Improvement_of_dup_zz_mignotte_bound(f, K)

sympy/polys/factortools.py

@@ -73,6 +73,7 @@
 
 from sympy.ntheory import nextprime, isprime, factorint
 from sympy.utilities import subsets
+from sympy import binomial
 
 from math import ceil as _ceil, log as _log
 
@@ -124,13 +125,33 @@ def dmp_trial_division(f, factors, u, K):
 
 
 def dup_zz_mignotte_bound(f, K):
-    """Mignotte bound for univariate polynomials in `K[x]`. """
-    a = dup_max_norm(f, K)
-    b = abs(dup_LC(f, K))
-    n = dup_degree(f)
+    """
+    The Knuth-Cohen variant of Mignotte bound for
+    univariate polynomials in `K[x]`.
 
-    return K.sqrt(K(n + 1))*2**n*a*b
+    References
+    ==========
+
+    ..[1] [Abbott2013]_
+
+    """
+    d = dup_degree(f)
+    delta = _ceil( d / 2 )
+
+    # euclidean-norm
+    eucl_norm = K.sqrt( sum( [cf**2 for cf in f] ) )
+
+    # biggest values of binomial coefficients (p. 538 of reference)
+    t1 = binomial( delta - 1, _ceil( delta / 2 ) )
+    t2 = binomial( delta - 1, _ceil( delta / 2 ) - 1 )
 
+    lc = abs( dup_LC(f, K) )   # leading coefficient
+
+    bound = t1 * eucl_norm + t2 * lc   # (p. 538 of reference)
+
+    bound = _ceil( bound / 2 ) * 2   # round up to even integer
+
+    return bound + dup_max_norm(f, K)  # add max_coeff for irreducible polys
 
 def dmp_zz_mignotte_bound(f, u, K):
     """Mignotte bound for multivariate polynomials in `K[X]`. """
@@ -1147,7 +1168,7 @@ def dmp_ext_factor(f, u, K):
         return lc, []
 
     f, F = dmp_sqf_part(f, u, K), f
-    s, g, r = dmp_sqf_norm(F, u, K)
+    s, g, r = dmp_sqf_norm(f, u, K)
 
     factors = dmp_factor_list_include(r, u, K.dom)
 

sympy/polys/tests/test_factortools.py

@@ -27,7 +27,7 @@ def test_dmp_trial_division():
 
 def test_dup_zz_mignotte_bound():
     R, x = ring("x", ZZ)
-    assert R.dup_zz_mignotte_bound(2*x**2 + 3*x + 4) == 32
+    assert R.dup_zz_mignotte_bound(2*x**2 + 3*x + 4) == 6
 
 
 def test_dmp_zz_mignotte_bound():