-DEFINE for(i=1,k, v=concat(apply(t->table[t+1], v)));
# GP-DEFINE v;
# GP-DEFINE }
# GP-Test my(v=alt_dir_morphism(5)); \
# GP-Test #v==9^5 && vector(#v,n,n--; alt_dir(n)%4) == v
# GP-DEFINE \\ WRONG needs 8 states to make 8 different triplets
# GP-DEFINE { my(table=[[0,1,0],
# GP-DEFINE [3,2,3],
# GP-DEFINE [0,3,0],
# GP-DEFINE [1,2,1]]);
# GP-DEFINE alt_dir_morphism3(k) =
# GP-DEFINE my(v=[0]);
# GP-DEFINE for(i=1,k, v=concat(apply(t->table[t+1], v)));
# GP-DEFINE v;
# GP-DEFINE }
# alt_dir_morphism3(4) - \
# vector(81,n,n--; alt_dir(n)%4)
# my(v=alt_dir_morphism3(4)); \
# #v==9^5; vector(#v,n,n--; alt_dir(n)%4) - v
# GP-DEFINE my(table=[0,1,0,3,2,3,0,1,0]); \
# GP-DEFINE alt_dir_plus(n) = vecsum(apply(d->table[1+d], digits(n,9)));
# vector(35,n,alt_dir_plus(n))
# not in OEIS: 1,0,3,2,3,0,1,0,1,2,1,4,3,4,1,2,1,0,1,0,3,2,3,0,1,0,3,4,3,6,5,6,3,4,3
# 1, -1,-1,-1, 1,1,1, -1
# GP-DEFINE alt_turn(n) = {
# GP-DEFINE n>=1 || error();
# GP-DEFINE while(n%9==0, n/=9);
# GP-DEFINE [1, -1,-1,-1, 1,1,1, -1][n%9];
# GP-DEFINE }
# vector(35,n,alt_turn(n))
# vector(27,n,alt_turn(n)>0)
# vector(27,n,alt_turn(n)<0)
# not in OEIS: 1,-1,-1,-1,1,1,1,-1,1,1,-1,-1,-1,1,1,1,-1,-1,1,-1,-1,-1,1,1,1,-1,-1
# not A216430 parity num 2s
# not in OEIS: 1,0,0,0,1,1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0,0,1,1,1,0,0
# not in OEIS: 0,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,1,1
#--------------------
# A332380 code
# GP-DEFINE \\ A332380 by rotate and position table
# GP-DEFINE { my(table=[[1,0], [I,1], [1,1+I],
# GP-DEFINE [-I,2+I], [-1,2], [-I,1],
# GP-DEFINE [1,1-I], [I,2-I], [1,2]]);
# GP-DEFINE table == vector(9,n, [table[n][1], sum(i=1,n-1, table[i][1])]) \
# GP-DEFINE || error();
# GP-DEFINE A332380_compact(n) =
# GP-DEFINE my(v=digits(n,9),rot=1);
# GP-DEFINE for(i=1,#v, [rot,v[i]] = rot*table[v[i]+1]);
# GP-DEFINE fromdigits(real(v),3);
# GP-DEFINE }
# GP-Test my(g=OEIS_bfile_gf("A332380")); \
# GP-Test g == Polrev(vector(poldegree(g)+1,n,n--;A332380_compact(n)))
#
# GP-DEFINE { my(table=[[1,0], [I,1], [1,1+I],
# GP-DEFINE [-I,2+I], [-1,2], [-I,1],
# GP-DEFINE [1,1-I], [I,2-I], [1,2]]);
# GP-DEFINE A332381_compact(n) =
# GP-DEFINE my(v=digits(n,9),rot=1);
# GP-DEFINE for(i=1,#v, [rot,v[i]] = rot*table[v[i]+1]);
# GP-DEFINE fromdigits(imag(v),3);
# GP-DEFINE }
# GP-Test my(g=OEIS_bfile_gf("A332381")); \
# GP-Test g == Polrev(vector(poldegree(g)+1,n,n--;A332381_compact(n)))
#------------------------------------------------------------------------------
# A332380,A332381 serpentine 010 101 010 - N on X=Y and X=-Y diagonals
# GP-DEFINE \\ 9x, 9x+2 and 9x-6
# GP-DEFINE alt_is_leadingdiag(n) = {
# GP-DEFINE while(n, if(n%9==0, ,
# GP-DEFINE n%9==2, n-=2,
# GP-DEFINE n%9==3, n+=6,
# GP-DEFINE return(0));
# GP-DEFINE n%9==0 || error(); n/=9);
# GP-DEFINE 1;
# GP-DEFINE }
# GP-Test vector(9^5,n,n--; alt_is_leadingdiag(n)) == \
# GP-Test vector(9^5,n,n--; A332380_compact(n) == A332381_compact(n))
# for(n=0,9^2, if(alt_is_leadingdiag(n) != (A332380(n)==A332381(n)), print(n)))
# GP-DEFINE balanced_ternary_digits(n) = {
# GP-DEFINE my(l=List([]));
# GP-DEFINE while(n, my(a=n%3); if(a==2, a=-1); listput(l,a); n=(n-a)/3);
# GP-DEFINE Vecrev(l);
# GP-DEFINE }
# GP-Test /* A072998 balanced ternary -1,0,1 coded as 0,1,2 decimal digits */ \
# GP-Test /* but 0 as one 0 digit so 1, an exception to all starting 2 */ \
# GP-Test my(want=OEIS_samples("A072998")); \
# GP-Test vector(#want,n,n--; \
# GP-Test if(n==0,1, \
# GP-Test fromdigits(apply(n->n+1,balanced_ternary_digits(n))))) \
# GP-Test == want
# GP-DEFINE A072998_compact(n) = \
# GP-DEFINE fromdigits(digits(n + (3^(1+if(n,logint(2*n,3))) - 1)/2, 3));
# GP-Test my(want=OEIS_samples("A072998")); \
# GP-Test vector(#want,n,n--; A072998_compact(n)) == want
# GP-Test vector(3^7,n,n--; A072998_compact(n)) == \
# GP-Test vector(3^7,n,n--; if(n==0,1, \
# GP-Test fromdigits(apply(n->n+1,balanced_ternary_digits(n)))))
# GP-DEFINE { my(table=[-6,0,2]);
# GP-DEFINE alt_leadingdiag_by_balanced_ternary(n) =
# GP-DEFINE my(v=balanced_ternary_digits(n));
# GP-DEFINE fromdigits(apply(d->table[d+2],v), 9);
# GP-DEFINE }
# GP-Test my(v=select(alt_is_leadingdiag, [0..9^5])); \
# GP-Test #v==122 && v == vector(#v,n,n--; alt_leadingdiag_by_balanced_ternary(n))
# GP-DEFINE { my(table=[[1,0],[1,2],[2,-6],[2,0]]);
# GP-DEFINE alt_leadingdiag_by_ternary(n) =
# GP-DEFINE my(v=concat(0,digits(n,3)), c=1);
# GP-DEFINE forstep(i=#v,1,-1, [c,v[i]]=table[c+v[i]]);
# GP-DEFINE fromdigits(v,9);
# GP-DEFINE }
# GP-Test vector(3^8,n,n--; alt_leadingdiag_by_balanced_ternary(n)) == \
# GP-Test vector(3^8,n,n--; alt_leadingdiag_by_ternary(n))
# GP-DEFINE { my(table=[-6,0,2]);
# GP-DEFINE alt_leadingdiag_by_offset(n) =
# GP-DEFINE fromdigits(apply(d->table[d+1],
# GP-DEFINE digits(n + (3^(1+if(n,logint(2*n,3))) - 1)/2, 3)), 9);
# GP-DEFINE }
# GP-Test vector(3^8,n,n--; alt_leadingdiag_by_offset(n)) == \
# GP-Test vector(3^8,n,n--; alt_leadingdiag_by_ternary(n))
#------------------------------------------------------------------------------
# Coordinates - Alternating
# GP-DEFINE want_AltX = [0,0,0,1,1,1,2,2,2,2,1,0,0,1,2,2,1,0,0,0,0,1,1,1,2,2,2,3,4,5,5,4,3,3,4,5,5,5,5,4,4,4,3,3,3,3,4,5,5,4,3,3,4,5,6,6,6,7,7,7,8,8,8,8,7,6,6,7,8,8,7,6,6,6,6,7,7,7,8,8,8,8,7,6,6,7,8,8,7,6,5,5,5,4,4,4,3,3,3,2,1,0,0,1,2,2,1,0,0,0,0,1,1,1,2,2,2,3,4,5,5,4,3,3,4,5,6,6,6,7,7,7,8,8,8,8,7,6,6,7,8,8,7,6,5,5,5,4,4,4,3,3,3,2,1,0,0,1,2,2,1,0,0,0,0,1,1,1,2,2,2,2,1,0,0,1,2,2,1,0,0,0,0,1,1,1,2,2,2,3,4,5,5,4,3,3,4,5,5,5,5,4,4,4,3,3,3,3,4,5,5,4,3,3,4,5,6,6,6,7,7,7,8,8,8,8,7,6,6,7,8,8,7,6,6,6,6,7,7,7,8,8,8,9,10,11,11,10,9,9,10,11,12,12,12,13,13,13,14,14,14,15,16,17,17,16,15,15,16,17,17,17,17,16,16,16,15,15,15,14,13,12,12,13,14,14,13,12,11,11,11,10,10,10,9,9,9,9,10,11,11,10,9,9,10,11,12,12,12,13,13,13,14,14,14,15,16,17,17,16,15,15,16,17,17,17,17,16,16,16,15,15,15,15,16,17,17,16,15,15,16,17,17,17,17,16,16,16,15,15,15,14,13,12,12,13,14,14,13,12,12,12,12,13,13,13,14,14,14,14,13,12,12,13,14,14,13,12,11,11,11,10,10,10,9,9,9,9,10,11,11,10,9,9,10,11,11,11,11,10,10,10,9,9,9,9,10,11,11,10,9,9,10,11,12,12,12,13,13,13,14,14,14,15,16,17,17,16,15,15,16,17,17,17,17,16,16,16,15,15,15,14,13,12,12,13,14,14,13,12,11,11,11,10,10,10,9,9,9,9,10,11,11,10,9,9,10,11,12,12,12,13,13,13,14,14,14,15,16,17,17,16,15,15,16,17,18,18,18,19,19,19,20,20,20,20,19,18,18,19,20,20,19,18,18,18,18,19,19,19,20,20,20,21,22,23,23,22,21,21,22,23,23,23,23,22,22,22,21,21,21,21,22,23,23,22,21,21,22,23,24,24,24,25,25,25,26,26,26,26,25,24,24,25,26,26,25,24,24,24,24,25,25,25,26,26,26,26,25,24,24,25,26,26,25,24,23,23,23,22,22,22,21,21,21,20,19,18,18,19,20,20,19,18,18,18,18,19,19,19,20,20,20,21,22,23,23,22,21,21,22,23,24,24,24,25,25,25,26,26,26,26,25,24,24,25,26,26,25,24,23,23,23,22,22,22,21,21,21,20,19,18,18,19,20,20,19,18,18,18,18,19,19,19,20,20,20,20,19,18,18,19,20,20,19,18,18,18,18,19,19,19,20,20,20,21,22,23,23,22,21,21,22,23,23,23,23,22,22,22,21,21,21,21,22,23,23,22,21,21,22,23,24,24,24,25,25,25,26,26,26,26,25,24,24,25,26,26,25,24,24,24,24,25,25,25,26,26,26,26];
# GP-DEFINE want_AltY = [0,1,2,2,1,0,0,1,2,3,3,3,4,4,4,5,5,5,6,7,8,8,7,6,6,7,8,8,8,8,7,7,7,6,6,6,5,4,3,3,4,5,5,4,3,2,2,2,1,1,1,0,0,0,0,1,2,2,1,0,0,1,2,3,3,3,4,4,4,5,5,5,6,7,8,8,7,6,6,7,8,9,9,9,10,10,10,11,11,11,11,10,9,9,10,11,11,10,9,9,9,9,10,10,10,11,11,11,12,13,14,14,13,12,12,13,14,14,14,14,13,13,13,12,12,12,12,13,14,14,13,12,12,13,14,15,15,15,16,16,16,17,17,17,17,16,15,15,16,17,17,16,15,15,15,15,16,16,16,17,17,17,18,19,20,20,19,18,18,19,20,21,21,21,22,22,22,23,23,23,24,25,26,26,25,24,24,25,26,26,26,26,25,25,25,24,24,24,23,22,21,21,22,23,23,22,21,20,20,20,19,19,19,18,18,18,18,19,20,20,19,18,18,19,20,21,21,21,22,22,22,23,23,23,24,25,26,26,25,24,24,25,26,26,26,26,25,25,25,24,24,24,24,25,26,26,25,24,24,25,26,26,26,26,25,25,25,24,24,24,23,22,21,21,22,23,23,22,21,21,21,21,22,22,22,23,23,23,23,22,21,21,22,23,23,22,21,20,20,20,19,19,19,18,18,18,18,19,20,20,19,18,18,19,20,20,20,20,19,19,19,18,18,18,17,16,15,15,16,17,17,16,15,14,14,14,13,13,13,12,12,12,11,10,9,9,10,11,11,10,9,9,9,9,10,10,10,11,11,11,12,13,14,14,13,12,12,13,14,15,15,15,16,16,16,17,17,17,17,16,15,15,16,17,17,16,15,14,14,14,13,13,13,12,12,12,11,10,9,9,10,11,11,10,9,8,8,8,7,7,7,6,6,6,6,7,8,8,7,6,6,7,8,8,8,8,7,7,7,6,6,6,5,4,3,3,4,5,5,4,3,3,3,3,4,4,4,5,5,5,5,4,3,3,4,5,5,4,3,2,2,2,1,1,1,0,0,0,0,1,2,2,1,0,0,1,2,2,2,2,1,1,1,0,0,0,0,1,2,2,1,0,0,1,2,3,3,3,4,4,4,5,5,5,6,7,8,8,7,6,6,7,8,8,8,8,7,7,7,6,6,6,5,4,3,3,4,5,5,4,3,2,2,2,1,1,1,0,0,0,0,1,2,2,1,0,0,1,2,3,3,3,4,4,4,5,5,5,6,7,8,8,7,6,6,7,8,9,9,9,10,10,10,11,11,11,11,10,9,9,10,11,11,10,9,9,9,9,10,10,10,11,11,11,12,13,14,14,13,12,12,13,14,14,14,14,13,13,13,12,12,12,12,13,14,14,13,12,12,13,14,15,15,15,16,16,16,17,17,17,17,16,15,15,16,17,17,16,15,15,15,15,16,16,16,17,17,17,18,19,20,20,19,18,18,19,20,21,21,21,22,22,22,23,23,23,24,25,26,26,25,24,24,25,26,26,26,26,25,25,25,24,24,24,23,22,21,21,22,23,23,22,21,20,20,20,19,19,19,18,18,18,18,19,20,20,19,18,18,19,20,21,21,21,22,22,22,23,23,23,24,25,26,26,25,24,24,25,26,27];
# GP-DEFINE AltY(n) = {
# GP-DEFINE my(v=digits(n,9), t=Mod(0,2), k=Mod(0,2));
# GP-DEFINE for(i=1,#v, my(d=v[i], y=if(t,d\3,d%3), c=d+y);
# GP-DEFINE v[i]=if((k+=c)+t*c, 2-y, y); t+=d);
# GP-DEFINE fromdigits(v,3);
# GP-DEFINE }
# GP-DEFINE AltY(n) = {
# GP-DEFINE my(v=digits(n,9), t=Mod(0,2), k=Mod(0,2));
# GP-DEFINE for(i=1,#v, my(p=divrem(v[i],3),y);
# GP-DEFINE if(t, y=if(k, 2-p[1],p[1]); k+=p[2],
# GP-DEFINE y=if(k+=p[1], 2-p[2],p[2]));
# GP-DEFINE t+=v[i]; v[i]=y);
# GP-DEFINE fromdigits(v,3);
# GP-DEFINE }
# GP-Test vector(#want_AltY,n,n--; AltY(n)) == want_AltY
# vector(161,n,n--; AltY(n)) - want_AltY[1..161]
# vector(10,n,n--; AltY(n))
# AltY(90)
# AltY(10)
# want_AltY[10 +1]
# digits(90,9)
# divrem(1,3) == [0,1]~
# GP-Test vector(9^3,n,n--; AltY(n)) == \
# GP-Test vector(9^3,n,n--; \
# GP-Test (A332380(n) + A332380(n+1) + A332381(n) + A332381(n+1) - 1)/2)
# GP-Test vector(9^5,n,n--; AltY(n)) == \
# GP-Test vector(9^5,n,n--; \
# GP-Test (A332380_compact(n) + A332380_compact(n+1) \
# GP-Test + A332381_compact(n) + A332381_compact(n+1) - 1)/2)
# real(('x+'y*I)/(1+I)) == 'x/2 + 'y/2
# GP-DEFINE \\ arithmetic transposing
# GP-DEFINE AltX(n) = {
# GP-DEFINE my(v=digits(n,9), t=Mod(0,2), k=Mod(0,2));
# GP-DEFINE for(i=1,#v, my(d=v[i], x=if(t,d%3,d\3), c=d+x);
# GP-DEFINE v[i]=if(k+t*c, 2-x, x); k+=c; t+=d);
# GP-DEFINE fromdigits(v,3);
# GP-DEFINE }
# GP-DEFINE \\ conditional transposing
# GP-DEFINE AltX(n) = {
# GP-DEFINE my(v=digits(n,9), t=Mod(1,2), k=Mod(0,2));
# GP-DEFINE for(i=1,#v, my(p=divrem(v[i],3),x);
# GP-DEFINE if(t, x=if(k, 2-p[1],p[1]); k+=p[2],
# GP-DEFINE x=if(k+=p[1], 2-p[2],p[2]));
# GP-DEFINE t+=v[i]; v[i]=x);
# GP-DEFINE fromdigits(v,3);
# GP-DEFINE }
# GP-Test vector(#want_AltX,n,n--; AltX(n)) == want_AltX
# vector(161,n,n--; AltX(n)) - want_AltX[1..161]
# vector(10,n,n--; AltX(n))
#
# GP-Test vector(9^3,n,n--; AltX(n)) == \
# GP-Test vector(9^3,n,n--; \
# GP-Test (A332380(n) + A332380(n+1) - A332381(n) - A332381(n+1) - 1)/2)
# GP-Test vector(9^5,n,n--; AltX(n)) == \
# GP-Test vector(9^5,n,n--; \
# GP-Test (A332380_compact(n) + A332380_compact(n+1) \
# GP-Test - A332381_compact(n) - A332381_compact(n+1) - 1)/2)
# GP-DEFINE dAltX(n) = AltX(n+1) - AltX(n);
# GP-DEFINE dAltY(n) = AltY(n+1) - AltY(n);
#
# GP-Test /* divining diagonal direction from dx,dy and parity */ \
# GP-Test vector(9^3,n,n--; A332380(n)) == \
# GP-Test vector(9^3,n,n--; real( (AltX(n) + AltY(n)*I)/(1+I) - (n%2)/2) \
# GP-Test + if(n%2==1 && dAltY(n)==1, 1, \
# GP-Test n%2==1 && dAltY(n)==-1, 1, \
# GP-Test n%2==0 && dAltY(n)==1, 0, \
# GP-Test n%2==0 && dAltY(n)==-1, 1, \
# GP-Test n%2==1 && dAltX(n)==1, 1, \
# GP-Test n%2==1 && dAltX(n)==-1, 1, \
# GP-Test n%2==0 && dAltX(n)==1, 0, \
# GP-Test n%2==0 && dAltX(n)==-1, 1, \
# GP-Test 'x))
#------------------------------------------------------------------------------
# A323258 -- X coordinate, Robert Dickau's variation.
# A323259 -- Y coordinate
#
# Wunderlich serpentine "alternating", but the least significant digit of N
# which 9 points in 3x3 has a transpose along its diagonal.
#
# Occurs since the base figure is an S orientation but then it and
# subsequent bigger 3^k x 3^k blocks are assembled in N orientation.
# In all cases rotations to make the ends join up.
#
# So in an "even" block which is leading diagonal, transpose lowest ternary
# digit of x,y. Or in odd block which is opposite diagonal, complement
# 2-y,2-x.
sub xy_low_transpose {
my ($x,$y) = @_;
my $xr = _divrem_mutate($x,3);
my $yr = _divrem_mutate($y,3);
if (($x+$y)&1) {
($xr,$yr) = (2-$yr,2-$xr);
} else {
($xr,$yr) = ($yr,$xr);
}
return (3*$x+$xr, 3*$y+$yr);
}
MyOEIS::compare_values
(anum => 'A323258',
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::WunderlichSerpentine->new;
my @got;
for (my $n = $path->n_start; @got < $count; $n++) {
my ($x,$y) = $path->n_to_xy($n);
($x,$y) = xy_low_transpose($x,$y);
push @got, $y;
}
return \@got;
});
MyOEIS::compare_values
(anum => 'A323259',
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::WunderlichSerpentine->new;
my @got;
for (my $n = $path->n_start; @got < $count; $n++) {
my ($x,$y) = $path->n_to_xy($n);
($x,$y) = xy_low_transpose($x,$y);
push @got, $x;
}
return \@got;
});
# without low transpose:
# not in OEIS: 0,1,2,2,1,0,0,1,2,3,3,3,4,4,4,5,5,5,6,7,8,8,7,6,6,7,8,8,8,8,7,7,7,6,6,6,5,4,3
# not in OEIS: 0,0,0,1,1,1,2,2,2,2,1,0,0,1,2,2,1,0,0,0,0,1,1,1,2,2,2,3,4,5,5,4,3,3,4,5,5,5,5,4,4,4,3,3,3,3,4,5,5,4,3
# ~/OEIS/a323258.png
# ~/OEIS/b323258.txt
# http://robertdickau.com/wunderlich.html
# my(g=OEIS_bfile_gf("A323258")); x(n) = polcoeff(g,n);
# my(g=OEIS_bfile_gf("A323259")); y(n) = polcoeff(g,n);
# plothraw(vector(9^3+10,n,n--; x(n)), \
# vector(9^3+10,n,n--; y(n)), 1+8+16+32)
# plothraw(vector(9^4+1,n,n--; x(n)), \
# vector(9^4+1,n,n--; y(n)), 1+8+16+32)
# plothraw(vector(9^3,n, y(9*n-4)), \
# vector(9^3,n, x(9*n-4)), 1+8+16+32)
#------------------------------------------------------------------------------
exit 0;
__END__
# my $xr = $x % 3;
# my $yr = $y % 3;
# return ($x - $xr + $yr,
# $y - $yr + $xr);
# sub xy_high_transpose {
# my ($x,$y) = @_;
# my @x = digit_split_lowtohigh($x,3);
# my @y = digit_split_lowtohigh($y,3);
# my $max = max($#x,$#y);
# if ($max >= 0) {
# push @x, (0) x ($max - $#x);
# push @y, (0) x ($max - $#y);
# ($x[$max],$y[$max]) = ($y[$max],$x[$max]);
# }
# return (digit_join_lowtohigh(\@y,3),
# digit_join_lowtohigh(\@x,3));
# }
|
