Introduce Integer1 = Integer(1)

@mmatera: a while back in branch not pushed, I also had other numbers
and in particular Integer(0) which is even more common.

I had problems somewhere along the line with that, so I didn't commit
any of this.

Since you introduced more locally IntegerOne, put this in for that one
case.

However rather than do more Integer symbols in this branch, let's merge
it in and do this as a follow on.

The number of changes in this branch is getting quite long.

Author: rocky

mathics/builtin/algebra.py

@@ -10,6 +10,7 @@
     Atom,
     Expression,
     Integer,
+    Integer1,
     Number,
     Symbol,
     SymbolFalse,
@@ -497,17 +498,17 @@ class FactorTermsList(Builtin):
     def apply_list(self, expr, vars, evaluation):
         "FactorTermsList[expr_, vars_List]"
         if expr == Integer(0):
-            return Expression("List", Integer(1), Integer(0))
+            return Expression("List", Integer1, Integer(0))
         elif isinstance(expr, Number):
-            return Expression("List", expr, Integer(1))
+            return Expression("List", expr, Integer1)
 
         for x in vars.leaves:
             if not (isinstance(x, Atom)):
                 return evaluation.message("CoefficientList", "ivar", x)
 
         sympy_expr = expr.to_sympy()
         if sympy_expr is None:
-            return Expression("List", Integer(1), expr)
+            return Expression("List", Integer1, expr)
         sympy_expr = sympy.together(sympy_expr)
 
         sympy_vars = [
@@ -1160,7 +1161,7 @@ def apply_noform(self, expr, evaluation):
 
     def apply(self, expr, form, evaluation):
         "Coefficient[expr_, form_]"
-        return _coefficient(self.__class__.__name__, expr, form, Integer(1), evaluation)
+        return _coefficient(self.__class__.__name__, expr, form, Integer1, evaluation)
 
     def apply_n(self, expr, form, n, evaluation):
         "Coefficient[expr_, form_, n_]"
@@ -1401,7 +1402,7 @@ class Exponent(Builtin):
 
     def apply_novar(self, expr, evaluation):
         "Exponent[expr_]"
-        return evaluation.message("Exponent", "argtu", Integer(1))
+        return evaluation.message("Exponent", "argtu", Integer1)
 
     def apply(self, expr, form, h, evaluation):
         "Exponent[expr_, form_, h_]"

mathics/builtin/arithmetic.py

@@ -26,6 +26,7 @@
     Complex,
     Expression,
     Integer,
+    Integer1,
     Number,
     Rational,
     Real,
@@ -113,7 +114,7 @@ def apply(self, z, evaluation):
                 if mpmath.isinf(result) and isinstance(result, mpmath.mpc):
                     result = Symbol("ComplexInfinity")
                 elif mpmath.isinf(result) and result > 0:
-                    result = Expression("DirectedInfinity", Integer(1))
+                    result = Expression("DirectedInfinity", Integer1)
                 elif mpmath.isinf(result) and result < 0:
                     result = Expression("DirectedInfinity", Integer(-1))
                 elif mpmath.isnan(result):
@@ -261,7 +262,7 @@ def negate(item):
             if item.has_form("Times", 1, None):
                 if isinstance(item.leaves[0], Number):
                     neg = -item.leaves[0]
-                    if neg.sameQ(Integer(1)):
+                    if neg.sameQ(Integer1):
                         if len(item.leaves) == 1:
                             return neg
                         else:
@@ -584,7 +585,7 @@ def inverse(item):
                 item.leaves[1], (Integer, Rational, Real)
             ):
                 neg = -item.leaves[1]
-                if neg.sameQ(Integer(1)):
+                if neg.sameQ(Integer1):
                     return item.leaves[0]
                 else:
                     return Expression("Power", item.leaves[0], neg)
@@ -604,7 +605,7 @@ def inverse(item):
                 negative.append(inverse(item))
             elif isinstance(item, Rational):
                 numerator = item.numerator()
-                if not numerator.sameQ(Integer(1)):
+                if not numerator.sameQ(Integer1):
                     positive.append(numerator)
                 negative.append(item.denominator())
             else:
@@ -619,7 +620,7 @@ def inverse(item):
         if positive:
             positive = create_infix(positive, op, 400, "None")
         else:
-            positive = Integer(1)
+            positive = Integer1
         if negative:
             negative = create_infix(negative, op, 400, "None")
             result = Expression(
@@ -681,15 +682,15 @@ def apply(self, items, evaluation):
                 and item.leaves[0].sameQ(leaves[-1])
             ):
                 leaves[-1] = Expression(
-                    "Power", leaves[-1], Expression("Plus", item.leaves[1], Integer(1))
+                    "Power", leaves[-1], Expression("Plus", item.leaves[1], Integer1)
                 )
             elif (
                 leaves
                 and leaves[-1].has_form("Power", 2)
                 and leaves[-1].leaves[0].sameQ(item)
             ):
                 leaves[-1] = Expression(
-                    "Power", item, Expression("Plus", Integer(1), leaves[-1].leaves[1])
+                    "Power", item, Expression("Plus", Integer1, leaves[-1].leaves[1])
                 )
             elif item.get_head().sameQ(SymbolDirectedInfinity):
                 infinity_factor = True
@@ -719,9 +720,9 @@ def apply(self, items, evaluation):
                 number = sympy.Mul(*[item.to_sympy() for item in numbers])
                 number = from_sympy(number)
         else:
-            number = Integer(1)
+            number = Integer1
 
-        if number.sameQ(Integer(1)):
+        if number.sameQ(Integer1):
             number = None
         elif number.is_zero:
             if infinity_factor:
@@ -743,7 +744,7 @@ def apply(self, items, evaluation):
         if not leaves:
             if infinity_factor:
                 return SymbolComplexInfinity
-            return Integer(1)
+            return Integer1
 
         if len(leaves) == 1:
             ret = leaves[0]
@@ -1354,7 +1355,7 @@ class I(Predefined):
     python_equivalent = 1j
 
     def evaluate(self, evaluation):
-        return Complex(Integer(0), Integer(1))
+        return Complex(Integer(0), Integer1)
 
 
 class NumberQ(Test):
@@ -2208,7 +2209,7 @@ def apply(self, expr, evaluation):
         "%(name)s[expr_]"
         if isinstance(expr, Symbol):
             if expr == SymbolTrue:
-                return Integer(1)
+                return Integer1
             elif expr == SymbolFalse:
                 return Integer(0)
         return None
@@ -2219,7 +2220,7 @@ class Assumptions(Predefined):
     <dl>
     <dt>'$Assumptions'
       <dd>is the default setting for the Assumptions option used in such
-   functions as Simplify, Refine, and Integrate. 
+   functions as Simplify, Refine, and Integrate.
     </dl>
     """
 

mathics/builtin/calculus.py

@@ -9,6 +9,7 @@
 from mathics.core.expression import (
     Expression,
     Integer,
+    Integer1,
     Number,
     SymbolTrue,
     SymbolFalse,
@@ -148,10 +149,10 @@ def apply(self, f, x, evaluation):
         "D[f_, x_?NotListQ]"
 
         if f == x:
-            return Integer(1)
+            return Integer1
         elif not f.is_atom() and len(f.leaves) == 1 and f.leaves[0] == x:
             return Expression(
-                Expression(Expression("Derivative", Integer(1)), f.head), x
+                Expression(Expression("Derivative", Integer1), f.head), x
             )
         elif not f.is_atom() and len(f.leaves) == 1:
             g = f.leaves[0]
@@ -170,7 +171,7 @@ def summand(leaf, index):
                                 "Derivative",
                                 *(
                                     [Integer(0)] * (index)
-                                    + [Integer(1)]
+                                    + [Integer1]
                                     + [Integer(0)] * (len(f.leaves) - index - 1)
                                 )
                             ),

mathics/builtin/comparison.py

@@ -20,6 +20,7 @@
     Complex,
     Expression,
     Integer,
+    Integer1,
     Number,
     Symbol,
     SymbolFalse,
@@ -243,7 +244,6 @@ def expr_equal(self, lhs, rhs, max_extra_prec=None) -> Optional[bool]:
         return True
 
     def infty_equal(self, lhs, rhs, max_extra_prec=None) -> Optional[bool]:
-        IntegerOne = Integer(1)
         if rhs.get_head().sameQ(SymbolDirectedInfinity):
             lhs, rhs = rhs, lhs
         if not lhs.get_head().sameQ(SymbolDirectedInfinity):
@@ -253,14 +253,14 @@ def infty_equal(self, lhs, rhs, max_extra_prec=None) -> Optional[bool]:
                 return True
             else:
                 return self.equal2(
-                    Expression("Sign", lhs._leaves[0]), IntegerOne, max_extra_prec
+                    Expression("Sign", lhs._leaves[0]), Integer1, max_extra_prec
                 )
         if rhs.is_numeric():
             return False
         elif rhs.is_atom():
             return None
         if rhs.get_head().sameQ(lhs.get_head()):
-            dir1 = dir2 = IntegerOne
+            dir1 = dir2 = Integer1
             if len(lhs._leaves) == 1:
                 dir1 = lhs._leaves[0]
             if len(rhs._leaves) == 1:

mathics/core/expression.py

@@ -2265,6 +2265,7 @@ def __neg__(self) -> "Integer":
     def is_zero(self) -> bool:
         return self.value == 0
 
+Integer1 = Integer(1)
 
 class Rational(Number):
     @lru_cache()