Fix PossibleZeroQ

mathics/builtin/arithmetic.py

@@ -1309,19 +1309,19 @@ class PossibleZeroQ(SympyFunction):
       <dd>returns 'True' if basic symbolic and numerical methods suggest that expr has value zero, and 'False' otherwise.
     </dl>
 
-    ## Test whether a numeric expression is zero:
-    ## >> PossibleZeroQ[E^(I Pi/4) - (-1)^(1/4)]
-    ##  = True
+    Test whether a numeric expression is zero:
+    >> PossibleZeroQ[E^(I Pi/4) - (-1)^(1/4)]
+     = True
 
-    ## The determination is approximate.
+    The determination is approximate.
 
     Test whether a symbolic expression is likely to be identically zero:
     >> PossibleZeroQ[(x + 1) (x - 1) - x^2 + 1]
      = True
 
 
-    ## >> PossibleZeroQ[(E + Pi)^2 - E^2 - Pi^2 - 2 E Pi]
-    ##  = True
+    >> PossibleZeroQ[(E + Pi)^2 - E^2 - Pi^2 - 2 E Pi]
+     = True
 
     Show that a numeric expression is nonzero:
     >> PossibleZeroQ[E^Pi - Pi^E]
@@ -1346,6 +1346,11 @@ def apply(self, expr, evaluation):
 
         sympy_expr = expr.to_sympy()
         result = _iszero(sympy_expr)
+        if result is None:
+        # try expanding the expression
+            exprexp = Expression("ExpandAll", expr).evaluate(evaluation)
+            exprexp = exprexp.to_sympy()
+            result = _iszero(exprexp)        
         if result is None:
             # Can't get exact answer, so try approximate equal
             numeric_val = Expression("N", expr).evaluate(evaluation)

mathics/core/evaluation.py

@@ -262,6 +262,7 @@ def parse(self, query):
 
         return self.parse_feeder(MathicsSingleLineFeeder(query))
 
+
     def parse_evaluate(self, query, timeout=None):
         expr = self.parse(query)
         if expr is not None:
@@ -273,7 +274,6 @@ def parse_feeder(self, feeder):
     def parse_feeder_returning_code(self, feeder):
         "Parse a single expression from feeder and print the messages."
         from mathics.core.parser.util import parse_returning_code
-
         try:
             result, source_code = parse_returning_code(self.definitions, feeder)
         except TranslateError:

mathics/core/expression.py

@@ -2109,7 +2109,7 @@ def __neg__(self) -> 'Rational':
 
     @property
     def is_zero(self) -> bool:
-        return self.numerator().is_zero
+        return self.numerator().is_zero and not self.denominator().is_zero()
 
 
 class Real(Number):
@@ -2257,9 +2257,10 @@ def is_zero(self) -> bool:
 
     @property
     def is_approx_zero(self) -> bool:
-        # FIXME: figure out how to hook int $MachinePrecision and
-        # what the right definition here would be.
-        return abs(self.value) <= 10**-14
+        # In WMA, Chop[10.^(-10)] == 0,
+        # so, lets take it.
+        res = abs(self.value) <= 1e-10
+        return res
 
 
 class PrecisionReal(Real):