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     e1 = 1+z+x+y*x+5
  49     e2 = 1+x*y+5+x+z
  50     assert e1 == e2
  51     assert e2 == 6+x+z+x*y
  52
  53 def test_mul():
  54     x = Symbol("x")
  55     y = Symbol("y")
  56     z = Symbol("z")
  57
  58     assert (x * y) * z == x * (y * z)
  59     assert (z * x) * y == x * (y * z)
  60     assert (z * x) * x != x * (y * z)
  61
  62     assert x * x == x ** Integer(2)
  63     assert ((x * y) * z) * x == ((x ** Integer(2)) * y) * z
  64
  65     e1 = 2*z*x*y**x*5
  66     e2 = 2*y**x*5*x*z
  67     assert e1 == e2
  68     assert e2 == 10*x*z*y**x
  69
  70 def test_arit():
  71     x = Symbol("x")
  72     y = Symbol("y")
  73     z = Symbol("z")
  74
  75     assert x+y == x + y
  76     assert x+y+z == (x + y) + z
  77
  78     assert x-y == x + (Integer(-1) * y)
  79     assert y-x == (Integer(-1) * x) + y
  80
  81     assert x*y == x * y
  82     assert x*y*z == z * (x * y)
  83
  84     assert x/y == x * (y ** Integer(-1))
  85     assert y/x == (x ** Integer(-1)) * y
  86
  87     assert x**Integer(2) == x ** Integer(2)
  88
  89     assert -x == Integer(-1) * x
  90     assert +x == x
  91
  92 def test_int_conversion():
  93     x = Symbol("x")
  94     assert x+1 == x + 1
  95     assert x*1 == x
  96     assert x**1 == x
  97     assert x/2 == x * (Integer(2) ** -1)
  98
  99 def test_expand1():
 100     x = Symbol("x")
 101     y = Symbol("y")
 102     z = Symbol("z")
 103
 104     assert ( (x+y)**2 ).expand() == x**2 + 2*x*y + y**2
 105     assert ( (x+y)**3 ).expand() == x**3 + 3*x**2*y +3*x*y**2 + y**3
 106
 107     assert ( (x+y+z)**2 ).expand() == x**2 + y**2 + z**2 + 2*x*y + 2*x*z + 2*y*z
 108
 109 def test_expand2():
 110     x = Symbol("x")
 111     y = Symbol("y")
 112     z = Symbol("z")
 113
 114     assert ( 2*x*y ).expand() == 2*x*y
 115     assert ( (x+y) * (x+z) ).expand() == x**2 + x*y + x*z + y*z
 116     assert ( x*(x+y)**2 ).expand() == x**3 + 2*x**2*y + x*y**2
 117     assert ( x*(x+y)**2 + z*(x+y)**2 ).expand() == \
 118             x**3 + 2*x**2*y + y**2*z + x**2*z + x*y**2 + 2*x*y*z
 119
 120     assert ( 2*x * (y*x + y*z) ).expand() == 2*x**2*y + 2*x*y*z
 121     assert ( (x+y)**2 * (x+z) ).expand() == \
 122             x**3 + 2*x**2*y + y**2*z + x**2*z + x*y**2 + 2*x*y*z
 123
 124 def test_canonicalization():
 125     x = Symbol("x")
 126     y = Symbol("y")
 127     z = Symbol("z")
 128
 129     assert x-x == 0
 130     assert x*1 == x
 131     assert x+0 == x
 132     assert x-0 == x
 133     assert x**1 == x
 134     assert 1**x == 1
 135     assert 0**x == 0
 136
 137 def test_pow():
 138     x = Symbol("x")
 139     y = Symbol("y")
 140     z = Symbol("z")
 141
 142     assert (x**2)**3 == x**6
 143     assert (x**y)**3 == x**(3*y)
 144     # this is maybe not mathematically correct:
 145     assert (x**y)**z == x**(y*z)
 146
 147     assert x*x == x**2
 148     assert x*x*x == x**3
 149
 150 def test_args_type():
 151     x = Symbol("x")
 152     y = Symbol("y")
 153     z = Symbol("z")
 154
 155     assert (x+y).type == ADD
 156     assert set((x+y).args) == set((x, y))
 157     assert set((x+y).args) != set((x, z))
 158
 159     assert (x*y*z).type == MUL
 160     assert set((x*y*z).args) == set((x, y, z))
 161
 162     assert (x**y).type == POW
 163     assert (x**y).args == (x, y)
 164     assert x.type == SYMBOL
 165     assert x.args in [(), None]
 166     assert Integer(5).type == INTEGER
 167     assert Integer(5).args in [(), None]
 168
 169     assert ( x-y ).type == ADD
 170     assert set(( x-y ).args) == set((x, -y))
 171
 172 def test_hash():
 173     x = Symbol("x")
 174     y = Symbol("y")
 175     z = Symbol("z")
 176     a = Symbol("x")
 177
 178     assert hash(x) != hash(y)
 179     assert hash(x) != hash(z)
 180     assert hash(x) == hash(a)
 181
 182     assert hash(Integer(3)) == hash(Integer(3))
 183     assert hash(Integer(3)) != hash(Integer(4))
 184
 185     assert hash(x*y) == hash(y*x)
 186     assert hash(x*y) == hash(y*a)
 187     assert hash(x*y) != hash(y*z)
 188     assert hash(x*y*z) == hash(y*z*x)
 189     assert hash(x*y*z) == hash(y*z*a)
 190
 191 def test_hash2():
 192     x = Symbol("x")
 193     y = Symbol("y")
 194     z = Symbol("z")
 195     a = Symbol("x")
 196
 197     assert x*y+y*x == 2*x*y
 198     assert x*y-y*x == 0
 199     assert x*y+y*a == 2*x*y
 200     assert x*y-y*a == 0
 201
 202 def test_hash3():
 203     x = Symbol("x")
 204     y = Symbol("y")
 205     z = Symbol("z")
 206     e1 = z+x+y*x
 207     e2 = x*y+x+z
 208
 209     d = {}
 210     d[e1] = 1
 211     assert e1 in d
 212     assert e2 in d