fix #431 and #274

mathics/builtin/arithmetic.py

@@ -1590,6 +1590,10 @@ class Sum(_IterationFunction, SympyFunction):
 
     #> a=Sum[x^k*Sum[y^l,{l,0,4}],{k,0,4}]]
      : "a=Sum[x^k*Sum[y^l,{l,0,4}],{k,0,4}]" cannot be followed by "]" (line 1 of "<test>").
+
+    ## Issue431
+    #> Sum[2^(-i), {i, 1, \[Infinity]}]
+     = 1
     """
 
     # Do not throw warning message for symbolic iteration bounds

mathics/builtin/linalg.py

@@ -15,7 +15,7 @@
 import sympy
 from mpmath import mp
 
-from mathics.builtin.base import Builtin
+from mathics.builtin.base import Builtin, SympyConstant
 from mathics.core.convert import from_sympy
 from mathics.core.expression import Expression, Integer, Symbol, Real
 
@@ -149,7 +149,7 @@ class VectorAngle(Builtin):
     }
 
 
-class Degree(Builtin):
+class Degree(SympyConstant):
     """
     <dl>
     <dt>'Degree'
@@ -158,11 +158,22 @@ class Degree(Builtin):
 
     >> Cos[60 Degree]
      = 1 / 2
+
+    Degree has the value of Pi / 180
+    >> Degree == Pi / 180
+     = True
+
+    #> Cos[Degree[x]]
+     = Cos[Degree[x]]
+
+    ## Issue 274
+    #> \[Degree] == ° == Degree
+     = True
     """
 
-    rules = {
-        'Degree': '(Pi/180)'
-    }
+    def to_sympy(self, expr):
+        if expr == Symbol('System`Degree'):
+            return sympy.pi / 180
 
 
 class Inverse(Builtin):

mathics/core/parser/parser.py

@@ -13,6 +13,16 @@
     inequality_ops, misc_ops)
 
 
+special_symbols = {
+    '\u03C0': 'Pi',         # Pi
+    '\uF74D': 'E',          # ExponentialE
+    '\uF74E': 'I',          # ImaginaryI
+    '\uF74F': 'I',          # ImaginaryJ
+    '\u221E': 'Infinity',   # Infinity
+    '\u00B0': 'Degree',     # Degree
+}
+
+
 class Parser(object):
     def __init__(self):
         # no implicit times on these tokens
@@ -287,7 +297,8 @@ def p_String(self, token):
         return result
 
     def p_Symbol(self, token):
-        result = Symbol(token.text, context=None)
+        symbol_name = special_symbols.get(token.text, token.text)
+        result = Symbol(symbol_name, context=None)
         self.consume()
         return result
 

test/test_parser/test_parser.py

@@ -89,6 +89,14 @@ def testSymbol(self):
         self.check('`name', Symbol('`name'))
         self.check('`context`name', Symbol('`context`name'))
 
+    def testSpecialSymbol(self):
+        self.check('\[Pi]', 'Pi')
+        self.check('\[Degree]', 'Degree')
+        self.check('\[ExponentialE]', 'E')
+        self.check('\[ImaginaryI]', 'I')
+        self.check('\[ImaginaryJ]', 'I')
+        self.check('\[Infinity]', 'Infinity')
+
     def testNumber(self):
         self.check_number('0')
         self.check_number('-1')