sympy/core/tests/test_assumptions.py

   1 import py
   2 from sympy.core import Symbol, S, Rational, Integer
   3 from sympy.utilities.pytest import XFAIL
   4
   5 def test_symbol_unset():
   6     x = Symbol('x',real=True, integer=True)
   7     assert x.is_real == True
   8     assert x.is_integer == True
   9     assert x.is_imaginary == False
  10     assert x.is_noninteger == False
  11
  12 def test_zero():
  13     z = Integer(0)
  14     assert z.is_commutative == True
  15     assert z.is_integer == True
  16     assert z.is_rational == True
  17     assert z.is_real == True
  18     assert z.is_complex == True
  19     assert z.is_noninteger == False
  20     assert z.is_irrational == False
  21     assert z.is_imaginary == False
  22     assert z.is_positive == False
  23     assert z.is_negative == False
  24     assert z.is_nonpositive == True
  25     assert z.is_nonnegative == True
  26     assert z.is_even == True
  27     assert z.is_odd == False
  28     assert z.is_bounded == True
  29     assert z.is_unbounded == False
  30     assert z.is_finite == False
  31     assert z.is_infinitesimal == True
  32     assert z.is_comparable == True
  33     assert z.is_prime == False
  34     assert z.is_composite == False
  35
  36 def test_one():
  37     z = Integer(1)
  38     assert z.is_commutative == True
  39     assert z.is_integer == True
  40     assert z.is_rational == True
  41     assert z.is_real == True
  42     assert z.is_complex == True
  43     assert z.is_noninteger == False
  44     assert z.is_irrational == False
  45     assert z.is_imaginary == False
  46     assert z.is_positive == True
  47     assert z.is_negative == False
  48     assert z.is_nonpositive == False
  49     assert z.is_nonnegative == True
  50     assert z.is_even == False
  51     assert z.is_odd == True
  52     assert z.is_bounded == True
  53     assert z.is_unbounded == False
  54     assert z.is_finite == True
  55     assert z.is_infinitesimal == False
  56     assert z.is_comparable == True
  57     assert z.is_prime == True
  58     assert z.is_composite == False
  59
  60 def test_negativeone():
  61     z = Integer(-1)
  62     assert z.is_commutative == True
  63     assert z.is_integer == True
  64     assert z.is_rational == True
  65     assert z.is_real == True
  66     assert z.is_complex == True
  67     assert z.is_noninteger == False
  68     assert z.is_irrational == False
  69     assert z.is_imaginary == False
  70     assert z.is_positive == False
  71     assert z.is_negative == True
  72     assert z.is_nonpositive == True
  73     assert z.is_nonnegative == False
  74     assert z.is_even == False
  75     assert z.is_odd == True
  76     assert z.is_bounded == True
  77     assert z.is_unbounded == False
  78     assert z.is_finite == True
  79     assert z.is_infinitesimal == False
  80     assert z.is_comparable == True
  81     assert z.is_prime == False
  82     assert z.is_composite == False
  83
  84 def test_infinity():
  85     oo = S.Infinity
  86
  87     assert oo.is_commutative    == True
  88     assert oo.is_integer        == None
  89     assert oo.is_rational       == None
  90     assert oo.is_real           == True
  91     assert oo.is_complex        == True
  92     assert oo.is_noninteger     == None
  93     assert oo.is_irrational     == None
  94     assert oo.is_imaginary      == False
  95     assert oo.is_positive       == True
  96     assert oo.is_negative       == False
  97     assert oo.is_nonpositive    == False
  98     assert oo.is_nonnegative    == True
  99     assert oo.is_even           == None
 100     assert oo.is_odd            == None
 101     assert oo.is_bounded        == False
 102     assert oo.is_unbounded      == True
 103     assert oo.is_finite         == False
 104     assert oo.is_infinitesimal  == False
 105     assert oo.is_comparable     == True
 106     assert oo.is_prime          == None
 107     assert oo.is_composite      == None
 108
 109 def test_neg_infinity():
 110     mm = S.NegativeInfinity
 111
 112     assert mm.is_commutative    == True
 113     assert mm.is_integer        == None
 114     assert mm.is_rational       == None
 115     assert mm.is_real           == True
 116     assert mm.is_complex        == True
 117     assert mm.is_noninteger     == None
 118     assert mm.is_irrational     == None
 119     assert mm.is_imaginary      == False
 120     assert mm.is_positive       == False
 121     assert mm.is_negative       == True
 122     assert mm.is_nonpositive    == True
 123     assert mm.is_nonnegative    == False
 124     assert mm.is_even           == None
 125     assert mm.is_odd            == None
 126     assert mm.is_bounded        == False
 127     assert mm.is_unbounded      == True
 128     assert mm.is_finite         == False
 129     assert mm.is_infinitesimal  == False
 130     assert mm.is_comparable     == True
 131     assert mm.is_prime          == False
 132     assert mm.is_composite      == False
 133
 134 def test_nan():
 135     nan = S.NaN
 136
 137     assert nan.is_commutative   == True
 138     assert nan.is_integer       == None
 139     assert nan.is_rational      == None
 140     assert nan.is_real          == None
 141     assert nan.is_complex       == None
 142     assert nan.is_noninteger    == None
 143     assert nan.is_irrational    == None
 144     assert nan.is_imaginary     == None
 145     assert nan.is_positive      == None
 146     assert nan.is_negative      == None
 147     assert nan.is_nonpositive   == None
 148     assert nan.is_nonnegative   == None
 149     assert nan.is_even          == None
 150     assert nan.is_odd           == None
 151     assert nan.is_bounded       == None
 152     assert nan.is_unbounded     == None
 153     assert nan.is_finite        == None
 154     assert nan.is_infinitesimal == None
 155     assert nan.is_comparable    == False
 156     assert nan.is_prime         == None
 157     assert nan.is_composite     == None
 158
 159 def test_pos_rational():
 160     r = Rational(3,4)
 161     assert r.is_commutative == True
 162     assert r.is_integer == False
 163     assert r.is_rational == True
 164     assert r.is_real == True
 165     assert r.is_complex == True
 166     assert r.is_noninteger == True
 167     assert r.is_irrational == False
 168     assert r.is_imaginary == False
 169     assert r.is_positive == True
 170     assert r.is_negative == False
 171     assert r.is_nonpositive == False
 172     assert r.is_nonnegative == True
 173     assert r.is_even == False
 174     assert r.is_odd == False
 175     assert r.is_bounded == True
 176     assert r.is_unbounded == False
 177     assert r.is_finite == True
 178     assert r.is_infinitesimal == False
 179     assert r.is_comparable == True
 180     assert r.is_prime == False
 181     assert r.is_composite == False
 182
 183     r = Rational(1,4)
 184     assert r.is_nonpositive == False
 185     assert r.is_positive == True
 186     assert r.is_negative == False
 187     assert r.is_nonnegative == True
 188     r = Rational(5,4)
 189     assert r.is_negative == False
 190     assert r.is_positive == True
 191     assert r.is_nonpositive == False
 192     assert r.is_nonnegative == True
 193     r = Rational(5,3)
 194     assert r.is_nonnegative == True
 195     assert r.is_positive == True
 196     assert r.is_negative == False
 197     assert r.is_nonpositive == False
 198
 199 def test_neg_rational():
 200     r = Rational(-3,4)
 201     assert r.is_positive == False
 202     assert r.is_nonpositive == True
 203     assert r.is_negative == True
 204     assert r.is_nonnegative == False
 205     r = Rational(-1,4)
 206     assert r.is_nonpositive == True
 207     assert r.is_positive == False
 208     assert r.is_negative == True
 209     assert r.is_nonnegative == False
 210     r = Rational(-5,4)
 211     assert r.is_negative == True
 212     assert r.is_positive == False
 213     assert r.is_nonpositive == True
 214     assert r.is_nonnegative == False
 215     r = Rational(-5,3)
 216     assert r.is_nonnegative == False
 217     assert r.is_positive == False
 218     assert r.is_negative == True
 219     assert r.is_nonpositive == True
 220
 221 def test_pi():
 222     z = S.Pi
 223     assert z.is_commutative == True
 224     assert z.is_integer == False
 225     assert z.is_rational == False
 226     assert z.is_real == True
 227     assert z.is_complex == True
 228     assert z.is_noninteger == True
 229     assert z.is_irrational == True
 230     assert z.is_imaginary == False
 231     assert z.is_positive == True
 232     assert z.is_negative == False
 233     assert z.is_nonpositive == False
 234     assert z.is_nonnegative == True
 235     assert z.is_even == False
 236     assert z.is_odd == False
 237     assert z.is_bounded == True
 238     assert z.is_unbounded == False
 239     assert z.is_finite == True
 240     assert z.is_infinitesimal == False
 241     assert z.is_comparable == True
 242     assert z.is_prime == False
 243     assert z.is_composite == False
 244
 245 def test_E():
 246     z = S.Exp1
 247     assert z.is_commutative == True
 248     assert z.is_integer == False
 249     assert z.is_rational == False
 250     assert z.is_real == True
 251     assert z.is_complex == True
 252     assert z.is_noninteger == True
 253     assert z.is_irrational == True
 254     assert z.is_imaginary == False
 255     assert z.is_positive == True
 256     assert z.is_negative == False
 257     assert z.is_nonpositive == False
 258     assert z.is_nonnegative == True
 259     assert z.is_even == False
 260     assert z.is_odd == False
 261     assert z.is_bounded == True
 262     assert z.is_unbounded == False
 263     assert z.is_finite == True
 264     assert z.is_infinitesimal == False
 265     assert z.is_comparable == True
 266     assert z.is_prime == False
 267     assert z.is_composite == False
 268
 269 def test_I():
 270     z = S.ImaginaryUnit
 271     assert z.is_commutative == True
 272     assert z.is_integer == False
 273     assert z.is_rational == False
 274     assert z.is_real == False
 275     assert z.is_complex == True
 276     assert z.is_noninteger == False
 277     assert z.is_irrational == False
 278     assert z.is_imaginary == True
 279     assert z.is_positive == False
 280     assert z.is_negative == False
 281     assert z.is_nonpositive == False
 282     assert z.is_nonnegative == False
 283     assert z.is_even == False
 284     assert z.is_odd == False
 285     assert z.is_bounded == True
 286     assert z.is_unbounded == False
 287     assert z.is_finite == True
 288     assert z.is_infinitesimal == False
 289     assert z.is_comparable == None
 290     assert z.is_prime == False
 291     assert z.is_composite == False
 292
 293 def test_symbol_zero():
 294     x = Symbol('x',zero=True)
 295     assert x.is_positive == False
 296     assert x.is_nonpositive == True
 297     assert x.is_negative == False
 298     assert x.is_nonnegative == True
 299     assert x.is_zero == True
 300     assert x.is_nonzero == False
 301
 302 def test_symbol_positive():
 303     x = Symbol('x',positive=True)
 304     assert x.is_positive == True
 305     assert x.is_nonpositive == False
 306     assert x.is_negative == False
 307     assert x.is_nonnegative == True
 308     assert x.is_zero == False
 309     assert x.is_nonzero == True
 310
 311 def test_neg_symbol_positive():
 312     x = -Symbol('x',positive=True)
 313     assert x.is_positive == False
 314     assert x.is_nonpositive == True
 315     assert x.is_negative == True
 316     assert x.is_nonnegative == False
 317
 318 def test_neg_symbol_positive2():
 319     x = -Symbol('x',positive=True)
 320     assert x.is_zero == False
 321     assert x.is_nonzero == True
 322
 323 def test_symbol_nonpositive():
 324     x = Symbol('x',nonpositive=True)
 325     assert x.is_positive == False
 326     assert x.is_nonpositive == True
 327     assert x.is_negative == None
 328     assert x.is_nonnegative == None
 329     assert x.is_zero == None
 330     assert x.is_nonzero == None
 331
 332 def test_neg_symbol_nonpositive():
 333     x = -Symbol('x',nonpositive=True)
 334     assert x.is_positive == None
 335     assert x.is_nonpositive == None
 336     assert x.is_negative == False
 337     assert x.is_nonnegative == True
 338     assert x.is_zero == None
 339     assert x.is_nonzero == None
 340
 341 def test_prime_symbol():
 342     x = Symbol('x', prime=True)
 343     assert x.is_prime == True
 344     assert x.is_integer == True
 345     assert x.is_positive == True
 346     assert x.is_negative == False
 347     assert x.is_nonpositive == False
 348     assert x.is_nonnegative == True
 349
 350     x = Symbol('x', prime=False)
 351     assert x.is_prime == False
 352     assert x.is_integer == None
 353     assert x.is_positive == None
 354     assert x.is_negative == None
 355     assert x.is_nonpositive == None
 356     assert x.is_nonnegative == None
 357
 358 def test_other_symbol():
 359     x = Symbol('x', integer=True)
 360     assert x.is_integer == True
 361     assert x.is_real == True
 362
 363     x = Symbol('x', integer=True, nonnegative=True)
 364     assert x.is_integer     == True
 365     assert x.is_nonnegative == True
 366     assert x.is_negative    == False
 367     assert x.is_positive    == None
 368
 369     x = Symbol('x', integer=True, nonpositive=True)
 370     assert x.is_integer     == True
 371     assert x.is_nonpositive == True
 372     assert x.is_positive    == False
 373     assert x.is_negative    == None
 374
 375     x = Symbol('x', odd=True)
 376     assert x.is_odd == True
 377     assert x.is_even == False
 378     assert x.is_integer == True
 379
 380     x = Symbol('x', even=True)
 381     assert x.is_even == True
 382     assert x.is_odd == False
 383     assert x.is_integer == True
 384
 385     x = Symbol('x', integer=True, nonnegative=True)
 386     assert x.is_integer == True
 387     assert x.is_nonnegative == True
 388
 389     x = Symbol('x', integer=True, nonpositive=True)
 390     assert x.is_integer == True
 391     assert x.is_nonpositive == True
 392
 393     py.test.raises(AttributeError, "x.is_real = False")
 394
 395
 396 def test_other_symbol_fail1():
 397     # XXX x.is_even currently will be True
 398     x = Symbol('x', odd=False)
 399     assert x.is_odd == False
 400     assert x.is_even == None
 401     assert x.is_integer == None
 402
 403 def test_other_symbol_fail2():
 404     # XXX x.is_odd currently will be True
 405     x = Symbol('x', even=False)
 406     assert x.is_even == False
 407     assert x.is_odd == None
 408     assert x.is_integer == None
 409
 410
 411 def test_issue749():
 412     a = Symbol('a', real=False)
 413
 414     assert a.is_real        == False
 415     assert a.is_integer     == False
 416     assert a.is_negative    == False
 417     assert a.is_positive    == False
 418     assert a.is_nonnegative == False
 419     assert a.is_nonpositive == False
 420     assert a.is_zero        == False
 421
 422
 423 def test_issue726():
 424     """catch: hash instability"""
 425     x = Symbol("x")
 426     y = Symbol("y")
 427     a1 = x+y
 428     a2 = y+x
 429     a2.is_comparable
 430
 431     h1 = hash(a1)
 432     h2 = hash(a2)
 433     assert h1 == h2
 434
 435
 436 def test_hash_vs_typeinfo():
 437     """seemingly different typeinfo, but in fact equal"""
 438     x = Symbol('x')
 439
 440     # the following two are semantically equal
 441     x1= Symbol('x', even=True)
 442     x2= Symbol('x', integer=True, odd=False)
 443
 444     assert hash(x1) == hash(x2)
 445     assert x1 == x2
 446
 447
 448 @XFAIL  # our __eq__ just does not look at it (yet)
 449 def test_hash_vs_typeinfo_2():
 450     """different typeinfo should mean !eq"""
 451     # the following two are semantically different
 452     x = Symbol('x')
 453     x1= Symbol('x', even=True)
 454
 455     assert x != x1
 456
 457
 458 def test_hash_vs_eq():
 459     """catch: different hash for equal objects"""
 460     a = 1 + S.Pi    # important: do not fold it into a Number instance
 461     ha= hash(a)     #            it should be Add/Mul/... to trigger the bug
 462
 463     a.is_positive   # this uses .evalf() and deduces it is positive
 464     assert a.is_positive == True
 465
 466     # be sure that hash stayed the same
 467     assert ha == hash(a)
 468
 469     # now b should be the same expression
 470     b = a.expand(trig=True)
 471     hb= hash(b)
 472
 473     assert a == b
 474     assert ha== hb
 475