Explicit Data For SO(5)



Every linear slice of SO(n) that we computed involved first choosing coefficients for the linear forms defining that slice. Here we keep a database of those coefficients as well as the results of the experiment for each coefficient.

The experiment ran in parallel, so below there are multiple threads. Each thread computed many packets. Each packet describes many linear cuts.
For example, if I open a `record' file, and I want to reproduce the result

{36, {5a, 2, 0}}

I would find the 1st line (experiments index at 0) of the second packet 5a002. It reads,

{-4.06667, .616667, .928571, -2.59091, 1.23016, .0416667, .283333, -.648352, 1.03968, .353535, -.766667, .666667, .472222, -.385965, -.658824, -1.41026, -.340909, .909091, .95, .361111, .95, -.20202, -.583333, .6875, -1.05263, .928571, -2.05, -2.06667, 1.26667, -.979798, .261905, .247368, -.390909, -.424242, -.571429, -2.3, -.225, -1.45882, 1.60784, -.677632, .2, .322368, -.183824, 1.17308, 6.91667, -.738095, -.45, -1.87143, 2.94737, -9.1, -1.45263, -.20202, -1.08333, .95, .923077, -1.75, -1.05263, .228571, -1.32143, .423077, .9375, -.527778, 2.60784, -.340909, .27451, -.74359, .277778, -4.05263, .1875, -.552632, 5.9375, -5.07143, -3.0625, 1.1875, .575, -2.09091, .804511, -1.33571, -.416667, -.975, -1.71667, -.618056, .4, .566667, -.519481, -1.8625, -.3125, -.196429, -2.07143, .283333, -.5625, .79798, 1.35, .694444, -.590909, -1.5625, 1.14737, .923077, -1.71667, -2.55, -4.57143, -.916667, 1.42308, -.9, .0897436, 1.0873, .544444, 1.45, -.276923, -2.30556, .504762, 3.93333, -1.72917, .394444, -1.22619, -.958824, -.281046, .928571, -1.0625, -.45, 1.0625, .447368, 1.16667, .428571, -.305556, -1.83333, 1.92308, 1.08036, 1.07576, 1.15, -.904762, .691176, .4375, -.276923, -4.05, -1.8, -1.06667, -.288889, -4.07692, 1.34524, -5.1, 1.71667, -.716667, -.716667, .623077, -.544444, -1.21667, -2.72222, .614035, .447368, -.960317, .8125, 1.04861, -1.1, -.571429, -.883333, 1.45, .0661765, 1.40909, -2.31667, .5, -1.08333, .230159, -10.0769, -1.45882, .183333, -2.1, -4.09091, -3.08333, .783333, .433333, .933333, 1.025, .694444, -1.0625, 1.61111, .447368, 3.43333, .344444, .6, .25641, -2.40476, -1.85556, -3.05, -2.1, -1.07143, .923077, -3.39583, -1.72549, -6.06667, -3.6, 1.94444, -1.27143, .941176, .807143, 6.95, 2.61404, .609091, -1.09091, .3, 1.27778, -2.05263, -.505495, .728571, -.308824, .790476, .516667, -1.08333, -2.55263, 1.40909, -1.55263, -.476923, -.715909, -7.05882, -.833333, 6.90909, 5.94444, .923077, -.933824, -1.07692, .4375, -.358824, .226891, -10.0833, -.766917, .95, 1.9375, -.74359, 2.25641, -.433333, -.571429, 2.2807, 4.4375, .128571, 1.55, .706349, -1.19444, -2.55263, -.830409, -.383333, 1.58333, .344444, 7.94118, .811966, -1.38333, -.933824, -1.5625, -.552632, -.276923, -2.1, -1.4, -.8, -.215909, .928571, -1.34091, -1.20168, -5.06667, -1.3125, .0595238, -1.08333}

These are the coefficients of the linear forms defining the linear slice in a particular order. This order corresponds to the order of parameters in the following Bertini files. To reproduce this run, one creates a 'final_parameters' file in Bertini with the above coefficients and then runs Bertini on a directory containing that file along with the three below. After performing the computation, one should see that 36 of the solutions are real.

Bertini Files


BertiniInput
BertiniStartParameters
BertiniStartPoints

Thread A



Record Tally

5a001 5a002 5a003 5a004 5a005 5a006 5a007 5a008 5a009
5a010 5a011 5a012 5a013 5a014 5a015 5a016 5a017 5a018 5a019

Thread B



Record Tally

5b001 5b002 5b003 5b004 5b005 5b006 5b007 5b008 5b009
5b010 5b011 5b012 5b013 5b014 5b015

Thread C



Record Tally

5c001 5c002 5c003 5c004 5c005 5c006 5c007 5c008 5c009
5c010 5c011 5c012 5c013 5c014 5c015 5c016 5c017 5c018 5c019
5c020 5c021 5c022 5c023 5c024 5c025 5c026 5c027 5c028 5c029
5c030 5c031 5c032 5c033 5c034 5c035 5c036 5c037 5c038 5c039
5c040 5c041 5c042 5c043 5c044 5c045 5c046 5c047 5c048 5c049
5c050 5c051 5c052 5c053 5c054 5c055 5c056 5c057 5c058 5c059
5c060 5c061 5c062 5c063 5c064 5c065 5c066 5c067 5c068 5c069
5c070 5c071 5c072 5c073 5c074 5c075 5c076 5c077 5c078 5c079
5c080 5c081 5c082 5c083 5c084 5c085 5c086 5c087 5c088 5c089
5c090 5c091 5c092 5c093 5c094 5c095 5c096 5c097 5c098 5c099
5c100 5c101 5c102 5c103 5c104 5c105 5c106 5c107 5c108 5c109
5c110 5c111 5c112 5c113 5c114 5c115 5c116 5c117 5c118 5c119
5c120 5c121 5c122 5c123 5c124

Thread D



Record Tally

5d001 5d002 5d003 5d004 5d005 5d006 5d007 5d008 5d009
5d010 5d011 5d012 5d013 5d014 5d015 5d016 5d017 5d018 5d019
5d020 5d021 5d022 5d023 5d024 5d025 5d026 5d027 5d028 5d029
5d030 5d031 5d032 5d033 5d034 5d035 5d036 5d037 5d038 5d039
5d040 5d041 5d042 5d043 5d044 5d045 5d046 5d047 5d048 5d049
5d050 5d051 5d052 5d053 5d054 5d055 5d056 5d057 5d058 5d059
5d060 5d061 5d062 5d063 5d064 5d065 5d066 5d067 5d068 5d069
5d070 5d071 5d072 5d073 5d074 5d075 5d076 5d077 5d078 5d079
5d080 5d081 5d082 5d083 5d084 5d085 5d086 5d087 5d088 5d089
5d090 5d091 5d092 5d093 5d094 5d095 5d096 5d097 5d098 5d099
5d100 5d101 5d102 5d103 5d104 5d105 5d106 5d107 5d108 5d109
5d110 5d111 5d112 5d113 5d114 5d115 5d116 5d117 5d118 5d119

Thread E



Record Tally

5e001 5e002 5e003 5e004 5e005 5e006 5e007 5e008 5e009
5e010 5e011 5e012 5e013 5e014 5e015 5e016 5e017 5e018 5e019
5e020 5e021 5e022 5e023 5e024 5e025 5e026 5e027 5e028 5e029
5e030 5e031 5e032 5e033 5e034 5e035 5e036 5e037 5e038 5e039
5e040 5e041 5e042 5e043 5e044 5e045 5e046 5e047 5e048 5e049
5e050 5e051 5e052 5e053 5e054 5e055 5e056 5e057 5e058 5e059
5e060 5e061 5e062 5e063 5e064 5e065 5e066 5e067 5e068 5e069
5e070 5e071 5e072 5e073 5e074 5e075 5e076 5e077 5e078 5e079
5e080 5e081 5e082 5e083 5e084 5e085 5e086 5e087 5e088 5e089
5e090 5e091 5e092 5e093 5e094 5e095 5e096 5e097 5e098 5e099
5e100 5e101 5e102 5e103 5e104 5e105 5e106

Thread F



Record Tally

5f001 5f002 5f003 5f004 5f005 5f006 5f007 5f008 5f009
5f010 5f011 5f012 5f013 5f014 5f015 5f016 5f017 5f018 5f019
5f020 5f021 5f022 5f023 5f024 5f025 5f026 5f027 5f028 5f029
5f030 5f031 5f032 5f033 5f034 5f035 5f036 5f037 5f038 5f039
5f040 5f041 5f042 5f043 5f044 5f045 5f046 5f047 5f048 5f049
5f050 5f051 5f052 5f053 5f054 5f055 5f056 5f057 5f058 5f059
5f060 5f061 5f062 5f063 5f064 5f065 5f066 5f067 5f068 5f069
5f070 5f071 5f072 5f073 5f074 5f075 5f076 5f077 5f078 5f079
5f080 5f081 5f082 5f083 5f084 5f085 5f086 5f087 5f088 5f089
5f090 5f091 5f092 5f093 5f094 5f095 5f096 5f097 5f098 5f099
5f100 5f101 5f102 5f103 5f104 5f105