gh-40720: fix ruff PERF in schemes
    
fix all suggestions of `ruff check --select=PERF src/sage/schemes`

about some loops

### 📝 Checklist

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
    
URL: #40720
Reported by: Frédéric Chapoton
Reviewer(s): David Coudert

Author: Release Manager

src/sage/schemes/curves/affine_curve.py

@@ -1744,14 +1744,13 @@ def tangent_line(self, p):
         Tp = self.tangent_space(p)
 
         if Tp.dimension() > 1:
-            raise ValueError("the curve is not smooth at {}".format(p))
+            raise ValueError(f"the curve is not smooth at {p}")
 
         from sage.schemes.curves.constructor import Curve
 
         # translate to p
-        I0 = []
-        for poly in Tp.defining_polynomials():
-            I0.append(poly.subs({x: x - c for x, c in zip(gens, p)}))
+        I0 = [poly.subs({x: x - c for x, c in zip(gens, p)})
+              for poly in Tp.defining_polynomials()]
 
         return Curve(I0, A)
 
@@ -2744,11 +2743,8 @@ def places_on(self, point):
         gs = [phi(g) for g in point.prime_ideal().gens()]
         fs = [g for g in gs if not g.is_zero()]
         f = fs.pop()
-        places = []
-        for p in f.zeros():
-            if all(f.valuation(p) > 0 for f in fs):
-                places.append(p)
-        return places
+        return [p for p in f.zeros()
+                if all(f.valuation(p) > 0 for f in fs)]
 
     def parametric_representation(self, place, name=None):
         """

src/sage/schemes/curves/projective_curve.py

@@ -2862,14 +2862,11 @@ def places_on(self, point):
 
         phi = self._map_to_function_field
         denom = self._coordinate_functions[i]
-        gs = [phi(f)/denom**f.degree() for f in prime.gens()]
+        gs = [phi(f) / denom**f.degree() for f in prime.gens()]
         fs = [g for g in gs if not g.is_zero()]
         f = fs.pop()
-        places = []
-        for p in f.zeros():
-            if all(f.valuation(p) > 0 for f in fs):
-                places.append(p)
-        return places
+        return [p for p in f.zeros()
+                if all(f.valuation(p) > 0 for f in fs)]
 
     def jacobian(self, model, base_div=None):
         """

src/sage/schemes/elliptic_curves/BSD.py

@@ -593,10 +593,12 @@ def prove_BSD(E, verbosity=0, two_desc='mwrank', proof=None, secs_hi=5,
                 if p >= 5 and D_K % p and len(K.factor(p)) == 1:
                     # p is inert in K
                     BSD.primes.append(p)
-            for p in heegner_primes:
-                if p >= 5 and D_E % p and D_K % p and len(K.factor(p)) == 1:
-                    # p is good for E and inert in K
-                    kolyvagin_primes.append(p)
+
+            kolyvagin_primes.extend(p for p in heegner_primes
+                                    # p is good for E and inert in K
+                                    if p >= 5 and D_E % p and D_K % p
+                                    and len(K.factor(p)) == 1)
+
             for p in prime_divisors(BSD.sha_an):
                 if p >= 5 and D_K % p and len(K.factor(p)) == 1:
                     if BSD.curve.is_good(p):

src/sage/schemes/elliptic_curves/ell_generic.py

@@ -3207,16 +3207,15 @@ def montgomery_model(self, twisted=False, morphism=False):
         R = self.base_ring()
         P = PolynomialRing(R, 'v')
 
-        sols = []
-        for r in P([b, a, 0, 1]).roots(multiplicities=False):
-            for s in P([3 * r**2 + a, 0, -1]).roots(multiplicities=False):
-                sols.append((r,s))
+        sols = [(r, s)
+                for r in P([b, a, 0, 1]).roots(multiplicities=False)
+                for s in P([3 * r**2 + a, 0, -1]).roots(multiplicities=False)]
 
         if not sols:
             raise ValueError(f'{self} has no Montgomery model')
 
         # square s allows us to take B=1
-        r,s = max(sols, key=lambda t: t[1].is_square())
+        r, s = max(sols, key=lambda t: t[1].is_square())
 
         A = 3 * r / s
         B = R.one() if s.is_square() else ~s

src/sage/schemes/generic/divisor.py

@@ -89,8 +89,7 @@ def CurvePointToIdeal(C, P):
                 polys.append(x[i])
             else:
                 polys.append(x[i]-ai)
-    for i in range(m+1,n):
-        polys.append(x[i])
+    polys.extend(x[i] for i in range(m + 1, n))
     return R.ideal(polys)
 
 

src/sage/schemes/hyperelliptic_curves/hyperelliptic_finite_field.py

@@ -1054,16 +1054,15 @@ def count_points_exhaustive(self, n=1, naive=False):
            [9, 27, 108, 675, 3069, 16302]
         """
         g = self.genus()
-        a = []
-        for i in range(1, min(n, g) + 1):
-            a.append(self.cardinality_exhaustive(extension_degree=i))
+        a = [self.cardinality_exhaustive(extension_degree=i)
+             for i in range(1, min(n, g) + 1)]
 
         if n <= g:
             return a
 
         if naive:
-            for i in range(g + 1, n + 1):
-                a.append(self.cardinality_exhaustive(extension_degree=i))
+            a.extend(self.cardinality_exhaustive(extension_degree=i)
+                     for i in range(g + 1, n + 1))
 
         # let's not be too naive and compute the frobenius polynomial
         f = self._frobenius_polynomial_cardinalities(a=a)

src/sage/schemes/hyperelliptic_curves/monsky_washnitzer.py

@@ -668,16 +668,8 @@ def transpose_list(input) -> list[list]:
         sage: transpose_list(L)
         [[1, 3, 5], [2, 4, 6]]
     """
-    h = len(input)
     w = len(input[0])
-
-    output = []
-    for i in range(w):
-        row = []
-        for j in range(h):
-            row.append(input[j][i])
-        output.append(row)
-    return output
+    return [[input_j[i] for input_j in input] for i in range(w)]
 
 
 def helper_matrix(Q):

src/sage/schemes/product_projective/rational_point.py

@@ -133,21 +133,20 @@ def enum_product_projective_rational_field(X, B):
 
     R = X.codomain().ambient_space()
     m = R.num_components()
-    iters = [ R[i].points_of_bounded_height(bound=B) for i in range(m) ]
+    iters = [R[i].points_of_bounded_height(bound=B) for i in range(m)]
     dim = [R[i].dimension_relative() + 1 for i in range(m)]
 
-    dim_prefix = [0, dim[0]] # prefixes dim list
+    dim_prefix = [0, dim[0]]  # prefixes dim list
     for i in range(1, len(dim)):
         dim_prefix.append(dim_prefix[i] + dim[i])
 
     pts = []
     P = []
     for i in range(m):
         pt = next(iters[i])
-        for j in range(dim[i]):
-            P.append(pt[j]) # initial value of P
+        P.extend(pt[j] for j in range(dim[i]))  # initial value of P
 
-    try: # add the initial point
+    try:  # add the initial point
         pts.append(X(P))
     except TypeError:
         pass
@@ -450,18 +449,12 @@ def points_modulo_primes(X, primes):
         Return a list of rational points modulo all `p` in primes,
         computed parallelly.
         """
-        normalized_input = []
-        for p in primes_list:
-            normalized_input.append(((X, p, ), {}))
+        normalized_input = [((X, p, ), {}) for p in primes_list]
         p_iter = p_iter_fork(ncpus())
 
         points_pair = list(p_iter(parallel_function, normalized_input))
         points_pair.sort()
-        modulo_points = []
-        for pair in points_pair:
-            modulo_points.append(pair[1])
-
-        return modulo_points
+        return [pair[1] for pair in points_pair]
 
     def parallel_function_combination(point_p_max):
         r"""
@@ -511,12 +504,10 @@ def lift_all_points():
         r"""
         Return list of all rational points lifted parallelly.
         """
-        normalized_input = []
-        points = modulo_points.pop() # remove the list of points corresponding to largest prime
+        points = modulo_points.pop()  # remove the list of points corresponding to largest prime
         len_modulo_points.pop()
 
-        for point in points:
-            normalized_input.append(( (point, ), {}))
+        normalized_input = [((point, ), {}) for point in points]
         p_iter = p_iter_fork(ncpus())
         points_satisfying = list(p_iter(parallel_function_combination, normalized_input))
 

src/sage/schemes/projective/proj_bdd_height.py

@@ -186,7 +186,7 @@ def IQ_points_of_bounded_height(PS, K, dim, bound):
     possible_norm_set = set()
     for i in range(class_number):
         for k in range(1, floor(bound + 1)):
-            possible_norm_set.add(k*class_group_ideal_norms[i])
+            possible_norm_set.add(k * class_group_ideal_norms[i])
 
     coordinate_space = {}
     coordinate_space[0] = [K(0)]
@@ -199,11 +199,9 @@ def IQ_points_of_bounded_height(PS, K, dim, bound):
         a_norm_bound = bound * a_norm
         a_coordinates = []
 
-        for m in coordinate_space:
+        for m, coord_m in coordinate_space.items():
             if m <= a_norm_bound:
-                for x in coordinate_space[m]:
-                    if x in a:
-                        a_coordinates.append(x)
+                a_coordinates.extend(x for x in coord_m if x in a)
 
         points_in_class_a = set()
         t = len(a_coordinates) - 1
@@ -213,7 +211,7 @@ def IQ_points_of_bounded_height(PS, K, dim, bound):
             if a == K.ideal(point_coordinates):
                 for p in itertools.permutations(point_coordinates):
                     for u in unit_tuples:
-                        point = PS([i*j for i, j in zip(u, p)] + [p[dim]])
+                        point = PS([i * j for i, j in zip(u, p)] + [p[dim]])
 
                         if point not in points_in_class_a:
                             points_in_class_a.add(point)
@@ -360,21 +358,18 @@ def points_of_bounded_height(PS, K, dim, bound, prec=53):
         vertex = sum([coefficient_tuple[i]*fund_unit_logs[i] for i in range(r)])
         fund_parallelotope_vertices.append(vertex)
 
-    D_numbers = []
-    for v in range(r + 1):
-        D_numbers.append(max([vertex[v] for vertex in fund_parallelotope_vertices]))
+    D_numbers = [max(vertex[v] for vertex in fund_parallelotope_vertices)
+                 for v in range(r + 1)]
 
-    A_numbers = []
-    for v in range(r + 1):
-        A_numbers.append(min([pr_ideal_gen_logs[y][v] for y in pr_ideal_gen_logs]))
+    A_numbers = [min(pr_ideal_gen_logs[y][v] for y in pr_ideal_gen_logs)
+                 for v in range(r + 1)]
 
-    aux_constant = (1/K_degree) * Reals(norm_bound).log()
+    aux_constant = (1 / K_degree) * Reals(norm_bound).log()
 
-    L_numbers = []
-    for v in range(r1):
-        L_numbers.append(aux_constant + D_numbers[v] - A_numbers[v])
-    for v in range(r1, r + 1):
-        L_numbers.append(2*aux_constant + D_numbers[v] - A_numbers[v])
+    L_numbers = [aux_constant + D_numbers[v] - A_numbers[v]
+                 for v in range(r1)]
+    L_numbers.extend(2 * aux_constant + D_numbers[v] - A_numbers[v]
+                     for v in range(r1, r + 1))
     L_numbers = vector(L_numbers).change_ring(QQ)
 
     T = column_matrix(fund_unit_logs).delete_rows([r]).change_ring(QQ)

src/sage/schemes/projective/projective_point.py

@@ -676,14 +676,14 @@ def dehomogenize(self, n):
             ...
             ValueError: can...t dehomogenize at 0 coordinate
         """
-        if self[n].is_zero():
+        sn = self[n]
+        if sn.is_zero():
             raise ValueError("can't dehomogenize at 0 coordinate")
         PS = self.codomain()
         A = PS.affine_patch(n)
-        Q = []
-        for i in range(PS.ambient_space().dimension_relative() + 1):
-            if i != n:
-                Q.append(self[i] / self[n])
+        Q = [self[i] / sn
+             for i in range(PS.ambient_space().dimension_relative() + 1)
+             if i != n]
         return A.point(Q)
 
     def global_height(self, prec=None):