gh-39556: Fixed issue where Partitions() was caching results when an error happens.
    
Fixes #38640. Partition used to cache the result even when an error was
given if provided with QQ instead of ZZ. To fix this we apply ZZ to
convert our input into integers during normalization. This has the added
side effect of making list(Partitions(4,parts_in=vector(QQ,[2,4]))) not
produce an error as seen in the added doctest. However providing
Partitions() with rational numbers that cannot be converted to integers
does crash as expected. This crash does not cache the result however so
the error is fixed.

### 📝 Checklist

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- [X] The title is concise and informative.
- [X] The description explains in detail what this PR is about.
- [X] I have linked a relevant issue or discussion.
- [X] I have created tests covering the changes.
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preview.

### ⌛ Dependencies
    
URL: #39556
Reported by: Noel-Roemmele
Reviewer(s): Noel-Roemmele, Travis Scrimshaw

Author: Release Manager

src/sage/combinat/partition.py

@@ -7596,8 +7596,19 @@ def __classcall_private__(cls, n, parts):
             sage: P2 = Partitions(4, parts_in=(1,2))
             sage: P is P2
             True
+
+        Ensure that :issue:`38640` is fixed::
+
+            sage: list(Partitions(4,parts_in=vector(QQ,[2,4])))
+            [[4], [2, 2]]
+            sage: list(Partitions(4,parts_in=vector(QQ,[2,1/4])))
+            Traceback (most recent call last):
+            ...
+            TypeError: no conversion of this rational to integer
+            sage: list(Partitions(4,parts_in=vector(ZZ,[2,4])))
+            [[4], [2, 2]]
         """
-        parts = tuple(sorted(parts))
+        parts = tuple(sorted(set(map(ZZ,parts))))
         return super().__classcall__(cls, Integer(n), parts)
 
     def __init__(self, n, parts):