fix(polys): fix multi factorisation over QQ<a>

doc/src/modules/polys/internals.rst

@@ -545,7 +545,9 @@ Polynomial factorization in characteristic zero:
 
 .. currentmodule:: sympy.polys.factortools
 
+.. autofunction:: dup_trial_division
 .. autofunction:: dmp_trial_division
+.. autofunction:: dup_zz_mignotte_bound
 .. autofunction:: dmp_zz_mignotte_bound
 .. autofunction:: dup_zz_hensel_step
 .. autofunction:: dup_zz_hensel_lift
@@ -559,16 +561,49 @@ Polynomial factorization in characteristic zero:
 .. autofunction:: dmp_zz_wang_non_divisors
 .. autofunction:: dmp_zz_wang_test_points
 .. autofunction:: dmp_zz_wang_lead_coeffs
+.. autofunction:: dup_zz_diophantine
 .. autofunction:: dmp_zz_diophantine
 .. autofunction:: dmp_zz_wang_hensel_lifting
 .. autofunction:: dmp_zz_wang
 .. autofunction:: dmp_zz_factor
+.. autofunction:: dup_qq_i_factor
+.. autofunction:: dup_zz_i_factor
+.. autofunction:: dmp_qq_i_factor
+.. autofunction:: dmp_zz_i_factor
+.. autofunction:: dup_ext_factor
 .. autofunction:: dmp_ext_factor
 .. autofunction:: dup_gf_factor
+.. autofunction:: dmp_gf_factor
+.. autofunction:: dup_factor_list
+.. autofunction:: dup_factor_list_include
 .. autofunction:: dmp_factor_list
 .. autofunction:: dmp_factor_list_include
+.. autofunction:: dup_irreducible_p
 .. autofunction:: dmp_irreducible_p
 
+Square-free factorization:
+
+.. currentmodule:: sympy.polys.sqfreetools
+
+.. autofunction:: dup_sqf_p
+.. autofunction:: dmp_sqf_p
+.. autofunction:: dup_sqf_norm
+.. autofunction:: dmp_sqf_norm
+.. autofunction:: dmp_norm
+.. autofunction:: dup_gf_sqf_part
+.. autofunction:: dmp_gf_sqf_part
+.. autofunction:: dup_sqf_part
+.. autofunction:: dmp_sqf_part
+.. autofunction:: dup_gf_sqf_list
+.. autofunction:: dmp_gf_sqf_list
+.. autofunction:: dup_sqf_list
+.. autofunction:: dup_sqf_list_include
+.. autofunction:: dmp_sqf_list
+.. autofunction:: dmp_sqf_list_include
+.. autofunction:: dup_gff_list
+.. autofunction:: dmp_gff_list
+
+
 Groebner basis algorithms
 *************************
 

doc/src/modules/polys/literature.rst

@@ -144,4 +144,16 @@ a theoretical foundation for implementing polynomials manipulation module.
     https://isc.tamu.edu/resources/preprints/1996/1996-02.pdf
 
 .. [Cohen93] Henri Cohen. "A Course in Computational Algebraic Number Theory",
-   Springer, 1993.
+    Springer, 1993.
+
+.. [Trager76] Barry M. Trager. "Algebraic factoriing and rational function
+    integration", Proceedings of SYMSAC 1976, pp. 219-226, ACM, 1976.
+    https://dl.acm.org/doi/abs/10.1145/800205.806338
+
+.. [Yun76] David Y.Y. Yun. "On square-free decomposition algorithms",
+    Proceedings of SYMSAC 1976, pp. 219-226, ACM, 1976.
+    https://dl.acm.org/doi/10.1145/800205.806320
+
+.. [Abbott13] John Abbott. "Bounds on factors in Z[x]".
+    Journal of Symbolic Computation 50 (2013), pp. 532-563
+    https://doi.org/10.1016/j.jsc.2012.09.004

sympy/polys/compatibility.py

@@ -101,6 +101,7 @@
 from sympy.polys.densetools import dup_mirror
 from sympy.polys.densetools import dup_scale
 from sympy.polys.densetools import dup_shift
+from sympy.polys.densetools import dmp_shift
 from sympy.polys.densetools import dup_transform
 from sympy.polys.densetools import dup_compose
 from sympy.polys.densetools import dmp_compose
@@ -209,9 +210,10 @@
 from sympy.polys.rootisolation import dup_isolate_all_roots
 
 from sympy.polys.sqfreetools import (
-    dup_sqf_p, dmp_sqf_p, dup_sqf_norm, dmp_sqf_norm, dup_gf_sqf_part, dmp_gf_sqf_part,
-    dup_sqf_part, dmp_sqf_part, dup_gf_sqf_list, dmp_gf_sqf_list, dup_sqf_list,
-    dup_sqf_list_include, dmp_sqf_list, dmp_sqf_list_include, dup_gff_list, dmp_gff_list)
+    dup_sqf_p, dmp_sqf_p, dmp_norm, dup_sqf_norm, dmp_sqf_norm,
+    dup_gf_sqf_part, dmp_gf_sqf_part, dup_sqf_part, dmp_sqf_part,
+    dup_gf_sqf_list, dmp_gf_sqf_list, dup_sqf_list, dup_sqf_list_include,
+    dmp_sqf_list, dmp_sqf_list_include, dup_gff_list, dmp_gff_list)
 
 from sympy.polys.galoistools import (
     gf_degree, gf_LC, gf_TC, gf_strip, gf_from_dict,
@@ -515,6 +517,8 @@ def dup_scale(self, f, a):
         return self.from_dense(dup_scale(self.to_dense(f), a, self.domain))
     def dup_shift(self, f, a):
         return self.from_dense(dup_shift(self.to_dense(f), a, self.domain))
+    def dmp_shift(self, f, a):
+        return self.from_dense(dmp_shift(self.to_dense(f), a, self.ngens-1, self.domain))
     def dup_transform(self, f, p, q):
         return self.from_dense(dup_transform(self.to_dense(f), self.to_dense(p), self.to_dense(q), self.domain))
 
@@ -877,6 +881,10 @@ def dup_sqf_p(self, f):
     def dmp_sqf_p(self, f):
         return dmp_sqf_p(self.to_dense(f), self.ngens-1, self.domain)
 
+    def dmp_norm(self, f):
+        n = dmp_norm(self.to_dense(f), self.ngens-1, self.domain)
+        return self.to_ground().from_dense(n)
+
     def dup_sqf_norm(self, f):
         s, F, R = dup_sqf_norm(self.to_dense(f), self.domain)
         return (s, self.from_dense(F), self.to_ground().from_dense(R))

sympy/polys/densetools.py

@@ -782,7 +782,7 @@ def dmp_ground_extract(f, g, u, K):
 
 def dup_real_imag(f, K):
     """
-    Return bivariate polynomials ``f1`` and ``f2``, such that ``f = f1 + f2*I``.
+    Find ``f1`` and ``f2``, such that ``f(x+I*y) = f1(x,y) + f2(x,y)*I``.
 
     Examples
     ========
@@ -793,6 +793,11 @@ def dup_real_imag(f, K):
     >>> R.dup_real_imag(x**3 + x**2 + x + 1)
     (x**3 + x**2 - 3*x*y**2 + x - y**2 + 1, 3*x**2*y + 2*x*y - y**3 + y)
 
+    >>> from sympy.abc import x, y, z
+    >>> from sympy import I
+    >>> (z**3 + z**2 + z + 1).subs(z, x+I*y).expand().collect(I)
+    x**3 + x**2 - 3*x*y**2 + x - y**2 + I*(3*x**2*y + 2*x*y - y**3 + y) + 1
+
     """
     if not K.is_ZZ and not K.is_QQ:
         raise DomainError("computing real and imaginary parts is not supported over %s" % K)
@@ -894,6 +899,44 @@ def dup_shift(f, a, K):
     return f
 
 
+def dmp_shift(f, a, u, K):
+    """
+    Evaluate efficiently Taylor shift ``f(X + A)`` in ``K[X]``.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols, ring, ZZ
+    >>> x, y = symbols('x y')
+    >>> R, _, _ = ring([x, y], ZZ)
+
+    >>> p = x**2*y + 2*x*y + 3*x + 4*y + 5
+
+    >>> R.dmp_shift(R(p), [ZZ(1), ZZ(2)])
+    x**2*y + 2*x**2 + 4*x*y + 11*x + 7*y + 22
+
+    >>> p.subs({x: x + 1, y: y + 2}).expand()
+    x**2*y + 2*x**2 + 4*x*y + 11*x + 7*y + 22
+    """
+    if not u:
+        return dup_shift(f, a[0], K)
+
+    if dmp_zero_p(f, u):
+        return f
+
+    a0, a1 = a[0], a[1:]
+
+    f = [ dmp_shift(c, a1, u-1, K) for c in f ]
+    n = len(f) - 1
+
+    for i in range(n, 0, -1):
+        for j in range(0, i):
+            afj = dmp_mul_ground(f[j], a0, u-1, K)
+            f[j + 1] = dmp_add(f[j + 1], afj, u-1, K)
+
+    return f
+
+
 def dup_transform(f, p, q, K):
     """
     Evaluate functional transformation ``q**n * f(p/q)`` in ``K[x]``.