Ticket #15243: 15243_uniformizer.patch

sage/libs/pari/decl.pxi

@@ -1365 +1365 @@
     void    pari_close()
     void    pari_init(size_t parisize, ulong maxprime)
     void    pari_init_opts(size_t parisize, ulong maxprime, ulong init_opts)
-    void    stackdummy(GEN x, long l)
     long    gsizebyte(GEN x)
     long    gsizeword(GEN x)
     long    timer()

sage/libs/pari/gen.pyx

@@ -7012 +7012 @@
     def idealappr(self, x, long flag=0):
         t0GEN(x)
         pari_catch_sig_on()
-        return self.new_gen(idealappr(self.g, t0))
+        return self.new_gen(idealappr0(self.g, t0, flag))
 
     def idealcoprime(self, x, y):
         """

sage/rings/number_field/number_field.py

@@ -5196 +5196 @@
             sage: P,Q = K.ideal(3).prime_factors()
             sage: P
             Fractional ideal (3, a + 1)
-            sage: pi=K.uniformizer(P); pi
+            sage: pi = K.uniformizer(P); pi
             a + 1
             sage: K.ideal(pi).factor()
             (Fractional ideal (2, a + 1)) * (Fractional ideal (3, a + 1))
-            sage: pi=K.uniformizer(P,'negative'); pi
+            sage: pi = K.uniformizer(P,'negative'); pi
             1/2*a + 1/2
             sage: K.ideal(pi).factor()
             (Fractional ideal (2, a + 1))^-1 * (Fractional ideal (3, a + 1))
@@ -5216 +5216 @@
             [1, 1, 1]
             sage: [ pilist[i] in Plist[i] for i in range(len(Plist)) ]
             [True, True, True]
+
+        ::
+
+            sage: K.<t> = NumberField(x^4 - x^3 - 3*x^2 - x + 1)
+            sage: [K.uniformizer(P) for P,e in factor(K.ideal(2))]
+            [2]
+            sage: [K.uniformizer(P) for P,e in factor(K.ideal(3))]
+            [t - 1]
+            sage: [K.uniformizer(P) for P,e in factor(K.ideal(5))]
+            [t^2 - t + 1, t + 2, t - 2]
+            sage: [K.uniformizer(P) for P,e in factor(K.ideal(7))]
+            [t^2 + 3*t + 1]
+            sage: [K.uniformizer(P) for P,e in factor(K.ideal(67))]
+            [t + 23, t + 26, t - 32, t - 18]
+
+        ALGORITHM:
+
+            Use PARI. More precisely, use the second component of
+            ``idealprimedec`` in the "positive" case. Use `idealappr`
+            with exponent of -1 and invert the result in the "negative"
+            case.
         """
         if not is_NumberFieldIdeal(P):
             P = self.ideal(P)
-        if not P.is_maximal():
-            raise ValueError, "P must be a nonzero prime"
-        if others == "negative":
-            P = ~P
-        elif others != "positive":
-            raise ValueError, "others must be 'positive' or 'negative'"
-        nf = self.pari_nf()
-        a = self(nf.idealappr(P.pari_hnf()))
-        if others == "negative":
-            a = ~a
-        return a
+        P = P.pari_prime()
+        if others == "positive":
+            return self(P[1])
+        elif others == "negative":
+            nf = self.pari_nf()
+            F = pari.matrix(1, 2, [P, -1])
+            return ~self(nf.idealappr(F, 1))
+        else:
+            raise ValueError("others must be 'positive' or 'negative'")
 
     def units(self, proof=None):
         """

sage/schemes/elliptic_curves/ell_number_field.py

@@ -595 +595 @@
             sage: K.<v> = NumberField(x^2 + 161*x - 150)
             sage: E = EllipticCurve([25105/216*v - 3839/36, 634768555/7776*v - 98002625/1296, 634768555/7776*v - 98002625/1296, 0, 0])
             sage: E.global_integral_model()
-            Elliptic Curve defined by y^2 + (33872485050625*v-31078224284250)*x*y + (2020602604156076340058146664245468750000*v-1871778534673615560803175189398437500000)*y = x^3 + (6933305282258321342920781250*v-6422644400723486559914062500)*x^2 over Number Field in v with defining polynomial x^2 + 161*x - 150
+            Elliptic Curve defined by y^2 + (-502639783*v+465618899)*x*y + (-6603604211463489399460860*v+6117229527723443603191500)*y = x^3 + (1526887622075335620*v-1414427901517840500)*x^2 over Number Field in v with defining polynomial x^2 + 161*x - 150
 
         :trac:`14476`::
 
@@ -603 +603 @@
             sage: K.<g> = NumberField(t^4 - t^3 - 3*t^2 - t + 1)
             sage: E = EllipticCurve([ -43/625*g^3 + 14/625*g^2 - 4/625*g + 706/625, -4862/78125*g^3 - 4074/78125*g^2 - 711/78125*g + 10304/78125,  -4862/78125*g^3 - 4074/78125*g^2 - 711/78125*g + 10304/78125, 0,0])
             sage: E.global_integral_model()
-            Elliptic Curve defined by y^2 + (-18*g^3+29*g^2+63*g+7)*x*y + (-704472*g^3-958584*g^2-166242*g+298101)*y = x^3 + (-2859*g^3-3978*g^2-669*g+1332)*x^2 over Number Field in g with defining polynomial t^4 - t^3 - 3*t^2 - t + 1
+            Elliptic Curve defined by y^2 + (15*g^3-48*g-42)*x*y + (-111510*g^3-162162*g^2-44145*g+37638)*y = x^3 + (-954*g^3-1134*g^2+81*g+576)*x^2 over Number Field in g with defining polynomial t^4 - t^3 - 3*t^2 - t + 1
 
         """
         K = self.base_field()