Changes between Initial Version and Version 8 of Ticket #11930


Ignore:
Timestamp:
12/18/11 14:00:44 (17 months ago)
Author:
mstreng
Comment:

Apply 11930_singular_hyperelliptic.patch and 11930_is_singular.patch

The first of these patches (written by Damiano and I) adds tests to the HyperellipticCurve? constructor. It tests whether the input polynomials f(x) and h(x) really make sense. In other words, it checks if there is some g such that, when f and h are homogenized wrt x to degrees 2g+2 and g+1 respectively, one gets a smooth projective curve. We compared it with the independent implementation in Magma, and the test turns out to be equivalent to Magma's test for all input polynomials over GF(2) and GF(3) where deg(f) is 5 or 6 and deg(h) <= 3.

The second patch is Daniel's function, but with a simpler algorithm that uses the fact that only smooth curves are constructed.

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  • Ticket #11930

    • Property Status changed from new to needs_work
    • Property Work issues changed from to add singular examples to the documentation of the constructor, do some tests
    • Property Authors changed from to Daniel Krenn, Marco Streng, Damiano Testa
    • Property Summary changed from function to check if hyperelliptitc curve is singular in the sense of hyperelliptic curves to function to check if hyperelliptic curve is singular in the sense of hyperelliptic curves
    • Property Keywords singular, sd35 added; singular removed
    • Property Reviewers changed from to Marco Streng, Damiano Testa

  • Ticket #11930 – Description

    initial v8  
    66True 
    77}}} 
    8 but `H` is a non-singular hyperelliptic curve. Although this is '''not''' an error, since all hyperelliptic curves, where the degree of the defining polynomial is at least 5, have a singularity at infinity.  
     8but `H` is a non-singular hyperelliptic curve. 
    99 
    10 The term non-singular hyperelliptic curve is used to say that all finite points are non-singular. Therefore it would be nice to have a function that returns the (non-)singularity of the finite points of an hyperelliptic curve. 
     10Hyperelliptic curves are smooth curves mathematically. In Sage, they are implemented as plane curves with a singularity at infinity, but that singularity can always be resolved. 
    1111 
     12Apply 
     13 
     14 * [attachment:11930_singular_hyperelliptic.patch] 
     15 * [attachment:11930_is_singular.patch]