Code for helping with math research
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README.md
hodge.py
hodge.sage
quintic_fields.sage
shioda.sage

README.md

math_research

Code for helping with math research (Hodge theory)

  1. hodge.py: compute hodge numbers for hypersurfaces in P^n

  2. hodge_numbers.sage: compute hodge numbers for hypersurfaces in P^n, in weighted projective space. Also compute hodge numbers for cyclic covers and hodge numbers of the eigenspaces of the covering automorphism.

  3. shioda.sage: for computing quantities associated with the character spaces which decompose the primitive cohomology of the Fermat hypersurface.

  4. quintic_fields.sage: for finding totally real quintic fields which produce cubic surfaces as in J. A. Carlson and D. Toledo, Cubic Surfaces with Special Periods, Proc. Amer. Math. Soc. 141 (2013), 1947-1962.

(2) is better developed than (1), and (2) does everything that (1) does. To download sage (free), go to http://sagemath.org

(1) and (2) replace the old Maple code in Hodgepack.