moving private doctests to pytests. Fix the compatibility issue 0. I-…

…> 0.

mathics/builtin/arithmetic.py

@@ -279,45 +279,6 @@ class Complex_(Builtin):
      = 1 + 2 I / 3
     >> Abs[Complex[3, 4]]
      = 5
-
-    #> OutputForm[Complex[2.0 ^ 40, 3]]
-     = 1.09951×10^12 + 3. I
-    #> InputForm[Complex[2.0 ^ 40, 3]]
-     = 1.099511627776*^12 + 3.*I
-
-    #> -2 / 3 - I
-     = -2 / 3 - I
-
-    #> Complex[10, 0]
-     = 10
-
-    #> 0. + I
-     = 0. + 1. I
-
-    #> 1 + 0 I
-     = 1
-    #> Head[%]
-     = Integer
-
-    #> Complex[0.0, 0.0]
-     = 0. + 0. I
-    #> 0. I
-     = 0.
-    #> 0. + 0. I
-     = 0.
-
-    #> 1. + 0. I
-     = 1.
-    #> 0. + 1. I
-     = 0. + 1. I
-
-    ## Check Nesting Complex
-    #> Complex[1, Complex[0, 1]]
-     = 0
-    #> Complex[1, Complex[1, 0]]
-     = 1 + I
-    #> Complex[1, Complex[1, 1]]
-     = I
     """
 
     summary_text = "head for complex numbers"
@@ -442,10 +403,6 @@ class Conjugate(MPMathFunction):
     >> Conjugate[{{1, 2 + I 4, a + I b}, {I}}]
      = {{1, 2 - 4 I, Conjugate[a] - I Conjugate[b]}, {-I}}
 
-    ## Issue #272
-    #> {Conjugate[Pi], Conjugate[E]}
-     = {Pi, E}
-
     >> Conjugate[1.5 + 2.5 I]
      = 1.5 - 2.5 I
     """
@@ -485,11 +442,6 @@ class DirectedInfinity(SympyFunction):
     >> DirectedInfinity[0]
      = ComplexInfinity
 
-    #> DirectedInfinity[1+I]+DirectedInfinity[2+I]
-     = (2 / 5 + I / 5) Sqrt[5] Infinity + (1 / 2 + I / 2) Sqrt[2] Infinity
-
-    #> DirectedInfinity[Sqrt[3]]
-     = Infinity
     """
 
     summary_text = "infinite quantity with a defined direction in the complex plane"
@@ -703,11 +655,6 @@ class Im(SympyFunction):
 
     >> Plot[{Sin[a], Im[E^(I a)]}, {a, 0, 2 Pi}]
      = -Graphics-
-
-    #> Re[0.5 + 2.3 I]
-     = 0.5
-    #> % // Precision
-     = MachinePrecision
     """
 
     summary_text = "imaginary part"
@@ -740,10 +687,6 @@ class Integer_(Builtin):
 
     >> Head[5]
      = Integer
-
-    ## Test large Integer comparison bug
-    #> {a, b} = {2^10000, 2^10000 + 1}; {a == b, a < b, a <= b}
-     = {False, True, True}
     """
 
     summary_text = "head for integer numbers"
@@ -789,10 +732,6 @@ class Product(IterationFunction, SympyFunction):
     >> primorial[12]
      = 7420738134810
 
-    ## Used to be a bug in sympy, but now it is solved exactly!
-    ## Again a bug in sympy - regressions between 0.7.3 and 0.7.6 (and 0.7.7?)
-    ## #> Product[1 + 1 / i ^ 2, {i, Infinity}]
-    ##  = 1 / ((-I)! I!)
     """
 
     summary_text = "discrete product"
@@ -847,9 +786,6 @@ class Rational_(Builtin):
 
     >> Rational[1, 2]
      = 1 / 2
-
-    #> -2/3
-     = -2 / 3
     """
 
     summary_text = "head for rational numbers"
@@ -878,11 +814,6 @@ class Re(SympyFunction):
 
     >> Plot[{Cos[a], Re[E^(I a)]}, {a, 0, 2 Pi}]
      = -Graphics-
-
-    #> Im[0.5 + 2.3 I]
-     = 2.3
-    #> % // Precision
-     = MachinePrecision
     """
 
     summary_text = "real part"
@@ -919,61 +850,6 @@ class Real_(Builtin):
     >> Head[x]
      = Real
 
-    ## Formatting tests
-    #> 1. * 10^6
-     = 1.×10^6
-    #> 1. * 10^5
-     = 100000.
-    #> -1. * 10^6
-     = -1.×10^6
-    #> -1. * 10^5
-     = -100000.
-    #> 1. * 10^-6
-     = 1.×10^-6
-    #> 1. * 10^-5
-     = 0.00001
-    #> -1. * 10^-6
-     = -1.×10^-6
-    #> -1. * 10^-5
-     = -0.00001
-
-    ## Mathematica treats zero strangely
-    #> 0.0000000000000
-     = 0.
-    #> 0.0000000000000000000000000000
-     = 0.×10^-28
-
-    ## Parse *^ Notation
-    #> 1.5×10^24
-     = 1.5×10^24
-    #> 1.5*^+24
-     = 1.5×10^24
-    #> 1.5*^-24
-     = 1.5×10^-24
-
-    ## Don't accept *^ with spaces
-    #> 1.5 *^10
-     : "1.5 *" cannot be followed by "^10" (line 1 of "<test>").
-    #> 1.5*^ 10
-     : "1.5*" cannot be followed by "^ 10" (line 1 of "<test>").
-
-    ## Issue654
-    #> 1^^2
-     : Requested base 1 in 1^^2 should be between 2 and 36.
-     : Expression cannot begin with "1^^2" (line 1 of "<test>").
-    #> 2^^0101
-     = 5
-    #> 2^^01210
-     : Digit at position 3 in 01210 is too large to be used in base 2.
-     : Expression cannot begin with "2^^01210" (line 1 of "<test>").
-    #> 16^^5g
-     : Digit at position 2 in 5g is too large to be used in base 16.
-     : Expression cannot begin with "16^^5g" (line 1 of "<test>").
-    #> 36^^0123456789abcDEFxyzXYZ
-     = 14142263610074677021975869033659
-    #> 37^^3
-     : Requested base 37 in 37^^3 should be between 2 and 36.
-     : Expression cannot begin with "37^^3" (line 1 of "<test>").
     """
 
     summary_text = "head for real numbers"
@@ -999,7 +875,7 @@ class RealNumberQ(Test):
     >> RealNumberQ[0 * I]
      = True
     >> RealNumberQ[0.0 * I]
-     = True
+     = False
     """
 
     attributes = A_NO_ATTRIBUTES
@@ -1076,12 +952,6 @@ class Sum(IterationFunction, SympyFunction):
     >> Sum[x ^ 2, {x, 1, y}] - y * (y + 1) * (2 * y + 1) / 6
      = 0
 
-    ## >> (-1 + a^n) Sum[a^(k n), {k, 0, m-1}] // Simplify
-    ## = -1 + (a ^ n) ^ m  # this is what I am getting
-    ## = Piecewise[{{m (-1 + a ^ n), a ^ n == 1}, {-1 + (a ^ n) ^ m, True}}]
-
-    #> 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>").
 
     ## Issue #302
     ## The sum should not converge since the first term is 1/0.

mathics/builtin/numbers/calculus.py

@@ -697,7 +697,6 @@ def diff(evaluation):
     def eval_with_x_tuple(self, f, xtuple, evaluation: Evaluation, options: dict):
         "%(name)s[f_, xtuple_, OptionsPattern[]]"
         f_val = f.evaluate(evaluation)
-
         if f_val.has_form("Equal", 2):
             f = Expression(SymbolPlus, f_val.elements[0], f_val.elements[1])
 

mathics/builtin/numbers/constants.py

@@ -263,14 +263,6 @@ class ComplexInfinity(_SympyConstant):
      = ComplexInfinity
     >> FullForm[ComplexInfinity]
      = DirectedInfinity[]
-
-    ## Issue689
-    #> ComplexInfinity + ComplexInfinity
-     : Indeterminate expression ComplexInfinity + ComplexInfinity encountered.
-     = Indeterminate
-    #> ComplexInfinity + Infinity
-     : Indeterminate expression ComplexInfinity + Infinity encountered.
-     = Indeterminate
     """
 
     summary_text = "infinite complex quantity of undetermined direction"
@@ -302,15 +294,6 @@ class Degree(_MPMathConstant, _NumpyConstant, _SympyConstant):
 
     >> N[\\[Degree]] == N[Degree]
      = True
-
-    #> Cos[Degree[x]]
-     = Cos[Degree[x]]
-
-
-    #> N[Degree]
-     = 0.0174533
-    #> N[Degree, 30]
-     = 0.0174532925199432957692369076849
     """
 
     summary_text = "conversion factor from radians to degrees"
@@ -367,9 +350,6 @@ class E(_MPMathConstant, _NumpyConstant, _SympyConstant):
      = 2.71828
     >> N[E, 50]
      = 2.7182818284590452353602874713526624977572470937000
-
-    #> 5. E
-     = 13.5914
     """
 
     summary_text = "exponential constant E ≃ 2.7182"
@@ -512,16 +492,6 @@ class Infinity(_SympyConstant):
     Use 'Infinity' in sum and limit calculations:
     >> Sum[1/x^2, {x, 1, Infinity}]
      = Pi ^ 2 / 6
-
-    #> FullForm[Infinity]
-     = DirectedInfinity[1]
-    #> (2 + 3.5*I) / Infinity
-     = 0.
-    #> Infinity + Infinity
-     = Infinity
-    #> Infinity / Infinity
-     : Indeterminate expression 0 Infinity encountered.
-     = Indeterminate
     """
 
     sympy_name = "oo"

mathics/core/convert/mpmath.py

@@ -18,7 +18,21 @@
 from mathics.core.systemsymbols import SymbolIndeterminate
 
 
-@lru_cache(maxsize=1024)
+# Another issue with the lru_cache: for mpmath, mpmath.mpc(0.,0.) and
+# mpmath.mpf(0.) produces the same hash. As a result, depending on
+# what is called first, the output of this function is different.
+#
+# note mmatera: When I start to pass the private doctests
+# to pytests, I realize that WMA evaluates `0. I`  to `Complex[0.,0.]`
+# instead of  `0.`. To fix this incompatibility, I removed from
+# `from_sympy` the lines that convert `mpc(0.,0.)` to `mpf(0.0)`,
+# and then this issue becomes evident.
+#
+# As we decide by now that performance comes after ensuring the compatibility
+# and clarity of the code, I propose here to conserve the right tests,
+# and commented out the cache and the lines that convert mpc(0,0) to MachineReal(0).
+#
+# @lru_cache(maxsize=1024)
 def from_mpmath(
     value: Union[mpmath.mpf, mpmath.mpc],
     precision: Optional[int] = None,
@@ -42,8 +56,8 @@ def from_mpmath(
         # HACK: use str here to prevent loss of precision
         return PrecisionReal(sympy.Float(str(value), precision=precision - 1))
     elif isinstance(value, mpmath.mpc):
-        if value.imag == 0.0:
-            return from_mpmath(value.real, precision=precision)
+        # if value.imag == 0.0:
+        #    return from_mpmath(value.real, precision=precision)
         val_re, val_im = value.real, value.imag
         if mpmath.isinf(val_re):
             if mpmath.isinf(val_im):

mathics/format/latex.py

@@ -234,7 +234,7 @@ def superscriptbox(self, **options):
         base = self.tex_block(tex1, True)
         superidx_to_tex = lookup_conversion_method(self.superindex, "latex")
         superindx = self.tex_block(superidx_to_tex(self.superindex, **options), True)
-        if isinstance(self.superindex, (String, StyleBox)):
+        if len(superindx) == 1 and isinstance(self.superindex, (String, StyleBox)):
             return "%s^%s" % (
                 base,
                 superindx,