Spaces:
Running
Running
File size: 20,189 Bytes
6a86ad5 |
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 |
from itertools import permutations
from copy import copy
from sympy.core.expr import unchanged
from sympy.core.numbers import Integer
from sympy.core.relational import Eq
from sympy.core.symbol import Symbol
from sympy.core.singleton import S
from sympy.combinatorics.permutations import \
Permutation, _af_parity, _af_rmul, _af_rmuln, AppliedPermutation, Cycle
from sympy.printing import sstr, srepr, pretty, latex
from sympy.testing.pytest import raises, warns_deprecated_sympy
rmul = Permutation.rmul
a = Symbol('a', integer=True)
def test_Permutation():
# don't auto fill 0
raises(ValueError, lambda: Permutation([1]))
p = Permutation([0, 1, 2, 3])
# call as bijective
assert [p(i) for i in range(p.size)] == list(p)
# call as operator
assert p(list(range(p.size))) == list(p)
# call as function
assert list(p(1, 2)) == [0, 2, 1, 3]
raises(TypeError, lambda: p(-1))
raises(TypeError, lambda: p(5))
# conversion to list
assert list(p) == list(range(4))
assert p.copy() == p
assert copy(p) == p
assert Permutation(size=4) == Permutation(3)
assert Permutation(Permutation(3), size=5) == Permutation(4)
# cycle form with size
assert Permutation([[1, 2]], size=4) == Permutation([[1, 2], [0], [3]])
# random generation
assert Permutation.random(2) in (Permutation([1, 0]), Permutation([0, 1]))
p = Permutation([2, 5, 1, 6, 3, 0, 4])
q = Permutation([[1], [0, 3, 5, 6, 2, 4]])
assert len({p, p}) == 1
r = Permutation([1, 3, 2, 0, 4, 6, 5])
ans = Permutation(_af_rmuln(*[w.array_form for w in (p, q, r)])).array_form
assert rmul(p, q, r).array_form == ans
# make sure no other permutation of p, q, r could have given
# that answer
for a, b, c in permutations((p, q, r)):
if (a, b, c) == (p, q, r):
continue
assert rmul(a, b, c).array_form != ans
assert p.support() == list(range(7))
assert q.support() == [0, 2, 3, 4, 5, 6]
assert Permutation(p.cyclic_form).array_form == p.array_form
assert p.cardinality == 5040
assert q.cardinality == 5040
assert q.cycles == 2
assert rmul(q, p) == Permutation([4, 6, 1, 2, 5, 3, 0])
assert rmul(p, q) == Permutation([6, 5, 3, 0, 2, 4, 1])
assert _af_rmul(p.array_form, q.array_form) == \
[6, 5, 3, 0, 2, 4, 1]
assert rmul(Permutation([[1, 2, 3], [0, 4]]),
Permutation([[1, 2, 4], [0], [3]])).cyclic_form == \
[[0, 4, 2], [1, 3]]
assert q.array_form == [3, 1, 4, 5, 0, 6, 2]
assert q.cyclic_form == [[0, 3, 5, 6, 2, 4]]
assert q.full_cyclic_form == [[0, 3, 5, 6, 2, 4], [1]]
assert p.cyclic_form == [[0, 2, 1, 5], [3, 6, 4]]
t = p.transpositions()
assert t == [(0, 5), (0, 1), (0, 2), (3, 4), (3, 6)]
assert Permutation.rmul(*[Permutation(Cycle(*ti)) for ti in (t)])
assert Permutation([1, 0]).transpositions() == [(0, 1)]
assert p**13 == p
assert q**0 == Permutation(list(range(q.size)))
assert q**-2 == ~q**2
assert q**2 == Permutation([5, 1, 0, 6, 3, 2, 4])
assert q**3 == q**2*q
assert q**4 == q**2*q**2
a = Permutation(1, 3)
b = Permutation(2, 0, 3)
I = Permutation(3)
assert ~a == a**-1
assert a*~a == I
assert a*b**-1 == a*~b
ans = Permutation(0, 5, 3, 1, 6)(2, 4)
assert (p + q.rank()).rank() == ans.rank()
assert (p + q.rank())._rank == ans.rank()
assert (q + p.rank()).rank() == ans.rank()
raises(TypeError, lambda: p + Permutation(list(range(10))))
assert (p - q.rank()).rank() == Permutation(0, 6, 3, 1, 2, 5, 4).rank()
assert p.rank() - q.rank() < 0 # for coverage: make sure mod is used
assert (q - p.rank()).rank() == Permutation(1, 4, 6, 2)(3, 5).rank()
assert p*q == Permutation(_af_rmuln(*[list(w) for w in (q, p)]))
assert p*Permutation([]) == p
assert Permutation([])*p == p
assert p*Permutation([[0, 1]]) == Permutation([2, 5, 0, 6, 3, 1, 4])
assert Permutation([[0, 1]])*p == Permutation([5, 2, 1, 6, 3, 0, 4])
pq = p ^ q
assert pq == Permutation([5, 6, 0, 4, 1, 2, 3])
assert pq == rmul(q, p, ~q)
qp = q ^ p
assert qp == Permutation([4, 3, 6, 2, 1, 5, 0])
assert qp == rmul(p, q, ~p)
raises(ValueError, lambda: p ^ Permutation([]))
assert p.commutator(q) == Permutation(0, 1, 3, 4, 6, 5, 2)
assert q.commutator(p) == Permutation(0, 2, 5, 6, 4, 3, 1)
assert p.commutator(q) == ~q.commutator(p)
raises(ValueError, lambda: p.commutator(Permutation([])))
assert len(p.atoms()) == 7
assert q.atoms() == {0, 1, 2, 3, 4, 5, 6}
assert p.inversion_vector() == [2, 4, 1, 3, 1, 0]
assert q.inversion_vector() == [3, 1, 2, 2, 0, 1]
assert Permutation.from_inversion_vector(p.inversion_vector()) == p
assert Permutation.from_inversion_vector(q.inversion_vector()).array_form\
== q.array_form
raises(ValueError, lambda: Permutation.from_inversion_vector([0, 2]))
assert Permutation(list(range(500, -1, -1))).inversions() == 125250
s = Permutation([0, 4, 1, 3, 2])
assert s.parity() == 0
_ = s.cyclic_form # needed to create a value for _cyclic_form
assert len(s._cyclic_form) != s.size and s.parity() == 0
assert not s.is_odd
assert s.is_even
assert Permutation([0, 1, 4, 3, 2]).parity() == 1
assert _af_parity([0, 4, 1, 3, 2]) == 0
assert _af_parity([0, 1, 4, 3, 2]) == 1
s = Permutation([0])
assert s.is_Singleton
assert Permutation([]).is_Empty
r = Permutation([3, 2, 1, 0])
assert (r**2).is_Identity
assert rmul(~p, p).is_Identity
assert (~p)**13 == Permutation([5, 2, 0, 4, 6, 1, 3])
assert p.max() == 6
assert p.min() == 0
q = Permutation([[6], [5], [0, 1, 2, 3, 4]])
assert q.max() == 4
assert q.min() == 0
p = Permutation([1, 5, 2, 0, 3, 6, 4])
q = Permutation([[1, 2, 3, 5, 6], [0, 4]])
assert p.ascents() == [0, 3, 4]
assert q.ascents() == [1, 2, 4]
assert r.ascents() == []
assert p.descents() == [1, 2, 5]
assert q.descents() == [0, 3, 5]
assert Permutation(r.descents()).is_Identity
assert p.inversions() == 7
# test the merge-sort with a longer permutation
big = list(p) + list(range(p.max() + 1, p.max() + 130))
assert Permutation(big).inversions() == 7
assert p.signature() == -1
assert q.inversions() == 11
assert q.signature() == -1
assert rmul(p, ~p).inversions() == 0
assert rmul(p, ~p).signature() == 1
assert p.order() == 6
assert q.order() == 10
assert (p**(p.order())).is_Identity
assert p.length() == 6
assert q.length() == 7
assert r.length() == 4
assert p.runs() == [[1, 5], [2], [0, 3, 6], [4]]
assert q.runs() == [[4], [2, 3, 5], [0, 6], [1]]
assert r.runs() == [[3], [2], [1], [0]]
assert p.index() == 8
assert q.index() == 8
assert r.index() == 3
assert p.get_precedence_distance(q) == q.get_precedence_distance(p)
assert p.get_adjacency_distance(q) == p.get_adjacency_distance(q)
assert p.get_positional_distance(q) == p.get_positional_distance(q)
p = Permutation([0, 1, 2, 3])
q = Permutation([3, 2, 1, 0])
assert p.get_precedence_distance(q) == 6
assert p.get_adjacency_distance(q) == 3
assert p.get_positional_distance(q) == 8
p = Permutation([0, 3, 1, 2, 4])
q = Permutation.josephus(4, 5, 2)
assert p.get_adjacency_distance(q) == 3
raises(ValueError, lambda: p.get_adjacency_distance(Permutation([])))
raises(ValueError, lambda: p.get_positional_distance(Permutation([])))
raises(ValueError, lambda: p.get_precedence_distance(Permutation([])))
a = [Permutation.unrank_nonlex(4, i) for i in range(5)]
iden = Permutation([0, 1, 2, 3])
for i in range(5):
for j in range(i + 1, 5):
assert a[i].commutes_with(a[j]) == \
(rmul(a[i], a[j]) == rmul(a[j], a[i]))
if a[i].commutes_with(a[j]):
assert a[i].commutator(a[j]) == iden
assert a[j].commutator(a[i]) == iden
a = Permutation(3)
b = Permutation(0, 6, 3)(1, 2)
assert a.cycle_structure == {1: 4}
assert b.cycle_structure == {2: 1, 3: 1, 1: 2}
# issue 11130
raises(ValueError, lambda: Permutation(3, size=3))
raises(ValueError, lambda: Permutation([1, 2, 0, 3], size=3))
def test_Permutation_subclassing():
# Subclass that adds permutation application on iterables
class CustomPermutation(Permutation):
def __call__(self, *i):
try:
return super().__call__(*i)
except TypeError:
pass
try:
perm_obj = i[0]
return [self._array_form[j] for j in perm_obj]
except TypeError:
raise TypeError('unrecognized argument')
def __eq__(self, other):
if isinstance(other, Permutation):
return self._hashable_content() == other._hashable_content()
else:
return super().__eq__(other)
def __hash__(self):
return super().__hash__()
p = CustomPermutation([1, 2, 3, 0])
q = Permutation([1, 2, 3, 0])
assert p == q
raises(TypeError, lambda: q([1, 2]))
assert [2, 3] == p([1, 2])
assert type(p * q) == CustomPermutation
assert type(q * p) == Permutation # True because q.__mul__(p) is called!
# Run all tests for the Permutation class also on the subclass
def wrapped_test_Permutation():
# Monkeypatch the class definition in the globals
globals()['__Perm'] = globals()['Permutation']
globals()['Permutation'] = CustomPermutation
test_Permutation()
globals()['Permutation'] = globals()['__Perm'] # Restore
del globals()['__Perm']
wrapped_test_Permutation()
def test_josephus():
assert Permutation.josephus(4, 6, 1) == Permutation([3, 1, 0, 2, 5, 4])
assert Permutation.josephus(1, 5, 1).is_Identity
def test_ranking():
assert Permutation.unrank_lex(5, 10).rank() == 10
p = Permutation.unrank_lex(15, 225)
assert p.rank() == 225
p1 = p.next_lex()
assert p1.rank() == 226
assert Permutation.unrank_lex(15, 225).rank() == 225
assert Permutation.unrank_lex(10, 0).is_Identity
p = Permutation.unrank_lex(4, 23)
assert p.rank() == 23
assert p.array_form == [3, 2, 1, 0]
assert p.next_lex() is None
p = Permutation([1, 5, 2, 0, 3, 6, 4])
q = Permutation([[1, 2, 3, 5, 6], [0, 4]])
a = [Permutation.unrank_trotterjohnson(4, i).array_form for i in range(5)]
assert a == [[0, 1, 2, 3], [0, 1, 3, 2], [0, 3, 1, 2], [3, 0, 1,
2], [3, 0, 2, 1] ]
assert [Permutation(pa).rank_trotterjohnson() for pa in a] == list(range(5))
assert Permutation([0, 1, 2, 3]).next_trotterjohnson() == \
Permutation([0, 1, 3, 2])
assert q.rank_trotterjohnson() == 2283
assert p.rank_trotterjohnson() == 3389
assert Permutation([1, 0]).rank_trotterjohnson() == 1
a = Permutation(list(range(3)))
b = a
l = []
tj = []
for i in range(6):
l.append(a)
tj.append(b)
a = a.next_lex()
b = b.next_trotterjohnson()
assert a == b is None
assert {tuple(a) for a in l} == {tuple(a) for a in tj}
p = Permutation([2, 5, 1, 6, 3, 0, 4])
q = Permutation([[6], [5], [0, 1, 2, 3, 4]])
assert p.rank() == 1964
assert q.rank() == 870
assert Permutation([]).rank_nonlex() == 0
prank = p.rank_nonlex()
assert prank == 1600
assert Permutation.unrank_nonlex(7, 1600) == p
qrank = q.rank_nonlex()
assert qrank == 41
assert Permutation.unrank_nonlex(7, 41) == Permutation(q.array_form)
a = [Permutation.unrank_nonlex(4, i).array_form for i in range(24)]
assert a == [
[1, 2, 3, 0], [3, 2, 0, 1], [1, 3, 0, 2], [1, 2, 0, 3], [2, 3, 1, 0],
[2, 0, 3, 1], [3, 0, 1, 2], [2, 0, 1, 3], [1, 3, 2, 0], [3, 0, 2, 1],
[1, 0, 3, 2], [1, 0, 2, 3], [2, 1, 3, 0], [2, 3, 0, 1], [3, 1, 0, 2],
[2, 1, 0, 3], [3, 2, 1, 0], [0, 2, 3, 1], [0, 3, 1, 2], [0, 2, 1, 3],
[3, 1, 2, 0], [0, 3, 2, 1], [0, 1, 3, 2], [0, 1, 2, 3]]
N = 10
p1 = Permutation(a[0])
for i in range(1, N+1):
p1 = p1*Permutation(a[i])
p2 = Permutation.rmul_with_af(*[Permutation(h) for h in a[N::-1]])
assert p1 == p2
ok = []
p = Permutation([1, 0])
for i in range(3):
ok.append(p.array_form)
p = p.next_nonlex()
if p is None:
ok.append(None)
break
assert ok == [[1, 0], [0, 1], None]
assert Permutation([3, 2, 0, 1]).next_nonlex() == Permutation([1, 3, 0, 2])
assert [Permutation(pa).rank_nonlex() for pa in a] == list(range(24))
def test_mul():
a, b = [0, 2, 1, 3], [0, 1, 3, 2]
assert _af_rmul(a, b) == [0, 2, 3, 1]
assert _af_rmuln(a, b, list(range(4))) == [0, 2, 3, 1]
assert rmul(Permutation(a), Permutation(b)).array_form == [0, 2, 3, 1]
a = Permutation([0, 2, 1, 3])
b = (0, 1, 3, 2)
c = (3, 1, 2, 0)
assert Permutation.rmul(a, b, c) == Permutation([1, 2, 3, 0])
assert Permutation.rmul(a, c) == Permutation([3, 2, 1, 0])
raises(TypeError, lambda: Permutation.rmul(b, c))
n = 6
m = 8
a = [Permutation.unrank_nonlex(n, i).array_form for i in range(m)]
h = list(range(n))
for i in range(m):
h = _af_rmul(h, a[i])
h2 = _af_rmuln(*a[:i + 1])
assert h == h2
def test_args():
p = Permutation([(0, 3, 1, 2), (4, 5)])
assert p._cyclic_form is None
assert Permutation(p) == p
assert p.cyclic_form == [[0, 3, 1, 2], [4, 5]]
assert p._array_form == [3, 2, 0, 1, 5, 4]
p = Permutation((0, 3, 1, 2))
assert p._cyclic_form is None
assert p._array_form == [0, 3, 1, 2]
assert Permutation([0]) == Permutation((0, ))
assert Permutation([[0], [1]]) == Permutation(((0, ), (1, ))) == \
Permutation(((0, ), [1]))
assert Permutation([[1, 2]]) == Permutation([0, 2, 1])
assert Permutation([[1], [4, 2]]) == Permutation([0, 1, 4, 3, 2])
assert Permutation([[1], [4, 2]], size=1) == Permutation([0, 1, 4, 3, 2])
assert Permutation(
[[1], [4, 2]], size=6) == Permutation([0, 1, 4, 3, 2, 5])
assert Permutation([[0, 1], [0, 2]]) == Permutation(0, 1, 2)
assert Permutation([], size=3) == Permutation([0, 1, 2])
assert Permutation(3).list(5) == [0, 1, 2, 3, 4]
assert Permutation(3).list(-1) == []
assert Permutation(5)(1, 2).list(-1) == [0, 2, 1]
assert Permutation(5)(1, 2).list() == [0, 2, 1, 3, 4, 5]
raises(ValueError, lambda: Permutation([1, 2], [0]))
# enclosing brackets needed
raises(ValueError, lambda: Permutation([[1, 2], 0]))
# enclosing brackets needed on 0
raises(ValueError, lambda: Permutation([1, 1, 0]))
raises(ValueError, lambda: Permutation([4, 5], size=10)) # where are 0-3?
# but this is ok because cycles imply that only those listed moved
assert Permutation(4, 5) == Permutation([0, 1, 2, 3, 5, 4])
def test_Cycle():
assert str(Cycle()) == '()'
assert Cycle(Cycle(1,2)) == Cycle(1, 2)
assert Cycle(1,2).copy() == Cycle(1,2)
assert list(Cycle(1, 3, 2)) == [0, 3, 1, 2]
assert Cycle(1, 2)(2, 3) == Cycle(1, 3, 2)
assert Cycle(1, 2)(2, 3)(4, 5) == Cycle(1, 3, 2)(4, 5)
assert Permutation(Cycle(1, 2)(2, 1, 0, 3)).cyclic_form, Cycle(0, 2, 1)
raises(ValueError, lambda: Cycle().list())
assert Cycle(1, 2).list() == [0, 2, 1]
assert Cycle(1, 2).list(4) == [0, 2, 1, 3]
assert Cycle(3).list(2) == [0, 1]
assert Cycle(3).list(6) == [0, 1, 2, 3, 4, 5]
assert Permutation(Cycle(1, 2), size=4) == \
Permutation([0, 2, 1, 3])
assert str(Cycle(1, 2)(4, 5)) == '(1 2)(4 5)'
assert str(Cycle(1, 2)) == '(1 2)'
assert Cycle(Permutation(list(range(3)))) == Cycle()
assert Cycle(1, 2).list() == [0, 2, 1]
assert Cycle(1, 2).list(4) == [0, 2, 1, 3]
assert Cycle().size == 0
raises(ValueError, lambda: Cycle((1, 2)))
raises(ValueError, lambda: Cycle(1, 2, 1))
raises(TypeError, lambda: Cycle(1, 2)*{})
raises(ValueError, lambda: Cycle(4)[a])
raises(ValueError, lambda: Cycle(2, -4, 3))
# check round-trip
p = Permutation([[1, 2], [4, 3]], size=5)
assert Permutation(Cycle(p)) == p
def test_from_sequence():
assert Permutation.from_sequence('SymPy') == Permutation(4)(0, 1, 3)
assert Permutation.from_sequence('SymPy', key=lambda x: x.lower()) == \
Permutation(4)(0, 2)(1, 3)
def test_resize():
p = Permutation(0, 1, 2)
assert p.resize(5) == Permutation(0, 1, 2, size=5)
assert p.resize(4) == Permutation(0, 1, 2, size=4)
assert p.resize(3) == p
raises(ValueError, lambda: p.resize(2))
p = Permutation(0, 1, 2)(3, 4)(5, 6)
assert p.resize(3) == Permutation(0, 1, 2)
raises(ValueError, lambda: p.resize(4))
def test_printing_cyclic():
p1 = Permutation([0, 2, 1])
assert repr(p1) == 'Permutation(1, 2)'
assert str(p1) == '(1 2)'
p2 = Permutation()
assert repr(p2) == 'Permutation()'
assert str(p2) == '()'
p3 = Permutation([1, 2, 0, 3])
assert repr(p3) == 'Permutation(3)(0, 1, 2)'
def test_printing_non_cyclic():
p1 = Permutation([0, 1, 2, 3, 4, 5])
assert srepr(p1, perm_cyclic=False) == 'Permutation([], size=6)'
assert sstr(p1, perm_cyclic=False) == 'Permutation([], size=6)'
p2 = Permutation([0, 1, 2])
assert srepr(p2, perm_cyclic=False) == 'Permutation([0, 1, 2])'
assert sstr(p2, perm_cyclic=False) == 'Permutation([0, 1, 2])'
p3 = Permutation([0, 2, 1])
assert srepr(p3, perm_cyclic=False) == 'Permutation([0, 2, 1])'
assert sstr(p3, perm_cyclic=False) == 'Permutation([0, 2, 1])'
p4 = Permutation([0, 1, 3, 2, 4, 5, 6, 7])
assert srepr(p4, perm_cyclic=False) == 'Permutation([0, 1, 3, 2], size=8)'
def test_deprecated_print_cyclic():
p = Permutation(0, 1, 2)
try:
Permutation.print_cyclic = True
with warns_deprecated_sympy():
assert sstr(p) == '(0 1 2)'
with warns_deprecated_sympy():
assert srepr(p) == 'Permutation(0, 1, 2)'
with warns_deprecated_sympy():
assert pretty(p) == '(0 1 2)'
with warns_deprecated_sympy():
assert latex(p) == r'\left( 0\; 1\; 2\right)'
Permutation.print_cyclic = False
with warns_deprecated_sympy():
assert sstr(p) == 'Permutation([1, 2, 0])'
with warns_deprecated_sympy():
assert srepr(p) == 'Permutation([1, 2, 0])'
with warns_deprecated_sympy():
assert pretty(p, use_unicode=False) == '/0 1 2\\\n\\1 2 0/'
with warns_deprecated_sympy():
assert latex(p) == \
r'\begin{pmatrix} 0 & 1 & 2 \\ 1 & 2 & 0 \end{pmatrix}'
finally:
Permutation.print_cyclic = None
def test_permutation_equality():
a = Permutation(0, 1, 2)
b = Permutation(0, 1, 2)
assert Eq(a, b) is S.true
c = Permutation(0, 2, 1)
assert Eq(a, c) is S.false
d = Permutation(0, 1, 2, size=4)
assert unchanged(Eq, a, d)
e = Permutation(0, 2, 1, size=4)
assert unchanged(Eq, a, e)
i = Permutation()
assert unchanged(Eq, i, 0)
assert unchanged(Eq, 0, i)
def test_issue_17661():
c1 = Cycle(1,2)
c2 = Cycle(1,2)
assert c1 == c2
assert repr(c1) == 'Cycle(1, 2)'
assert c1 == c2
def test_permutation_apply():
x = Symbol('x')
p = Permutation(0, 1, 2)
assert p.apply(0) == 1
assert isinstance(p.apply(0), Integer)
assert p.apply(x) == AppliedPermutation(p, x)
assert AppliedPermutation(p, x).subs(x, 0) == 1
x = Symbol('x', integer=False)
raises(NotImplementedError, lambda: p.apply(x))
x = Symbol('x', negative=True)
raises(NotImplementedError, lambda: p.apply(x))
def test_AppliedPermutation():
x = Symbol('x')
p = Permutation(0, 1, 2)
raises(ValueError, lambda: AppliedPermutation((0, 1, 2), x))
assert AppliedPermutation(p, 1, evaluate=True) == 2
assert AppliedPermutation(p, 1, evaluate=False).__class__ == \
AppliedPermutation
|