"""Built-in examples: port of sphericalExamples.pm. The lambdas are Perl numeric literals in the original (3/4 is the number 0.75, .33 the number 0.33), so they are given here as the same Python numbers. """ def getExamples(): """Return (types, lambdas, titles, comments), keyed 1..9.""" types = dict((i, "C") for i in range(1, 10)) lambdas = { 1: [2, 1], 2: [1, 0], 3: [1, .1], 4: [3, 2, 1], 5: [3 / 4, .33, 0], 6: [3 / 4, 1 / 8, 0], 7: [2, 1, 1, 0], 8: [5 / 4, 5 / 4, 1 / 4, 1 / 4, 3 / 4, 3 / 4], 9: [5 / 4, 5 / 4, 5 / 4, 1 / 4, 1 / 4, 1 / 4, 3 / 4, 3 / 4, 3 / 4], } titles = { 1: "trivial of Sp(4)", 2: "Sp(4) example 1", 3: "Sp(4) example 2", 4: "trivial of Sp(6)", 5: "Sp(6) example 1", 6: "Sp(6) example 2", 7: "Sp(8) example 1", 8: "Sp(12)", 9: "Sp(18)", } comments = { 1: "Example: Trivial representation of Sp(4)", 2: "Example: Unitary point for Sp(4). This is a corner of the square " "which is the corner of the open\nregion containing 0. Note that " "no complementary series are allowed since Z contains O(2). See " "Sp(4) example 3.", 3: "Example: Non-unitary point for Sp(4). This is close to the point " "(1,0), at which the complementary series is empty. Compare " "Sp(4) example 3.", 4: "Example: Trivial representation of Sp(6)", 5: "Example: Unitary 0-complementary series of Sp(6). This is not in " "the obvious open facet \ncontaining 0. See example 6.", 6: "Example: Non-Unitary 0-complementary series of Sp(6). This is not " "in the obvious open facet containing 0.\nSee Example 5.", 7: "Example: Distinguished nilpotent orbit.", 8: "Example: Unitary representation of Sp(12). The centralizer " "contains a factor O(4) of type D2.\nCompare Sp(18) " "example.", 9: "Non-unitary representation of Sp(18). This is non-unitary since\n" "the centralizer contains a factor O(6) of type D_3, and the " "corresponding factor of nu \ndoes not have a 0--coordinate, and " "is therefore not fixed by w0. Compare Sp(12) example.", } return types, lambdas, titles, comments def getFileExamples(): """Return (typeAndRanks, files, fileTitles). Only the entries that were active in the original program are listed. ``files`` are paths relative to /dissemination/spherical/; of these only the B2 and D4 files exist on the site (:data:`AVAILABLE`). """ typeAndRanks = {5: "B2", 6: "B2", 11: "A3", 15: "C3", 16: "C3", 19: "A4", 21: "B4", 22: "B4", 23: "C4", 24: "C4", 25: "D4"} files = {5: "B2/psd_barbasch", 6: "B2/ptlist_std", 11: "A3/psd_barbasch", 15: "C3/psd_barbasch", 16: "C3/ptlist_std", 19: "A4/psd_barbasch", 20: "A4/ptlist_std", 21: "B4/psd_barbasch", 22: "B4/ptlist_std", 23: "C4/psd_barbasch", 24: "C4/ptlist_std", 25: "D4/psd_barbasch"} fileTitles = {5: "B2 unitary facets", 6: "B2 all facets", 11: "A3 unitary facets", 15: "C3 unitary facets", 16: "C3 all facets", 19: "A4 unitary facets", 20: "A4 all facets", 21: "B4 unitary facets", 22: "B4 all facets", 23: "C4 unitary facets", 24: "C4 all facets", 25: "D4 unitary facets"} return typeAndRanks, files, fileTitles # File examples whose data files are on the site. AVAILABLE = [5, 6, 25]