add note about non-removable unused imports

Author: fchapoton

src/sage/libs/mpmath/ext_libmp.pyx

@@ -4,6 +4,7 @@ Faster versions of some key functions in mpmath.libmp
 from .ext_impl cimport *
 from sage.libs.gmp.all cimport *
 
+# the next line is used by mpmath
 from .ext_impl import exp_fixed, cos_sin_fixed, log_int_fixed
 
 # Note: not thread-safe
@@ -12,6 +13,7 @@ cdef MPF tmp2
 MPF_init(&tmp1)
 MPF_init(&tmp2)
 
+
 def mpf_add(tuple x, tuple y, int prec=0, str rnd='d'):
     cdef MPopts opts
     MPF_set_tuple(&tmp1, x)
@@ -21,6 +23,7 @@ def mpf_add(tuple x, tuple y, int prec=0, str rnd='d'):
     MPF_add(&tmp1, &tmp1, &tmp2, opts)
     return MPF_to_tuple(&tmp1)
 
+
 def mpf_sub(tuple x, tuple y, int prec=0, str rnd='d'):
     cdef MPopts opts
     MPF_set_tuple(&tmp1, x)
@@ -30,6 +33,7 @@ def mpf_sub(tuple x, tuple y, int prec=0, str rnd='d'):
     MPF_sub(&tmp1, &tmp1, &tmp2, opts)
     return MPF_to_tuple(&tmp1)
 
+
 def mpf_mul(tuple x, tuple y, int prec=0, str rnd='d'):
     cdef MPopts opts
     MPF_set_tuple(&tmp1, x)
@@ -39,6 +43,7 @@ def mpf_mul(tuple x, tuple y, int prec=0, str rnd='d'):
     MPF_mul(&tmp1, &tmp1, &tmp2, opts)
     return MPF_to_tuple(&tmp1)
 
+
 def mpf_div(tuple x, tuple y, int prec, str rnd='d'):
     cdef MPopts opts
     MPF_set_tuple(&tmp1, x)
@@ -48,9 +53,10 @@ def mpf_div(tuple x, tuple y, int prec, str rnd='d'):
     MPF_div(&tmp1, &tmp1, &tmp2, opts)
     return MPF_to_tuple(&tmp1)
 
+
 def mpf_sqrt(tuple x, int prec, str rnd='d'):
     """
-    Computes sqrt(x) with mpf value tuples.
+    Compute sqrt(x) with mpf value tuples.
 
     EXAMPLES::
 
@@ -59,7 +65,6 @@ def mpf_sqrt(tuple x, int prec, str rnd='d'):
         sage: y = mpf_sqrt(x, 53, 'n')
         sage: to_float(y)
         1.4142135623730951
-
     """
     if x[0]:
         import mpmath.libmp as libmp
@@ -71,9 +76,10 @@ def mpf_sqrt(tuple x, int prec, str rnd='d'):
     MPF_sqrt(&tmp1, &tmp1, opts)
     return MPF_to_tuple(&tmp1)
 
+
 def mpf_log(tuple x, int prec, str rnd='d'):
     """
-    Computes log(x) with mpf value tuples.
+    Compute log(x) with mpf value tuples.
 
     EXAMPLES::
 
@@ -82,7 +88,6 @@ def mpf_log(tuple x, int prec, str rnd='d'):
         sage: y = mpf_log(x, 53, 'n')
         sage: to_float(y)
         0.6931471805599453
-
     """
     if x[0]:
         import mpmath.libmp as libmp
@@ -94,9 +99,10 @@ def mpf_log(tuple x, int prec, str rnd='d'):
     MPF_log(&tmp1, &tmp1, opts)
     return MPF_to_tuple(&tmp1)
 
+
 def mpf_exp(tuple x, int prec, str rnd='d'):
     """
-    Computes exp(x) with mpf value tuples.
+    Compute exp(x) with mpf value tuples.
 
     EXAMPLES::
 
@@ -105,7 +111,6 @@ def mpf_exp(tuple x, int prec, str rnd='d'):
         sage: z = mpf_exp(x, 53, 'n')
         sage: to_float(z)
         7.38905609893065
-
     """
     cdef MPopts opts
     MPF_set_tuple(&tmp1, x)
@@ -114,9 +119,10 @@ def mpf_exp(tuple x, int prec, str rnd='d'):
     MPF_exp(&tmp1, &tmp1, opts)
     return MPF_to_tuple(&tmp1)
 
+
 def mpf_cos(tuple x, int prec, str rnd='d'):
     """
-    Computes cos(x) with mpf value tuples.
+    Compute cos(x) with mpf value tuples.
 
     EXAMPLES::
 
@@ -125,7 +131,6 @@ def mpf_cos(tuple x, int prec, str rnd='d'):
         sage: y = mpf_cos(x, 53, 'n')
         sage: to_float(y)
         0.5403023058681398
-
     """
     cdef MPopts opts
     MPF_set_tuple(&tmp1, x)
@@ -134,9 +139,10 @@ def mpf_cos(tuple x, int prec, str rnd='d'):
     MPF_cos(&tmp1, &tmp1, opts)
     return MPF_to_tuple(&tmp1)
 
+
 def mpf_sin(tuple x, int prec, str rnd='d'):
     """
-    Computes sin(x) with mpf value tuples.
+    Compute sin(x) with mpf value tuples.
 
     EXAMPLES::
 
@@ -145,7 +151,6 @@ def mpf_sin(tuple x, int prec, str rnd='d'):
         sage: y = mpf_sin(x, 53, 'n')
         sage: to_float(y)
         0.8414709848078965
-
     """
     cdef MPopts opts
     MPF_set_tuple(&tmp1, x)
@@ -154,9 +159,10 @@ def mpf_sin(tuple x, int prec, str rnd='d'):
     MPF_sin(&tmp1, &tmp1, opts)
     return MPF_to_tuple(&tmp1)
 
+
 def mpc_sqrt(tuple z, int prec, str rnd='d'):
     """
-    Computes sqrt(z) with mpc value tuples.
+    Compute sqrt(z) with mpc value tuples.
 
     EXAMPLES::
 
@@ -176,9 +182,10 @@ def mpc_sqrt(tuple z, int prec, str rnd='d'):
     MPF_complex_sqrt(&tmp1, &tmp2, &tmp1, &tmp2, opts)
     return MPF_to_tuple(&tmp1), MPF_to_tuple(&tmp2)
 
+
 def mpc_exp(tuple z, int prec, str rnd='d'):
     """
-    Computes exp(z) with mpc value tuples.
+    Compute exp(z) with mpc value tuples.
 
     EXAMPLES::
 
@@ -198,9 +205,10 @@ def mpc_exp(tuple z, int prec, str rnd='d'):
     MPF_complex_exp(&tmp1, &tmp2, &tmp1, &tmp2, opts)
     return MPF_to_tuple(&tmp1), MPF_to_tuple(&tmp2)
 
+
 def mpf_pow(tuple x, tuple y, int prec, str rnd='d'):
     """
-    Computes x ^ y with mpf value tuples.
+    Compute x ^ y with mpf value tuples.
 
     EXAMPLES::