#20774: Basic singularity analysis for algebraic curves
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Reporter: gjorgenson | Owner:
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-7.3
Component: algebraic | Resolution:
geometry | Merged in:
Keywords: gsoc2016 | Reviewers: Ben Hutz
Authors: Grayson Jorgenson | Work issues:
Report Upstream: N/A | Commit:
Branch: | e6f1a9364395b0507ba872b4addf5b11d3e17ef8
u/gjorgenson/ticket/20774 | Stopgaps:
Dependencies: |
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Comment (by gjorgenson):
Thanks. I added some examples with different fields. It looks like
multiplicity works with RR and CC, and with finite fields. I think only
number fields work with the tangents functions though, since they use the
function factor().
I implemented an is_singular function which just uses the is_smooth
functions of affine/projective subschemes. If given a point it returns
whether it's singular or not, otherwise it returns whether the curve is
singular or not. I added a singular_subscheme function as well.
Currently, only plane curves over general rings can be defined. In the
space curve initialization, dimension is checked. Could we get around this
by checking the dimension of the new curve created by embedding the
defining polynomials of the original curve into the polynomial ring with
coefficients from the field of fractions of the base ring (assuming it's
an integral domain)?
If we add classes for curves over rings, would the naming scheme
AffineCurve_ring, ProjectiveCurve_ring for generic curves over rings, and
renaming
AffineCurve --> AffineCurve_field
ProjectiveCurve --> ProjectiveCurve_field
be okay?
I haven't yet implemented the corresponding singularity analysis functions
for points on curves; do you think it might be good for me to create
classes for points on general curves first? Maybe similar to what's done
in ell_point.py for points on elliptic curves?
--
Ticket URL: <http://trac.sagemath.org/ticket/20774#comment:7>
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