Ticket #3946: 3946.patch

a/sage/quadratic_forms/binary_qf.py

@@ -9 +9 @@
-    x^2 + 2*x*y  + 3*y^2
-    sage: Q.discriminant()
-    -8
-
+d_form
-    x^2 + 2*y^2
-    sage: Q(1, 1)
-    6
@@ -81 +81 @@
-        self.a = ZZ(abc_triple[0])
-        self.b = ZZ(abc_triple[1])
-        self.c = ZZ(abc_triple[2])
-        self._reduced_form = None
-
-    def __getitem__(self, n):
-        """
@@ -269 +268 @@
-        """
-        return is_fundamental_discriminant(self.discriminant())
-
-
-    def is_weakly_reduced(self):
-        """
-        Checks if the form $ax^2 + bxy + cy^2$  satisfies
@@ -289 +287 @@
-            True
-        """
-        if self.discriminant() >= 0:
-egative discriminant
+agative discriminants
-        return (abs(self.b) <= self.a) and (self.a <= self.c)
-
+    def reduced_form(self):
+        """
+        EXAMPLES:
+            sage: a = BinaryQF([33,11,5])
+            sage: a.is_reduced()
+            False
+            sage: b = a.reduced_form(); b
+            5*x^2 - x*y + 27*y^2
+            sage: b.is_reduced()
+            True
+            
+            sage: a = BinaryQF([15,0,15])
+            sage: a.is_reduced()
+            True
+            sage: b = a.reduced_form(); b
+            15*x^2 + 15*y^2
+            sage: b.is_reduced()
+            True
+        """
+        if self.discriminant() >= 0 or self.a < 0:
+            raise NotImplementedError, "only implemented for positive definite forms"
+        if not self.is_reduced():
+            v = list(pari('Vec(qfbred(Qfb(%s,%s,%s)))'%(self.a,self.b,self.c)))
+            return BinaryQF(v)
+        else:
+            return self
+    
-    def reduce(self):
-        """
-        EXAMPLES:
-            sage: a = BinaryQF([37,17,2])
-            sage: a.is_reduced()
-            False
-b = a.reduce(); b
+a.reduce(); a 
-            x^2 + x*y + 2*y^2
-b
+a
-            True
-        """
-
-
-
-
+
+
+
-
-    def is_reduced(self):
-        """
@@ -331 +355 @@
-            sage: Q.is_reduced()
-            True
-        """
-
+
+
-
-    def complex_point(self):
-        """