Merge branch 't/23331/allow_exact_defining_polynomials_for_p_adic_ext…

…ensions' into t/20310/change_precision

src/sage/rings/padics/padic_extension_generic.py

@@ -183,11 +183,11 @@ def defining_polynomial(self):
             return self._given_poly
 
     def exact_field(self):
-        """
+        r"""
         Return a number field with the same defining polynomial.
 
-        Note that this method always returns a field, even for
-        a p-adic ring.
+        Note that this method always returns a field, even for a `p`-adic
+        ring.
 
         EXAMPLES::
 
@@ -206,7 +206,7 @@ def exact_field(self):
         return self.base_ring().exact_field().extension(self._exact_modulus, self.variable_name())
 
     def modulus(self, exact=False):
-        """
+        r"""
         Returns the polynomial defining this extension.
 
         INPUT:

src/sage/rings/padics/padic_extension_leaves.py

@@ -100,21 +100,21 @@ def __init__(self, exact_modulus, poly, prec, print_mode, shift_seed, names, imp
 
         INPUT:
 
-            - exact_modulus -- The original polynomial defining the
-              extension.  This could be a polynomial with integer
-              coefficients, for example, while poly has coefficients
-              in Zp.
+        - ``exact_modulus`` -- the original polynomial defining the extension.
+          This could be a polynomial with integer coefficients, for example,
+          while ``poly`` has coefficients in a `p`-adic ring.
 
-            - poly -- The polynomial with coefficients in
-              self.base_ring() defining this extension.
+        - ``poly`` -- t polynomial with coefficients in :meth:`base_ring`
+          defining this extension
 
-            - prec -- The precision cap of this ring.
+        - ``prec`` -- the precision cap of this ring
 
-            - print_mode -- A dictionary of print options.
+        - ``print_mode`` -- a dictionary of print options
 
-            - shift_seed -- unused
+        - ``shift_seed`` -- unused
 
-            - names -- a 4-tuple, (variable_name, residue_name, unramified_subextension_variable_name, uniformizer_name)
+        - ``names`` -- a 4-tuple, ``(variable_name, residue_name,
+          unramified_subextension_variable_name, uniformizer_name)``
 
         EXAMPLES::
 
@@ -153,26 +153,26 @@ class UnramifiedExtensionFieldCappedRelative(UnramifiedExtensionGeneric, pAdicCa
         sage: TestSuite(R).run(skip='_test_log',max_runs=4)
     """
     def __init__(self, exact_modulus, poly, prec, print_mode, shift_seed, names, implementation='FLINT'):
-        """
+        r"""
         A representation of Qq.
 
         INPUT:
 
-            - exact_modulus -- The original polynomial defining the
-              extension.  This could be a polynomial with integer
-              coefficients, for example, while poly has coefficients
-              in Qp.
+        - ``exact_modulus`` -- the original polynomial defining the extension.
+          This could be a polynomial with rational coefficients, for example,
+          while ``poly`` has coefficients in a `p`-adic field.
 
-            - poly -- The polynomial with coefficients in
-              self.base_ring() defining this extension.
+        - ``poly`` -- the polynomial with coefficients in :meth:`base_ring`
+          defining this extension
 
-            - prec -- The precision cap of this ring.
+        - ``prec`` -- the precision cap of this ring
 
-            - print_mode -- A dictionary of print options.
+        - ``print_mode`` -- a dictionary of print options
 
-            - shift_seed -- unused
+        - ``shift_seed`` -- unused
 
-            - names -- a 4-tuple, (variable_name, residue_name, unramified_subextension_variable_name, uniformizer_name)
+        - ``names`` -- a 4-tuple, ``(variable_name, residue_name,
+          unramified_subextension_variable_name, uniformizer_name)``
 
         EXAMPLES::
 
@@ -217,21 +217,21 @@ def __init__(self, exact_modulus, poly, prec, print_mode, shift_seed, names, imp
 
         INPUT:
 
-            - exact_modulus -- The original polynomial defining the
-              extension.  This could be a polynomial with integer
-              coefficients, for example, while poly has coefficients
-              in Zp.
+        - ``exact_modulus`` -- the original polynomial defining the extension.
+          This could be a polynomial with integer coefficients, for example,
+          while poly has coefficients in a `p`-adic ring.
 
-            - poly -- The polynomial with coefficients in
-              self.base_ring() defining this extension.
+        - ``poly`` -- the polynomial with coefficients in :meth:`base_ring`
+          defining this extension
 
-            - prec -- The precision cap of this ring.
+        - ``prec`` -- the precision cap of this ring
 
-            - print_mode -- A dictionary of print options.
+        - ``print_mode`` -- A dictionary of print options
 
-            - shift_seed -- unused
+        - ``shift_seed`` -- unused
 
-            - names -- a 4-tuple, (variable_name, residue_name, unramified_subextension_variable_name, uniformizer_name)
+        - ``names`` -- a 4-tuple, ``(variable_name, residue_name,
+          unramified_subextension_variable_name, uniformizer_name)``
 
         EXAMPLES::
 
@@ -276,21 +276,20 @@ def __init__(self, exact_modulus, poly, prec, print_mode, shift_seed, names, imp
 
         INPUT:
 
-            - exact_modulus -- The original polynomial defining the
-              extension.  This could be a polynomial with integer
-              coefficients, for example, while poly has coefficients
-              in Qp.
+        - ``exact_modulus`` -- the original polynomial defining the extension.
+          This could be a polynomial with integer coefficients, for example,
+          while ``poly`` has coefficients in a `p`-adic field.
 
-            - poly -- The polynomial with coefficients in
-              self.base_ring() defining this extension.
+        - ``poly`` -- the polynomial with coefficients in :meth:`base_ring`
+          defining this extension
 
-            - prec -- The precision cap of this ring.
+        - ``prec`` -- the precision cap of this ring
 
-            - print_mode -- A dictionary of print options.
+        - ``print_mode`` -- a dictionary of print options
 
-            - shift_seed -- unused
+        - ``shift_seed`` -- unused
 
-            - names -- a 4-tuple, (variable_name, residue_name, unramified_subextension_variable_name, uniformizer_name)
+        - ``names`` -- a 4-tuple, ``(variable_name, residue_name, unramified_subextension_variable_name, uniformizer_name)``
 
         EXAMPLES::
 
@@ -339,21 +338,20 @@ def __init__(self, exact_modulus, poly, prec, print_mode, shift_seed, names, imp
 
         INPUT:
 
-            - exact_modulus -- The original polynomial defining the
-              extension.  This could be a polynomial with integer
-              coefficients, for example, while poly has coefficients
-              in Zp.
+        - ``exact_modulus`` -- the original polynomial defining the extension.
+          This could be a polynomial with integer coefficients, for example,
+          while ``poly`` has coefficients in Zp.
 
-            - poly -- The polynomial with coefficients in
-              self.base_ring() defining this extension.
+        - ``poly`` -- the polynomial with coefficients in :meth:`base_ring`
+          defining this extension
 
-            - prec -- The precision cap of this ring.
+        - ``prec`` -- the precision cap of this ring
 
-            - print_mode -- A dictionary of print options.
+        - ``print_mode`` -- a dictionary of print options
 
-            - shift_seed -- unused
+        - ``shift_seed`` -- unused
 
-            - names -- a 4-tuple, (variable_name, residue_name, unramified_subextension_variable_name, uniformizer_name)
+        - ``names`` -- a 4-tuple, ``(variable_name, residue_name, unramified_subextension_variable_name, uniformizer_name)``
 
         EXAMPLES::
 
@@ -388,21 +386,20 @@ def __init__(self, exact_modulus, poly, prec, print_mode, shift_seed, names, imp
 
         INPUT:
 
-            - exact_modulus -- The original polynomial defining the
-              extension.  This could be a polynomial with integer
-              coefficients, for example, while poly has coefficients
-              in Qp.
+        - ``exact_modulus`` -- the original polynomial defining the extension.
+          This could be a polynomial with rational coefficients, for example,
+          while ``poly`` has coefficients in a `p`-adic field.
 
-            - poly -- The polynomial with coefficients in
-              self.base_ring() defining this extension.
+        - ``poly`` -- the polynomial with coefficients in :meth:`base_ring`
+          defining this extension
 
-            - prec -- The precision cap of this ring.
+        - ``prec`` -- the precision cap of this ring
 
-            - print_mode -- A dictionary of print options.
+        - ``print_mode`` -- a dictionary of print options
 
-            - shift_seed -- unused
+        - ``shift_seed`` -- unused
 
-            - names -- a 4-tuple, (variable_name, residue_name, unramified_subextension_variable_name, uniformizer_name)
+        - ``names`` -- a 4-tuple, ``(variable_name, residue_name, unramified_subextension_variable_name, uniformizer_name)``
 
         EXAMPLES::
 
@@ -439,21 +436,20 @@ def __init__(self, exact_modulus, poly, prec, print_mode, shift_seed, names, imp
 
         INPUT:
 
-            - exact_modulus -- The original polynomial defining the
-              extension.  This could be a polynomial with integer
-              coefficients, for example, while poly has coefficients
-              in Zp.
+        - ``exact_modulus`` -- the original polynomial defining the extension.
+          This could be a polynomial with integer coefficients, for example,
+          while ``poly`` has coefficients in a `p`-adic ring.
 
-            - poly -- The polynomial with coefficients in
-              self.base_ring() defining this extension.
+        - ``poly`` -- the polynomial with coefficients in :meth:`base_ring`
+          defining this extension
 
-            - prec -- The precision cap of this ring.
+        - ``prec`` -- the precision cap of this ring
 
-            - print_mode -- A dictionary of print options.
+        - ``print_mode`` -- a dictionary of print options
 
-            - shift_seed -- unused
+        - ``shift_seed`` -- unused
 
-            - names -- a 4-tuple, (variable_name, residue_name, unramified_subextension_variable_name, uniformizer_name)
+        - ``names`` -- a 4-tuple, ``(variable_name, residue_name, unramified_subextension_variable_name, uniformizer_name)``
 
         EXAMPLES::
 
@@ -495,21 +491,20 @@ def __init__(self, exact_modulus, poly, prec, print_mode, shift_seed, names, imp
 
         INPUT:
 
-            - exact_modulus -- The original polynomial defining the
-              extension.  This could be a polynomial with integer
-              coefficients, for example, while poly has coefficients
-              in Qp.
+        - ``exact_modulus`` -- the original polynomial defining the extension.
+          This could be a polynomial with rational coefficients, for example,
+          while ``poly`` has coefficients in a `p`-adic field.
 
-            - poly -- The polynomial with coefficients in
-              self.base_ring() defining this extension.
+        - ``poly`` -- the polynomial with coefficients in :meth:`base_ring`
+          defining this extension
 
-            - prec -- The precision cap of this ring.
+        - ``prec`` -- the precision cap of this ring
 
-            - print_mode -- A dictionary of print options.
+        - ``print_mode`` -- a dictionary of print options
 
-            - shift_seed -- unused
+        - ``shift_seed`` -- unused
 
-            - names -- a 4-tuple, (variable_name, residue_name, unramified_subextension_variable_name, uniformizer_name)
+        - ``names`` -- a 4-tuple, ``(variable_name, residue_name, unramified_subextension_variable_name, uniformizer_name)``
 
         EXAMPLES::
 
@@ -552,21 +547,20 @@ def __init__(self, exact_modulus, poly, prec, print_mode, shift_seed, names, imp
 
         INPUT:
 
-            - exact_modulus -- The original polynomial defining the
-              extension.  This could be a polynomial with integer
-              coefficients, for example, while poly has coefficients
-              in Zp.
+        - ``exact_modulus`` -- the original polynomial defining the extension.
+          This could be a polynomial with integer coefficients, for example,
+          while ``poly`` has coefficients in a `p`-adic ring.
 
-            - poly -- The polynomial with coefficients in
-              self.base_ring() defining this extension.
+        - ``poly`` -- the polynomial with coefficients in :meth:`base_ring`
+          defining this extension
 
-            - prec -- The precision cap of this ring.
+        - ``prec`` -- the precision cap of this ring
 
-            - print_mode -- A dictionary of print options.
+        - ``print_mode`` -- a dictionary of print options
 
-            - shift_seed -- unused
+        - ``shift_seed`` -- unused
 
-            - names -- a 4-tuple, (variable_name, residue_name, unramified_subextension_variable_name, uniformizer_name)
+        - ``names`` -- a 4-tuple, ``(variable_name, residue_name, unramified_subextension_variable_name, uniformizer_name)``
 
         EXAMPLES::
 
@@ -608,21 +602,20 @@ def __init__(self, exact_modulus, poly, prec, print_mode, shift_seed, names, imp
 
         INPUT:
 
-            - exact_modulus -- The original polynomial defining the
-              extension.  This could be a polynomial with integer
-              coefficients, for example, while poly has coefficients
-              in Zp.
+        - ``exact_modulus`` -- the original polynomial defining the extension.
+          This could be a polynomial with integer coefficients, for example,
+          while ``poly`` has coefficients in a `p`-adic ring.
 
-            - poly -- The polynomial with coefficients in
-              self.base_ring() defining this extension.
+        - ``poly`` -- the polynomial with coefficients in :meth:`base_ring`
+          defining this extension
 
-            - prec -- The precision cap of this ring.
+        - ``prec`` -- the precision cap of this ring
 
-            - print_mode -- A dictionary of print options.
+        - ``print_mode`` -- a dictionary of print options
 
-            - shift_seed -- unused
+        - ``shift_seed`` -- unused
 
-            - names -- a 4-tuple, (variable_name, residue_name, unramified_subextension_variable_name, uniformizer_name)
+        - ``names`` -- a 4-tuple, ``(variable_name, residue_name, unramified_subextension_variable_name, uniformizer_name)``
 
         EXAMPLES::
 

src/sage/rings/padics/padic_generic_element.pyx

@@ -1495,7 +1495,7 @@ cdef class pAdicGenericElement(LocalGenericElement):
 
     def rational_reconstruction(self):
         r"""
-        Returns a rational approximation to this p-adic number
+        Returns a rational approximation to this `p`-adic number
 
         This will raise an ArithmeticError if there are no valid
         approximations to the unit part with numerator and
@@ -1505,10 +1505,6 @@ cdef class pAdicGenericElement(LocalGenericElement):
 
             :meth:`_rational_`
 
-        INPUT:
-
-        - ``self`` -- a p-adic element
-
         OUTPUT:
 
         rational -- an approximation to self
@@ -1533,7 +1529,7 @@ cdef class pAdicGenericElement(LocalGenericElement):
 
     def _rational_(self):
         r"""
-        Return a rational approximation to this p-adic number.
+        Return a rational approximation to this `p`-adic number.
 
         If there is no good rational approximation to the unit part,
         will just return the integer approximation.