Revision history [back]
 | 1 | initial version |
The height functions you refer to are available as methods of some objects, rather than as functions in the global namespace.
To use them, first define an object of the appropriate class, giving it a name; then apply the method.
For instance, for a point on an elliptic curve, first define it, naming it P:
sage: E = EllipticCurve([0, 0, 0, -36, 0])
sage: P = E(-3, 9)
Then ask its heights:
sage: P.height()
0.888625874839619
sage: P.local_height(v=5)
0.000000000000000
sage: P.global_height()
2.19722457733622
sage: P.archimedean_local_height()
1.98723816350773
sage: P.non_archimedean_local_height()
-log(3)
