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Exact Line Packings from Numerical Solutions. (arXiv:1902.00552v2 [math.MG] UPDATED)
来源于:arXiv
Recent progress in Zauner's conjecture has leveraged deep conjectures in
algebraic number theory to promote numerical line packings to exact and
verifiable solutions to the line packing problem. We introduce a
numerical-to-exact technique in the real setting that does not require such
conjectures. Our approach is completely reproducible, matching Sloane's
database of putatively optimal numerical line packings with Mathematica's
built-in implementation of cylindrical algebraic decomposition. As a proof of
concept, we promote a putatively optimal numerical packing of eight points in
the real projective plane to an exact packing, whose optimality we establish in
a forthcoming paper. 查看全文>>