Typing experiments

src/mypy.ini

@@ -3,5 +3,5 @@
 python_version = 3.12
 
 # https://github.com/sagemath/sage/issues/36198#issuecomment-1709521850
-follow_imports = skip
+follow_imports = silent
 ignore_missing_imports = True

src/sage/categories/morphism.pyi

@@ -0,0 +1,3 @@
+
+class Morphism:
+    ...

src/sage/rings/factorint_pari.pyi

@@ -1,4 +1,13 @@
-from typing import Union
+from typing import overload, Literal
+from sage.rings.integer import Int
 
-def factor_using_pari(n: Union[int, Integer], int_: bool = False, debug_level: int = 0, proof: bool | None = None) -> list[tuple[Union[int, Integer], int]]:
+@overload
+def factor_using_pari(n: Int, int_: Literal[True], debug_level: int = 0, proof: bool | None = None) -> list[tuple[int, int]]:
+    ...
+
+@overload
+def factor_using_pari(n: Int, int_: Literal[False], debug_level: int = 0, proof: bool | None = None) -> list[tuple[Integer, int]]:
+    ...
+
+def factor_using_pari(n: Int, int_: bool = False, debug_level: int = 0, proof: bool | None = None) -> list[tuple[Int, int]]:
     ...

src/sage/rings/integer.pyi

@@ -1,72 +1,56 @@
-from sage.libs.gmp.types import __mpz_struct, mpz_t, mpz_ptr
-from sage.libs.gmp.mpz import mpz_set
+from typing import overload
 
 from sage.structure.element import EuclideanDomainElement, RingElement
-from sage.categories.morphism import Morphism
 
 class Integer(EuclideanDomainElement):
-    value: __mpz_struct[1]
-
-    def set_from_mpz(self, value: mpz_t) -> None:
-        ...
-
-    def hash_c(self) -> int:
-        ...
-
-    def __pari__(self) -> object:
-        ...
-
-    def _shift_helper(self, y: object, sign: int) -> object:
-        ...
-
-    def _add_(self, other: object) -> object:
-        ...
-
-    def _mul_(self, other: object) -> object:
-        ...
-
-    def _pow_(self, other: object) -> object:
-        ...
-
-    def _and(self, other: 'Integer') -> 'Integer':
-        ...
-
-    def _or(self, other: 'Integer') -> 'Integer':
-        ...
-
-    def _xor(self, other: 'Integer') -> 'Integer':
-        ...
-
-    def _exact_log_log2_iter(self, m: 'Integer') -> int:
-        ...
-
-    def _exact_log_mpfi_log(self, m: object) -> int:
-        ...
-
-    def _valuation(self, p: 'Integer') -> RingElement:
-        ...
-
-    def _val_unit(self, p: 'Integer') -> object:
-        ...
-
-    def _divide_knowing_divisible_by(self, right: 'Integer') -> 'Integer':
-        ...
-
-    def _is_power_of(self, n: 'Integer') -> bool:
-        ...
-
-    def _pseudoprime_is_prime(self, proof: object) -> bool:
-        ...
-
-def mpz_set_str_python(z: mpz_ptr, s: str, base: int) -> int:
-    ...
-
-def smallInteger(value: int) -> 'Integer':
-    ...
-
-_small_primes_table: list[bool]
-
-def _Integer_from_mpz(e: mpz_t) -> 'Integer':
-    z = Integer.__new__(Integer)
-    mpz_set(z.value, e)
-    return z
+    def __init__(self, x: object = None, base: Int = 0) -> None: ...
+    def __pari__(self) -> object: ...
+    def _shift_helper(self, y: object, sign: int) -> object: ...
+    def _add_(self, other: Integer) -> Integer: ...
+    def _sub_(self, other: Integer) -> Integer: ...
+    def _mul_(self, other: Integer) -> Integer: ...
+    def _pow_(self, other: Integer) -> Integer: ...
+    def _exact_log_log2_iter(self, m: Integer) -> int: ...
+    def _exact_log_mpfi_log(self, m: object) -> int: ...
+    def _valuation(self, p: Integer) -> RingElement: ...
+    def valuation(self, p: Int) -> RingElement: ...
+
+    ord = valuation
+
+    def val_unit(self, p: Int) -> object: ...
+    def divide_knowing_divisible_by(self, right: Int) -> Integer: ...
+    def is_power_of(self, n: Integer) -> bool: ...
+    def is_pseudoprime(self) -> bool: ...
+    @overload
+    def __add__(self, other: Int) -> Integer: ...
+    @overload
+    def __add__(self, other: object) -> object: ...
+    @overload
+    def __sub__(self, other: Int) -> Integer: ...
+    @overload
+    def __sub__(self, other: object) -> object: ...
+    @overload
+    def __rsub__(self, other: int) -> Integer: ...
+    @overload
+    def __rsub__(self, other: object) -> object: ...
+    @overload
+    def __radd__(self, other: int) -> Integer: ...
+    @overload
+    def __radd__(self, other: object) -> object: ...
+    @overload
+    def __mul__(self, other: Int) -> Integer: ...
+    @overload
+    def __mul__(self, other: object) -> object: ...
+    @overload
+    def __rmul__(self, other: int) -> Integer: ...
+    @overload
+    def __rmul__(self, other: object) -> object: ...
+    @overload
+    def __pow__(self, other: Int) -> Integer: ...
+    @overload
+    def __pow__(self, other: Int, modulo: Int | None) -> Integer: ...
+    @overload
+    def __pow__(self, other: object, modulo: object | None) -> object: ...
+
+# This type alias is not available at runtime
+type Int = Integer | int

src/sage/rings/integer.pyx

@@ -4586,8 +4586,15 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):
             107326510974310118493
             sage: a.divide_knowing_divisible_by(11) # way off and possibly random
             43215361478743422388970455040
+
+        TESTS:
+
+        Make sure the methods works for Python ints::
+
+            sage: 10.divide_knowing_divisible_by(5r)
+            2
         """
-        return self._divide_knowing_divisible_by(right)
+        return self._divide_knowing_divisible_by(as_Integer(right))
 
     def _lcm(self, Integer n):
         """
@@ -5213,7 +5220,7 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):
             else:
                 return 0
 
-    def is_power_of(Integer self, n):
+    def is_power_of(self, n) -> bool:
         r"""
         Return ``True`` if there is an integer `b` with
         `\mathtt{self} = n^b`.

src/sage/rings/rational.pyi

@@ -0,0 +1,4 @@
+from sage.structure.element import FieldElement
+
+class Rational(FieldElement):
+    ...

src/sage/structure/element.pyi

@@ -0,0 +1,78 @@
+from sage.structure.sage_object import SageObject
+
+class Element(SageObject):
+
+    def __add__(self, other): ...
+
+    def __sub__(self, other): ...
+
+    def __neg__(self): ...
+
+    def __mul__(self, other): ...
+
+    def __matmul__(self, other): ...
+
+    def __truediv__(self, other): ...
+
+    def __floordiv__(self, other): ...
+
+    def __mod__(self, other): ...
+
+    def __pow__(self, other, modulo): ...
+
+class ElementWithCachedMethod(Element):
+    ...
+
+class ModuleElement(Element):
+    ...
+
+class ModuleElementWithMutability(ModuleElement):
+    ...
+
+class MonoidElement(Element):
+    ...
+
+class AdditiveGroupElement(ModuleElement):
+    ...
+
+class MultiplicativeGroupElement(MonoidElement):
+    ...
+
+class RingElement(ModuleElement):
+    ...
+
+class CommutativeRingElement(RingElement):
+    ...
+
+class Expression(CommutativeRingElement):
+    ...
+
+class Vector(ModuleElementWithMutability):
+    ...
+
+class Matrix(ModuleElement):
+    ...
+
+class IntegralDomainElement(CommutativeRingElement):
+    ...
+
+class DedekindDomainElement(IntegralDomainElement):
+    ...
+
+class PrincipalIdealDomainElement(DedekindDomainElement):
+    ...
+
+class EuclideanDomainElement(PrincipalIdealDomainElement):
+    ...
+
+class FieldElement(CommutativeRingElement):
+    ...
+
+class AlgebraElement(RingElement):
+    ...
+
+class CommutativeAlgebraElement(CommutativeRingElement):
+    ...
+
+class InfinityElement(RingElement):
+    ...