Ticket #11868: trac_11868-get_nf.patch

sage/libs/pari/gen.pyx

@@ -710 +710 @@
         # stored.
         return self.new_gen(gel(self.g, 1))
 
-    def get_nf(self):
-        """
-        Given a PARI object `self`, convert it to a proper PARI number
-        field (nf) structure.
+    def nf_get_pol(self):
+        """
+        Returns the defining polynomial of this number field.
 
         INPUT:
 
         - ``self`` -- A PARI number field being the output of ``nfinit()``,
                       ``bnfinit()`` or ``bnrinit()``.
 
-        TESTS:
-
-        We test this indirectly through `nf_get_pol()`::
+        EXAMPLES::
+
+            sage: K.<a> = NumberField(x^4 - 4*x^2 + 1)
+            sage: pari(K).nf_get_pol()
+            y^4 - 4*y^2 + 1
+            sage: bnr = pari("K = bnfinit(x^4 - 4*x^2 + 1); bnrinit(K, 2*x)")
+            sage: bnr.nf_get_pol()
+            x^4 - 4*x^2 + 1
+
+        For relative extensions, this returns the absolute polynomial,
+        not the relative one::
+
+            sage: L.<b> = K.extension(x^2 - 5)
+            sage: pari(L).nf_get_pol()   # Absolute polynomial
+            y^8 - 28*y^6 + 208*y^4 - 408*y^2 + 36
+            sage: L.pari_rnf().nf_get_pol()
+            x^8 - 28*x^6 + 208*x^4 - 408*x^2 + 36
+
+        TESTS::
 
             sage: x = polygen(QQ)
             sage: K.<a> = NumberField(x^4 - 4*x^2 + 1)
@@ -730 +745 @@
             y^4 - 4*y^2 + 1
             sage: K.pari_bnf().nf_get_pol()
             y^4 - 4*y^2 + 1
-            sage: bnr = pari("K = bnfinit(x^4 - 4*x^2 + 1); bnrinit(K, 2*x)")
-            sage: bnr.nf_get_pol()
-            x^4 - 4*x^2 + 1
-
-        It does not work with ``rnfinit()`` or garbage input::
-
-            sage: K.extension(x^2 - 5, 'b').pari_rnf().nf_get_pol()
-            Traceback (most recent call last):
-            ...
-            TypeError: Not a PARI number field
+
+        An error is raised for invalid input::
+
             sage: pari("[0]").nf_get_pol()
             Traceback (most recent call last):
             ...
-            TypeError: Not a PARI number field
-        """
-        cdef GEN nf
-        cdef long nftyp
-        pari_catch_sig_on()
-        nf = get_nf(self.g, &nftyp)
-        if not nf:
-            pari_catch_sig_off()
-            raise TypeError("Not a PARI number field")
-        return P.new_gen(nf)
-
-    def nf_get_pol(self):
-        """
-        Returns the defining polynomial of this number field.
-
-        INPUT:
-
-        - ``self`` -- A PARI number field being the output of ``nfinit()``,
-                      ``bnfinit()`` or ``bnrinit()``.
-
-        EXAMPLES::
-            
-            sage: K.<a> = NumberField(x^4 - 4*x^2 + 1)
-            sage: pari(K).nf_get_pol()
-            y^4 - 4*y^2 + 1
-            sage: bnr = pari("K = bnfinit(x^4 - 4*x^2 + 1); bnrinit(K, 2*x)")
-            sage: bnr.nf_get_pol()
-            x^4 - 4*x^2 + 1
-
-        For relative extensions, we can only get the absolute polynomial,
-        not the relative one::
-
-            sage: L.<b> = K.extension(x^2 - 5)
-            sage: pari(L).nf_get_pol()   # Absolute polynomial
-            y^8 - 28*y^6 + 208*y^4 - 408*y^2 + 36
-            sage: L.pari_rnf().nf_get_pol()
-            Traceback (most recent call last):
-            ...
-            TypeError: Not a PARI number field
-        """
-        cdef gen nf = self.get_nf()
-        pari_catch_sig_on()
-        return P.new_gen(nf_get_pol(nf.g))
+            PariError: incorrect type in pol
+        """
+        pari_catch_sig_on()
+        return P.new_gen(member_pol(self.g))
 
     def nf_get_diff(self):
         """
@@ -802 +771 @@
             sage: pari(K).nf_get_diff()
             [12, 0, 0, 0; 0, 12, 8, 0; 0, 0, 4, 0; 0, 0, 0, 4]
         """
-        cdef gen nf = self.get_nf()
-        pari_catch_sig_on()
-        # Very bad code, but there doesn't seem to be a better way
-        return P.new_gen(gel(gel(nf.g, 5), 5))
+        pari_catch_sig_on()
+        return P.new_gen(member_diff(self.g))
 
     def nf_get_sign(self):
         """
@@ -831 +798 @@
         """
         cdef long r1
         cdef long r2
-        cdef gen nf = self.get_nf()
-        nf_get_sign(nf.g, &r1, &r2)
+        cdef GEN sign
+        pari_catch_sig_on()
+        sign = member_sign(self.g)
+        r1 = itos(gel(sign, 1))
+        r2 = itos(gel(sign, 2))
+        pari_catch_sig_off()
         return [r1, r2]
 
     def nf_get_zk(self):
@@ -851 +822 @@
             sage: pari(K).nf_get_zk()
             [1, y, y^3 - 4*y, y^2 - 2]
         """
-        cdef gen nf = self.get_nf()
-        pari_catch_sig_on()
-        return P.new_gen(nf_get_zk(nf.g))
+        pari_catch_sig_on()
+        return P.new_gen(member_zk(self.g))
 
     def bnf_get_no(self):
         """
@@ -8896 +8866 @@
             [2]
         """
         pari_catch_sig_on()
-        cdef gen nf = self.get_nf()
         cdef GEN t0 = P.toGEN(z)
-        return P.new_gen(gsubst(self.g, nf_get_varn(nf.g), t0))
+        return P.new_gen(gsubst(self.g, gvar(self.g), t0))
 
     def taylor(self, v=-1):
         pari_catch_sig_on()