test_basic.py

   1 from sympy import Symbol, Add, Mul, Pow, Integer, SYMBOL, ADD, MUL, POW, \
   2         INTEGER
   3
   4 def test_eq():
   5
   6     x = Symbol("x")
   7     y = Symbol("y")
   8     z = Symbol("z")
   9     a = Symbol("x")
  10
  11     assert x == x
  12     assert not (x != x)
  13     assert x == a
  14     assert not (x != a)
  15     assert x != y
  16
  17     assert x + y == x + y
  18     assert a + y == x + y
  19     assert x + y == y + x
  20     assert x + y != y + z
  21
  22     assert x * y == x * y
  23     assert a * y == x * y
  24     assert x * y == y * x
  25     assert x * y != y * z
  26
  27     assert x ** y == x ** y
  28     assert a ** y == x ** y
  29     assert x ** y != y ** x
  30     assert x ** y != y ** z
  31     assert a ** y != x ** z
  32
  33     assert Integer(3) == Integer(3)
  34     assert Integer(3) != Integer(4)
  35
  36 def test_add():
  37     x = Symbol("x")
  38     y = Symbol("y")
  39     z = Symbol("z")
  40
  41     assert (x + y) + z == x + (y + z)
  42     assert (z + x) + y == x + (y + z)
  43     assert (z + x) + x != x + (y + z)
  44
  45     assert x + x == Integer(2) * x
  46     assert ((x + y) + z) + x == (Integer(2)*x + y) + z
  47
  48 def test_mul():
  49     x = Symbol("x")
  50     y = Symbol("y")
  51     z = Symbol("z")
  52
  53     assert (x * y) * z == x * (y * z)
  54     assert (z * x) * y == x * (y * z)
  55     assert (z * x) * x != x * (y * z)
  56
  57     assert x * x == x ** Integer(2)
  58     assert ((x * y) * z) * x == ((x ** Integer(2)) * y) * z
  59
  60 def test_arit():
  61     x = Symbol("x")
  62     y = Symbol("y")
  63     z = Symbol("z")
  64
  65     assert x+y == x + y
  66     assert x+y+z == (x + y) + z
  67
  68     assert x-y == x + (Integer(-1) * y)
  69     assert y-x == (Integer(-1) * x) + y
  70
  71     assert x*y == x * y
  72     assert x*y*z == z * (x * y)
  73
  74     assert x/y == x * (y ** Integer(-1))
  75     assert y/x == (x ** Integer(-1)) * y
  76
  77     assert x**Integer(2) == x ** Integer(2)
  78
  79     assert -x == Integer(-1) * x
  80     assert +x == x
  81
  82 def test_int_conversion():
  83     x = Symbol("x")
  84     assert x+1 == x + 1
  85     assert x*1 == x
  86     assert x**1 == x
  87     assert x/2 == x * (Integer(2) ** -1)
  88
  89 def test_expand1():
  90     x = Symbol("x")
  91     y = Symbol("y")
  92     z = Symbol("z")
  93
  94     assert ( (x+y)**2 ).expand() == x**2 + 2*x*y + y**2
  95     assert ( (x+y)**3 ).expand() == x**3 + 3*x**2*y +3*x*y**2 + y**3
  96
  97     assert ( (x+y+z)**2 ).expand() == x**2 + y**2 + z**2 + 2*x*y + 2*x*z + 2*y*z
  98
  99 def test_expand2():
 100     x = Symbol("x")
 101     y = Symbol("y")
 102     z = Symbol("z")
 103
 104     assert ( 2*x*y ).expand() == 2*x*y
 105     assert ( (x+y) * (x+z) ).expand() == x**2 + x*y + x*z + y*z
 106     assert ( x*(x+y)**2 ).expand() == x**3 + 2*x**2*y + x*y**2
 107     assert ( x*(x+y)**2 + z*(x+y)**2 ).expand() == \
 108             x**3 + 2*x**2*y + y**2*z + x**2*z + x*y**2 + 2*x*y*z
 109
 110     assert ( 2*x * (y*x + y*z) ).expand() == 2*x**2*y + 2*x*y*z
 111     assert ( (x+y)**2 * (x+z) ).expand() == \
 112             x**3 + 2*x**2*y + y**2*z + x**2*z + x*y**2 + 2*x*y*z
 113
 114 def test_canonicalization():
 115     x = Symbol("x")
 116     y = Symbol("y")
 117     z = Symbol("z")
 118
 119     assert x-x == 0
 120     assert x*1 == x
 121     assert x+0 == x
 122     assert x-0 == x
 123     assert x**1 == x
 124     assert 1**x == 1
 125     assert 0**x == 0
 126
 127 def test_pow():
 128     x = Symbol("x")
 129     y = Symbol("y")
 130     z = Symbol("z")
 131
 132     assert (x**2)**3 == x**6
 133     assert (x**y)**3 == x**(3*y)
 134     # this is maybe not mathematically correct:
 135     assert (x**y)**z == x**(y*z)
 136
 137     assert x*x == x**2
 138     assert x*x*x == x**3
 139
 140 def test_args_type():
 141     x = Symbol("x")
 142     y = Symbol("y")
 143     z = Symbol("z")
 144
 145     assert (x+y).type == ADD
 146     assert set((x+y).args) == set((x, y))
 147     assert set((x+y).args) != set((x, z))
 148
 149     assert (x*y*z).type == MUL
 150     assert set((x*y*z).args) == set((x, y, z))
 151
 152     assert (x**y).type == POW
 153     assert (x**y).args == (x, y)
 154     assert x.type == SYMBOL
 155     assert x.args == ()
 156     assert Integer(5).type == INTEGER
 157     assert Integer(5).args == ()
 158
 159     assert ( x-y ).type == ADD
 160     assert set(( x-y ).args) == set((x, -y))
 161
 162 def test_hash():
 163     x = Symbol("x")
 164     y = Symbol("y")
 165     z = Symbol("z")
 166     a = Symbol("x")
 167
 168     assert hash(x) != hash(y)
 169     assert hash(x) != hash(z)
 170     assert hash(x) == hash(a)
 171
 172     assert hash(Integer(3)) == hash(Integer(3))
 173     assert hash(Integer(3)) != hash(Integer(4))
 174
 175     assert hash(x*y) == hash(y*x)
 176     assert hash(x*y) == hash(y*a)
 177     assert hash(x*y) != hash(y*z)
 178     assert hash(x*y*z) == hash(y*z*x)
 179     assert hash(x*y*z) == hash(y*z*a)
 180
 181 def test_hash2():
 182     x = Symbol("x")
 183     y = Symbol("y")
 184     z = Symbol("z")
 185     a = Symbol("x")
 186
 187     assert x*y+y*x == 2*x*y
 188     assert x*y-y*x == 0
 189     assert x*y+y*a == 2*x*y
 190     assert x*y-y*a == 0