Tweaked some logarithmic rules.

src/rules/__init__.py

@@ -22,7 +22,7 @@ from .derivatives import match_zero_derivative, \
         match_goniometric, match_sum_product_rule, match_quotient_rule
 from .logarithmic import match_constant_logarithm, \
         match_add_logarithms, match_raised_base, match_factor_out_exponent, \
-        match_factor_in_multiplicant
+        match_factor_in_multiplicant, match_expand_terms
 from .integrals import match_solve_indef, match_constant_integral, \
         match_integrate_variable_power, match_factor_out_constant, \
         match_division_integral, match_function_integral
@@ -56,7 +56,8 @@ RULES = {
                  match_variable_power, match_const_deriv_multiplication,
                  match_logarithmic, match_goniometric, match_sum_product_rule,
                  match_quotient_rule],
-        OP_LOG: [match_constant_logarithm, match_factor_out_exponent],
+        OP_LOG: [match_constant_logarithm, match_factor_out_exponent,
+                 match_expand_terms],
         OP_INT: [match_integrate_variable_power, match_constant_integral,
                  match_factor_out_constant, match_division_integral,
                  match_function_integral],

src/rules/logarithmic.py

@@ -1,8 +1,8 @@
-from itertools import combinations, product
+from itertools import combinations, product, ifilterfalse
 
-from .utils import find_variables, partition
+from .utils import find_variables, partition, divides, is_numeric_node
 from ..node import ExpressionLeaf as L, OP_LOG, OP_ADD, OP_MUL, OP_POW, \
-        Scope, log
+        Scope, log, DEFAULT_LOGARITHM_BASE, E, OP_DIV
 from ..possibilities import Possibility as P, MESSAGES
 from ..translate import _
 
@@ -11,8 +11,8 @@ def match_constant_logarithm(node):
     """
     log_1(a)   ->  # raise ValueError for base 1
     log(1)     ->  0
-    log(a, a)  ->  1  # Explicit possibility to prevent cycles
-    log(a, a)  ->  log(a) / log(a)  # ->  1
+    log(a, a)  ->  1
+    log(a, b) and b not in  (10, e)  ->  log(a) / log(b)
     """
     assert node.is_op(OP_LOG)
 
@@ -30,8 +30,9 @@ def match_constant_logarithm(node):
     if raised == base:
         # log(a, a)  ->  1
         p.append(P(node, base_equals_raised))
-        # log(a, a)  ->  log(a) / log(a)  # ->  1
-        # TODO: When to do this except for this case?
+        p.append(P(node, divide_same_base))
+    elif base not in (DEFAULT_LOGARITHM_BASE, E):
+        # log(a, b)  ->  log(a) / log(b)
         p.append(P(node, divide_same_base))
 
     return p
@@ -56,12 +57,12 @@ def base_equals_raised(root, args):
     return L(1).negate(root.negated)
 
 
-MESSAGES[base_equals_raised] = _('Logarithm {0} recuces to 1.')
+MESSAGES[base_equals_raised] = _('Logarithm {0} reduces to 1.')
 
 
 def divide_same_base(root, args):
     """
-    log(a, b)  ->  log(a) / log(b)
+    log(a, b) and b != 10  ->  log(a) / log(b)
     """
     raised, base = root
 
@@ -73,10 +74,10 @@ MESSAGES[divide_same_base] = _('Apply log_b(a) = log(a) / log(b) on {0}.')
 
 def match_add_logarithms(node):
     """
-    log(a) + log(b)   ->  log(ab)
-    -log(a) - log(b)  ->  -(log(a) + log(b))  # ->  -log(ab)
-    log(a) - log(b)   ->  log(a / b)
-    -log(a) + log(b)  ->  log(b / a)
+    log(a) + log(b) and a,b in Z   ->  log(ab)
+    -log(a) - log(b) and a,b in Z  ->  -(log(a) + log(b))  # ->  -log(ab)
+    log(a) - log(b) and a/b in Z   ->  log(a / b)
+    -log(a) + log(b) and a/b in Z  ->  log(b / a)
     """
     assert node.is_op(OP_ADD)
 
@@ -86,7 +87,10 @@ def match_add_logarithms(node):
 
     for log_a, log_b in combinations(logarithms, 2):
         # Compare base
-        if log_a[1] != log_b[1]:
+        (a, base_a), (b, base_b) = log_a, log_b
+
+        if base_a != base_b or not a.is_numeric() \
+                or not b.is_numeric():  # pragma: nocover
             continue
 
         a_negated = log_a.negated == 1
@@ -98,10 +102,10 @@ def match_add_logarithms(node):
         elif a_negated and b_negated:
             # -log(a) - log(b)  ->  -(log(a) + log(b))
             p.append(P(node, expand_negations, (scope, log_a, log_b)))
-        elif not log_a.negated and b_negated:
+        elif not log_a.negated and b_negated and divides(b.value, a.value):
             # log(a) - log(b)  ->  log(a / b)
             p.append(P(node, subtract_logarithms, (scope, log_a, log_b)))
-        elif a_negated and not log_b.negated:
+        elif a_negated and not log_b.negated and  divides(a.value, b.value):
             # -log(a) + log(b)  ->  log(b / a)
             p.append(P(node, subtract_logarithms, (scope, log_b, log_a)))
 
@@ -161,8 +165,8 @@ MESSAGES[subtract_logarithms] = _('Apply log(a) - log(b) = log(a / b).')
 
 def match_raised_base(node):
     """
-    g ^ log_g(a)     ->  a
-    g ^ (blog_g(a))  ->  g ^ log_g(a ^ b)
+    g ^ log_g(a)        ->  a
+    g ^ (b * log_g(a))  ->  g ^ log_g(a ^ b)
     """
     assert node.is_op(OP_POW)
 
@@ -188,11 +192,18 @@ def match_raised_base(node):
 
 
 def factor_in_exponent_multiplicant(root, args):
+    """
+    g ^ (b * log_g(a))  ->  g ^ log_g(a ^ b)
+    """
     r, e = root
 
     return r ** factor_in_multiplicant(e, args)
 
 
+MESSAGES[factor_in_exponent_multiplicant] = \
+        _('Bring {2} into {3} as exponent so that the power can be removed.')
+
+
 def raised_base(root, args):
     """
     g ^ log_g(a)  ->  a
@@ -285,3 +296,53 @@ def factor_in_multiplicant(root, args):
 
 MESSAGES[factor_in_multiplicant] = \
         _('Bring multiplicant {2} into {3} as the exponent of {3[0]}.')
+
+
+def match_expand_terms(node):
+    """
+    log(ab) and a not in Z  ->  log(a) + log(b)
+    log(a / b)              ->  log(a) - log(b)
+    """
+    assert node.is_op(OP_LOG)
+
+    exp = node[0]
+
+    if exp.is_op(OP_MUL):
+        scope = Scope(exp)
+
+        return [P(node, expand_multiplication_terms, (scope, n)) \
+                for n in ifilterfalse(is_numeric_node, scope)]
+
+    if exp.is_op(OP_DIV):
+        return [P(node, expand_division_terms)]
+
+    return []
+
+
+def expand_multiplication_terms(root, args):
+    """
+    log(ab) and a not in Z  ->  log(a) + log(b)
+    """
+    scope, n = args
+    scope.remove(n)
+    base = root[1]
+    addition = log(n, base=base) + log(scope.as_nary_node(), base=base)
+
+    return addition.negate(root.negated)
+
+
+MESSAGES[expand_multiplication_terms] = _('Extract {2} from {0}.')
+
+
+def expand_division_terms(root, args):
+    """
+    log(a / b)  ->  log(a) - log(b)
+    """
+    division, base = root
+    n, d = division
+    addition = log(n.negate(division.negated), base=base) - log(d, base=base)
+
+    return addition.negate(root.negated)
+
+
+MESSAGES[expand_division_terms] = _('Expand {0} to a subtraction.')

tests/test_rules_logarithmic.py

@@ -4,7 +4,9 @@ from src.rules.logarithmic import log, match_constant_logarithm, \
         subtract_logarithms, match_raised_base, raised_base, \
         match_factor_out_exponent, split_negative_exponent, \
         factor_out_exponent, match_factor_in_multiplicant, \
-        factor_in_multiplicant
+        factor_in_multiplicant, match_expand_terms, \
+        expand_multiplication_terms, expand_division_terms, \
+        factor_in_exponent_multiplicant
 from src.node import Scope
 from src.possibilities import Possibility as P
 from tests.rulestestcase import RulesTestCase, tree
@@ -30,10 +32,21 @@ class TestRulesLogarithmic(RulesTestCase):
                 [P(root, base_equals_raised),
                  P(root, divide_same_base)])
 
+        root = tree('log(a, b)')
+        self.assertEqualPos(match_constant_logarithm(root),
+                [P(root, divide_same_base)])
+
     def test_logarithm_of_one(self):
         root = tree('log 1')
         self.assertEqual(logarithm_of_one(root, ()), 0)
 
+    def test_base_equals_raised(self):
+        root, expect = tree('log(a, a), 1')
+        self.assertEqual(base_equals_raised(root, ()), expect)
+
+        root, expect = tree('-log(a, a), -1')
+        self.assertEqual(base_equals_raised(root, ()), expect)
+
     def test_divide_same_base(self):
         root, l5, l6 = tree('log(5, 6), 5, 6')
         self.assertEqual(divide_same_base(root, ()), log(l5) / log(l6))
@@ -42,19 +55,27 @@ class TestRulesLogarithmic(RulesTestCase):
         root = tree('log a + ln b')
         self.assertEqualPos(match_add_logarithms(root), [])
 
-        log_a, log_b = root = tree('log a + log b')
+        # log(ab) is not desired if ab is not reduceable
+        root = tree('log a + log b')
+        self.assertEqualPos(match_add_logarithms(root), [])
+
+        log_a, log_b = root = tree('log 2 + log 3')
         self.assertEqualPos(match_add_logarithms(root),
                 [P(root, add_logarithms, (Scope(root), log_a, log_b))])
 
-        log_a, log_b = root = tree('-log a - log b')
+        log_a, log_b = root = tree('-log 2 - log 3')
         self.assertEqualPos(match_add_logarithms(root),
                 [P(root, expand_negations, (Scope(root), log_a, log_b))])
 
-        log_a, log_b = root = tree('log a - log b')
+        # log(2 / 3) is not desired because 2 / 3 cannot be reduced
+        log_a, log_b = root = tree('log 2 - log 3')
+        self.assertEqualPos(match_add_logarithms(root), [])
+
+        log_a, log_b = root = tree('log 4 - log 2')
         self.assertEqualPos(match_add_logarithms(root),
                 [P(root, subtract_logarithms, (Scope(root), log_a, log_b))])
 
-        log_a, log_b = root = tree('-log a + log b')
+        log_a, log_b = root = tree('-log 2 + log 4')
         self.assertEqualPos(match_add_logarithms(root),
                 [P(root, subtract_logarithms, (Scope(root), log_b, log_a))])
 
@@ -93,6 +114,18 @@ class TestRulesLogarithmic(RulesTestCase):
         root = tree('2 ^ log_3(a)')
         self.assertEqualPos(match_raised_base(root), [])
 
+        root = tree('e ^ (2ln x)')
+        l2, lnx = mul = root[1]
+        self.assertEqualPos(match_raised_base(root),
+                [P(root, factor_in_exponent_multiplicant,
+                   (Scope(mul), l2, lnx))])
+
+    def test_factor_in_exponent_multiplicant(self):
+        root, expect = tree('e ^ (2ln x), e ^ ln x ^ 2')
+        l2, lnx = mul = root[1]
+        self.assertEqual(factor_in_exponent_multiplicant(root,
+                         (Scope(mul), l2, lnx)), expect)
+
     def test_raised_base(self):
         root, a = tree('2 ^ log_2(a), a')
         self.assertEqual(raised_base(root, (root[1][0],)), a)
@@ -136,3 +169,25 @@ class TestRulesLogarithmic(RulesTestCase):
         l2, log3 = root
         self.assertEqual(factor_in_multiplicant(root, (Scope(root), l2, log3)),
                          expect)
+
+    def test_match_expand_terms(self):
+        ab, base = root = tree('log(2x)')
+        a, b = ab
+        self.assertEqualPos(match_expand_terms(root),
+                [P(root, expand_multiplication_terms, (Scope(ab), b))])
+
+        root = tree('log(2 * 3)')
+        self.assertEqualPos(match_expand_terms(root), [])
+
+        root = tree('log(2 / a)')
+        self.assertEqualPos(match_expand_terms(root),
+                [P(root, expand_division_terms)])
+
+    def test_expand_multiplication_terms(self):
+        root, expect = tree('log(2x), log x + log 2')
+        self.assertEqual(expand_multiplication_terms(root,
+                         (Scope(root[0]), root[0][1])), expect)
+
+    def test_expand_division_terms(self):
+        root, expect = tree('log(2 / x), log 2 - log x')
+        self.assertEqual(expand_division_terms(root, ()), expect)