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| = Polytopes requests = * packages: lrs, cddlib, porta, 4ti2, polymake, coin/or * optimal performance: important algorithms are reverse search (as in lrs, uses less memory), double description (track the duals, as in cdd and 4ti2) * optimization: linear and integer programming (coin/or), semidefinite programming (any good software for this?) * combinatorial aspects * polymake puts a lot of these things together, but it does not build! === Bernstein's theorem === (this is coming from Daniel Erman). {{{ R.<a,b>=QQ[] f1=a^2+a*b+b^2+1 f2=a*b^2+a^2*b+11 N1=f1.newton_polytope() N2=f2.newton_polytope() S=[N1,N2] }}} I would like to be able to compute the mixed volume of the collection of polytopes: {{{ S.mixed_volume() }}} [[Note from Marshall Hampton: this is possible using the optional phc package: {{{ from sage.interfaces.phc import phc phc.mixed_volume([f1,f2]) }}} ]] The reason I want to do this is because I want to apply Bernstein's theorem to a polynomial system in affine space. So conceivably I'd like to ask: {{{ F=[f1,f2] F.bernstein_bound() }}} In addition I'd like to be able to compute anything about N1 that can be done in polymake. For instance f-vector: {{{ N1.f_vector() }}} [[Another note from M. Hampton: I have a patch for computing face lattices and f-vectors that I am hoping to put up on trac this week.]] |
