trs/tests/test_node.py

# This file is part of TRS (http://math.kompiler.org)
#
# TRS is free software: you can redistribute it and/or modify it under the
# terms of the GNU Affero General Public License as published by the Free
# Software Foundation, either version 3 of the License, or (at your option) any
# later version.
#
# TRS 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 Affero General Public License for more
# details.
#
# You should have received a copy of the GNU Affero General Public License
# along with TRS.  If not, see <http://www.gnu.org/licenses/>.
from src.node import ExpressionNode as N, ExpressionLeaf as L, Scope, \
        nary_node, get_scope, OP_ADD, infinity, absolute, sin, cos, tan, log, \
        ln, der, integral, int_def, eq
from tests.rulestestcase import RulesTestCase, tree


class TestNode(RulesTestCase):

    def setUp(self):
        self.l = [L(1), N('*', L(2), L(3)), L(4), L(5)]
        self.n, self.f = tree('a + b + cd,f')
        (self.a, self.b), self.cd = self.n
        self.c, self.d = self.cd
        self.scope = Scope(self.n)

    def test___lt__(self):
        self.assertTrue(L(1) < L(2))
        self.assertFalse(L(1) < L(1))
        self.assertFalse(L(2) < L(1))

        self.assertTrue(L(2) < N('+', L(1), L(2)))
        self.assertFalse(N('+', L(1), L(2)) < L(1))

        self.assertTrue(N('^', L('a'), L(2)) < N('^', L('a'), L(3)))
        self.assertTrue(N('^', L(2), L('a')) < N('^', L(3), L('a')))
        self.assertTrue(N('*', L(2), N('^', L('a'), L('b')))
                        < N('*', L(3), N('^', L('a'), L('b'))))
        self.assertFalse(N('^', L('a'), L(3)) < N('^', L('a'), L(2)))

    def test_is_op(self):
        self.assertTrue(N('+', *self.l[:2]).is_op(OP_ADD))
        self.assertFalse(N('-', *self.l[:2]).is_op(OP_ADD))

    def test_is_leaf(self):
        self.assertTrue(L(2).is_leaf)
        self.assertFalse(N('+', *self.l[:2]).is_leaf)

    def test_is_power(self):
        self.assertTrue(N('^', *self.l[2:]).is_power())
        self.assertFalse(N('+', *self.l[2:]).is_power())

    def test_is_power_exponent(self):
        self.assertTrue(N('^', *self.l[2:]).is_power(5))
        self.assertFalse(N('^', *self.l[2:]).is_power(2))

    def test_is_nary(self):
        self.assertTrue(N('+', *self.l[:2]).is_nary())
        self.assertTrue(N('-', *self.l[:2]).is_nary())
        self.assertTrue(N('*', *self.l[:2]).is_nary())
        self.assertFalse(N('^', *self.l[:2]).is_nary())

    def test_is_identifier(self):
        self.assertTrue(L('a').is_identifier())
        self.assertFalse(L(1).is_identifier())

    def test_is_int(self):
        self.assertTrue(L(1).is_int())
        self.assertFalse(L(1.5).is_int())
        self.assertFalse(L('a').is_int())

    def test_is_float(self):
        self.assertTrue(L(1.5).is_float())
        self.assertFalse(L(1).is_float())
        self.assertFalse(L('a').is_float())

    def test_is_numeric(self):
        self.assertTrue(L(1).is_numeric())
        self.assertTrue(L(1.5).is_numeric())
        self.assertFalse(L('a').is_numeric())

    def test_extract_polynome_properties_identifier(self):
        self.assertEqual(L('a').extract_polynome_properties(),
                         (L(1), L('a'), L(1)))

    def test_extract_polynome_properties_None(self):
        self.assertIsNone(N('+').extract_polynome_properties())

    def test_extract_polynome_properties_power(self):
        power = N('^', L('a'), L(2))
        self.assertEqual(power.extract_polynome_properties(),
                         (L(1), L('a'), L(2)))

    def test_extract_polynome_properties_coefficient_exponent_int(self):
        times = N('*', L(3), N('^', L('a'), L(2)))
        self.assertEqual(times.extract_polynome_properties(),
                         (L(3), L('a'), L(2)))

    def test_extract_polynome_properties_coefficient_exponent_id(self):
        times = N('*', L(3), N('^', L('a'), L('b')))
        self.assertEqual(times.extract_polynome_properties(),
                         (L(3), L('a'), L('b')))

    def test_get_scope_binary(self):
        plus = N('+', *self.l[:2])
        self.assertEqual(get_scope(plus), self.l[:2])

    def test_get_scope_nested_left(self):
        plus = N('+', N('+', *self.l[:2]), self.l[2])
        self.assertEqual(get_scope(plus), self.l[:3])

    def test_get_scope_nested_right(self):
        plus = N('+', self.l[0], N('+', *self.l[1:3]))
        self.assertEqual(get_scope(plus), self.l[:3])

    def test_get_scope_nested_deep(self):
        plus = N('+', N('+', N('+', *self.l[:2]), self.l[2]), self.l[3])
        self.assertEqual(get_scope(plus), self.l)

    def test_get_scope_negation(self):
        root, a, b, c, d = tree('ab * -cd, a, b, -c, d')
        self.assertEqual(get_scope(root), [a, b, c, d])

    def test_get_scope_index(self):
        self.assertEqual(self.scope.index(self.a), 0)
        self.assertEqual(self.scope.index(self.b), 1)
        self.assertEqual(self.scope.index(self.cd), 2)

    def test_equals_node_leaf(self):
        a, b = plus = tree('a + b')

        self.assertFalse(a.equals(plus))
        self.assertFalse(plus.equals(a))

    def test_equals_other_op(self):
        plus, mul = tree('a + b, a * b')

        self.assertFalse(plus.equals(mul))

    def test_equals_add(self):
        p0, p1, p2, p3 = tree('a + b,a + b,b + a, a + c')

        self.assertTrue(p0.equals(p1))
        self.assertTrue(p0.equals(p2))
        self.assertFalse(p0.equals(p3))
        self.assertFalse(p2.equals(p3))

    def test_equals_mul(self):
        m0, m1, m2, m3 = tree('a * b,a * b,b * a, a * c')

        self.assertTrue(m0.equals(m1))
        self.assertTrue(m0.equals(m2))
        self.assertFalse(m0.equals(m3))
        self.assertFalse(m2.equals(m3))

    def test_equals_nary(self):
        p0, p1, p2, p3, p4 = \
                tree('a + b + c,a + c + b,b + a + c,b + c + a,a + b + d')

        self.assertTrue(p0.equals(p1))
        self.assertTrue(p0.equals(p2))
        self.assertTrue(p0.equals(p3))
        self.assertTrue(p1.equals(p2))
        self.assertTrue(p1.equals(p3))
        self.assertTrue(p2.equals(p3))
        self.assertFalse(p2.equals(p4))

    def test_equals_nary_mary(self):
        m0, m1 = tree('ab,2ab')

        self.assertFalse(m0.equals(m1))

    def test_equals_div(self):
        d0, d1, d2 = tree('a / b,a / b,b / a')

        self.assertTrue(d0.equals(d1))
        self.assertFalse(d0.equals(d2))

    def test_equals_neg(self):
        a0, a1 = tree('-a,a')
        self.assertFalse(a0.equals(a1))

        a0, a1 = tree('-a,-a')
        self.assertTrue(a0.equals(a1))

        m0, m1 = tree('-5 * -3,-5 * 6')
        self.assertFalse(m0.equals(m1))

    def test_equals_ignore_negation(self):
        p0, p1 = tree('-(a + b), a + b')
        self.assertTrue(p0.equals(p1, ignore_negation=True))

        a0, a1 = tree('-a,a')
        self.assertTrue(a0.equals(a1, ignore_negation=True))

    def test_scope___init__(self):
        self.assertEqual(self.scope.node, self.n)
        self.assertEqual(self.scope.nodes, [self.a, self.b, self.cd])

    def test_scope_remove_leaf(self):
        self.scope.remove(self.b)
        self.assertEqual(self.scope.nodes, [self.a, self.cd])

    def test_scope_remove_node(self):
        self.scope.remove(self.cd)
        self.assertEqual(self.scope.nodes, [self.a, self.b])

    def test_scope_remove_error(self):
        self.assertRaises(ValueError, self.scope.remove, self.f)

    def test_scope_replace(self):
        self.scope.replace(self.cd, self.f)
        self.assertEqual(self.scope.nodes, [self.a, self.b, self.f])

    def test_nary_node(self):
        a, b, c, d = tree('a,b,c,d')

        self.assertEqualNodes(nary_node('+', [a]), a)
        self.assertEqualNodes(nary_node('+', [a, b]), N('+', a, b))
        self.assertEqualNodes(nary_node('+', [a, b, c]),
                              N('+', N('+', a, b), c))
        self.assertEqualNodes(nary_node('+', [a, b, c, d]),
                              N('+', N('+', N('+', a, b), c), d))

    def test_scope_as_nary_node(self):
        self.assertEqualNodes(self.scope.as_nary_node(), self.n)

    def test_scope_as_nary_node_negated(self):
        n = tree('-(a + b)')
        self.assertEqualNodes(Scope(n).as_nary_node(), n)
        self.assertEqualNodes(Scope(-n).as_nary_node(), -n)

    def test_contains(self):
        a, ab, bc, ln0, ln1, ma = tree('a, ab, bc, ln(a) + 1, ln(b) + 1, -a')

        self.assertTrue(a.contains(a))
        self.assertTrue(ab.contains(a))
        self.assertFalse(bc.contains(a))
        self.assertTrue(ln0.contains(a))
        self.assertFalse(ln1.contains(a))
        self.assertTrue(ma.contains(a))

    def test_construct_function_derivative(self):
        self.assertEqual(str(tree("(x ^ 2)'")), "[x ^ 2]'")
        self.assertEqual(str(tree("(x ^ 2)''")), "[x ^ 2]''")
        self.assertEqual(str(tree('d/dx x ^ 2')), 'd/dx x ^ 2')

    def test_construct_function_integral(self):
        self.assertEqual(str(tree('int x ^ 2')), 'int x ^ 2 dx')
        self.assertEqual(str(tree('int x ^ 2 dx')), 'int x ^ 2 dx')
        self.assertEqual(str(tree('int x ^ 2 dy')), 'int x ^ 2 dy')
        self.assertEqual(str(tree('int x ^ 2 dy')), 'int x ^ 2 dy')
        self.assertEqual(str(tree('int x + 1')), 'int x dx + 1')

        self.assertEqual(str(tree('int_a^b x ^ 2')), 'int_a^b x ^ 2 dx')
        self.assertEqual(str(tree('int_(a-b)^(a+b) x ^ 2')),
                         'int_(a - b)^(a + b) x ^ 2 dx')

    def test_construct_function_int_def(self):
        self.assertEqual(str(tree('[x ^ 2]_a^b')), '[x ^ 2]_a^b')
        self.assertEqual(str(tree('[x ^ 2]_(a-b)^(a+b)')),
                         '[x ^ 2]_(a - b)^(a + b)')

    def test_construct_function_absolute_child(self):
        self.assertEqual(str(tree('ln(|x|)')), 'ln(|x|)')
        self.assertEqual(str(tree('sin(|x|)')), 'sin(|x|)')

    def test_construct_logarithm(self):
        self.assertEqual(str(tree('log n')), 'log(n)')
        self.assertEqual(str(tree('log(n)')), 'log(n)')

        self.assertEqual(str(tree('ln n')), 'ln(n)')
        self.assertEqual(str(tree('ln(n)')), 'ln(n)')

        self.assertEqual(str(tree('log_2 n')), 'log_2(n)')
        self.assertEqual(str(tree('log_2(n)')), 'log_2(n)')

        self.assertEqual(str(tree('log_g n')), 'log_g(n)')
        self.assertEqual(str(tree('log_(g + h) n')), 'log_(g + h)(n)')

    def test_infinity(self):
        self.assertEqual(infinity(), tree('oo'))

    def test_absolute(self):
        self.assertEqual(absolute(tree('x^2')), tree('|x^2|'))

    def test_sin(self):
        self.assertEqual(sin(tree('x')), tree('sin(x)'))

    def test_cos(self):
        self.assertEqual(cos(tree('x')), tree('cos(x)'))

    def test_tan(self):
        self.assertEqual(tan(tree('x')), tree('tan(x)'))

    def test_log(self):
        x = tree('x')
        self.assertEqual(log(x, 'e'), tree('ln x'))
        self.assertEqual(log(x, 2), tree('log_2 x'))
        self.assertEqual(log(x), tree('log x'))
        self.assertEqual(log(x, 10), tree('log x'))

    def test_ln(self):
        self.assertEqual(ln(tree('x')), tree('ln x'))

    def test_der(self):
        x2, x, y = tree('x ^ 2, x, y')
        self.assertEqual(der(x2), tree('[x ^ 2]\''))
        self.assertEqual(der(x2, x), tree('d/dx x ^ 2'))
        self.assertEqual(der(x2, y), tree('d/dy x ^ 2'))

    def test_integral(self):
        x2, x, y, a, b = tree('x ^ 2, x, y, a, b')
        self.assertEqual(integral(x2, x), tree('int x^2 dx'))
        self.assertEqual(integral(x2, x, a, b), tree('int_a^b x^2 dx'))
        self.assertEqual(integral(x2, y, a, b), tree('int_a^b x^2 dy'))

    def test_int_def(self):
        x2, a, b, expect = tree('x ^ 2, a, b, [x ^ 2]_a^b')
        self.assertEqual(int_def(x2, a, b), expect)

    def test_eq(self):
        x, a, b, expect = tree('x, a, b, x + a = b')
        self.assertEqual(eq(x + a, b), expect)