So in Bart de Smit's talk at Sage Days 23 he gave in an example the integer 103^100-1 which had to be factored in order to proceed. There is a very interesting difference between the performance of Sage 4.4 and Magma 2.15-4 here:
sage: time factor(103^100-1) CPU times: user 270.59 s, sys: 0.64 s, total: 271.23 s Wall time: 271.39 s 2^5 * 3 * 5^3 * 11 * 13 * 17 * 41 * 101 * 701 * 1061 * 1171 * 1801 * 5101 * 95191 * 10332211 * 10928101 * 484075001 * 8151355651 * 56592946951 * 577700122751 * 3582676889101 * 61787838410341 * 7067700288486601 * 44598886554623988985262651 * 20551228788109132062441192793719196434330727301 and > time Factorization(103^100-1); [ <2, 5>, <3, 1>, <5, 3>, <11, 1>, <13, 1>, <17, 1>, <41, 1>, <101, 1>, <701, 1>, <1061, 1>, <1171, 1>, <1801, 1>, <5101, 1>, <95191, 1>, <10332211, 1>, <10928101, 1>, <484075001, 1>, <8151355651, 1>, <56592946951, 1>, <577700122751, 1>, <3582676889101, 1>, <61787838410341, 1>, <7067700288486601, 1>, <44598886554623988985262651, 1>, <205512287881091320624411927937191964343307273\ 01, 1> ] Time: 0.140 There is a significant difference here. Now the Magma implementation recognizes that this is a Cunningham number and the documentation says that it uses a "combination of table- lookups and attempts at `algebraic' factorization (Aurifeuillian techniques)". I believe that Jeroen Demeyer is writing code to work with Cunningham numbers and was wondering if this should be made part of the standard factoring command. I also noticed that there is a "hidden" method _factor_cunningham for integers, and I think that it should be un-hidden (there was some debate about this in tickets #7240 and #7239. best wishes, Lloyd. -- Numero deus impare gaudet (The god delights in odd numbers). Virgil, the Eclogues. -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
