{"action":"opened","issue":{"url":"https://api.github.com/repos/Macaulay2/M2/issues/330","labels_url":"https://api.github.com/repos/Macaulay2/M2/issues/330/labels{/name}","comments_url":"https://api.github.com/repos/Macaulay2/M2/issues/330/comments","events_url":"https://api.github.com/repos/Macaulay2/M2/issues/330/events","html_url":"https://github.com/Macaulay2/M2/issues/330","id":100838270,"number":330,"title":"Bug in computing Segre classes?","user":{"login":"mikestillman","id":102215,"avatar_url":"https://avatars.githubusercontent.com/u/102215?v=3","gravatar_id":"","url":"https://api.github.com/users/mikestillman","html_url":"https://github.com/mikestillman","followers_url":"https://api.github.com/users/mikestillman/followers","following_url":"https://api.github.com/users/mikestillman/following{/other_user}","gists_url":"https://api.github.com/users/mikestillman/gists{/gist_id}","starred_url":"https://api.github.com/users/mikestillman/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/mikestillman/subscriptions","organizations_url":"https://api.github.com/users/mikestillman/orgs","repos_url":"https://api.github.com/users/mikestillman/repos","events_url":"https://api.github.com/users/mikestillman/events{/privacy}","received_events_url":"https://api.github.com/users/mikestillman/received_events","type":"User","site_admin":false},"labels":[],"state":"open","locked":false,"assignee":null,"milestone":null,"comments":0,"created_at":"2015-08-13T18:34:46Z","updated_at":"2015-08-13T18:34:46Z","closed_at":null,"body":"The following example/bug report was reported by Paolo Aluffi.  I need to decide still what the problem is.  I'm making it an issue so I don't forget to look into it.\r\n\r\nIf F is a vector bundle over a base X,  Y = P(F) its projectivization, and K is the first \r\nChern class of the tautological O_Y(1), then the push-forward of  (1 + K + K^2 + ... )\r\nshould equal the Segre class of F. (This is the formula at the bottom of p.47 in\r\nFulton's book.)\r\n\r\nI see that `segre' in Schubert2 differs from Fulton's convention, but this formula should\r\nstill hold up to signs. For example:\r\n\r\n```\r\ni1 : load(\"Schubert2.m2\")\r\n\r\ni2 : X = projectiveBundle 4;\r\n\r\ni3 : F = OO_X(2) ++ OO_X(3);\r\n\r\ni4 : segre F\r\n\r\no4 = 1 + 5H    + 19H    + 65H    + 211H\r\n          2,1      2,2      2,3       2,4\r\n\r\ni5 : Y = projectiveBundle F;\r\n\r\ni6 : p = Y.StructureMap;\r\n\r\ni7 : K = chern(1,OO_Y(1));\r\n\r\ni8 : p_*(1+K+K^2+K^3+K^4+K^5+K^6)\r\n\r\no8 = 1 + 5H    + 19H    + 65H    + 211H\r\n          2,1      2,2      2,3       2,4\r\n\r\no4 and o8 agree, as expected. I am actually a little confused by the signs, since the \r\ndifferent convention should lead to discrepancies, but never mind. What worries me more \r\nis the same computation, but performed on a rank-3 bundle (I am using this example \r\nbecause it matches the example given on \r\nhttp://www.math.uiuc.edu/Macaulay2/doc/Macaulay2-1.6/share/doc/Macaulay2/Schubert2/html/_projective__Bundle.html):\r\n\r\ni1 : load(\"Schubert2.m2\")\r\n\r\ni2 : X = projectiveBundle 4;\r\n\r\ni3 : F = OO_X(2) ++ OO_X(3) ++ OO_X(4);\r\n\r\ni4 : segre F\r\n\r\no4 = 1 + 9H    + 55H    + 285H    + 1351H\r\n          2,1      2,2       2,3        2,4\r\n\r\ni5 : Y = projectiveBundle F;\r\n\r\ni6 : p = Y.StructureMap;\r\n\r\ni7 : K = chern(1,OO_Y(1));\r\n\r\ni8 : p_*(1+K+K^2+K^3+K^4+K^5+K^6)\r\n\r\no8 = 1 + 18H    + 217H    + 2190H    + 19981H\r\n           2,1       2,2        2,3         2,4\r\n\r\nI really am not sure what is going on here. Shouldn't o4 and o8 agree (maybe up to signs), \r\nby Fulton's formula, just as they do in the rank-2 case? (I haven't tried this on the older \r\nSchubert maple package, I don't have easy access to it.) \r\n```"}}