Changeset 7507:de39c2037850

Timestamp:

12/02/07 02:20:33 (5 years ago)

Author:

Craig Citro <craigcitro@…>

Branch:

default

Message:

More fixes & changes for trac #1129.

File:

• sage/rings/polynomial/polynomial_element.pyx (modified) (3 diffs)

sage/rings/polynomial/polynomial_element.pyx

@@ -1483 +1483 @@
             sage: expand(F)
             T^6 + 10/7*T^5 + (-867/49)*T^4 + (-76/245)*T^3 + 3148/35*T^2 + (-25944/245)*T + 48771/1225
+
+            sage: f = x^2 - 1/3 ; K.<a> = NumberField(f) ; A.<T> = K[] ; g = A(x^2-1)
+            sage: g.factor()
+            (T - 1) * (T + 1)
+
+            sage: h = A(3*x^2-1) ; h.factor()
+            (3) * (T - a) * (T + a)
+
+            sage: h = A(x^2-1/3) ; h.factor()
+            (T - a) * (T + a)
         
         Over the real double field:
@@ -1553 +1563 @@
         G = None
         
-        from sage.rings.number_field.all import is_NumberField, is_RelativeNumberField
+        from sage.rings.number_field.all import is_NumberField, \
+             is_RelativeNumberField, NumberField
         from sage.rings.finite_field import is_FiniteField
 
@@ -1582 +1593 @@
 
             
-        elif is_NumberField(R) or is_FiniteField(R):
-            v = [x._pari_("a") for x in self.list()]
-            f = pari(v).Polrev()
-            G = list(R.pari_polynomial("a").nfinit().nffactor(f))
+        elif is_NumberField(R):
+            if (R.defining_polynomial().denominator() == 1) and \
+                   (self.denominator() == 1):
+                v = [ x._pari_("a") for x in self.list() ]
+                f = pari(v).Polrev()
+                Rpari = R.pari_nf()
+                if (Rpari.variable() != "a"):
+                    Rpari = Rpari.copy()
+                    Rpari[0] = Rpari[0]("a")
+                    Rpari[6] = [ x("a") for x in Rpari[6] ]
+                G = list(Rpari.nffactor(f))
+
+            else:
+
+                Rdenom = R.defining_polynomial().denominator()
+
+                new_Rpoly = (R.defining_polynomial() * Rdenom).change_variable_name("a")
+
+                Rpari, Rdiff = new_Rpoly._pari_().nfinit(3)
+
+                AZ = polynomial_ring.PolynomialRing(QQ,'z')
+                Raux = NumberField(AZ(Rpari[0]),'alpha')
+
+                S, gSRaux, fRauxS = Raux.change_generator(Raux(Rdiff))
+
+                phi_RS = R.Hom(S)([S.gen(0)])
+                phi_SR = S.Hom(R)([R.gen(0)])
+
+                unit = self.leading_coefficient()
+                temp_f = self * 1/unit
+
+                v = [ gSRaux(phi_RS(x))._pari_("a") for x in temp_f.list() ]
+                f = pari(v).Polrev()
+
+                pari_factors = Rpari.nffactor(f)
+
+                factors = [ ( self.parent([ phi_SR(fRauxS(Raux(pari_factors[0][i][j])))
+                                            for j in range(len(pari_factors[0][i])) ]) ,
+                             int(pari_factors[1][i]) )
+                            for i in range(pari_factors.nrows()) ]
+
+                return Factorization(factors, unit)
+        
 
         elif is_RealField(R):