gh-40860: some care for pbori
    
just a few details ; converting the "main" function of `blocks` into a
doctest

### 📝 Checklist

- [ ] The title is concise and informative.
- [ ] The description explains in detail what this PR is about.
    
URL: #40860
Reported by: Frédéric Chapoton
Reviewer(s): Dima Pasechnik

Author: Release Manager

src/sage/rings/polynomial/pbori/__init__.py

@@ -29,7 +29,6 @@
 Electronic Proceedings of the MEGA 2007 - Effective Methods in Algebraic Geometry, Strobl, Austria, June 2007.
 http://www.ricam.oeaw.ac.at/mega2007/electronic/electronic.html
 """
-from sage.misc.lazy_import import lazy_import
 from .PyPolyBoRi import Ring, Polynomial, Monomial, Variable
 
 # Get all-inclusive groebner routine

src/sage/rings/polynomial/pbori/blocks.py

@@ -1,4 +1,3 @@
-import sys
 from itertools import chain, islice
 
 from sage.rings.polynomial.pbori.pbori import (
@@ -157,7 +156,7 @@ class HigherOrderBlock:
     r"""
     HigherOrderBlocks are multidimensional blocks of variables.
 
-    For each dimension a separate start_index and size can be specified.
+    For each dimension a separate ``start_index`` and ``size`` can be specified.
 
     var_name : variables will be called <var_name>(multiindex), where
     multiindex is a tuple of the size <size_tuple>
@@ -353,23 +352,22 @@ def if_then(i, t, supposed_to_be_valid=True):
 
 def declare_ring(blocks, context=None):
     r"""
-    Declare Ring is the preferred function to create a ring and declare a variable scheme,
-    the number of variables is automatically determined, usually you pass globals() as context
-    argument to store the ring and the variable mapping.
+    Declare Ring is the preferred function to create a ring and declare a variable scheme.
+
+    The number of variables is automatically determined. Usually you
+    pass ``globals()`` as context argument to store the ring and the
+    variable mapping.
 
     EXAMPLES::
 
         sage: from sage.rings.polynomial.pbori import *
         sage: declare_ring([Block("x",10),Block("y",5)],globals())
         Boolean PolynomialRing in x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, y0, y1, y2, y3, y4
 
-    gives  a ring with x(0..9),y(0..4) and registers the ring as r, and the variable
-    blocks x and y in the context dictionary globals(), which consists of the global
-    variables of the python module
+    gives a ring with x(0..9),y(0..4) and registers the ring as r, and
+    the variable blocks x and y in the context dictionary ``globals()``,
+    which consists of the global variables of the python module
     """
-    if context is None:
-        context = sys.modules['__main__'].__dict__
-
     def canonicalize(blocks):
         for elt in blocks:
             if isinstance(elt, str):
@@ -408,39 +406,92 @@ def declare_block_scheme(blocks, context):
     context["number_of_declared_vars"] = start
 
 
-def main():
+def main_test():
+    """
+    EXAMPLES::
+
+        sage: from sage.rings.polynomial.pbori.blocks import main_test
+        sage: main_test()
+        x(0)
+        x(1)
+        x(2)
+        x(3)
+        x(4)
+        x(5)
+        x(6)
+        x(7)
+        x(8)
+        x(9)
+        ['a(0)', 'b(0)', 'c(0)', 'a(1)', 'b(1)', ...]
+        x(0)
+        x(1)
+        x(2)
+        x(3)
+        x(4)
+        x(5)
+        x(6)
+        x(7)
+        x(8)
+        x(9)
+        x(364) x(367) x(370) x(365) x(368) x(366)
+        x(99)
+        x(98)
+        x(97)
+        x(96)
+        x(95)
+        x(94)
+        x(93)
+        x(92)
+        x(91)
+        x(90)
+        x(0) x(1) x(2)
+    """
     r = Ring(1000)
+    dic = {"r": r}
+    dic["internalVariable"] = VariableFactory(r)
+
+    # first test
     ablock = AlternatingBlock(["a", "b", "c"], 100)
-    declare_block_scheme([ablock], globals())
+    declare_block_scheme([ablock], dic)
     for i in range(10):
         print(r.variable(i))
-
     print(list(ablock))
+
+    # second test
     declare_block_scheme([Block(var_name="x", size=100),
                           HigherOrderBlock("y", (3, 4, 11, 2)),
                           AlternatingBlock(["a", "b", "c"], 100)],
-                         globals())
+                         dic)
+    x = dic['x']
+    a, b, c = dic['a'], dic['b'], dic['c']
     for i in range(10):
         print(x(i))
-    print(y(0, 0, 0, 0))
-    print(y(0, 0, 0, 1))
-    print(y(0, 0, 1, 0))
-    print(y(0, 0, 1, 1))
+    # y are currently broken ?
+    # print(y(0, 0, 0, 0))
+    # print(y(0, 0, 0, 1))
+    # print(y(0, 0, 1, 0))
+    # print(y(0, 0, 1, 1))
     print(a(0), a(1), a(2), b(0), b(1), c(0))
+
+    # third test
     declare_block_scheme([Block(var_name="x", size=100, reverse=True),
                           HigherOrderBlock("y", (3, 4, 11, 2), reverse=True),
                           AlternatingBlock(["a", "b", "c"], 100, reverse=True)],
-                         globals())
+                         dic)
+    x = dic['x']
+    a, b, c = dic['a'], dic['b'], dic['c']
     for i in range(10):
         print(x(i))
-    print(y(0, 0, 0, 0))
-    print(y(0, 0, 0, 1))
-    print(y(0, 0, 1, 0))
-    print(y(0, 0, 1, 1))
-    print(a(0), a(1), a(2), b(0), b(1), c(0))
-    declare_block_scheme(["a", "b", "c"], globals())
+    # y are currently broken ?
+    # print(y(0, 0, 0, 0))
+    # print(y(0, 0, 0, 1))
+    # print(y(0, 0, 1, 0))
+    # print(y(0, 0, 1, 1))
+
+    # a also broken ?
+    # print(a(0), a(1), a(2), b(0), b(1), c(0))
+
+    # fourth test
+    declare_block_scheme(["a", "b", "c"], dic)
+    a, b, c = dic['a'], dic['b'], dic['c']
     print(a, b, c)
-
-
-if __name__ == '__main__':
-    main()

src/sage/rings/polynomial/pbori/cnf.py

@@ -45,13 +45,12 @@ def choose(s):
                 if e.constant() and not e.terminal_one():
                     indices.append(nav.value())
                     nav = t
-                else:
-                    if self.random_generator.randint(0, 1):
-                        indices.append(nav.value())
-                        nav = t
+                elif self.random_generator.randint(0, 1):
+                    indices.append(nav.value())
+                    nav = t
 
-                    else:
-                        nav = e
+                else:
+                    nav = e
             assert nav.terminal_one()
             res = self.one_set
             for i in reversed(indices):

src/sage/rings/polynomial/pbori/fglm.py

@@ -22,13 +22,13 @@ def fglm(I, from_ring, to_ring):
 
         sage: from sage.rings.polynomial.pbori import *
         sage: from sage.rings.polynomial.pbori.PyPolyBoRi import OrderCode
+        sage: from sage.rings.polynomial.pbori.fglm import fglm
         sage: dp_asc = OrderCode.dp_asc
-        sage: r=declare_ring(['x','y','z'],dict())
+        sage: r = declare_ring(['x','y','z'],dict())
         sage: old_ring = r
         sage: new_ring = old_ring.clone(ordering=dp_asc)
-        sage: (x,y,z) = [old_ring.variable(i) for i in range(3)]
-        sage: ideal=[x+z, y+z]# lp Groebner basis
-        sage: from sage.rings.polynomial.pbori.fglm import fglm
+        sage: x,y,z = (old_ring.variable(i) for i in range(3))
+        sage: ideal = [x+z, y+z]  # lp Groebner basis
         sage: list(fglm(ideal, old_ring, new_ring))
         [y + x, z + x]
     """

src/sage/rings/polynomial/pbori/frontend.py

@@ -31,7 +31,6 @@
 """
 
 
-from sage.features import FeatureNotPresentError
 from sage.rings.polynomial.pbori.blocks import declare_ring as orig_declare_ring
 from sage.rings.polynomial.pbori.pbori import VariableFactory
 from sage.rings.polynomial.pbori.PyPolyBoRi import Ring

src/sage/rings/polynomial/pbori/gbcore.py

@@ -26,7 +26,7 @@
 
 
 def get_options_from_function(f):
-    (argnames, varargs, varopts, defaults) = getargspec(f)[:4]
+    argnames, varargs, varopts, defaults = getargspec(f)[:4]
     return dict(zip(argnames[-len(defaults):], defaults))
 
 
@@ -221,8 +221,8 @@ def wrapper(I, **kwds):
                     print("preprocessing for option:", option)
 
                 local_symbols = copy(locals())
-                (I, state) = pre(**{k: v for (k, v) in local_symbols.items()
-                                    if k in pre_args})
+                I, state = pre(**{k: v for (k, v) in local_symbols.items()
+                                  if k in pre_args})
             I = f(I, **kwds)
             if option_set and post:
                 post_args = getargspec(post)[0]
@@ -271,7 +271,7 @@ def invert_all_post(I, state):
 
 
 def llfirst_pre(I, prot):
-    (eliminated, llnf, I) = eliminate(I, on_the_fly=False, prot=prot)
+    eliminated, llnf, I = eliminate(I, on_the_fly=False, prot=prot)
     return (I, eliminated)
 
 
@@ -396,7 +396,7 @@ def other_ordering_pre(I, option_set, kwds):
 
 
 def llfirstonthefly_pre(I, prot):
-    (eliminated, llnf, I) = eliminate(I, on_the_fly=True)
+    eliminated, llnf, I = eliminate(I, on_the_fly=True)
     return (I, eliminated)
 
 

src/sage/rings/polynomial/pbori/nf.py

@@ -146,8 +146,7 @@ def build_and_print_matrices_deg_colored(v, strat):
     polys_in_mat.sort(key=pkey)
     global mat_counter
     mat_counter = mat_counter + 1
-    from PIL import Image
-    from PIL import ImageColor
+    from PIL import Image, ImageColor
 
     rows = len(polys_in_mat)
     cols = len(m2i)

src/sage/rings/polynomial/pbori/parallel.py

@@ -6,6 +6,7 @@
 Copyright 2008 The PolyBoRi Team
 """
 import copyreg
+import os
 from zlib import compress, decompress
 
 from sage.rings.polynomial.pbori.gbcore import groebner_basis
@@ -23,9 +24,10 @@
 )
 
 
-def to_fast_pickable(l):
+def to_fast_pickable(l) -> list:
     r"""
-    Convert a list of polynomials into a builtin Python value, which is fast pickable and compact.
+    Convert a list of polynomials into a builtin Python value,
+    which is fast pickable and compact.
 
     INPUT:
 
@@ -98,7 +100,7 @@ def find_navs(nav):
 
     nodes_sorted = sorted(nodes, key=CCuddNavigator.value)
     nodes2i = {one: 1, zero: 0}
-    for (i, n) in enumerate(nodes_sorted):
+    for i, n in enumerate(nodes_sorted):
         nodes2i[n] = i + 2
 
     for i in range(len(nodes_sorted)):
@@ -110,7 +112,7 @@ def find_navs(nav):
     return [[nodes2i[f.set().navigation()] for f in l], nodes_sorted]
 
 
-def from_fast_pickable(l, r):
+def from_fast_pickable(l, r) -> list:
     r"""
     Undo the operation :func:`to_fast_pickable`.
 
@@ -151,10 +153,10 @@ def from_fast_pickable(l, r):
         [x(0)*x(1), 0, 1, x(3)]
     """
     i2poly = {0: r.zero(), 1: r.one()}
-    (indices, terms) = l
+    indices, terms = l
 
-    for i in reversed(range(len(terms))):
-        (v, t, e) = terms[i]
+    for i in range(len(terms) - 1, -1, - 1):
+        v, t, e = terms[i]
         t = i2poly[t]
         e = i2poly[e]
         terms[i] = if_then_else(v, t, e)
@@ -163,7 +165,7 @@ def from_fast_pickable(l, r):
 
 
 def _calculate_gb_with_keywords(args):
-    (I, kwds_as_single_arg) = args
+    I, kwds_as_single_arg = args
     return groebner_basis(I, **kwds_as_single_arg)
 
 
@@ -204,18 +206,17 @@ def pickle_var(self):
 
 
 def _decode_ring(code):
-    import os
-    (identifier, data, varnames, blocks) = code
+    identifier, data, varnames, blocks = code
 
     global _polybori_parallel_rings
     try:
         _polybori_parallel_rings
     except NameError:
         _polybori_parallel_rings = {}
 
-    for key in [key for key in _polybori_parallel_rings
-                if not _polybori_parallel_rings[key][0]()]:
-        del _polybori_parallel_rings[key]
+    for key in list(_polybori_parallel_rings):
+        if not _polybori_parallel_rings[key][0]():
+            del _polybori_parallel_rings[key]
 
     if identifier in _polybori_parallel_rings:
         ring = _polybori_parallel_rings[identifier][0]()
@@ -224,7 +225,7 @@ def _decode_ring(code):
 
     if not ring:
         varnames = decompress(varnames).split('\n')
-        (nvars, ordercode) = data
+        nvars, ordercode = data
         ring = Ring(nvars, ordercode, names=varnames, blocks=blocks)
         storage_data = (WeakRingRef(ring), code)
         _polybori_parallel_rings[identifier] = storage_data
@@ -234,7 +235,6 @@ def _decode_ring(code):
 
 
 def _encode_ring(ring):
-    import os
     identifier = (ring.id(), os.getpid())
 
     global _polybori_parallel_rings
@@ -243,9 +243,9 @@ def _encode_ring(ring):
     except NameError:
         _polybori_parallel_rings = {}
 
-    for key in [key for key in _polybori_parallel_rings
-                if not _polybori_parallel_rings[key][0]()]:
-        del _polybori_parallel_rings[key]
+    for key in list(_polybori_parallel_rings):
+        if not _polybori_parallel_rings[key][0]():
+            del _polybori_parallel_rings[key]
 
     if identifier in _polybori_parallel_rings:
         code = _polybori_parallel_rings[identifier][1]

src/sage/rings/polynomial/pbori/specialsets.py

@@ -83,7 +83,7 @@ def power_set(variables):
 
 
 if __name__ == '__main__':
-    from .blocks import declare_ring, Block
+    from .blocks import Block, declare_ring
     r = declare_ring([Block("x", 10000)], globals())
     print(list(all_monomials_of_degree_d(0, [Variable(i) for i in range(100)])))
     print(list(all_monomials_of_degree_d(1, [Variable(i) for i in range(10)])))