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As an example of genus2reduction's functionality, let C be a proper smooth curve of genus 2 defined by a hyperelliptic equation y^2+Q(x)y=P(x), where P(x) and Q(x) are polynomials with rational coefficients such that deg(Q(x))<4, deg(P(x))<7. Let J(C) be the Jacobian of C, let X be the minimal regular model of C over the ring of integers Z.
This program determines the reduction of C at any prime number p (that is the special fiber X_p of X over p), and the exponent f of the conductor of J(C) at p.
************* genus2reduction ************* November 7th, 1994 WHAT THIS PROGRAM DOES............................................. Let C be a proper smooth curve of genus 2 defined by a hyperelliptic equation y^2+Q(x)y=P(x) where P(x) and Q(x) are polynomials with rational coeffic more»
genus2reduction (0.3-2.2) unstable; urgency=low * Non-maintainer upload. * Fix "Unversioned build-dependency on libpari-dev": make it versioned. (Closes: #644091) * Fix "Please allow building with ld --as-needed": add patch from Ubuntu / Andreas Moog: - Libraries needed to link the package should go into LDADD and after sources on the linker command line to fix an issue wi more»
Some bugs have been fixed and modifications have been done according to new syntaxes in pari 2.0.
Well, it is obvious that the incomplete case p=2 is irritating. Also it should be interesting to get more»
Many thanks to Henri Cohen who started writing this program. After this program is available, many more»