diff --git a/src/sage/rings/polynomial/pbori/easy_polynomials.py b/src/sage/rings/polynomial/pbori/easy_polynomials.py
index a5ee335b98b..270e3db06d4 100644
--- a/src/sage/rings/polynomial/pbori/easy_polynomials.py
+++ b/src/sage/rings/polynomial/pbori/easy_polynomials.py
@@ -6,7 +6,7 @@ def easy_linear_polynomials(p):
     r"""
     Get linear polynomials implied by given polynomial.
 
-    TESTS::
+    EXAMPLES::
 
         sage: from sage.rings.polynomial.pbori.frontend import *
         sage: from sage.rings.polynomial.pbori.easy_polynomials import easy_linear_polynomials
diff --git a/src/sage/rings/polynomial/pbori/frontend.py b/src/sage/rings/polynomial/pbori/frontend.py
index 2a0d29c2018..7314e09db63 100644
--- a/src/sage/rings/polynomial/pbori/frontend.py
+++ b/src/sage/rings/polynomial/pbori/frontend.py
@@ -31,7 +31,8 @@
 """
 
 
-from . import *
+from .PyPolyBoRi import Ring, Monomial, Polynomial
+from .pbori import VariableFactory
 from .blocks import declare_ring as orig_declare_ring
 
 
diff --git a/src/sage/rings/polynomial/pbori/gbcore.py b/src/sage/rings/polynomial/pbori/gbcore.py
index 4a9d47777de..6776dbc58df 100644
--- a/src/sage/rings/polynomial/pbori/gbcore.py
+++ b/src/sage/rings/polynomial/pbori/gbcore.py
@@ -1,17 +1,17 @@
+from copy import copy
+from itertools import chain
+from inspect import getfullargspec as getargspec
+
 from .nf import GeneratorLimitExceeded, symmGB_F2_C, symmGB_F2_python
 from .PyPolyBoRi import (Monomial, Polynomial,
                          GroebnerStrategy, OrderCode, ll_red_nf_redsb)
 from .ll import eliminate, ll_encode
-from copy import copy
-from itertools import chain
 from .statistics import used_vars_set
 from .heuristics import dense_system, gauss_on_linear
 from .easy_polynomials import easy_linear_polynomials
 from .interpolate import lex_groebner_basis_for_polynomial_via_variety
 from .fglm import _fglm
 
-from inspect import getfullargspec as getargspec
-
 
 def get_options_from_function(f):
     (argnames, varargs, varopts, defaults) = getargspec(f)[:4]
@@ -22,7 +22,7 @@ def filter_oldstyle_options(**options):
     filtered = dict()
     for key in options:
         newkey = key
-        for prefix in ['', 'use_', 'opt_allow_', 'opt_']:
+        for prefix in ['use_', 'opt_allow_', 'opt_']:
             newkey = newkey.replace(prefix, '')
         filtered[newkey] = options[key]
     return filtered
@@ -197,13 +197,9 @@ def make_wrapper(f):
     return make_wrapper
 
 
-def clean_polys(I):
-    I = list(set((Polynomial(p) for p in I if not Polynomial(p).is_zero())))
-    return I
-
-
 def clean_polys_pre(I):
-    return (clean_polys(I), None)
+    wrap = (Polynomial(p) for p in I)
+    return (list(set(p for p in wrap if not p.is_zero())), None)
 
 
 def gb_with_pre_post_option(option, pre=None,
@@ -259,14 +255,14 @@ def wrapper(I, **kwds):
 
 
 def redsb_post(I, state):
-    if I == []:
+    if not I:
         return []
     else:
         return I.minimalize_and_tail_reduce()
 
 
 def minsb_post(I, state):
-    if I == []:
+    if not I:
         return []
     else:
         return I.minimalize()
diff --git a/src/sage/rings/polynomial/pbori/ll.py b/src/sage/rings/polynomial/pbori/ll.py
index c9795ddd3ca..48c43220a89 100644
--- a/src/sage/rings/polynomial/pbori/ll.py
+++ b/src/sage/rings/polynomial/pbori/ll.py
@@ -109,15 +109,15 @@ def identity(p):
         else:
             reduction_function = ll_red_nf_redsb
 
-    def llnf(p):
-        return reduction_function(p, reductors)
-    reduced_list = []
     if optimized:
         llnf, reduced_list = eliminate_ll_ranked(linear_leads, rest,
                                                  reduction_function=reduction_function,
                                                  reduce_ll_system=(not on_the_fly),
                                                  prot=prot)
     else:
+        def llnf(p):
+            return reduction_function(p, reductors)
+        reduced_list = []
         reductors = ll_encode(linear_leads, reduce=(not on_the_fly), prot=prot)
         for p in rest:
             p = reduction_function(p, reductors)