Floating-point nu\ mbers

\n\n" ), chaptitle := rec( 1 := "Licensing", 2 := "Float package", 3 := "Polynomials", 4 := "Implemented packages" ), content := [ rec( content := "xml version=\"1.0\" encoding=\"UTF-8\"", count := [ 0, 0, 0, 1 ], name := "XMLPI", root := ~ ), rec( content := "Book SYSTEM \"gapdoc.dtd\" [\n $\\to$--&tgt;'>\n \n\n\n]", count := [ 0, 0, 0, 1 ], name := "XMLDOCTYPE", root := ~ ), rec( attributes := rec( Name := "FLOAT" ), content := [ rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Floating-point numbers", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], name := "Title", next := 286, root := ~, start := 249, stop := 285 ), rec( attributes := rec( ), content := [ rec( content := "Version 1.0.1", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 1 ], name := "Version", next := 325, root := ~, start := 289, stop := 324 ), rec( attributes := rec( ), content := [ rec( content := "\n Integration of mpfr, mpfi, \ mpc, fplll and cxsc in GAP\n ", count := [ 0, 0, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 2 ], name := "TitleComment", next := 418, root := ~, start := 328, stop := 417 ), rec( attributes := rec( ), content := [ rec( content := "Laurent Bartholdi\n ", count := [ 0, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Only := "HTML" ), content := [ rec( HTML := true, content := "laurent.barthold\ i@gmail.com", count := [ 0, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 3 ], mathmode := "Text", name := "Alt", next := 514, root := ~, start := 464, stop := 513 ), rec( content := "\n\t\t ", count := [ 0, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "HTML" ), content := [ rec( content := "laurent.bartholdi\ @gmail.com", count := [ 0, 0, 0, 3 ], name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 3 ], mathmode := "Text", name := "Alt", next := 567, root := ~, start := 518, stop := 566 ) ], count := [ 0, 0, 0, 3 ], mathmode := "Text", name := "Email", next := 575, root := ~, start := 457, stop := 574 ), rec( content := " \n\t ", count := [ 0, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "https://www.math.uni-sb.d\ e/ag/bartholdi/", count := [ 0, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 3 ], mathmode := "Text", name := "Homepage", next := 641, root := ~, start := 580, stop := 640 ), rec( content := "\n ", count := [ 0, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 3 ], name := "Author", next := 653, root := ~, start := 421, stop := 652 ), rec( attributes := rec( ), content := [ rec( content := "26/11/2021", count := [ 0, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 3 ], name := "Date", next := 675, root := ~, start := 656, stop := 674 ), rec( attributes := rec( ), content := [ rec( content := "\n FR Mathematik", count := [ 0, 0, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 0, 0, 0, 4 ], mathmode := "Text", name := "Br", next := 708, root := ~, start := 703, stop := 707 ), rec( content := "D-66041 Saarbrþcken", count := [ 0, 0, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 0, 0, 0, 4 ], mathmode := "Text", name := "Br", next := 733, root := ~, start := 728, stop := 732 ), rec( content := "Germany\n ", count := [ 0, 0, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 0, 4 ], name := "Address", next := 753, root := ~, start := 678, stop := 752 ), rec( attributes := rec( ), content := [ rec( content := "\n This document describes the\ package ", count := [ 0, 0, 1, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Float", count := [ 0, 0, 1, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 1 ], mathmode := "Text", name := "Package", next := 831, root := ~, start := 807, stop := 830 ), rec( content := ", which\n implements in ", count := [ 0, 0, 1, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "GAP", count := [ 0, 0, 1, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 1 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := " arbitrary-precision floating-po\ int numbers.\n ", count := [ 0, 0, 1, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Only := "HTML" ), content := [ rec( HTML := true, content := "\n ", count := [ 0, 0, 1, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 0, 0, 1, 2 ], mathmode := "Text", name := "P", next := 933, root := ~, start := 929, stop := 932 ), rec( HTML := true, content := "\n The computer algebra\ system ", count := [ 0, 0, 1, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( HTML := true, content := "GAP", count := [ 0, 0, 1, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 2 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( HTML := true, content := " is available at\n ", count := [ 0, 0, 1, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( HTML := true, content := "https://gap-syst\ em.org", count := [ 0, 0, 1, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 2 ], mathmode := "Text", name := "URL", next := 1021, root := ~, start := 988, stop := 1020 ), rec( HTML := true, content := ".\n ", count := [ 0, 0, 1, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 0, 0, 1, 3 ], mathmode := "Text", name := "P", next := 1029, root := ~, start := 1025, stop := 1028 ), rec( HTML := true, content := "\n This documentation f\ or ", count := [ 0, 0, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( HTML := true, content := "Float", count := [ 0, 0, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 3 ], mathmode := "Text", name := "Package", next := 1079, root := ~, start := 1055, stop := 1078 ), rec( HTML := true, content := " is available at\n ", count := [ 0, 0, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( HTML := true, content := "https://www.gap-\ system.org/Manuals/pkg/float-1.0.1/doc/manual.pdf", count := [ 0, 0, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 3 ], mathmode := "Text", name := "URL", next := 1178, root := ~, start := 1098, stop := 1177 ), rec( HTML := true, content := " in PDF format, and may \ be\n accessed online at ", count := [ 0, 0, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( HTML := true, content := "https://gap-pack\ ages.github.io/float/", count := [ 0, 0, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 3 ], mathmode := "Text", name := "URL", next := 1274, root := ~, start := 1226, stop := 1273 ), rec( HTML := true, content := ".\n ", count := [ 0, 0, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "P", next := 1282, root := ~, start := 1278, stop := 1281 ), rec( HTML := true, content := "\n The latest release o\ f the package may be downloaded as\n ", count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( HTML := true, content := "https://github.c\ om/gap-packages/float/releases/download/v1.0.1/float-1.0.1.tar.gz", count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "URL", next := 1442, root := ~, start := 1342, stop := 1441 ), rec( HTML := true, content := " (tar, gzipped).\n The \ latest repository version (possibly unstable) may be downloaded as\n ", count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( HTML := true, content := "https://github.c\ om/gap-packages/float/tarball/master", count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "URL", next := 1597, root := ~, start := 1534, stop := 1596 ), rec( HTML := true, content := " (tar, gzipped),\n ", count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( HTML := true, content := "https://github.c\ om/gap-packages/float.git", count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "URL", next := 1668, root := ~, start := 1616, stop := 1667 ), rec( HTML := true, content := " (git repository),\n ", count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( HTML := true, content := "https://packages\ .debian.org/search?keywords=gap-float&searchon=names&suite=all§ion=all", count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "URL", next := 1802, root := ~, start := 1689, stop := 1801 ), rec( HTML := true, content := " (debian package), or\n \ explored at ", count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( HTML := true, content := "https://github.c\ om/gap-packages/float/tree/master/", count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "URL", next := 1899, root := ~, start := 1838, stop := 1898 ), rec( HTML := true, content := ".\n ", count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 1 ], name := "Alt", next := 1909, root := ~, start := 909, stop := 1908 ), rec( content := "\n ", count := [ 0, 0, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 0, 0, 1, 5 ], mathmode := "Text", name := "P", next := 1916, root := ~, start := 1912, stop := 1915 ), rec( content := "\n For comments or questions \ on ", count := [ 0, 0, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Float", count := [ 0, 0, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 5 ], mathmode := "Text", name := "Package", next := 1974, root := ~, start := 1950, stop := 1973 ), rec( content := " please contact\n the author.\ \n ", count := [ 0, 0, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 1, 1 ], name := "Abstract", next := 2019, root := ~, start := 756, stop := 2018 ), rec( attributes := rec( ), content := [ rec( content := "© 2011-2021 by Laurent Bartholdi\ \n ", count := [ 0, 0, 2, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 2, 1 ], name := "Copyright", next := 2090, root := ~, start := 2022, stop := 2089 ), rec( attributes := rec( ), content := [ rec( content := "Part of this work was supported b\ y the \"Swiss\n National Fund for Scientific Research (SNF)\", the \"German N\ ational Science Foundation (DFG)\",\n and the Courant Research Centre \"Highe\ r Order Structures\" of the University of Göttingen.\n ", count := [ 0, 0, 3, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 0, 0, 3, 1 ], name := "Acknowledgements", next := 2367, root := ~, start := 2093, stop := 2366 ) ], count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "TitlePage", next := 2381, root := ~, start := 235, stop := 2380 ), rec( attributes := rec( ), content := 0, count := [ 0, 0, 4, 1 ], mathmode := "Text", name := "TableOfContents", next := 2401, root := ~, start := 2383, stop := 2400 ), rec( attributes := rec( ), content := [ rec( content := "\n\n", count := [ 0, 0, 4, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Licensing", count := [ 1, 0, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 0, 0, 2 ], mathmode := "Text", name := "Heading", next := 2448, root := ~, start := 2420, stop := 2447 ), rec( content := "\n\nThis program is free softwar\ e; you can redistribute it and/or modify\nit under the terms of the GNU Genera\ l Public License as published by\nthe Free Software Foundation; either version\ 2 of the License, or any\nlater version.\n\n", count := [ 1, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 1, 0, 0, 4 ], mathmode := "Text", name := "P", next := 2678, root := ~, start := 2674, stop := 2677 ), rec( content := " This program is distributed in \ the hope that it will be useful,\nbut WITHOUT ANY WARRANTY; without even the i\ mplied warranty of\nMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See \ the GNU\nGeneral Public License for more details.\n\n", count := [ 1, 0, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 1, 0, 0, 5 ], mathmode := "Text", name := "P", next := 2918, root := ~, start := 2914, stop := 2917 ), rec( content := " You should have received a copy\ of the GNU General Public\nLicense along with this program, in the file COPYI\ NG. If not, see\n", count := [ 1, 0, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "https://www.gnu.org/licen\ ses/", count := [ 1, 0, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 0, 0, 5 ], mathmode := "Text", name := "URL", next := 3084, root := ~, start := 3044, stop := 3083 ), rec( content := ".\n\n", count := [ 1, 0, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 1, 0, 0, 1 ], mathmode := "Text", name := "Chapter", next := 3097, root := ~, start := 2411, stop := 3096 ), rec( content := "\n\n", count := [ 1, 0, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "floatpackage" ), content := [ rec( attributes := rec( ), content := [ rec( content := "Float package", count := [ 2, 0, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 0, 0, 2 ], mathmode := "Text", name := "Heading", next := 3161, root := ~, start := 3129, stop := 3160 ), rec( content := "\n\n", count := [ 2, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "sample" ), content := [ rec( attributes := rec( ), content := [ rec( content := "A sample run", count := [ 2, 1, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 2 ], mathmode := "Text", name := "Heading", next := 3218, root := ~, start := 3187, stop := 3217 ), rec( content := "\n\nThe extended floatin\ g-point capabilities of ", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "GAP", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := " are installed by loadin\ g the package\nvia ", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "LoadPackage(\"flo\ at\");", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "C", next := 3339, root := ~, start := 3311, stop := 3338 ), rec( content := " and selecting new float\ ing-point handlers via\n", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "SetFloats(MPFR)", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "C", next := 3408, root := ~, start := 3386, stop := 3407 ), rec( content := ", ", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "SetFloats(MPFI)", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "C", next := 3432, root := ~, start := 3410, stop := 3431 ), rec( content := ", ", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "SetFloats(MPC)", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "C", next := 3455, root := ~, start := 3434, stop := 3454 ), rec( content := " or", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "SetFloats(CXSC)", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "C", next := 3480, root := ~, start := 3458, stop := 3479 ), rec( content := ",\ndepending on whether \ high-precision real, interval or complex arithmetic are desired, or\nwhether a\ fast package containing all four real/complex element/interval arithmetic is \ desired:\n", count := [ 2, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\ngap> LoadPackag\ e(\"float\");\nLoading FLOAT 0.7.0 ...\ntrue\ngap> SetFloats(MPFR); # floating\ -point\ngap> x := 4*Atan(1.0);\n.314159e1\ngap> Sin(x);\n.169569e-30\ngap> Set\ Floats(MPFR,1000); # 1000 bits\ngap> x := 4*Atan(1.0);\n.314159e1\ngap> Sin(x)\ ;\n.125154e-300\ngap> String(x,300);\n\".3141592653589793238462643383279502884\ 197169399375105820974944592307816406286\\\n20899862803482534211706798214808651\ 3282306647093844609550582231725359408128481\\\n1174502841027019385211055596446\ 22948954930381964428810975665933446128475648233\\\n786783165271201909145648566\ 92346034861045432664821339360726024914127e1\"\ngap>\ngap> SetFloats(MPFI); # i\ ntervals\ngap> x := 4*Atan(1.0);\n.314159e1(99)\ngap> AbsoluteDiameter(x); Sup\ (x); Inf(x);\n.100441e-29\n.314159e1\n.314159e1\ngap> Sin(x);\n-.140815e-29(97\ )\ngap> 0.0 in last;\ntrue\ngap> 1.0; # exact representation\n.1e1(∞)\ngap> \ IncreaseInterval(last,0.001); # now only 8 significant bits\n.1e1(8)\ngap> Inc\ reaseInterval(last,-0.002); # now becomes empty\n∅\ngap> r2 := Sqrt(2.0);\n.\ 141421e1(99)\ngap> MinimalPolynomial(Rationals,r2);\n-2*x_1^2+1\ngap> Cyc(r2);\ \nE(8)-E(8)^3\ngap>\ngap> SetFloats(MPC); # complex numbers\ngap> z := 5.0-1.0\ i;\n.5e1-.1e1i\ngap> (1+1.0i)*last^4*(239+1.0i);\n.228488e6\ngap> Exp(6.2835i)\ ;\n.1e1+.314693e-3i\n", count := [ 2, 1, 0, 4 ], name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 4 ], mathmode := "Text", name := "Example", next := 4926, root := ~, start := 3667, stop := 4925 ), rec( content := "\n\n", count := [ 2, 1, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 1 ], mathmode := "Text", name := "Section", next := 4938, root := ~, start := 3163, stop := 4937 ), rec( content := "\n\n", count := [ 2, 1, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 0, 0, 1 ], mathmode := "Text", name := "Chapter", next := 4950, root := ~, start := 3099, stop := 4949 ), rec( content := "\n\n", count := [ 2, 1, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "poly" ), content := [ rec( attributes := rec( ), content := [ rec( content := "Polynomials", count := [ 3, 0, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 0, 0, 2 ], mathmode := "Text", name := "Heading", next := 5004, root := ~, start := 4974, stop := 5003 ), rec( content := "\n\n", count := [ 3, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "The Floats pseudo\ -field", count := [ 3, 1, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 0, 2 ], mathmode := "Text", name := "Heading", next := 5057, root := ~, start := 5015, stop := 5056 ), rec( content := "\n\nPolynomials with flo\ ating-point coefficients may be manipulated in\n", count := [ 3, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "GAP", count := [ 3, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 0, 3 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := "; though they behave, in\ subtle ways, quite differently than\npolynomials over rings. A \"pseudo-field\ \" of floating-point numbers\nis available to create them using the standard " , count := [ 3, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "GAP", count := [ 3, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 0, 3 ], mathmode := "Text", name := "Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := " syntax.\n", count := [ 3, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 1, 0, 4 ], mathmode := "Text", name := "P", next := 5324, root := ~, start := 5320, stop := 5323 ), rec( content := "\n\n", count := [ 3, 1, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Name := "FLOAT_PSEUDOFIE\ LD" ), content := 0, count := [ 3, 1, 1, 2 ], mathmode := "Text", name := "Var", next := 5372, root := ~, start := 5341, stop := 5371 ), rec( attributes := rec( ), content := [ rec( content := "\n The\ \"pseudo-field\" of floating-point numbers, containing all\n floating-poin\ t numbers in the current implementation.\n ", count := [ 3, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 1, 1, 4 ], mathmode := "Text", name := "P", next := 5520, root := ~, start := 5516, stop := 5519 ), rec( content := "\n No\ te that it is not really a field, e.g. because addition of\n floating-point\ numbers is not associative. It is mainly used to\n create indeterminates, \ as in the following example:\n", count := [ 3, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ ngap> x := Indeterminate(FLOAT_PSEUDOFIELD,\"x\");\nx\ngap> 2*x^2+3;\n2.0*x^2+\ 3.0\ngap> Value(last,10);\n203.0\n", count := [ 3, 1, 1, 5 ], name := "PCDATA" , root := ~ ) ], count := [ 3, 1, 1, 5 ], mathmode := "Text", name := "Example", next := 5845, root := ~, start := 5710, stop := 5844 ), rec( content := "\n ", count := [ 3, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 1, 3 ], mathmode := "Text", name := "Description", next := 5862, root := ~, start := 5375, stop := 5861 ) ], count := [ 3, 1, 1, 1 ], mathmode := "Text", name := "ManSection", next := 5876, root := ~, start := 5326, stop := 5875 ), rec( content := "\n\n", count := [ 3, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 0, 1 ], mathmode := "Text", name := "Section", next := 5888, root := ~, start := 5006, stop := 5887 ), rec( content := "\n\n", count := [ 3, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Roots of polynomi\ als", count := [ 3, 2, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 0, 2 ], mathmode := "Text", name := "Heading", next := 5938, root := ~, start := 5899, stop := 5937 ), rec( content := "\n\nThe Jenkins-Traub al\ gorithm has been implemented, in arbitrary\nprecision for MPFR and MPC.\n", count := [ 3, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 2, 0, 4 ], mathmode := "Text", name := "P", next := 6035, root := ~, start := 6031, stop := 6034 ), rec( content := "\nFurthermore, CXSC can \ provide complex enclosures for the roots of a\ncomplex polynomial.\n\n", count := [ 3, 2, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 0, 1 ], mathmode := "Text", name := "Section", next := 6135, root := ~, start := 5890, stop := 6134 ), rec( content := "\n\n", count := [ 3, 2, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "Finding integer r\ elations", count := [ 3, 3, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 0, 2 ], mathmode := "Text", name := "Heading", next := 6190, root := ~, start := 6146, stop := 6189 ), rec( content := "\nThe PSLQ algorithm has\ been implemented by Steve A. Linton, as an external\r\ncontribution to ", count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "Float", count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "Package", next := 6307, root := ~, start := 6283, stop := 6306 ), rec( content := ". This algorithm receive\ s as\r\ninput a vector of floats ", count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x", count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "M", next := 6370, root := ~, start := 6362, stop := 6369 ), rec( content := " and a required precisio\ n ", count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\epsilon", count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "M", next := 6411, root := ~, start := 6396, stop := 6410 ), rec( content := ",\r\nand seeks an intege\ r vector ", count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v", count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "M", next := 6450, root := ~, start := 6442, stop := 6449 ), rec( content := " such that\r\n", count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "|x\\cdot v|<\\eps\ ilon", count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "M", next := 6491, root := ~, start := 6462, stop := 6490 ), rec( content := ". The implementation fol\ lows quite closely the\r\noriginal article ", count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Key := "MR1836930" ), content := 0, count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "Cite", next := 6579, root := ~, start := 6556, stop := 6578 ), rec( content := ".\r\n\r\n", count := [ 3, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Arg := "x, epsilon[, gam\ ma]", Name := "PSLQ" ), content := 0, count := [ 3, 3, 1, 2 ], mathmode := "Text", name := "Func", next := 6645, root := ~, start := 6600, stop := 6644 ), rec( attributes := rec( Arg := "x, epsilon[, gam\ ma [,beta]]", Name := "PSLQ_MP" ), content := 0, count := [ 3, 3, 1, 4 ], mathmode := "Text", name := "Func", next := 6705, root := ~, start := 6649, stop := 6704 ), rec( attributes := rec( ), content := [ rec( content := "An intege\ r vector ", count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "v\ ", count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "M", next := 6744, root := ~, start := 6736, stop := 6743 ), rec( content := " with ", count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "|\ x\\cdot v|<\\epsilon", count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "PCD\ ATA", root := ~ ) ], count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "M", next := 6779, root := ~, start := 6750, stop := 6778 ), rec( content := ".", count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "Returns", next := 6790, root := ~, start := 6709, stop := 6789 ), rec( attributes := rec( ), content := [ rec( content := "\r\n T\ he PSLQ algorithm by Bailey and Broadhurst (see ", count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Key := "MR183693\ 0" ), content := 0, count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "Cite", next := 6885, root := ~, start := 6862, stop := 6884 ), rec( content := ")\r\n \ searches for an integer relation between the entries in ", count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "x\ ", count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "M", next := 6956, root := ~, start := 6948, stop := 6955 ), rec( content := ".\r\n\r\\ n ", count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 1, 6 ], mathmode := "Text", name := "P", next := 6969, root := ~, start := 6965, stop := 6968 ), rec( attributes := rec( ), content := [ rec( content := "\\ \beta", count := [ 3, 3, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 1, 6 ], mathmode := "Text", name := "M", next := 6981, root := ~, start := 6969, stop := 6980 ), rec( content := " and ", count := [ 3, 3, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ \gamma", count := [ 3, 3, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 1, 6 ], mathmode := "Text", name := "M", next := 6999, root := ~, start := 6986, stop := 6998 ), rec( content := " are alg\ orithm tuning parameters, and\r\n default to ", count := [ 3, 3, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "4\ /10", count := [ 3, 3, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 1, 6 ], mathmode := "Text", name := "M", next := 7064, root := ~, start := 7053, stop := 7063 ), rec( content := " and ", count := [ 3, 3, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "2\ /\\sqrt(3)", count := [ 3, 3, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 1, 6 ], mathmode := "Text", name := "M", next := 7086, root := ~, start := 7069, stop := 7085 ), rec( content := " respect\ ively.\r\n\r\n ", count := [ 3, 3, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 3, 1, 7 ], mathmode := "Text", name := "P", next := 7112, root := ~, start := 7108, stop := 7111 ), rec( content := "The seco\ nd form implements the \"Multi-pair\" variant of the algorithm, which is\r\n \ better suited to parallelization.\r\n", count := [ 3, 3, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "\\ r\ngap> PSLQ([1.0,(1+Sqrt(5.0))/2],1.e-2);\r\n[ 55, -34 ] # Fibonacci numbers\ \r\ngap> RootsFloat([1,-4,2]*1.0);\r\n[ 0.292893, 1.70711 ] # roots of 2x^2-4x\ +1\r\ngap> PSLQ(List([0..2],i->last[1]^i),1.e-7);\r\n[ 1, -4, 2 ] # a degree-2\ polynomial fitting well\r\n", count := [ 3, 3, 1, 8 ], name := "PCDATA", root := ~ ) ], count := [ 3, 3, 1, 8 ], mathmode := "Text", name := "Example", next := 7510, root := ~, start := 7231, stop := 7509 ), rec( content := "\r\n ", count := [ 3, 3, 1, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 1, 5 ], mathmode := "Text", name := "Description", next := 7528, root := ~, start := 6794, stop := 7527 ) ], count := [ 3, 3, 1, 1 ], mathmode := "Text", name := "ManSection", next := 7543, root := ~, start := 6584, stop := 7542 ), rec( content := "\r\n\n", count := [ 3, 3, 1, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 0, 1 ], mathmode := "Text", name := "Section", next := 7556, root := ~, start := 6137, stop := 7555 ), rec( content := "\n\n", count := [ 3, 3, 1, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "LLL lattice reduc\ tion", count := [ 3, 4, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 0, 2 ], mathmode := "Text", name := "Heading", next := 7607, root := ~, start := 7567, stop := 7606 ), rec( content := "\n\nA faster implementat\ ion of the LLL lattice reduction algorithm has\nalso been implemented. It is a\ ccessible via the commands\n", count := [ 3, 4, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "FPLLLReducedBasis\ (m)", count := [ 3, 4, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 0, 3 ], mathmode := "Text", name := "C", next := 7760, root := ~, start := 7733, stop := 7759 ), rec( content := " and \n", count := [ 3, 4, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( content := "FPLLLShortestVect\ or(m)", count := [ 3, 4, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 0, 3 ], mathmode := "Text", name := "C", next := 7795, root := ~, start := 7766, stop := 7794 ), rec( content := ".\n", count := [ 3, 4, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 3, 4, 0, 4 ], mathmode := "Text", name := "P", next := 7801, root := ~, start := 7797, stop := 7800 ), rec( content := "\n\n", count := [ 3, 4, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 0, 1 ], mathmode := "Text", name := "Section", next := 7813, root := ~, start := 7558, stop := 7812 ), rec( content := "\n\n", count := [ 3, 4, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 0, 0, 1 ], mathmode := "Text", name := "Chapter", next := 7825, root := ~, start := 4952, stop := 7824 ), rec( content := "\n\n", count := [ 3, 4, 0, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "impl" ), content := [ rec( attributes := rec( ), content := [ rec( content := "Implemented packages", count := [ 4, 0, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 0, 0, 2 ], mathmode := "Text", name := "Heading", next := 7888, root := ~, start := 7849, stop := 7887 ), rec( content := "\n\n", count := [ 4, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "MPFR", count := [ 4, 1, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 2 ], mathmode := "Text", name := "Heading", next := 7922, root := ~, start := 7899, stop := 7921 ), rec( content := "\n", count := [ 4, 1, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Name := "IsMPFRFloat" ), content := 0, count := [ 4, 1, 1, 2 ], mathmode := "Text", name := "Filt", next := 7964, root := ~, start := 7938, stop := 7963 ), rec( attributes := rec( Name := "TYPE_MPFR" ) , content := 0, count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "Var", next := 7990, root := ~, start := 7967, stop := 7989 ), rec( attributes := rec( ), content := [ rec( content := "\n The\ category of floating-point numbers.\n\n ", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 4, 1, 1, 6 ], mathmode := "Text", name := "P", next := 8060, root := ~, start := 8056, stop := 8059 ), rec( content := " Note th\ at they are treated as commutative and scalar, but are\n not necessarily as\ sociative.\n ", count := [ 4, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "Description", next := 8172, root := ~, start := 7993, stop := 8171 ) ], count := [ 4, 1, 1, 1 ], mathmode := "Text", name := "ManSection", next := 8186, root := ~, start := 7923, stop := 8185 ), rec( content := "\n\n", count := [ 4, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 1 ], mathmode := "Text", name := "Section", next := 8198, root := ~, start := 7890, stop := 8197 ), rec( content := "\n\n", count := [ 4, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "MPFI", count := [ 4, 2, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 2, 0, 2 ], mathmode := "Text", name := "Heading", next := 8232, root := ~, start := 8209, stop := 8231 ), rec( content := "\n", count := [ 4, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Name := "IsMPFIFloat" ), content := 0, count := [ 4, 2, 1, 2 ], mathmode := "Text", name := "Filt", next := 8274, root := ~, start := 8248, stop := 8273 ), rec( attributes := rec( Name := "TYPE_MPFI" ) , content := 0, count := [ 4, 2, 1, 4 ], mathmode := "Text", name := "Var", next := 8300, root := ~, start := 8277, stop := 8299 ), rec( attributes := rec( ), content := [ rec( content := "\n The\ category of intervals of floating-point numbers.\n\n ", count := [ 4, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 4, 2, 1, 6 ], mathmode := "Text", name := "P", next := 8383, root := ~, start := 8379, stop := 8382 ), rec( content := " Note th\ at they are treated as commutative and scalar, but are\n not necessarily as\ sociative.\n ", count := [ 4, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 2, 1, 5 ], mathmode := "Text", name := "Description", next := 8495, root := ~, start := 8303, stop := 8494 ) ], count := [ 4, 2, 1, 1 ], mathmode := "Text", name := "ManSection", next := 8509, root := ~, start := 8233, stop := 8508 ), rec( content := "\n\n", count := [ 4, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 2, 0, 1 ], mathmode := "Text", name := "Section", next := 8521, root := ~, start := 8200, stop := 8520 ), rec( content := "\n\n", count := [ 4, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "MPC", count := [ 4, 3, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 3, 0, 2 ], mathmode := "Text", name := "Heading", next := 8554, root := ~, start := 8532, stop := 8553 ), rec( content := "\n", count := [ 4, 3, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Name := "IsMPCFloat" ), content := 0, count := [ 4, 3, 1, 2 ], mathmode := "Text", name := "Filt", next := 8595, root := ~, start := 8570, stop := 8594 ), rec( attributes := rec( Name := "TYPE_MPC" ), content := 0, count := [ 4, 3, 1, 4 ], mathmode := "Text", name := "Var", next := 8620, root := ~, start := 8598, stop := 8619 ), rec( attributes := rec( ), content := [ rec( content := "\n The\ category of intervals of floating-point numbers.\n\n ", count := [ 4, 3, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 4, 3, 1, 6 ], mathmode := "Text", name := "P", next := 8703, root := ~, start := 8699, stop := 8702 ), rec( content := " Note th\ at they are treated as commutative and scalar, but are\n not necessarily as\ sociative.\n ", count := [ 4, 3, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 3, 1, 5 ], mathmode := "Text", name := "Description", next := 8815, root := ~, start := 8623, stop := 8814 ) ], count := [ 4, 3, 1, 1 ], mathmode := "Text", name := "ManSection", next := 8829, root := ~, start := 8555, stop := 8828 ), rec( content := "\n\n", count := [ 4, 3, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 3, 0, 1 ], mathmode := "Text", name := "Section", next := 8841, root := ~, start := 8523, stop := 8840 ), rec( content := "\n\n", count := [ 4, 3, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "CXSC", count := [ 4, 4, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 4, 0, 2 ], mathmode := "Text", name := "Heading", next := 8875, root := ~, start := 8852, stop := 8874 ), rec( content := "\n", count := [ 4, 4, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( Name := "IsCXSCReal" ), content := 0, count := [ 4, 4, 1, 2 ], mathmode := "Text", name := "Filt", next := 8916, root := ~, start := 8891, stop := 8915 ), rec( attributes := rec( Name := "IsCXSCComplex" ), content := 0, count := [ 4, 4, 1, 4 ], mathmode := "Text", name := "Filt", next := 8947, root := ~, start := 8919, stop := 8946 ), rec( attributes := rec( Name := "IsCXSCInterval"\ ), content := 0, count := [ 4, 4, 1, 6 ], mathmode := "Text", name := "Filt", next := 8979, root := ~, start := 8950, stop := 8978 ), rec( attributes := rec( Name := "IsCXSCBox" ) , content := 0, count := [ 4, 4, 1, 8 ], mathmode := "Text", name := "Filt", next := 9006, root := ~, start := 8982, stop := 9005 ), rec( attributes := rec( Name := "TYPE_CXSC_RP" ) , content := 0, count := [ 4, 4, 1, 10 ], mathmode := "Text", name := "Var", next := 9035, root := ~, start := 9009, stop := 9034 ), rec( attributes := rec( Name := "TYPE_CXSC_CP" ) , content := 0, count := [ 4, 4, 1, 12 ], mathmode := "Text", name := "Var", next := 9064, root := ~, start := 9038, stop := 9063 ), rec( attributes := rec( Name := "TYPE_CXSC_RI" ) , content := 0, count := [ 4, 4, 1, 14 ], mathmode := "Text", name := "Var", next := 9093, root := ~, start := 9067, stop := 9092 ), rec( attributes := rec( Name := "TYPE_CXSC_CI" ) , content := 0, count := [ 4, 4, 1, 16 ], mathmode := "Text", name := "Var", next := 9122, root := ~, start := 9096, stop := 9121 ), rec( attributes := rec( ), content := [ rec( content := "\n The\ category of floating-point numbers.\n\n ", count := [ 4, 4, 1, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := 0, count := [ 4, 4, 1, 18 ], mathmode := "Text", name := "P", next := 9192, root := ~, start := 9188, stop := 9191 ), rec( content := " Note th\ at they are treated as commutative and scalar, but are\n not necessarily as\ sociative.\n ", count := [ 4, 4, 1, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 4, 1, 17 ], mathmode := "Text", name := "Description", next := 9304, root := ~, start := 9125, stop := 9303 ) ], count := [ 4, 4, 1, 1 ], mathmode := "Text", name := "ManSection", next := 9318, root := ~, start := 8876, stop := 9317 ), rec( content := "\n\n", count := [ 4, 4, 1, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 4, 0, 1 ], mathmode := "Text", name := "Section", next := 9330, root := ~, start := 8843, stop := 9329 ), rec( content := "\n\n", count := [ 4, 4, 1, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( ), content := [ rec( attributes := rec( ), content := [ rec( content := "FPLLL", count := [ 4, 5, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 5, 0, 2 ], mathmode := "Text", name := "Heading", 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\n

FPLLLReduced\
Basis

4.5-1
\nFPLLLShortestVector 4.5-2
\nIsCXSCBox 4.4-1
\n

IsCXSCCom\
plex

4.4-1
\nIsCXSCInterval 4.4-1
\nIsCXSCReal 4.4-1
\n

IsMPCFloat  4.3-1  
\nIsMPFIFloat  4.2-1  
\nIsMPFRFloat  4.1-1  
\nPSLQ  3.3-1  
\nPSLQ_MP\
  3.3-1  
\nTYPE_CXSC_CI  4.4-\
1  
\nTYPE_CXSC_CP  4.4-1  
\nTYPE_CXSC_RI

  4.4-1  
\nTYPE_CXSC_RP  4.4-1 \
 
\nTYPE_MPC  4.3-1  
\nTYPE_MPFI  4.2-1  
\nTYPE_MP\
FR  4.1-1  
\n", 
  input := "\n\n$\\to$--&tgt;'>\n \n\n\n]>\n\n\n\n  Floating-point nu\
mbers\n  Version &Version;\n  \n    I\
ntegration of mpfr, mpfi, mpc, fplll and cxsc in GAP\n  \n  Laurent Bartholdi\n          laurent.bartholdi@\
gmail.com\n\t\t laurent.bartholdi@gmail.com \n\t  https://www.math.uni-sb.de/ag/bartholdi/\n  \n  &Date;\n  \n  FR Mathematik
D-66041 Saarbr\
þcken
Germany\n  
\n  \n    This document describes th\
e package Float, which\n    implements in &GAP; arbitrary-p\
recision floating-point numbers.\n  \n  \n  The compute\
r algebra system &GAP; is available at\n  https://gap-system.org.\n\
  
\n  This documentation for Float is available at\n  <\
URL>https://www.gap-system.org/Manuals/pkg/float-&Version;/doc/manual.pdf in PDF format, and may be\n  accessed online at https://gap-packages.gi\
thub.io/float/.\n  
\n  The latest release of the package may be down\
loaded as\n  https://github.com/gap-packages/float/releases/download/v&Ve\
rsion;/float-&Version;.tar.gz (tar, gzipped).\n  The latest repository v\
ersion (possibly unstable) may be downloaded as\n  https://github.com/gap\
-packages/float/tarball/master (tar, gzipped),\n  https://github.co\
m/gap-packages/float.git (git repository),\n  https://packages.debi\
an.org/search?keywords=gap-float&searchon=names&suite=all&section=\
all (debian package), or\n  explored at https://github.com/gap-pack\
ages/float/tree/master/.\n  \n  
\n    For comments or question\
s on Float please contact\n    the author.\n  \n\
  ©right; 2011-2021 by Laurent Bartholdi\n  \n  Part of this work was supported by the \"Swiss\n  National Fund\
 for Scientific Research (SNF)\", the \"German National Science Foundation (DF\
G)\",\n  and the Courant Research Centre \"Higher Order Structures\" of the Un\
iversity of Göttingen.\n  \n\n\n\n\n\n\n\nLicensing\n\nThis program is f\
ree software; you can redistribute it and/or modify\nit under the terms of the\
 GNU General Public License as published by\nthe Free Software Foundation; eit\
her version 2 of the License, or any\nlater version.\n\n
 This program is d\
istributed in the hope that it will be useful,\nbut WITHOUT ANY WARRANTY; with\
out even the implied warranty of\nMERCHANTABILITY or FITNESS FOR A PARTICULAR \
PURPOSE.  See the GNU\nGeneral Public License for more details.\n\n
 You sh\
ould have received a copy of the GNU General Public\nLicense along with this p\
rogram, in the file COPYING.  If not, see\nhttps://www.gnu.org/licenses/<\
/URL>.\n\n\n\nFloat package\
\n\n
A sample run\n\nThe\
 extended floating-point capabilities of &GAP; are installed by loading the pa\
ckage\nvia LoadPackage(\"float\"); and selecting new floating-point han\
dlers via\nSetFloats(MPFR), SetFloats(MPFI), SetFloats(MPC) orSetFloats(CXSC),\ndepending on whether high-precision real, interv\
al or complex arithmetic are desired, or\nwhether a fast package containing al\
l four real/complex element/interval arithmetic is desired:\n LoadPackage(\"float\");\nLoading FLOAT 0.7.0 ...\ntrue\ngap> SetFloats\
(MPFR); # floating-point\ngap> x := 4*Atan(1.0);\n.314159e1\ngap> Sin(x);\n.16\
9569e-30\ngap> SetFloats(MPFR,1000); # 1000 bits\ngap> x := 4*Atan(1.0);\n.314\
159e1\ngap> Sin(x);\n.125154e-300\ngap> String(x,300);\n\".3141592653589793238\
462643383279502884197169399375105820974944592307816406286\\\n20899862803482534\
2117067982148086513282306647093844609550582231725359408128481\\\n1174502841027\
01938521105559644622948954930381964428810975665933446128475648233\\\n786783165\
27120190914564856692346034861045432664821339360726024914127e1\"\ngap>\ngap> Se\
tFloats(MPFI); # intervals\ngap> x := 4*Atan(1.0);\n.314159e1(99)\ngap> Absolu\
teDiameter(x); Sup(x); Inf(x);\n.100441e-29\n.314159e1\n.314159e1\ngap> Sin(x)\
;\n-.140815e-29(97)\ngap> 0.0 in last;\ntrue\ngap> 1.0; # exact representation\
\n.1e1(∞)\ngap> IncreaseInterval(last,0.001); # now only 8 significant bits\
\n.1e1(8)\ngap> IncreaseInterval(last,-0.002); # now becomes empty\n∅\ngap> \
r2 := Sqrt(2.0);\n.141421e1(99)\ngap> MinimalPolynomial(Rationals,r2);\n-2*x_1\
^2+1\ngap> Cyc(r2);\nE(8)-E(8)^3\ngap>\ngap> SetFloats(MPC); # complex numbers\
\ngap> z := 5.0-1.0i;\n.5e1-.1e1i\ngap> (1+1.0i)*last^4*(239+1.0i);\n.228488e6\
\ngap> Exp(6.2835i);\n.1e1+.314693e-3i\n]]>\n\n
\n\n\n\nPolynomials\n\nThe Floats pseudo-field\n\nPolynomials with floating-point coef\
ficients may be manipulated in\n&GAP;; though they behave, in subtle ways, qui\
te differently than\npolynomials over rings. A \"pseudo-field\" of floating-po\
int numbers\nis available to create them using the standard &GAP; syntax.\n\n\n\n  \n  \n    T\
he \"pseudo-field\" of floating-point numbers, containing all\n    floating-po\
int numbers in the current implementation.\n    
\n    Note that it is not \
really a field, e.g. because addition of\n    floating-point numbers is not as\
sociative. It is mainly used to\n    create indeterminates, as in the followin\
g example:\n x := Indeterminate(FLOAT_PSEUDOFIELD,\"x\
\");\nx\ngap> 2*x^2+3;\n2.0*x^2+3.0\ngap> Value(last,10);\n203.0\n]]>\n  \n\n\n
\n\nRoots of\
 polynomials\n\nThe Jenkins-Traub algorithm has been implemented, in\
 arbitrary\nprecision for MPFR and MPC.\n\nFurthermore, CXSC can provide c\
omplex enclosures for the roots of a\ncomplex polynomial.\n\n
\n\nFinding integer relations\nThe PSLQ algorithm has bee\
n implemented by Steve A. Linton, as an external\r\ncontribution to F\
loat. This algorithm receives as\r\ninput a vector of floats x and a required precision \\epsilon,\r\nand seeks an integer vector v such that\r\n|x\\cdot v|<\\epsilon. The implementation follow\
s quite closely the\r\noriginal article .\r\n\r\n\r\n  \r\n  \r\n  An integer v\
ector v with |x\\cdot v|<\\epsilon.\r\n  \r\n    The PSLQ algorithm by Bailey and Broadhurst (see )\r\n    searches for an integer relation between the entries in x.\r\n\r\n    \\beta and \\gamma are algorithm tuning param\
eters, and\r\n    default to 4/10 and 2/\\sqrt(3) respectively.\
\r\n\r\n    
The second form implements the \"Multi-pair\" variant of the a\
lgorithm, which is\r\n    better suited to parallelization.\r\n PSLQ([1.0,(1+Sqrt(5.0))/2],1.e-2);\r\n[ 55, -34 ] # Fibonacci numb\
ers\r\ngap> RootsFloat([1,-4,2]*1.0);\r\n[ 0.292893, 1.70711 ] # roots of 2x^2\
-4x+1\r\ngap> PSLQ(List([0..2],i->last[1]^i),1.e-7);\r\n[ 1, -4, 2 ] # a degre\
e-2 polynomial fitting well\r\n]]>\r\n  \r\n\r\n\n\n\n
LLL lattice reduction\n\nA \
faster implementation of the LLL lattice reduction algorithm has\nalso been im\
plemented. It is accessible via the commands\nFPLLLReducedBasis(m) and \
\nFPLLLShortestVector(m).\n\n\n
\n\n\n\nImplemented packages\n\nM\
PFR\n\n  \n  \n  \n    The category of floating-point numbers.\n\n  \
   Note that they are treated as commutative and scalar, but are\n    not \
necessarily associative.\n  \n\n\n
\n\nMPFI\n\n  \n \
 \n  \n    The category of intervals of \
floating-point numbers.\n\n     Note that they are treated as commutative \
and scalar, but are\n    not necessarily associative.\n  \n\n\n\n\n
MPC\n\n  \n  \n  \n    The\
 category of intervals of floating-point numbers.\n\n     Note that they a\
re treated as commutative and scalar, but are\n    not necessarily associative\
.\n  \n\n\n
\n\nCXSC\n\n  \n  \n  \n  \n  \n  \n  \n  \n  \n    The categor\
y of floating-point numbers.\n\n     Note that they are treated as commuta\
tive and scalar, but are\n    not necessarily associative.\n  \n\
\n\n
\n\nFPLLL\n\
\n  \n  A matrix spanning\
 the same lattice as m.\n  \n    This function i\
mplements the LLL (Lenstra-Lenstra-Lovász) lattice\n    reduction algorithm v\
ia the external library fplll.\n\n     The result is gu\
aranteed to be optimal up to 1%.\n  \n\n\n\n  \n  A short vect\
or in the lattice spanned by m.\n  \n    This fu\
nction implements the LLL (Lenstra-Lenstra-Lovász) lattice\n    reduction alg\
orithm via the external library fplll,\n    and then comput\
es a short vector in this lattice.\n\n    
 The result is guaranteed to be \
optimal up to 1%.\n  \n\n\n\n\n\
\n\n\n\n\n\n\n\n", 
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  toctext := "1 Licensing\n
\n2 Float pa\
ckage\n 2.1 A sample run\n\n
\n
\n3 P\
olynomials\n 3.1 The Floats pseudo-field\n\n\n
  \
3.1-1 FLOAT_PSEUDOFIELD\n
\n 3.2 Roots of polynomials\n\n
\n 3.3 Finding integer\
 relations\n\n\n
  3.3-1 PSLQ\n
\n<\
span class=\"tocline\"> 3.4 LLL lattice reduction<\
/a>\n\n
\n
\n4 Implemented packages\n 4.1 MPFR\n\n\n
\
  4.1-1 IsMPFRFloat\n
\n 4.2 MPFI\n\n\n
 \
 4.2-1 IsMPFIFloat\n
\n 4.3 MPC\n\n\n
  4.3-1 IsMPCFloat\n
\n 4.4 CXSC\n\n\n
  4.4-\
1 IsCXSCReal\n
\n 4.5 FPLLL\n\n\n
  4.5-1 FPLLLReducedBasis\n
  4.5-2 FPLLLShortestVector\n
\n
\nReferences
\nIndex
\n1 Lic\
ensing\n
\n2 Float package\n 2.1 A sample run\n\n
\n
\n3 Polynomials\n <\
a href=\"chap3.html#X7BDA2E7C85ECC18C\">3.1 The Floats\
 pseudo-field\n\n\n
  3.1-1 FLOAT_PSEUDOFIELD\n
\n 3.2 Roots of poly\
nomials\n\n
\n 3.3 Finding integer relations\n\
\n\n
  3.3-1 PSLQ\
\n
\n 3.4 LLL lattice reduction\n\n
\n\n\
4 Implemented packages\n 4.1 MPFR\n\n\n
 &n\
bsp;4.1-1 IsMPFRFloat\n
\n 4.2 MPFI\n\n\n
  4.2-1 IsMPFIFloat\n
\n 4.3 MPC\
\n\n\n
  4.3-1\
 IsMPCFloat\n
\n 4.4 CXSC\n\n\n
  4.4-1 IsCXSCReal\n
\n 4.5 FPLLL\n\n\n
  4.5-1 FPLLLReducedBasis\n  4.5-2 FPLLLShortestVector\n
\n
\nReferences
\nIndex\n" )
gap> gap> #W dlopen() error: /builddir/build/BUILD/float-1.0.1/../pkg/float-1.0.1/bin/po\
werpc64le-redhat-linux-gnu-default64-kv7/float.so: undefined symbol: cpoly_MPC
Error, module '/builddir/build/BUILD/float-1.0.1/../pkg/float-1.0.1/bin/powerpc64le-r\
edhat-linux-gnu-default64-kv7/float.so' not found in
  LOAD_DYN( arg[1], false ) at /usr/lib/gap/lib/files.gd:587 called from 
LoadDynamicModule( f 
 ); at /builddir/build/BUILD/float-1.0.1/../pkg/float-1.0.1/init.g:43 called from
(  )
 called from read-eval loop at /builddir/build/BUILD/float-1.0.1/../pkg/float-1.0.1/init.g:45
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
Error, was not in any namespace at /usr/lib/gap/lib/variable.g:292 called from
LEAVE_NAMESPACE(  ); at /usr/lib/gap/lib/package.gi:1303 called from
ReadPackage( pkgname, "init.g" ); at /usr/lib/gap/lib/package.gi:1670 called from
LoadPackage( pkgname ); at /usr/lib/gap/lib/package.gi:2081 called from
(  )
 called from read-eval loop at *stdin*:9
brk> brk> + rm -fr ../pkg
+ RPM_EC=0
++ jobs -p
+ exit 0
Executing(%install): /bin/sh -e /var/tmp/rpm-tmp.QcGaHc
+ umask 022
+ cd /builddir/build/BUILD
+ '[' /builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le '!=' / ']'
+ rm -rf /builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le
++ dirname /builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le
+ mkdir -p /builddir/build/BUILDROOT
+ mkdir /builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le
+ cd float-1.0.1
+ /usr/bin/make install DESTDIR=/builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le 'INSTALL=/usr/bin/install -p'
Making install in src
make[1]: Entering directory '/builddir/build/BUILD/float-1.0.1/src'
make[2]: Entering directory '/builddir/build/BUILD/float-1.0.1/src'
 /usr/bin/mkdir -p '/builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le/usr/lib/gap/pkg/float/bin/powerpc64le-redhat-linux-gnu-default64-kv7'
 /bin/sh ../libtool   --mode=install /usr/bin/install -p   float.la '/builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le/usr/lib/gap/pkg/float/bin/powerpc64le-redhat-linux-gnu-default64-kv7'
libtool: install: /usr/bin/install -p .libs/float.so /builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le/usr/lib/gap/pkg/float/bin/powerpc64le-redhat-linux-gnu-default64-kv7/float.so
libtool: install: /usr/bin/install -p .libs/float.lai /builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le/usr/lib/gap/pkg/float/bin/powerpc64le-redhat-linux-gnu-default64-kv7/float.la
libtool: warning: remember to run 'libtool --finish /usr/lib/gap/pkg/float/bin/powerpc64le-redhat-linux-gnu-default64-kv7'
make[2]: Nothing to be done for 'install-data-am'.
make[2]: Leaving directory '/builddir/build/BUILD/float-1.0.1/src'
make[1]: Leaving directory '/builddir/build/BUILD/float-1.0.1/src'
make[1]: Entering directory '/builddir/build/BUILD/float-1.0.1'
make[2]: Entering directory '/builddir/build/BUILD/float-1.0.1'
make[2]: Nothing to be done for 'install-exec-am'.
make[2]: Nothing to be done for 'install-data-am'.
make[2]: Leaving directory '/builddir/build/BUILD/float-1.0.1'
make[1]: Leaving directory '/builddir/build/BUILD/float-1.0.1'
+ mv /builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le/usr/lib/gap/pkg/float /builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le/usr/lib/gap/pkg/float-1.0.1
+ rm -f /builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le/usr/lib/gap/pkg/float-1.0.1/bin/powerpc64le-redhat-linux-gnu-default64-kv7/float.la
+ cp -a PackageInfo.g init.g makedoc.g read.g lib tst /builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le/usr/lib/gap/pkg/float-1.0.1
+ rm -f /builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le/usr/lib/gap/pkg/float-1.0.1/lib/Makefile.am /builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le/usr/lib/gap/pkg/float-1.0.1/tst/Makefile.am
+ mkdir -p /builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le/usr/lib/gap/pkg/float-1.0.1/doc
+ cp -p doc/floatbib.xml.bib doc/lefttoc.css doc/manual.css doc/nocolorprompt.css doc/ragged.css doc/times.css doc/toggless.css doc/chap0.html doc/chap1.html doc/chap2.html doc/chap3.html doc/chap4.html doc/chapBib.html doc/chapInd.html doc/chooser.html doc/manual.js doc/rainbow.js doc/toggless.js doc/manual.lab doc/manual.pdf doc/manual.six doc/float.toc doc/chap0.txt doc/chap1.txt doc/chap2.txt doc/chap3.txt doc/chap4.txt doc/chapBib.txt doc/chapInd.txt doc/float.xml doc/floatbib.xml /builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le/usr/lib/gap/pkg/float-1.0.1/doc
+ /usr/bin/find-debuginfo -j8 --strict-build-id -m -i --build-id-seed 1.0.1-1.fc35 --unique-debug-suffix -1.0.1-1.fc35.ppc64le --unique-debug-src-base gap-pkg-float-1.0.1-1.fc35.ppc64le --run-dwz --dwz-low-mem-die-limit 10000000 --dwz-max-die-limit 50000000 -S debugsourcefiles.list /builddir/build/BUILD/float-1.0.1
extracting debug info from /builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le/usr/lib/gap/pkg/float-1.0.1/bin/powerpc64le-redhat-linux-gnu-default64-kv7/float.so
original debug info size: 2116kB, size after compression: 1984kB
/usr/bin/sepdebugcrcfix: Updated 1 CRC32s, 0 CRC32s did match.
280 blocks
+ /usr/lib/rpm/check-buildroot
+ /usr/lib/rpm/redhat/brp-ldconfig
+ /usr/lib/rpm/brp-compress
+ /usr/lib/rpm/redhat/brp-strip-lto /usr/bin/strip
+ /usr/lib/rpm/brp-strip-static-archive /usr/bin/strip
+ /usr/lib/rpm/check-rpaths
+ /usr/lib/rpm/redhat/brp-mangle-shebangs
+ /usr/lib/rpm/redhat/brp-python-bytecompile '' 1 0
+ /usr/lib/rpm/redhat/brp-python-hardlink
Executing(%check): /bin/sh -e /var/tmp/rpm-tmp.jstv4C
+ umask 022
+ cd /builddir/build/BUILD
+ cd float-1.0.1
+ gap -l '/builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le/usr/lib/gap;/usr/lib/gap'
 *********   GAP 4.11.1 of 2021-03-02
 *  GAP  *   https://www.gap-system.org
 *********   Architecture: powerpc64le-redhat-linux-gnu-default64-kv7
 Configuration:  gmp 6.2.0, GASMAN, readline
 Loading the library and packages ...
#I  autpgrp package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  alnuth package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  crisp package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  ctbllib package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  factint package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  fga package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  irredsol package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  laguna package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  polenta package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  polycyclic package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  resclasses package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  sophus package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  tomlib package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
 Packages:   GAPDoc 1.6.4, PrimGrp 3.4.1, SmallGrp 1.4.2, TransGrp 3.3
 Try '??help' for help. See also '?copyright', '?cite' and '?authors'
gap> #W dlopen() error: /builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64l\
e/usr/lib/gap/pkg/float-1.0.1/bin/powerpc64le-redhat-linux-gnu-default64-kv7/f\
loat.so: undefined symbol: cpoly_MPC
Error, module '/builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le/usr/lib/g\
ap/pkg/float-1.0.1/bin/powerpc64le-redhat-linux-gnu-default64-kv7/float.so' no\
t found in
  LOAD_DYN( arg[1], false ) at /usr/lib/gap/lib/files.gd:587 called from 
LoadDynamicModule( f 
 ); at /builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le/usr/lib/ga\
p/pkg/float-1.0.1/init.g:43 called from
(  )
 called from read-eval loop at /builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le/usr/lib/gap/pk\
g/float-1.0.1/init.g:45
Error, was not in any namespace at /usr/lib/gap/lib/variable.g:292 called from
LEAVE_NAMESPACE(  ); at /usr/lib/gap/lib/package.gi:1303 called from
ReadPackage( pkgname, "init.g" ); at /usr/lib/gap/lib/package.gi:1670 called from
(  )
 called from read-eval loop at *stdin*:1
brk> you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk> Syntax warning: Unbound global variable in *errin*:2
dirs := DirectoriesPackageLibrary("float","tst");
^^^^
[ dir("/builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le/usr/lib/ga\
p/pkg/float-1.0.1/tst/") ]
brk> brk> Syntax warning: Unbound global variable in *errin*:4
success := true;
^^^^^^^
true
brk> brk> brk> brk> arithmetic
msecs: 1
true
brk> brk> > > > > > #I  WARNING: skipping tests for MPFR
> brk> brk> > > > > > #I  WARNING: skipping tests for MPFI
> brk> brk> > > > > > > > > #I  WARNING: skipping tests for MPC
> brk> brk> > > > > > > > > #I  WARNING: skipping tests for CXSC
> brk> brk> > > > > #I  WARNING: skipping tests for FPLLL
> brk> brk> brk> > #I  No errors detected while testing package float
> > > > > + RPM_EC=0
++ jobs -p
+ exit 0
Processing files: gap-pkg-float-1.0.1-1.fc35.ppc64le
Executing(%doc): /bin/sh -e /var/tmp/rpm-tmp.x5nVDw
+ umask 022
+ cd /builddir/build/BUILD
+ cd float-1.0.1
+ DOCDIR=/builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le/usr/share/doc/gap-pkg-float
+ export LC_ALL=C
+ LC_ALL=C
+ export DOCDIR
+ /usr/bin/mkdir -p /builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le/usr/share/doc/gap-pkg-float
+ cp -pr README.md /builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le/usr/share/doc/gap-pkg-float
+ cp -pr THANKS /builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le/usr/share/doc/gap-pkg-float
+ RPM_EC=0
++ jobs -p
+ exit 0
Executing(%license): /bin/sh -e /var/tmp/rpm-tmp.tfl4nb
+ umask 022
+ cd /builddir/build/BUILD
+ cd float-1.0.1
+ LICENSEDIR=/builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le/usr/share/licenses/gap-pkg-float
+ export LC_ALL=C
+ LC_ALL=C
+ export LICENSEDIR
+ /usr/bin/mkdir -p /builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le/usr/share/licenses/gap-pkg-float
+ cp -pr COPYING /builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le/usr/share/licenses/gap-pkg-float
+ RPM_EC=0
++ jobs -p
+ exit 0
Provides: gap-pkg-float = 1.0.1-1.fc35 gap-pkg-float(ppc-64) = 1.0.1-1.fc35
Requires(rpmlib): rpmlib(CompressedFileNames) <= 3.0.4-1 rpmlib(FileDigests) <= 4.6.0-1 rpmlib(PayloadFilesHavePrefix) <= 4.0-1
Requires: libc.so.6()(64bit) libc.so.6(GLIBC_2.17)(64bit) libcxsc.so.2()(64bit) libfplll.so.7()(64bit) libgcc_s.so.1()(64bit) libgcc_s.so.1(GCC_3.0)(64bit) libgcc_s.so.1(GCC_3.3.1)(64bit) libm.so.6()(64bit) libm.so.6(GLIBC_2.17)(64bit) libm.so.6(GLIBC_2.29)(64bit) libmpc.so.3()(64bit) libmpfi.so.0()(64bit) libmpfr.so.6()(64bit) libstdc++.so.6()(64bit) libstdc++.so.6(CXXABI_1.3)(64bit) libstdc++.so.6(CXXABI_1.3.8)(64bit) libstdc++.so.6(CXXABI_1.3.9)(64bit) libstdc++.so.6(GLIBCXX_3.4)(64bit) libstdc++.so.6(GLIBCXX_3.4.11)(64bit) libstdc++.so.6(GLIBCXX_3.4.9)(64bit) rtld(GNU_HASH)
Processing files: gap-pkg-float-doc-1.0.1-1.fc35.noarch
Provides: gap-pkg-float-doc = 1.0.1-1.fc35
Requires(rpmlib): rpmlib(CompressedFileNames) <= 3.0.4-1 rpmlib(FileDigests) <= 4.6.0-1 rpmlib(PayloadFilesHavePrefix) <= 4.0-1
Processing files: gap-pkg-float-debugsource-1.0.1-1.fc35.ppc64le
Provides: gap-pkg-float-debugsource = 1.0.1-1.fc35 gap-pkg-float-debugsource(ppc-64) = 1.0.1-1.fc35
Requires(rpmlib): rpmlib(CompressedFileNames) <= 3.0.4-1 rpmlib(FileDigests) <= 4.6.0-1 rpmlib(PayloadFilesHavePrefix) <= 4.0-1
Processing files: gap-pkg-float-debuginfo-1.0.1-1.fc35.ppc64le
Provides: debuginfo(build-id) = 78cd2cbec4e2c6ed832dae392ff4d0cf916f027f gap-pkg-float-debuginfo = 1.0.1-1.fc35 gap-pkg-float-debuginfo(ppc-64) = 1.0.1-1.fc35
Requires(rpmlib): rpmlib(CompressedFileNames) <= 3.0.4-1 rpmlib(FileDigests) <= 4.6.0-1 rpmlib(PayloadFilesHavePrefix) <= 4.0-1
Recommends: gap-pkg-float-debugsource(ppc-64) = 1.0.1-1.fc35
Checking for unpackaged file(s): /usr/lib/rpm/check-files /builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le
Wrote: /builddir/build/RPMS/gap-pkg-float-doc-1.0.1-1.fc35.noarch.rpm
Wrote: /builddir/build/RPMS/gap-pkg-float-debugsource-1.0.1-1.fc35.ppc64le.rpm
Wrote: /builddir/build/RPMS/gap-pkg-float-1.0.1-1.fc35.ppc64le.rpm
Wrote: /builddir/build/RPMS/gap-pkg-float-debuginfo-1.0.1-1.fc35.ppc64le.rpm
Executing(%clean): /bin/sh -e /var/tmp/rpm-tmp.X21Wev
+ umask 022
+ cd /builddir/build/BUILD
+ cd float-1.0.1
+ /usr/bin/rm -rf /builddir/build/BUILDROOT/gap-pkg-float-1.0.1-1.fc35.ppc64le
+ RPM_EC=0
++ jobs -p
+ exit 0
Child return code was: 0