various small details in padics

Author: fchapoton

src/sage/rings/padics/common_conversion.pyx

@@ -127,7 +127,8 @@ cdef long get_ordp(x, PowComputer_class prime_pow) except? -10000:
             else:
                 curterm = get_ordp(a, prime_pow)
                 k = min(k, curterm + shift, maxordp)
-            if e != 1: shift += 1
+            if e != 1:
+                shift += 1
         # We don't want to multiply by e again.
         return k
     elif isinstance(x, pAdicGenericElement):
@@ -206,7 +207,8 @@ cdef long get_preccap(x, PowComputer_class prime_pow) except? -10000:
             else:
                 curterm = get_preccap(a, prime_pow)
                 k = min(k, curterm + shift)
-            if e != 1: shift += 1
+            if e != 1:
+                shift += 1
         # We don't want to multiply by e again.
         return k
     elif isinstance(x, pAdicGenericElement):
@@ -242,7 +244,8 @@ cdef long comb_prec(iprec, long prec) except? -10000:
 
     - ``prec`` -- a long
     """
-    if iprec is infinity: return prec
+    if iprec is infinity:
+        return prec
     cdef Integer intprec
     if isinstance(iprec, Integer):
         intprec = <Integer>iprec
@@ -302,13 +305,13 @@ cdef int _process_args_and_kwds(long *aprec, long *rprec, args, kwds, bint absol
             raise TypeError("_call_with_args() got multiple values for keyword argument 'relprec'")
         relprec = args[1]
     else:
-        relprec = kwds.get("relprec",infinity)
+        relprec = kwds.get("relprec", infinity)
     if len(args) >= 1:
         if "absprec" in kwds:
             raise TypeError("_call_with_args() got multiple values for keyword argument 'absprec'")
         absprec = args[0]
     else:
-        absprec = kwds.get("absprec",infinity)
+        absprec = kwds.get("absprec", infinity)
     if absolute:
         aprec[0] = comb_prec(absprec, prime_pow.ram_prec_cap)
         rprec[0] = comb_prec(relprec, maxordp)

src/sage/rings/padics/local_generic_element.pyx

@@ -377,7 +377,7 @@ cdef class LocalGenericElement(CommutativeRingElement):
 
         # make sure that start and stop are nonnegative
         if start<0:
-            i += -start # fix the value of ppow below
+            i += -start  # fix the value of ppow below
             start = 0
         stop = max(stop, 0)
 

src/sage/rings/padics/morphism.pyx

@@ -259,12 +259,11 @@ cdef class FrobeniusEndomorphism_padics(RingHomomorphism):
             sage: f * g
             Frobenius endomorphism on 5-adic Unramified Extension ... lifting a |--> a^(5^7) on the residue field
         """
-        if isinstance(right,FrobeniusEndomorphism_padics):
-            return self.__class__(self.domain(), self._power+right.power())
-        else:
-            return RingHomomorphism._composition(self,right)
+        if isinstance(right, FrobeniusEndomorphism_padics):
+            return self.__class__(self.domain(), self._power + right.power())
+        return RingHomomorphism._composition(self, right)
 
-    def is_injective(self):
+    def is_injective(self) -> bool:
         """
         Return ``True`` since any power of the Frobenius endomorphism
         over an unramified `p`-adic field is always injective.
@@ -278,7 +277,7 @@ cdef class FrobeniusEndomorphism_padics(RingHomomorphism):
         """
         return True
 
-    def is_surjective(self):
+    def is_surjective(self) -> bool:
         """
         Return ``True`` since any power of the Frobenius endomorphism
         over an unramified `p`-adic field is always surjective.
@@ -292,7 +291,7 @@ cdef class FrobeniusEndomorphism_padics(RingHomomorphism):
         """
         return True
 
-    def is_identity(self):
+    def is_identity(self) -> bool:
         """
         Return ``True`` if this morphism is the identity morphism.
 

src/sage/rings/padics/padic_ZZ_pX_CR_element.pyx

@@ -462,9 +462,11 @@ cdef class pAdicZZpXCRElement(pAdicZZpXElement):
                     else:
                         poly = x._ntl_rep_abs()[0]
                         if absprec is infinity:
-                            self._set_from_ZZ_pX_rel(&(<ntl_ZZ_pX>poly).x,(<ntl_ZZ_pX>poly).c, rprec)
+                            self._set_from_ZZ_pX_rel(&(<ntl_ZZ_pX>poly).x,
+                                                     (<ntl_ZZ_pX>poly).c, rprec)
                         else:
-                            self._set_from_ZZ_pX_both(&(<ntl_ZZ_pX>poly).x,(<ntl_ZZ_pX>poly).c, aprec, rprec)
+                            self._set_from_ZZ_pX_both(&(<ntl_ZZ_pX>poly).x,
+                                                      (<ntl_ZZ_pX>poly).c, aprec, rprec)
             elif x.parent() is parent.fraction_field():
                 _x = <pAdicZZpXCRElement>x
                 if _x.relprec < 0:
@@ -963,7 +965,7 @@ cdef class pAdicZZpXCRElement(pAdicZZpXElement):
             mpz_set(tmp_m, den_unit)
             mpz_to_ZZ(&den_zz, tmp_m)
             mpz_clear(tmp_m)
-            #The context has been restored in setting self.relprec
+            # The context has been restored in setting self.relprec
             ZZ_p_div(tmp_zp, ZZ_to_ZZ_p(num_zz), ZZ_to_ZZ_p(den_zz))
             ZZ_pX_SetCoeff(self.unit, 0, tmp_zp)
             self.ordp = 0
@@ -1062,13 +1064,15 @@ cdef class pAdicZZpXCRElement(pAdicZZpXElement):
         cdef long curval
         cdef ZZ_c tmp_z
         while mini == -1:
-            if not ZZ_IsZero(ZZX_coeff(poly,i)):
-                minval = ZZ_remove(tmp_z, ZZX_coeff(poly, i), self.prime_pow.pow_ZZ_tmp(1)[0])
+            if not ZZ_IsZero(ZZX_coeff(poly, i)):
+                minval = ZZ_remove(tmp_z, ZZX_coeff(poly, i),
+                                   self.prime_pow.pow_ZZ_tmp(1)[0])
                 mini = i
             i += 1
         while i <= deg:
-            if not ZZ_IsZero(ZZX_coeff(poly,i)):
-                curval = ZZ_remove(tmp_z, ZZX_coeff(poly, i), self.prime_pow.pow_ZZ_tmp(1)[0])
+            if not ZZ_IsZero(ZZX_coeff(poly, i)):
+                curval = ZZ_remove(tmp_z, ZZX_coeff(poly, i),
+                                   self.prime_pow.pow_ZZ_tmp(1)[0])
                 if curval < minval:
                     minval = curval
                     mini = i
@@ -2978,7 +2982,8 @@ cdef class pAdicZZpXCRElement(pAdicZZpXElement):
             v = self._new_c(rp)
         cdef pAdicZZpXCRElement u = self.unit_part()
         cdef long goal
-        if n is not None: goal = rp - n + self.ordp
+        if n is not None:
+            goal = rp - n + self.ordp
         while u.relprec > 0:
             v = self._new_c(rp)
             self.prime_pow.teichmuller_set_c(&v.unit, &u.unit, rp)
@@ -2987,11 +2992,13 @@ cdef class pAdicZZpXCRElement(pAdicZZpXElement):
                 L.append(v)
             elif rp == goal:
                 return v
-            if rp == 1: break
+            if rp == 1:
+                break
             ZZ_pX_sub(u.unit, u.unit, v.unit)
             u.relprec = -u.relprec
             u._normalize()
-            if u.relprec == 0: break
+            if u.relprec == 0:
+                break
             rp -= 1
             u.ordp -= 1
             while u.ordp > 0:

src/sage/rings/padics/padic_ext_element.pyx

@@ -377,15 +377,16 @@ cdef class pAdicExtElement(pAdicGenericElement):
         R = self.parent()
         if R.absolute_e() != 1:
             raise NotImplementedError("Frobenius automorphism only implemented for unramified extensions")
-        if self.is_zero(): return self
+        if self.is_zero():
+            return self
         L = self.teichmuller_expansion()
         ppow = R.uniformizer_pow(self.valuation())
         if arithmetic:
             exp = R.prime()
         else:
             exp = R.prime()**(R.absolute_degree()-1)
         ans = ppow * L[0]**exp
-        for m in range(1,len(L)):
+        for m in range(1, len(L)):
             ppow = ppow << 1
             ans += ppow * L[m]**exp
         return ans
@@ -504,7 +505,7 @@ cdef class pAdicExtElement(pAdicGenericElement):
 
         if absprec == 0:
             from sage.rings.finite_rings.integer_mod import Mod
-            return Mod(0,1)
+            return Mod(0, 1)
         elif absprec == 1:
             return R.residue_field()(self.expansion(0))
         else:

src/sage/rings/padics/padic_generic_element.pyx

@@ -1017,13 +1017,14 @@ cdef class pAdicGenericElement(LocalGenericElement):
             elt = self
             while True:
                 poly = elt.polynomial()
-                vector = V([ poly[i] for i in range(deg) ])
-                if vector in W: break
+                vector = V([poly[i] for i in range(deg)])
+                if vector in W:
+                    break
                 vectors.append(vector)
                 W += V.span([vector])
                 elt *= self
             W = V.span_of_basis(vectors)
-            coeffs = [ -c for c in W.coordinate_vector(vector) ] + [K(1)]
+            coeffs = [-c for c in W.coordinate_vector(vector)] + [K(1)]
             return polring(coeffs)
         else:
             raise NotImplementedError
@@ -1492,10 +1493,12 @@ cdef class pAdicGenericElement(LocalGenericElement):
         if self.parent().is_field():
             return self.parent().one()
 
-        if min(self.valuation(),other.valuation()) >= min(self.precision_absolute(),other.precision_absolute()):
-            return self.parent().zero().add_bigoh(min(self.precision_absolute(),other.precision_absolute()))
+        if min(self.valuation(), other.valuation()) >= min(self.precision_absolute(), other.precision_absolute()):
+            return self.parent().zero().add_bigoh(
+                min(self.precision_absolute(), other.precision_absolute()))
 
-        return self.parent().uniformiser_pow( min(self.valuation(),other.valuation()) )
+        return self.parent().uniformiser_pow(
+            min(self.valuation(),other.valuation()))
 
     @coerce_binop
     def xgcd(self, other):
@@ -2380,7 +2383,8 @@ cdef class pAdicGenericElement(LocalGenericElement):
                 a += 1
                 p2a = p2a*p
                 upper_u = ((aprec+a*e)/(alpha*p2a)).floor()
-                if a >= mina and upper_u <= 0: break
+                if a >= mina and upper_u <= 0:
+                    break
 
                 # We perform this last operation after the test
                 # because it is costly and may raise OverflowError
@@ -3755,9 +3759,8 @@ cdef class pAdicGenericElement(LocalGenericElement):
         root = (~root) << (val // n)
 
         if all:
-            return [ parent(root*zeta) for zeta in K.roots_of_unity(n) ]
-        else:
-            return parent(root)
+            return [parent(root*zeta) for zeta in K.roots_of_unity(n)]
+        return parent(root)
 
     def _inverse_pth_root(self, twist=None, hint=None):
         r"""
@@ -3844,7 +3847,8 @@ cdef class pAdicGenericElement(LocalGenericElement):
             # we can alternatively update it after each update of x
             # (which is theoretically a bit faster)
             b = ainv - x**p
-            if b == 0: break
+            if b == 0:
+                break
             curprec = b.valuation()
             bexp = iter(b.unit_part().expansion())
             maxprec = prec
@@ -3903,7 +3907,7 @@ cdef class pAdicGenericElement(LocalGenericElement):
                     x *= invroottwist**exponent
             from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
             S = PolynomialRing(k, name='x')
-            AS = S([ coeff, rho ] + (p-2)*[0] + [1])
+            AS = S([coeff, rho] + (p-2)*[0] + [1])
             roots = AS.roots()
             if len(roots) == 0:
                 return x, curprec
@@ -4364,7 +4368,7 @@ def _AHE_coefficients(p, N, prec):
         cache_internal_prec = 0
     if cache_internal_prec < internal_prec:
         parent = ZpFM(p, internal_prec)
-        values = [ parent(1) ]
+        values = [parent(1)]
     for i in range(len(values), N):
         c = 0
         dec = 1
@@ -4484,7 +4488,7 @@ cpdef dwork_mahler_coeffs(R, int bd=20):
     for k in range(1, p):
         v.append(v[-1] / R(k))
     if bd > 1:
-        R1 = Qp(p, prec=bd) # Need divisions in this calculation
+        R1 = Qp(p, prec=bd)  # Need divisions in this calculation
         u = [R1(x) for x in v]
         for i in range(1, bd):
             u[0] = ((u[-1] + u[0]) / i) >> 1
@@ -4573,7 +4577,7 @@ cpdef gauss_table(long long p, int f, int prec, bint use_longs):
     cdef long long q, q1, q3, r, r1, r2, s1, s2, k
     cdef array.array vv, ans1
 
-    if (f == 1 and prec == 1): # Shortcut for this key special case
+    if (f == 1 and prec == 1):  # Shortcut for this key special case
         ans1 = array.array('l', [0]) * p
         ans1[0] = p-1
         for r in range(1, p-1):
@@ -4585,7 +4589,7 @@ cpdef gauss_table(long long p, int f, int prec, bint use_longs):
     q1 = q - 1
     bd = (p*prec+p-2) // (p-1) - 1
     R = Zp(p, prec, 'fixed-mod')
-    if p == 2: # Dwork expansion has denominators when p = 2
+    if p == 2:  # Dwork expansion has denominators when p = 2
         R1 = Qp(p, prec)
         use_longs = False
     else:
@@ -4606,7 +4610,8 @@ cpdef gauss_table(long long p, int f, int prec, bint use_longs):
         ans = [0 for r in range(q1)]
         ans[0] = -u
     for r in range(1, q1):
-        if ans[r]: continue
+        if ans[r]:
+            continue
         if use_longs:
             s1 = 1
         else:
@@ -4615,7 +4620,7 @@ cpdef gauss_table(long long p, int f, int prec, bint use_longs):
         for j in range(1, f+1):
             k = r1 % p
             r1 = (r1 + k * q1) // p
-            if use_longs: # Use Dwork expansion to compute p-adic Gamma
+            if use_longs:  # Use Dwork expansion to compute p-adic Gamma
                 s1 *= -evaluate_dwork_mahler_long(vv, r1*r2 % q3,
                                                   p, bd, k, q3)
                 s1 %= q3
@@ -4634,7 +4639,8 @@ cpdef gauss_table(long long p, int f, int prec, bint use_longs):
                 s **= f // j
             ans[r] = -s
         for i in range(j-1):
-            r1 = r1 * p % q1 # Initially r1 == r
+            r1 = r1 * p % q1  # Initially r1 == r
             ans[r1] = ans[r]
-    if p != 2: return ans
+    if p != 2:
+        return ans
     return [R(x) for x in ans]

src/sage/rings/padics/padic_printing.pyx

@@ -105,7 +105,9 @@ class pAdicPrinterDefaults(SageObject):
         self._max_terse_terms = int(max_terse_terms)
         self._sep = sep
         if alphabet is None:
-            self._alphabet = ('0','1','2','3','4','5','6','7','8','9','A','B','C','D','E','F','G','H','I','J','K','L','M','N','O','P','Q','R','S','T','U','V','W','X','Y','Z','a','b','c','d','e','f','g','h','i','j','k','l','m','n','o','p','q','r','s','t','u','v','w','x','y','z')
+            txt = '0123456789'
+            txt += 'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz'
+            self._alphabet = tuple(txt)
         else:
             self._alphabet = alphabet
 
@@ -144,11 +146,11 @@ class pAdicPrinterDefaults(SageObject):
         """
         if mode is None:
             return self._mode
+
+        if mode in ['val-unit', 'series', 'terse', 'digits', 'bars']:
+            self._mode = mode
         else:
-            if mode in ['val-unit','series','terse','digits','bars']:
-                self._mode = mode
-            else:
-                raise ValueError("invalid printing mode")
+            raise ValueError("invalid printing mode")
 
     def allow_negatives(self, neg=None):
         r"""
@@ -1041,7 +1043,8 @@ cdef class pAdicPrinter_class(SageObject):
                     s += "^{%s})" % (elt.precision_absolute())
                 else:
                     s += "^%s)" % (elt.precision_absolute())
-        if s == "": s = "0"
+        if s == "":
+            return "0"
         return s
 
     cdef _repr_spec(self, pAdicGenericElement elt, bint do_latex, bint pos, int mode, bint paren, ram_name):

src/sage/rings/padics/padic_template_element_header.pxi

@@ -19,16 +19,16 @@ AUTHORS:
 - David Roe (2012-03-01) -- initial version
 """
 
-#*****************************************************************************
+# ***************************************************************************
 #       Copyright (C) 2012 David Roe <[email protected]>
 #                          William Stein <[email protected]>
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
 #  as published by the Free Software Foundation; either version 2 of
 #  the License, or (at your option) any later version.
 #
-#                  http://www.gnu.org/licenses/
-#*****************************************************************************
+#                  https://www.gnu.org/licenses/
+# ***************************************************************************
 
 from sage.structure.element cimport ModuleElement, RingElement
 from sage.rings.padics.padic_generic_element cimport pAdicGenericElement
@@ -43,7 +43,6 @@ cdef class pAdicTemplateElement(pAdicGenericElement):
     cdef int _get_unit(self, celement value) except -1
     cdef pAdicTemplateElement _lshift_c(self, long shift)
     cdef pAdicTemplateElement _rshift_c(self, long shift)
-    #cpdef RingElement _floordiv_c_impl(self, RingElement right)
     cdef int check_preccap(self) except -1
     cdef pAdicTemplateElement lift_to_precision_c(self, long absprec)
     cpdef pAdicTemplateElement unit_part(self)