Ticket #12173: trac_12173-ffixes.patch

sage/libs/flint/nmod_poly_linkage.pxi

@@ -495 +495 @@
     elif e == 1:
         nmod_poly_set(res, x)
     elif e == 2:
-        nmod_poly_mul(res, x, x)
+        nmod_poly_pow(res, x, 2)
     else:
         if res == x:
             nmod_poly_set(tmp, x)
@@ -509 +509 @@
             nmod_poly_set_coeff_ui(res, 0, 1)
         e = e >> 1
         while(e != 0):
-            nmod_poly_mul(pow2, pow2, pow2)
+            nmod_poly_pow(pow2, pow2, 2)
             if e % 2:
                 nmod_poly_mul(res, res, pow2)
             e = e >> 1

sage/rings/fraction_field_FpT.pyx

@@ -9 +9 @@
 
 from sage.rings.all import GF
 from sage.libs.flint.nmod_poly cimport *
+from sage.libs.flint.ulong_extras cimport n_jacobi
 from sage.structure.element cimport Element, ModuleElement, RingElement
 from sage.rings.integer_ring import ZZ
 from sage.rings.fraction_field import FractionField_generic, FractionField_1poly_field
@@ -648 +649 @@
                 finally:
                     nmod_poly_clear(g)
         return next
-        
+
     cpdef _sqrt_or_None(self):
         """
         Returns the squre root of self, or None. Differs from sqrt() by not raising an exception. 
@@ -686 +687 @@
             []
 
         """
-        if nmod_poly_degree(self._numer) == -1:
+        if nmod_poly_is_zero(self._numer):
             return self
+
+        if not nmod_poly_sqrt_check(self._numer) or not nmod_poly_sqrt_check(self._denom):
+            return None
+
         cdef nmod_poly_t numer
         cdef nmod_poly_t denom
         cdef long a
@@ -1640 +1645 @@
         d -= 1
     return 0
 
+cdef bint nmod_poly_sqrt_check(nmod_poly_t poly):
+     """
+     Quick check to see if poly could possibly be a square.
+     """
+     # We could use Sage's jacobi_int which is for 32 bits integers rather
+     # than FLINT's n_jacobi which is for longs as the FpT class is crafted
+     # for primes 2 < p < 2^16
+     return (nmod_poly_degree(poly) % 2 == 0
+         and n_jacobi(nmod_poly_leading(poly), poly.mod.n) == 1
+         and n_jacobi(nmod_poly_get_coeff_ui(poly, 0), poly.mod.n) != -1)
+
 def unpickle_FpT_element(K, numer, denom):
     """
     Used for pickling.

sage/rings/polynomial/polynomial_zmod_flint.pyx

@@ -152 +152 @@
 
         INPUT:
 
-        - ``x`` - a list of coefficients
+        - ``x`` - a list of coefficients - the coefficients are assumed to be
+          reduced already and the list contains no trailing zeroes.
+
 
         EXAMPLES::
 
@@ -178 +180 @@
         sig_off()
 
         sig_on()
+        # The following depends on the internals of FLINT
         for i from 0 <= i < length:
-            nmod_poly_set_coeff_ui(&self.x, i, l_in[i])
+            self.x.coeffs[i] = l_in[i]
+        self.x.length = length
         sig_off()
         return 0