Changeset 7684:efff27d56eb3

Timestamp:

11/20/07 03:38:04 (6 years ago)

Author:

Robert Bradshaw <robertwb@…>

Branch:

default

Message:

Translate points back to curve for Simon's two descent

Location:

sage/schemes/elliptic_curves

Files:

• ell_generic.py (modified) (4 diffs)
• ell_number_field.py (modified) (2 diffs)
• ell_rational_field.py (modified) (4 diffs)
• weierstrass_morphism.py (modified) (1 diff)

sage/schemes/elliptic_curves/ell_generic.py

@@ -1284 +1284 @@
     division_polynomial = torsion_polynomial
 
-    def isomporphism_to(self, other):
+    def isomorphism_to(self, other):
         """
         Given another weierstrass model \code{other} of self, return a morphism
@@ -1294 +1294 @@
             sage: E = EllipticCurve('37a')
             sage: F = E.weierstrass_model()
-            sage: w = E.isomporphism_to(F); w
+            sage: w = E.isomorphism_to(F); w
             Generic morphism:
               From: Abelian group of points on Elliptic Curve defined by y^2 + y = x^3 - x over Rational Field
@@ -1310 +1310 @@
           We can also handle injections to different base rings: 
               sage: K.<a> = NumberField(x^3-7)
-              sage: E.isomporphism_to(E.change_ring(K))
+              sage: E.isomorphism_to(E.change_ring(K))
               Generic morphism:
                 From: Abelian group of points on Elliptic Curve defined by y^2 + y = x^3 - x over Rational Field
@@ -1337 +1337 @@
         else:
             try:
-                phi = self.isomporphism_to(other)
+                phi = self.isomorphism_to(other)
                 return True
             except ValueError:

sage/schemes/elliptic_curves/ell_number_field.py

@@ -79 +79 @@
         
         If the curve has 2-torsion, only the probable rank is returned. 
-
-        \note{The points are not translated back to self only because
-        I haven't written code to do this yet.}
         
         INPUT:
@@ -129 +126 @@
             (1, -1, [])
         """
-        #Should this really be here?
-        #if self.torsion_order() % 2 == 0:
-        #    raise ArithmeticError, "curve must not have rational 2-torsion\nThe *only* reason for this is that I haven't finished implementing the wrapper\nin this case.  It wouldn't be too difficult.\nPerhaps you could do it?!  Email me (wstein@gmail.com)."
-        # F = self.integral_weierstrass_model()
-        # a1,a2,a3,a4,a6 = F.a_invariants()
         x = PolynomialRing(self.base_ring(), 'x').gen(0)
         t = simon_two_descent(self,

sage/schemes/elliptic_curves/ell_rational_field.py

@@ -789 +789 @@
         Given a curve with no 2-torsion, computes (probably) the rank
         of the Mordell-Weil group, with certainty the rank of the
-        2-Selmer group, and a list of independent points on
-        some mysterious model of the curve.
-
-        \note{The points are not translated back to self only because
-        nobody has written code to do this yet.  Implement it and send 
-        a patch.}
-        
+        2-Selmer group, and a list of independent points on the curve.
+
         INPUT:
             verbose -- integer, 0,1,2,3; (default: 0), the verbosity level
@@ -810 +805 @@
             integer -- "probably" the rank of self
             integer -- the 2-rank of the Selmer group
-            list    -- list of independent points on some (myserious!!) model for the curve.
+            list    -- list of independent points on the curve.
 
         IMPLEMENTATION: Uses {\bf Denis Simon's} GP/PARI scripts from
@@ -1599 +1594 @@
         for a in ai:
             if not a.is_integral():
-      ### Is there really no prime_factors() function?
-               pj=[fi[0] for fi in a.denom().factor()]
-               for p in pj:
+               for p, _ in a.denom().factor():
                   e  = min([(ai[i].valuation(p)/[1,2,3,4,6][i]) for i in range(5)]).floor()
                   ai = [ai[i]/p**(e*[1,2,3,4,6][i]) for i in range(5)]
@@ -1607 +1600 @@
 
     integral_model = global_integral_model
+    
+    def integral_model(self):
+        F = self.global_integral_model()
+        return F, self.isomorphism_to(F)
 
     def integral_weierstrass_model(self):

sage/schemes/elliptic_curves/weierstrass_morphism.py

@@ -76 +76 @@
             sage: F = E.change_weierstrass_model([2,3,4,5]); F
             Elliptic Curve defined by y^2 - 8*x*y + 22*y = x^3 - 25*x^2 + 3*x + 588 over Rational Field
-            sage: w = E.isomporphism_to(F)
+            sage: w = E.isomorphism_to(F)
             sage: P = E(-2,3,1)
             sage: w(P)