sage: minor improvements and document some stuff

script/research/ec/ordp.sage

@@ -76,7 +76,11 @@ def ordp(P, original_f, debug=False):
     g = g[0]
     assert u(Px, Py) == 0
     assert f(Px, Py) != 0
-    #assert g(Px, Py) != 0
+    assert g(Px, Py) != 0
+    if debug:
+        print(f"u = {u}")
+        print(f"f = {f}")
+        print(f"g = {g}")
 
     return k
 

script/research/ec/valuate.sage

@@ -125,7 +125,11 @@ g = g[0]
 fprime = b0^k * f/g
 assert fprime == S(original_f)
 # to convert fprime back again:
-#f, g = fprime.numerator().lift(), fprime.denominator().lift()
+#   f, g = fprime.numerator().lift(), fprime.denominator().lift()
+# to get the parent ring use:
+#   f.parent()
+# to move up the hierarchy
+#   S.ring().cover_ring()
 assert g(Px, Py) != 0
 assert f(Px, Py) != 0
 assert b0(Px, Py) == 0