Added possibility to multiply denominators of division addition.

src/rules/fractions.py

@@ -70,17 +70,20 @@ MESSAGES[division_by_self] = _('Division of {1} by {1} reduces to 1.')
 def match_add_constant_fractions(node):
     """
     1 / 2 + 3 / 4  ->  2 / 4 + 3 / 4  # Equalize denominators
+    2 / 2 - 3 / 4  ->  4 / 4 - 3 / 4
     2 / 4 + 3 / 4  ->  5 / 4          # Equal denominators, so nominators can
                                       # be added
-    2 / 2 - 3 / 4  ->  4 / 4 - 3 / 4  # Equalize denominators
-    2 / 4 - 3 / 4  ->  -1 / 4         # Equal denominators, so nominators can
-                                      # be subtracted
+    2 / 4 - 3 / 4  ->  -1 / 4
+    1 / 2 + 3 / 4  ->  4 / 8 + 6 / 8  # Equalize denominators by multiplying
+                                      # them with eachother
+
     """
     assert node.is_op(OP_ADD)
 
     p = []
+    scope = Scope(node)
 
-    fractions = filter(lambda node: node.is_op(OP_DIV), Scope(node))
+    fractions = filter(lambda node: node.is_op(OP_DIV), scope)
 
     for a, b in combinations(fractions, 2):
         na, da = a
@@ -94,7 +97,12 @@ def match_add_constant_fractions(node):
             # least common multiple of their denominators. Later, the
             # nominators will be added
             denom = least_common_multiple(da.value, db.value)
-            p.append(P(node, equalize_denominators, (a, b, denom)))
+            p.append(P(node, equalize_denominators, (scope, a, b, denom)))
+
+            # Also, add the (non-recommended) possibility to multiply the
+            # denominators
+            p.append(P(node, equalize_denominators, (scope, a, b,
+                                                     da.value * db.value)))
 
     return p
 
@@ -104,10 +112,9 @@ def equalize_denominators(root, args):
     1 / 2 + 3 / 4  ->  2 / 4 + 3 / 4
     a / 2 + b / 4  ->  2a / 4 + b / 4
     """
-    denom = args[2]
-    scope = Scope(root)
+    scope, denom = args[::3]
 
-    for fraction in args[:2]:
+    for fraction in args[1:3]:
         n, d = fraction
         mult = denom / d.value
 
@@ -125,8 +132,8 @@ def equalize_denominators(root, args):
     return scope.as_nary_node()
 
 
-MESSAGES[equalize_denominators] = _('Equalize the denominators of division'
-    ' of {1} by {2}.')
+MESSAGES[equalize_denominators] = _('Equalize the denominators of divisions'
+    ' {2} and {3} to {4}.')
 
 
 def add_nominators(root, args):

tests/test_rules_fractions.py

 from src.rules.fractions import match_constant_division, division_by_one, \
         division_of_zero, division_by_self, match_add_constant_fractions, \
         equalize_denominators, add_nominators
+from src.node import Scope
 from src.possibilities import Possibility as P
 from tests.rulestestcase import RulesTestCase, tree
 
@@ -51,12 +52,14 @@ class TestRulesFractions(RulesTestCase):
         n0, n1 = root = l1 / l2 + l3 / l4
         possibilities = match_add_constant_fractions(root)
         self.assertEqualPos(possibilities,
-                [P(root, equalize_denominators, (n0, n1, 4))])
+                [P(root, equalize_denominators, (Scope(root), n0, n1, 4)),
+                 P(root, equalize_denominators, (Scope(root), n0, n1, 8))])
 
         (((n0, n1), n2), n3), n4 = root = a + l1 / l2 + b + l3 / l4 + c
         possibilities = match_add_constant_fractions(root)
         self.assertEqualPos(possibilities,
-                [P(root, equalize_denominators, (n1, n3, 4))])
+                [P(root, equalize_denominators, (Scope(root), n1, n3, 4)),
+                 P(root, equalize_denominators, (Scope(root), n1, n3, 8))])
 
         n0, n1 = root = l2 / l4 + l3 / l4
         possibilities = match_add_constant_fractions(root)
@@ -74,7 +77,8 @@ class TestRulesFractions(RulesTestCase):
         (((n0, n1), n2), n3), n4 = root = a + l2 / l2 + b + (-l3 / l4) + c
         possibilities = match_add_constant_fractions(root)
         self.assertEqualPos(possibilities,
-                [P(root, equalize_denominators, (n1, n3, 4))])
+                [P(root, equalize_denominators, (Scope(root), n1, n3, 4)),
+                 P(root, equalize_denominators, (Scope(root), n1, n3, 8))])
 
         (((n0, n1), n2), n3), n4 = root = a + l2 / l4 + b + (-l3 / l4) + c
         possibilities = match_add_constant_fractions(root)
@@ -85,22 +89,23 @@ class TestRulesFractions(RulesTestCase):
         a, b, l1, l2, l3, l4 = tree('a,b,1,2,3,4')
 
         n0, n1 = root = l1 / l2 + l3 / l4
-        self.assertEqualNodes(equalize_denominators(root, (n0, n1, 4)),
-                              l2 / l4 + l3 / l4)
+        self.assertEqualNodes(equalize_denominators(root,
+                              (Scope(root), n0, n1, 4)), l2 / l4 + l3 / l4)
 
         n0, n1 = root = a / l2 + b / l4
-        self.assertEqualNodes(equalize_denominators(root, (n0, n1, 4)),
-                              (l2 * a) / l4 + b / l4)
+        self.assertEqualNodes(equalize_denominators(root,
+                              (Scope(root), n0, n1, 4)), (l2 * a) / l4 + b /
+                              l4)
 
         #2 / 2 - 3 / 4  ->  4 / 4 - 3 / 4  # Equalize denominators
         n0, n1 = root = l1 / l2 + (-l3 / l4)
-        self.assertEqualNodes(equalize_denominators(root, (n0, n1, 4)),
-                              l2 / l4 + (-l3 / l4))
+        self.assertEqualNodes(equalize_denominators(root,
+            (Scope(root), n0, n1, 4)), l2 / l4 + (-l3 / l4))
 
         #2 / 2 - 3 / 4  ->  4 / 4 - 3 / 4  # Equalize denominators
         n0, n1 = root = a / l2 + (-b / l4)
-        self.assertEqualNodes(equalize_denominators(root, (n0, n1, 4)),
-                              (l2 * a) / l4 + (-b / l4))
+        self.assertEqualNodes(equalize_denominators(root,
+            (Scope(root), n0, n1, 4)), (l2 * a) / l4 + (-b / l4))
 
     def test_add_nominators(self):
         a, b, c = tree('a,b,c')