"""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]