suggested details

Author: fchapoton

src/sage/coding/binary_code.pyx

@@ -3373,14 +3373,16 @@ cdef class BinaryCodeClassifier:
                 e[k] = 0 # see state 12 and 17
                 state = 2 # continue down the tree
 
-            elif state == 5:  # same as state 3, but in the case where we haven't yet defined zeta
-                             # i.e. this is our first time down the tree. Once we get to the bottom,
-                             # we will have zeta = nu = rho, so we do:
+            elif state == 5:
+                # same as state 3, but in the case where we haven't yet defined zeta
+                # i.e. this is our first time down the tree. Once we get to the bottom,
+                # we will have zeta = nu = rho, so we do:
                 zf__Lambda_zeta[k] = Lambda[k]
                 zb__Lambda_rho[k] = Lambda[k]
                 state = 4
 
-            elif state == 6: # at this stage, there is no reason to continue downward, so backtrack
+            elif state == 6:
+                # at this stage, there is no reason to continue downward, so backtrack
                 j = k
 
                 # return to the longest ancestor nu[i] of nu that could have a
@@ -3401,9 +3403,10 @@ cdef class BinaryCodeClassifier:
                     else:
                         k = hh-1
                 # TODO: is the following line necessary?
-                if k == -1: k = 0
+                if k == -1:
+                    k = 0
 
-                if hb > k:# update hb since we are backtracking
+                if hb > k:  # update hb since we are backtracking
                     hb = k
                 # if j == hh, then all nodes lower than our current position are equivalent, so bail out
                 if j == hh:

src/sage/libs/singular/singular.pyx

@@ -104,7 +104,7 @@ cdef Rational si2sa_QQ(number *n, number **nn, ring *_ring):
     nom = nlGetNumerator(n, _ring.cf)
     mpz_init(nom_z)
 
-    if (SR_HDL(nom) & SR_INT):
+    if SR_HDL(nom) & SR_INT:
         mpz_set_si(nom_z, SR_TO_INT(nom))
     else:
         mpz_set(nom_z,nom.z)
@@ -116,7 +116,7 @@ cdef Rational si2sa_QQ(number *n, number **nn, ring *_ring):
     denom = nlGetDenom(n, _ring.cf)
     mpz_init(denom_z)
 
-    if (SR_HDL(denom) & SR_INT):
+    if SR_HDL(denom) & SR_INT:
         mpz_set_si(denom_z, SR_TO_INT(denom))
     else:
         mpz_set(denom_z,denom.z)

src/sage/rings/finite_rings/element_base.pyx

@@ -88,14 +88,12 @@ cdef class FiniteRingElement(CommutativeRingElement):
         if self.is_one():
             if gcd == 1:
                 return [self] if all else self
-            else:
-                nthroot = K.zeta(gcd)
-                return [nthroot**a for a in range(gcd)] if all else nthroot
+            nthroot = K.zeta(gcd)
+            return [nthroot**a for a in range(gcd)] if all else nthroot
         if gcd == q-1:
             if all:
                 return []
-            else:
-                raise ValueError("no nth root")
+            raise ValueError("no nth root")
         gcd, alpha, _ = n.xgcd(q-1)  # gcd = alpha*n + beta*(q-1), so 1/n = alpha/gcd (mod q-1)
         if gcd == 1:
             return [self**alpha] if all else self**alpha
@@ -105,8 +103,7 @@ cdef class FiniteRingElement(CommutativeRingElement):
         if self**q1overn != 1:
             if all:
                 return []
-            else:
-                raise ValueError("no nth root")
+            raise ValueError("no nth root")
         self = self**alpha
         if cunningham:
             from sage.rings.factorint import factor_cunningham
@@ -136,12 +133,11 @@ cdef class FiniteRingElement(CommutativeRingElement):
             if all:
                 nthroot = K.zeta(n)
                 L = [self]
-                for i in range(1,n):
+                for i in range(1, n):
                     self *= nthroot
                     L.append(self)
                 return L
-            else:
-                return self
+            return self
         else:
             raise ValueError("unknown algorithm")
 
@@ -243,10 +239,11 @@ cdef class FinitePolyExtElement(FiniteRingElement):
             from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
             R = PolynomialRing(self.parent().prime_subfield(), var)
             return R(self.__pari__().minpoly('x').lift())
-        elif algorithm == 'matrix':
+        
+        if algorithm == 'matrix':
             return self.matrix().minpoly(var)
-        else:
-            raise ValueError("unknown algorithm '%s'" % algorithm)
+
+        raise ValueError("unknown algorithm '%s'" % algorithm)
 
     # We have two names for the same method
     # for compatibility with sage.matrix
@@ -505,8 +502,7 @@ cdef class FinitePolyExtElement(FiniteRingElement):
         """
         if self.parent().degree()>1:
             return self.polynomial()._latex_()
-        else:
-            return str(self)
+        return str(self)
 
     def __pari__(self, var=None):
         r"""
@@ -626,10 +622,11 @@ cdef class FinitePolyExtElement(FiniteRingElement):
             from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
             R = PolynomialRing(self.parent().prime_subfield(), var)
             return R(self.__pari__().charpoly('x').lift())
-        elif algorithm == 'matrix':
+
+        if algorithm == 'matrix':
             return self.matrix().charpoly(var)
-        else:
-            raise ValueError("unknown algorithm '%s'" % algorithm)
+
+        raise ValueError("unknown algorithm '%s'" % algorithm)
 
     def norm(self):
         """
@@ -659,10 +656,7 @@ cdef class FinitePolyExtElement(FiniteRingElement):
         """
         f = self.charpoly('x')
         n = f[0]
-        if f.degree() % 2:
-            return -n
-        else:
-            return n
+        return -n if f.degree() % 2 else n
 
     def trace(self):
         """
@@ -926,8 +920,7 @@ cdef class FinitePolyExtElement(FiniteRingElement):
             if n <= 0:
                 if all:
                     return []
-                else:
-                    raise ValueError
+                raise ValueError
             return [self] if all else self
         if n < 0:
             self = ~self
@@ -936,13 +929,11 @@ cdef class FinitePolyExtElement(FiniteRingElement):
             if self == 1:
                 if all:
                     return [a for a in self.parent().list() if a != 0]
-                else:
-                    return self
+                return self
             else:
                 if all:
                     return []
-                else:
-                    raise ValueError
+                raise ValueError
         if extend:
             raise NotImplementedError
         n = Integer(n)

src/sage/rings/finite_rings/integer_mod.pyx

@@ -1507,19 +1507,16 @@ cdef class IntegerMod_abstract(FiniteRingElement):
             if self == 1:
                 if all:
                     return [K(a) for a in range(1, K.order())]
-                else:
-                    return self
+                return self
             else:
                 if all:
                     return []
-                else:
-                    raise ValueError
+                raise ValueError
         F = K.factored_order()
         if len(F) == 0:
             if all:
                 return [self]
-            else:
-                return self
+            return self
         if len(F) != 1:
             if all:
                 # we should probably do a first pass to see if there are any solutions so that we don't get giant intermediate lists and waste time...
@@ -1539,24 +1536,20 @@ cdef class IntegerMod_abstract(FiniteRingElement):
             if n < 0:
                 if all:
                     return []
-                else:
-                    raise ValueError
+                raise ValueError
             if all:
                 if k == 1:
                     return [self]
-                else:
-                    minval = max(1, (k/n).ceil())
-                    return [K(a*p**minval) for a in range(p**(k-minval))]
-            else:
-                return self
+                minval = max(1, (k/n).ceil())
+                return [K(a*p**minval) for a in range(p**(k-minval))]
+            return self
         if n < 0:
             try:
                 self = ~self
             except ZeroDivisionError:
                 if all:
                     return []
-                else:
-                    raise ValueError
+                raise ValueError
             n = -n
         if p == 2 and k == 1:
             return [self] if all else self
@@ -1565,8 +1558,7 @@ cdef class IntegerMod_abstract(FiniteRingElement):
             if not n.divides(pval):
                 if all:
                     return []
-                else:
-                    raise ValueError("no nth root")
+                raise ValueError("no nth root")
             if pval > 0:
                 if all:
                     return [K(a.lift()*p**(pval // n) + p**(k - (pval - pval//n)) * b) for a in mod(upart, p**(k-pval)).nth_root(n, all=True, algorithm=algorithm) for b in range(p**(pval - pval//n))]
@@ -1580,27 +1572,23 @@ cdef class IntegerMod_abstract(FiniteRingElement):
                     if n % 2 == 0:
                         if all:
                             return []
-                        else:
-                            raise ValueError("no nth root")
+                        raise ValueError("no nth root")
                     else:
                         sign = [-1]
                         self = -self
                 elif n % 2 == 0:
                     if k > 2 and self % 8 == 5:
                         if all:
                             return []
-                        else:
-                            raise ValueError("no nth root")
+                        raise ValueError("no nth root")
                     sign = [1, -1]
                 if k == 2:
                     if all:
                         return [K(s) for s in sign[:2]]
-                    else:
-                        return K(sign[0])
+                    return K(sign[0])
                 if all:
-                    modp = [mod(self,8)]
-                else:
-                    modp = mod(self,8)
+                    modp = [mod(self, 8)]
+                modp = mod(self, 8)
             else:
                 sign = [1]
                 modp = self % p
@@ -1614,13 +1602,11 @@ cdef class IntegerMod_abstract(FiniteRingElement):
                 if self == 1:
                     if all:
                         return [s*K(p*a+m.lift()) for a in range(p**(k-(2 if p==2 else 1))) for m in modp for s in sign]
-                    else:
-                        return K(modp.lift())
+                    return K(modp.lift())
                 else:
                     if all:
                         return []
-                    else:
-                        raise ValueError("no nth root")
+                    raise ValueError("no nth root")
             if all:
                 ans = [plog // n + p**(k - nval) * i for i in range(p**nval)]
                 ans = [s*K(R.teichmuller(m) * a.exp()) for a in ans for m in modp for s in sign]

src/sage/rings/polynomial/polynomial_element.pyx

@@ -1175,8 +1175,7 @@ cdef class Polynomial(CommutativePolynomial):
         cdef Py_ssize_t d = self.degree()
         if 0 <= i <= d:
             return self.get_unsafe(i)
-        else:
-            return self._parent._base.zero()
+        return self._parent._base.zero()
 
     cdef get_unsafe(self, Py_ssize_t i):
         """
@@ -1822,13 +1821,14 @@ cdef class Polynomial(CommutativePolynomial):
         cdef Polynomial _right = right
         if self.is_term():
             return _right._mul_term(self, term_on_right=False)
-        elif _right.is_term():
+
+        if _right.is_term():
             return self._mul_term(_right, term_on_right=True)
 
-        elif self._parent.is_exact():
+        if self._parent.is_exact():
             return self._mul_karatsuba(right)
-        else:
-            return self._mul_generic(right)
+
+        return self._mul_generic(right)
 
     cpdef Polynomial _mul_trunc_(self, Polynomial right, long n):
         r"""
@@ -6814,8 +6814,7 @@ cdef class Polynomial(CommutativePolynomial):
         if len(e) == 1:
             if e[0] == 0:
                 return []
-            else:
-                return [(infinity.infinity, e[0])]
+            return [(infinity.infinity, e[0])]
 
         if e[0] == 0:
             slopes = []
@@ -6831,8 +6830,8 @@ cdef class Polynomial(CommutativePolynomial):
                 slopes = slopes[:-1]
                 points = points[:-1]
                 s = -(v-points[-1][1])/(e[i]-points[-1][0])
-            slopes.append((s,e[i]-points[-1][0]))
-            points.append((e[i],v))
+            slopes.append((s, e[i]-points[-1][0]))
+            points.append((e[i], v))
 
         return slopes