{"shas":[["b99a429795c90f19cd2b39c502af49c04c33be80","1e9756e77b7f49f0f72fef2b4ba1416b3cc8dcc8@gmx.de","This version replaces the Hull operation by a combinatorial operation that does not involve quotiens\nby binomials.  It does so by detecting embedded lattices and throwing in the corresponding\nmonomials.  This idea is based on knowledge about mesoprimary decompositions and more features like\nthis will be implemented in future versions.\n\nFirst release in the 0.7 branch.\n\nIt is not entirely clear whether the new procedure is faster.  It should work best if there are many\nembedded lattices and the old \"minimalPrimaryComponent\" function would call itself recursively many\ntimes.  The benchmarks give confusing results anyway, e.g. performance on the third ideal has gotten\nmuch worse lately, even if nothing about the Macaulay2 installation changed.\n\nThis new approach also circumenvents a problem where in the old version one would need to saturate a\nnon-pure difference lattice ideal.  The problem is demonstrated in the following example:\n\nR = QQ[x,y,z,a,b]\n\nI = ideal (x*y*(a^2-1),\n           x*z*(b^2-1),\n\t   y*z*(a^2-b^2),\n\t   x*y*z*(a-1), x*y*z*(b-1),\n\t   x^2,y^2,z^2)\nBPD I\n\nIn the old version there would arise a call to the saturate function which was failing because\nI+P^(b) was not pure difference but had embedded non-saturated partial characters to be saturated.\nThe new approach avoids this problem since it directly removes embedded lattices without saturating\nthem.\n\nFor now the old minimalPrimaryComponent function was renamed to minimalPrimaryComponent2 and\nsurvives in the source code.","Thomas Kahle"]],"repo":"tom111/Binomials","actor":"tom111","ref":"refs/heads/master","size":1,"head":"b99a429795c90f19cd2b39c502af49c04c33be80","actor_gravatar":"14bf3e382e054733311b74ae4231e23f","push_id":23858967}