some little changes in polynomials (ruff PERF)

Author: fchapoton

src/sage/rings/polynomial/binary_form_reduce.py

@@ -202,8 +202,7 @@ def covariant_z0(F, z0_cov=False, prec=53, emb=None, error_limit=0.000001):
         for p, e in L1:
             if e >= d / 2:
                 raise ValueError('cannot have a root with multiplicity >= %s/2' % d)
-            for _ in range(e):
-                L.append(p)
+            L.extend(p for _ in range(e))
         RCF = PolynomialRing(CF, 'u,t')
         a = RCF.zero()
         c = RCF.zero()

src/sage/rings/polynomial/complex_roots.py

@@ -290,8 +290,7 @@ def complex_roots(p, skip_squarefree=False, retval='interval', min_prec=0):
                 break
             if retval != 'interval':
                 factor = QQbar.common_polynomial(factor)
-            for irt in irts:
-                all_rts.append((irt, factor, exp))
+            all_rts.extend((irt, factor, exp) for irt in irts)
 
         if ok and intervals_disjoint([rt for (rt, fac, mult) in all_rts]):
             all_rts = sort_complex_numbers_for_display(all_rts)

src/sage/rings/polynomial/groebner_fan.py

@@ -643,11 +643,7 @@ def verts_for_normal(normal, poly):
     expmat = matrix(exps)
     vals = expmat * vector(QQ, normal)
     maxval = max(vals)
-    outverts = []
-    for i in range(len(exps)):
-        if vals[i] == maxval:
-            outverts.append(exps[i])
-    return outverts
+    return [exps[i] for i in range(len(exps)) if vals[i] == maxval]
 
 
 class TropicalPrevariety(PolyhedralFan):
@@ -1316,16 +1312,13 @@ def render(self, file=None, larger=False, shift=0, rgbcolor=(0, 0, 0),
             xs = x.split(' ')
             y = []
             if x[0:3] != '2 3' and len(xs) > 1:
-                for q in xs:
-                    if q != '':
-                        y.append(q)
+                y.extend(q for q in xs if q)
                 sp2.append(y)
         sp3 = []
         for j in range(len(sp2)):
-            temp = []
-            for i in range(0, len(sp2[j]) - 1, 2):
-                temp.append([float(sp2[j][i]) / 1200.0,
-                             float(sp2[j][i + 1]) / 1200.0])
+            temp = [[float(sp2[j][i]) / 1200.0,
+                     float(sp2[j][i + 1]) / 1200.0]
+                    for i in range(0, len(sp2[j]) - 1, 2)]
             sp3.append(temp)
         r_lines = Graphics()
         for x in sp3:
@@ -1370,10 +1363,7 @@ def _cone_to_ieq(self, facet_list):
             sage: gf._cone_to_ieq([[1,2,3,4]])
             [[0, 1, 2, 3, 4]]
         """
-        ieq_list = []
-        for q in facet_list:
-            ieq_list.append([0] + q)
-        return ieq_list
+        return [[0] + q for q in facet_list]
 
     def _embed_tetra(self, fpoint):
         """
@@ -1505,8 +1495,7 @@ def render3d(self, verbose=False):
             except Exception:
                 print(cone_data._rays)
                 raise RuntimeError
-            for a_line in cone_lines:
-                all_lines.append(a_line)
+            all_lines.extend(a_line for a_line in cone_lines)
         return sum([line3d(a_line) for a_line in all_lines])
 
     def _gfan_stats(self):

src/sage/rings/polynomial/multi_polynomial_ideal.py

@@ -605,9 +605,8 @@ def _groebner_cover(self):
         from sage.libs.singular.function import lib, singular_function
         lib("grobcov.lib")
         grobcov = singular_function("grobcov")
-        polynomials = []
-        for f in self.gens():
-            polynomials.append(f * lcm([c.denominator() for c in f.coefficients()]))
+        polynomials = [f * lcm([c.denominator() for c in f.coefficients()])
+                       for f in self.gens()]
         return grobcov(self.ring().ideal(polynomials))
 
 
@@ -2853,10 +2852,8 @@ def _variety(T, V, v=None):
         from sage.misc.converting_dict import KeyConvertingDict
         V = []
         for t in T:
-            Vbar = _variety([P(f) for f in t], [])
-
-            for v in Vbar:
-                V.append(KeyConvertingDict(P, v))
+            V.extend(KeyConvertingDict(P, v)
+                     for v in _variety([P(f) for f in t], []))
         return V
 
     @require_field
@@ -5586,8 +5583,8 @@ def weil_restriction(self):
         map_ideal = [a]
 
         variables = iter(intermediate_ring.gens()[1:])
-        for _ in range(nvars):
-            map_ideal.append(sum([a**i * next(variables) for i in range(r)]))
+        map_ideal.extend(sum([a**i * next(variables) for i in range(r)])
+                         for _ in range(nvars))
 
         myminpoly = myminpoly(*map_ideal)
         l = [f(*map_ideal).reduce([myminpoly]) for f in l]

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

@@ -57,10 +57,7 @@ def __init__(self, var_names, size_per_variable, start_index=0,
 
         if reverse:
             indices = reversed(indices)
-        names = []
-        for i in indices:
-            for n in var_names:
-                names.append(n + "(" + str(i) + ")")
+        names = [f"{n}({str(i)})" for i in indices for n in var_names]
         self.indices = indices
         self.index2pos = {v: k for k, v in enumerate(indices)}
         self.names = names

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

@@ -144,18 +144,14 @@ def dimacs_encode_polynomial(self, p):
         TESTS::
 
             sage: from sage.rings.polynomial.pbori import *
-            sage: d=dict()
+            sage: d = {}
             sage: r = declare_ring(["x", "y", "z"], d)
             sage: from sage.rings.polynomial.pbori.cnf import CNFEncoder
             sage: e = CNFEncoder(r)
             sage: sorted(e.dimacs_encode_polynomial(d["x"]+d["y"]+d["z"]))
             ['-1 -2 -3 0', '-1 2 3 0', '1 -2 3 0', '1 2 -3 0']
         """
-        clauses = self.clauses(p)
-        res = []
-        for c in clauses:
-            res.append(self.dimacs_encode_clause(c))
-        return res
+        return [self.dimacs_encode_clause(c) for c in self.clauses(p)]
 
     def dimacs_cnf(self, polynomial_system):
         r"""
@@ -174,13 +170,12 @@ def dimacs_cnf(self, polynomial_system):
             'c cnf generated by PolyBoRi\np cnf 3 3\n-1 -2 -3 0\n1 -2 0\n-1 2 0'
         """
         clauses_list = [c for p in polynomial_system for c in self.
-            dimacs_encode_polynomial(p)]
+                        dimacs_encode_polynomial(p)]
         res = ["c cnf generated by PolyBoRi"]
         r = polynomial_system[0].ring()
         n_variables = r.n_variables()
         res.append("p cnf %s %s" % (n_variables, len(clauses_list)))
-        for c in clauses_list:
-            res.append(c)
+        res.extend(clauses_list)
         return "\n".join(res)
 
 
@@ -239,6 +234,6 @@ def dimacs_cnf(self, polynomial_system):
         """
         uv = list(used_vars_set(polynomial_system).variables())
         res = super().dimacs_cnf(polynomial_system)
-        res = res + "\n" + "\n".join(["c v %s %s" % (self.to_dimacs_index(v),
-            v) for v in uv])
+        res += "\n" + "\n".join("c v %s %s" % (self.to_dimacs_index(v), v)
+                                for v in uv)
         return res

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

@@ -20,9 +20,7 @@ def easy_linear_polynomials(p):
     res = []
     if p.deg() >= 2:
         if p.vars_as_monomial().deg() > 8:
-            opp = p + 1
-            for q in easy_linear_factors(opp):
-                res.append(q + 1)
+            res.extend(q + 1 for q in easy_linear_factors(p + 1))
         else:
             res = easy_linear_polynomials_via_interpolation(p)
     return res

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

@@ -488,14 +488,14 @@ def eliminate_identical_variables_pre(I, prot):
 
         def my_sort_key(l):
             return l.navigation().value()
+
         for (t, leads) in rules.items():
             if len(leads) > 1:
                 changed = True
                 leads = sorted(leads, key=my_sort_key, reverse=True)
                 chosen = leads[0]
-                for v in leads[1:]:
-                    ll_system.append(chosen + v)
-    if len(ll_system) > 0:
+                ll_system.extend(chosen + v for v in leads[1:])
+    if ll_system:
         ll_encoded = ll_encode(ll_system, reduce=True)
         I = set(ll_red_nf_redsb(p, ll_encoded) for p in I)
     return (I, ll_system)
@@ -592,15 +592,15 @@ def call_algorithm(I, max_generators=None):
 
     if clean_and_restart_algorithm:
         for max_generators in [1000, 10000, 50000, 100000, 200000, 300000,
-                400000, None]:
+                               400000, None]:
             try:
                 return call_algorithm(I, max_generators=max_generators)
             except GeneratorLimitExceeded as e:
                 I = list(e.strat.all_generators())
                 del e.strat
                 if prot:
                     print("generator limit exceeded:", max_generators,
-                        "restarting algorithm")
+                          "restarting algorithm")
     else:
         return call_algorithm(I)
 

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

@@ -67,10 +67,8 @@ def sparse_random_system(ring, number_of_polynomials, variables_per_polynomial,
     if random_seed is not None:
         set_random_seed(random_seed)
     random_generator = Random(random_seed)
-    solutions = []
     variables = [ring.variable(i) for i in range(ring.n_variables())]
-    for v in variables:
-        solutions.append(v + random_generator.randint(0, 1))
+    solutions = [v + random_generator.randint(0, 1) for v in variables]
     solutions = ll_encode(solutions)
     res = []
     while len(res) < number_of_polynomials:

src/sage/rings/polynomial/polynomial_quotient_ring.py

@@ -1362,11 +1362,12 @@ def _S_decomposition(self, S):
             if not seen_before:
                 S_abs = []
                 for p in S:
-                    abs_gens = []
-                    for g in D.ideal(p.gens()).gens(): # this line looks a bit silly, due to inconsistency over QQ - see # 7596
-                        abs_gens.append(D_abs.structure()[1](g))
-                    S_abs += [pp for pp,_ in D_abs.ideal(abs_gens).factor()]
-                iso_classes.append((D_abs,S_abs))
+                    # next line looks a bit silly,
+                    # due to inconsistency over QQ - see # 7596
+                    abs_gens = [D_abs.structure()[1](g)
+                                for g in D.ideal(p.gens()).gens()]
+                    S_abs += [pp for pp, _ in D_abs.ideal(abs_gens).factor()]
+                iso_classes.append((D_abs, S_abs))
             isos.append((D_abs.embeddings(D_abs)[0], j))
         return fields, isos, iso_classes