Changeset 7506:e44cd1715483

Timestamp:

12/01/07 15:28:51 (5 years ago)

Author:

Craig Citro <craigcitro@…>

Branch:

default

Message:

Fix for trac ticket #1129.

Location:

sage/rings

Files:

• number_field/number_field.py (modified) (2 diffs)
• polynomial/polynomial_element.pyx (modified) (2 diffs)

sage/rings/number_field/number_field.py

@@ -1356 +1356 @@
             return False
 
-    def pari_polynomial(self):
+    def pari_polynomial(self, name='x'):
         """
         PARI polynomial corresponding to polynomial that defines
-        this field.   This is always a polynomial in the variable "x".
+        this field. By default, this is a polynomial in the
+        variable "x".
 
         EXAMPLES:
@@ -1365 +1366 @@
             sage: k.<a> = NumberField(y^2 - 3/2*y + 5/3)
             sage: k.pari_polynomial()
-            x^2 - 3/2*x + 5/3        
+            x^2 - 3/2*x + 5/3
+            sage: k.pari_polynomial('a')
+            a^2 - 3/2*a + 5/3
         """
         try:
-            return self.__pari_polynomial
+            if (self.__pari_polynomial_var == name):
+                return self.__pari_polynomial
+            else:
+                self.__pari_polynomial = self.__pari_polynomial(name)
+                self.__pari_polynomial_var = name
+                return self.__pari_polynomial
         except AttributeError:
             poly = self.polynomial()
-            with localvars(poly.parent(), 'x'):
+            with localvars(poly.parent(), name):
                 self.__pari_polynomial = poly._pari_()
+                self.__pari_polynomial_var = name
             return self.__pari_polynomial
 

sage/rings/polynomial/polynomial_element.pyx

@@ -1576 +1576 @@
             return Factorization(v, from_M(F.unit()))
 
-
+        elif is_FiniteField(R):
+            v = [x._pari_("a") for x in self.list()]
+            f = pari(v).Polrev()
+            G = list(f.factor())
+
+            
         elif is_NumberField(R) or is_FiniteField(R):
             v = [x._pari_("a") for x in self.list()]
             f = pari(v).Polrev()
-            G = list(f.factor())
+            G = list(R.pari_polynomial("a").nfinit().nffactor(f))
 
         elif is_RealField(R):
@@ -2916 +2921 @@
             sage: R(4).is_irreducible()
             True
+
+        TESTS:
+            sage: F.<t> = NumberField(x^2-5)
+            sage: Fx.<xF> = PolynomialRing(F)
+            sage: f = Fx([2*t - 5, 5*t - 10, 3*t - 6, -t, -t + 2, 1])
+            sage: f.is_irreducible()
+            False
+            sage: f = Fx([2*t - 3, 5*t - 10, 3*t - 6, -t, -t + 2, 1])
+            sage: f.is_irreducible()
+            True            
         """
         if self.is_zero():