Miscellaneous fixes (#1153)

This just fixes a few crashes I was seeing running Mathics through OEIS
programs, with corresponding doctests (and a few more type error fixes)

mathics/builtin/atomic/numbers.py

@@ -486,11 +486,14 @@ def eval_with_base(self, n, b, evaluation, nr_elements=None, pos=None):
         digits = []
         if not py_b == 10:
             digits = convert_float_base(py_n, py_b, display_len - exp)
-            # truncate all the leading 0's
-            i = 0
-            while digits and digits[i] == 0:
-                i += 1
-            digits = digits[i:]
+            if all(d == 0 for d in digits):
+                digits = [0]
+            else:
+                # truncate all the leading 0's
+                i = 0
+                while digits and digits[i] == 0:
+                    i += 1
+                digits = digits[i:]
 
             if not isinstance(n, Integer):
                 if len(digits) > display_len:

mathics/builtin/list/constructing.py

@@ -184,14 +184,21 @@ class Normal(Builtin):
       <dd> Brings special expressions to a normal expression from different special \
            forms.
     </dl>
+
+    >> Normal[Pi]
+     = Pi
+    >> Series[Exp[x], {x, 0, 5}]
+     = 1 + x + 1 / 2 x ^ 2 + 1 / 6 x ^ 3 + 1 / 24 x ^ 4 + 1 / 120 x ^ 5 + O[x] ^ 6
+    >> Normal[%]
+     = 1 + x + x ^ 2 / 2 + x ^ 3 / 6 + x ^ 4 / 24 + x ^ 5 / 120
     """
 
     summary_text = "convert objects to normal expressions"
 
     def eval_general(self, expr: Expression, evaluation: Evaluation):
         "Normal[expr_]"
         if isinstance(expr, Atom):
-            return
+            return expr
         if expr.has_form("RootSum", 2):
             return from_sympy(expr.to_sympy().doit(roots=True))
         return Expression(

mathics/builtin/list/rearrange.py

@@ -8,11 +8,12 @@
 import functools
 from collections import defaultdict
 from itertools import chain
-from typing import Callable
+from typing import Callable, Optional
 
-from mathics.core.atoms import Integer, Integer0
+from mathics.core.atoms import Integer, Integer0, Number
 from mathics.core.attributes import A_FLAT, A_ONE_IDENTITY, A_PROTECTED
 from mathics.core.builtin import Builtin, MessageException
+from mathics.core.element import BaseElement
 from mathics.core.evaluation import Evaluation
 from mathics.core.expression import Expression, structure
 from mathics.core.expression_predefined import MATHICS3_INFINITY
@@ -655,6 +656,7 @@ class Flatten(Builtin):
             "Level `1` specified in `2` exceeds the levels, `3`, "
             "which can be flattened together in `4`."
         ),
+        "normal": "Nonatomic expression expected at position `1` in `2`.",
     }
 
     rules = {
@@ -759,21 +761,25 @@ def insert_element(elements):
 
         return Expression(h, *insert_element(elements))
 
-    def eval(self, expr, n, h, evaluation):
+    def eval(self, expr: BaseElement, n: Number, h, evaluation):
         "Flatten[expr_, n_, h_]"
 
+        n_int: Optional[int]
         if n.sameQ(MATHICS3_INFINITY):
-            n = -1  # a negative number indicates an unbounded level
+            n_int = -1  # a negative number indicates an unbounded level
         else:
             n_int = n.get_int_value()
             # Here we test for negative since in Mathics Flatten[] as opposed to flatten_with_respect_to_head()
             # negative numbers (and None) are not allowed.
             if n_int is None or n_int < 0:
                 evaluation.message("Flatten", "flpi", n)
                 return
-            n = n_int
 
-        return expr.flatten_with_respect_to_head(h, level=n)
+        if not isinstance(expr, Expression):
+            evaluation.message("Flatten", "normal", 1, expr)
+            return
+
+        return expr.flatten_with_respect_to_head(h, level=n_int)
 
 
 class GatherBy(_GatherOperation):
@@ -814,14 +820,15 @@ class GatherBy(_GatherOperation):
     summary_text = "gather based on values of a function applied to elements"
     _bin = _GatherBin
 
-    def eval(self, values, func, evaluation: Evaluation):
+    def eval(self, values: BaseElement, func, evaluation: Evaluation):
         "%(name)s[values_, func_]"
 
         if not self._check_list(values, func, evaluation):
             return
 
         keys = Expression(SymbolMap, func, values).evaluate(evaluation)
-        if len(keys.elements) != len(values.elements):
+        assert keys is not None
+        if len(keys.get_elements()) != len(values.get_elements()):
             return
 
         return self._gather(keys, values, _FastEquivalence())

mathics/builtin/numbers/algebra.py

@@ -899,6 +899,8 @@ class CoefficientList(Builtin):
      = {{{0, 0, 0, 27}, {0, 0, -54, 0}, {0, 36, 0, 0}, {-8, 0, 0, 0}}, {{0, 0, 27, 0}, {0, -36, 0, 0}, {12, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 9, 0, 0}, {-6, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{1, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}
     >> CoefficientList[Series[Log[1-x], {x, 0, 9}], x]
      = {0, -1, -1 / 2, -1 / 3, -1 / 4, -1 / 5, -1 / 6, -1 / 7, -1 / 8, -1 / 9}
+    >> CoefficientList[Series[2x, {x, 0, 9}], x]
+     = {0, 2}
     """
 
     messages = {
@@ -944,7 +946,9 @@ def eval(self, expr: Expression, form: Expression, evaluation: Evaluation):
                 return ListExpression(
                     *[
                         coeffs.elements[i - nmin.value] if i >= nmin.value else Integer0
-                        for i in range(0, nmax.value)
+                        for i in range(
+                            0, min(nmax.value, nmin.value + len(coeffs.elements))
+                        )
                     ]
                 )
 

mathics/builtin/numbers/calculus.py

@@ -1818,6 +1818,8 @@ class SeriesCoefficient(Builtin):
      = 31 / 5760
     >> SeriesCoefficient[Exp[-x], {x, 0, 5}]
      = -1 / 120
+    >> SeriesCoefficient[2x, {x, 0, 2}]
+     = 0
 
     >> SeriesCoefficient[SeriesData[x, c, Table[i^2, {i, 10}], 7, 17, 3], 14/3]
      = 64
@@ -1842,10 +1844,10 @@ def eval(self, series: Expression, n: Rational, evaluation: Evaluation):
         den: Integer
         coeffs, nmin, nmax, den = series.elements[2:]
         index = n.value * den.value - nmin.value
-        if index < 0:
-            return Integer0
         if index >= nmax.value - nmin.value:
             return SymbolIndeterminate
+        if index < 0 or index >= len(coeffs.elements):
+            return Integer0
         return coeffs[index]
 
 

mathics/builtin/numbers/numbertheory.py

@@ -217,6 +217,8 @@ class EulerPhi(SympyFunction):
     'EulerPhi' of a negative integer is same as its positive counterpart:
     >> EulerPhi[-11] == EulerPhi[11]
     = True
+    >> EulerPhi[0]
+    = 0
 
     Large arguments are computed quickly:
     >> EulerPhi[40!]
@@ -238,8 +240,16 @@ class EulerPhi(SympyFunction):
 
     def eval(self, n: Integer, evaluation: Evaluation):
         "EulerPhi[n_Integer]"
+        if n.is_zero:
+            return Integer0
         return super().eval(abs(n), evaluation)
 
+    def to_sympy(self, expr, **kwargs):
+        try:
+            return super().to_sympy(expr, **kwargs)
+        except ValueError:  # n must be a positive integer
+            return None
+
 
 class FactorInteger(Builtin):
     """
@@ -441,7 +451,7 @@ class IntegerPartitions(Builtin):
         "IntegerPartitions[n_Integer, All]": "IntegerPartitions[n, n]",
         "IntegerPartitions[n_Integer, k_Integer]": "IntegerPartitions[n, {1, k}]",
         "IntegerPartitions[n_Integer, {k_Integer}]": "IntegerPartitions[n, {k, k}]",
-        "IntegerPartitions[n_Integer, kspec_, s_List] /; SubsetQ[Range[n], s]": "Select[IntegerPartitions[n, kspec], SubsetQ[s, #] &]",
+        "IntegerPartitions[n_Integer, kspec_, s_List] /; SubsetQ[Range[n], s] && s == Union[s]": "Select[IntegerPartitions[n, kspec], SubsetQ[s, #] &]",
         "IntegerPartitions[n_Integer, kspec_, All]": "IntegerPartitions[n, kspec]",
         "IntegerPartitions[n_Integer, kspec_, sspec_, m_]": "Take[IntegerPartitions[n, kspec, sspec], m]",
         "IntegerPartitions[n_Integer, {k_Integer}, s_List]": "ReverseSort@Select[Union[ReverseSort /@ Tuples[s, k]], Total[#] == n &]",

mathics/core/element.py

@@ -301,7 +301,7 @@ def get_head_name(self) -> str:
     def get_float_value(self, permit_complex=False):
         return None
 
-    def get_int_value(self):
+    def get_int_value(self) -> Optional[int]:
         return None
 
     def get_lookup_name(self) -> str:

mathics/core/expression.py

@@ -662,7 +662,7 @@ def sequence(element):
         return self._flatten_sequence(sequence, evaluation)
 
     def flatten_with_respect_to_head(
-        self, head, pattern_only=False, callback=None, level=100
+        self, head: Symbol, pattern_only=False, callback=None, level=100
     ) -> "Expression":
         """
         Flatten elements in self which have `head` in them.
@@ -1304,6 +1304,7 @@ def flatten_callback(new_elements, old):
                 element.unevaluated = old.unevaluated
 
         if A_FLAT & attributes:
+            assert isinstance(new._head, Symbol)
             new = new.flatten_with_respect_to_head(new._head, callback=flatten_callback)
             if new.elements_properties is None:
                 new._build_elements_properties()