1 / Fix issues with pattern matching for Rubi

mathics/core/pattern.py

@@ -701,7 +701,12 @@ def match_expression_with_one_identity(
             isinstance(pat_elem, PatternObject)
             and pat_elem.get_head() == SymbolOptional
         ):
-            if len(pat_elem.elements) == 2:
+            if optionals:
+                # A default pattern already exists
+                # Do not use the second one
+                if new_pattern is None:
+                    new_pattern = pat_elem
+            elif len(pat_elem.elements) == 2:
                 pat, value = pat_elem.elements
                 if isinstance(pat, Pattern):
                     key = pat.elements[0].atom.name  # type: ignore[attr-defined]
@@ -724,8 +729,12 @@ def match_expression_with_one_identity(
                 result = defaultvalue_expr.evaluate(evaluation)
                 assert result is not None
                 if result.sameQ(defaultvalue_expr):
-                    return
-                optionals[key] = result
+                    if new_pattern is None:
+                        # The optional pattern has no default value
+                        # for the given position
+                        new_pattern = pat_elem
+                else:
+                    optionals[key] = result
             else:
                 return
         elif new_pattern is not None:
@@ -757,6 +766,8 @@ def match_expression_with_one_identity(
     del parms["attributes"]
     assert new_pattern is not None
     new_pattern.match(expression=expression, pattern_context=parms)
+    for optional in optionals:
+        vars_dict.pop(optional)
 
 
 def basic_match_expression(

test/core/test_patterns.py

@@ -0,0 +1,52 @@
+# -*- coding: utf-8 -*-
+"""
+Unit tests for mathics pattern matching
+"""
+
+import sys
+import time
+from test.helper import check_evaluation, evaluate
+
+import pytest
+
+
+@pytest.mark.parametrize(
+    ("str_expr", "msgs", "str_expected", "fail_msg"),
+    [
+        # Two default arguments (linear)
+        ("MatchQ[1, a_.+b_.*x_]", None, "True", None),
+        ("MatchQ[x, a_.+b_.*x_]", None, "True", None),
+        ("MatchQ[2*x, a_.+b_.*x_]", None, "True", None),
+        ("MatchQ[1+x, a_.+b_.*x_]", None, "True", None),
+        ("MatchQ[1+2*x, a_.+b_.*x_]", None, "True", None),
+        # Default argument (power)
+        ("MatchQ[1, x_^m_.]", None, "True", None),
+        ("MatchQ[x, x_^m_.]", None, "True", None),
+        ("MatchQ[x^1, x_^m_.]", None, "True", None),
+        ("MatchQ[x^2, x_^m_.]", None, "True", None),
+        # Two default arguments (power)
+        ("MatchQ[1, x_.^m_.]", None, "True", None),
+        ("MatchQ[x, x_.^m_.]", None, "True", None),
+        ("MatchQ[x^1, x_.^m_.]", None, "True", None),
+        ("MatchQ[x^2, x_.^m_.]", None, "True", None),
+        # Two default arguments (no non-head)
+        ("MatchQ[1, a_.+b_.]", None, "True", None),
+        ("MatchQ[x, a_.+b_.]", None, "True", None),
+        ("MatchQ[1+x, a_.+b_.]", None, "True", None),
+        ("MatchQ[1+2*x, a_.+b_.]", None, "True", None),
+        ("MatchQ[1, a_.+b_.]", None, "True", None),
+        ("MatchQ[x, a_.*b_.]", None, "True", None),
+        ("MatchQ[2*x, a_.*b_.]", None, "True", None),
+    ],
+)
+def test_patterns(str_expr, msgs, str_expected, fail_msg):
+    """patterns"""
+    check_evaluation(
+        str_expr,
+        str_expected,
+        to_string_expr=True,
+        to_string_expected=True,
+        hold_expected=True,
+        failure_message=fail_msg,
+        expected_messages=msgs,
+    )