I am new to sagemath.
I followed the steps for installing sagemath 9.6 from:
sagemanifolds[DOT]obspm[DOT]fr/install_ubuntu[DOT]html
However, while testing out the included functions, I noticed that I do not have any height functions:
height(); local_height(); global_height(); archimedean_local_height(); non_archimedean_local_height();
etc.
How do I add these missing functions?
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)
thanks for the assist.
after defining the elliptic curve, and point, I receive the following errors:
P.height(): AttributeError: 'EllipticCurvePoint_finite_field' object has no attribute 'height'.
P.local_height(v=5): TypeError: must be over a number field or a number field order.
P.global_height(): NotImplementedError: not implemented for subschemes.
P.archimedean_local_height() is not present.
P.local_height_arch(): TypeError: local_height_arch() missing 1 required positional argument: 'i'.
P.local_height_arch(i=5): TypeError: must be over a number field or a number field order.
p = order of field.
P.local_height_arch(i=p): TypeError: must be over a number field or a number field order.
P.non_archimedean_local_height() is not present.
Please make the code self-contained - add the definition of P.
edited for simpler version with same result:
p = 37
K = GF(p)
E = EllipticCurve(K,[0, 0, 0, -36, 0])
P = E(-3, 9)
P.height(): AttributeError: 'EllipticCurvePoint_finite_field' object has no attribute 'height'.
P.local_height(v=5): TypeError: must be over a number field or a number field order.
P.global_height(): NotImplementedError: not implemented for subschemes.
P.archimedean_local_height() is not present.
P.local_height_arch(i=p): TypeError: must be over a number field or a number field order.
P.non_archimedean_local_height():is not present
it seems once I add the Galois Field, the height functions don't apply.
is this correct?
Asked: 2022-08-02 03:14:44 +0100
Seen: 288 times
Last updated: Aug 04 '22
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Height of what object? Do you want to add functions locally in your code, or globally in next version of Sage?
locally in my code. it seems to be in Sage already, just not in my version
You need to provide a minimal example illustrating the issue. See https://en.wikipedia.org/wiki/Minimal...
I started with
apt install sagemath apt install sagemath-doc
then followed the steps from the link in my question:
sudo apt install [...too large for comment...]
git clone --branch master https://github.com/sagemath/sage.git
cd sage/
make configure ./configure MAKE="make -j8" make
then deleted the first installed binary :
sudo rm /usr/bin/sage
then moved the new binary to my PATH:
sudo ln -sf $(pwd)/sage /usr/local/bin
sudo ln -sf $(pwd)/sage /usr/bin
When I run sage -v it says:
SageMath version 9.6, Release Date: 2022-05-15
yet I receive the errors listed in response to slelievre's answer