Most Sage objects are immutable. Nevertheless, copy and deepcopy make copies (through pickling/unpickling) for them because we have not provided the classes with __copy__ methods (which should just return the object) and __deepcopy__ methods (which in many cases should just return the object).

sage: a = 0
sage: copy(a) is a
False

Another symptom (from the original ticket description): Copying of (immutable!) LazyFamily objects only works for families that can be pickled:

   sage: def unpicklableFamily():
   ...       x = 10
   ...       return LazyFamily([1,2,3], lambda n: x*n)
   sage: f = unpicklableFamily() 
   sage: copy(f)
   Traceback (most recent call last):
   ...
   ValueError: Cannot pickle code objects from closures

The case of __deepcopy__ of immutable container-like objects (like Family or Sequence) is a bit trickier: Is immutability intended to imply that the elements are immutable too? In this ticket, we make no such assumption.

Tickets:

• trivial __copy__ and __deepcopy__ methods for number types #32454 trivial __copy__ and __deepcopy__ methods for number types
• trivial __copy__ and __deepcopy__ methods for number field elements #32478 trivial __copy__ and __deepcopy__ methods for number field elements
• trivial __copy__ and __deepcopy__ methods for symbolic expressions and functions #32480 trivial __copy__ and __deepcopy__ methods for symbolic expressions and functions
• trivial __copy__ and __deepcopy__ methods for Family and Set #32462 trivial __copy__ and __deepcopy__ methods for Family and Set
• __copy__ methods for all classes that define "copy" methods (outside of sage.tensor, sage.manifolds) #32453 __copy__ methods for all classes that define copy methods
• sage.tensor, sage.manifolds: __copy__, __deepcopy__ methods for all classes that define "copy" methods #32476 sage.tensor, sage.manifolds: __copy__, __deepcopy__ methods for all classes that define copy methods
• copy(CombinatorialFreeModule.Element) broken by #22632 #23075 copy(CombinatorialFreeModule.Element) broken by Cythonize CombinatorialFreeModuleElement #22632
• Fix some more deepcopy/caching issues in the quadratic forms code (followup to #5403) #5417 Fix some more deepcopy/caching issues in the quadratic forms code
  Related:
• sage.structure.mutability: Add global is_mutable, is_immutable functions #30387

Depends on #32454

CC: @tscrim @mjungmath @nbruin @kwankyu @williamstein @mwageringel @kcrisman

Component: pickling

Keywords: LazyFamily, copy, pickle

Author: Matthias Koeppe

Branch/Commit: u/mkoeppe/__copy___and___deepcopy___methods_for_all_immutable_sage_objects @ 2bd01ae

Issue created by migration from https://trac.sagemath.org/ticket/13811