SSL aboutPoincareSeriesII.html

Interaktion und
PortierbarkeitHTML

products/Sources/formale Sprachen/GAP/pkg/hap/www/SideLinks/About/aboutPoincareSeriesII.html

<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
<head>
 <meta http-equiv="content-type"
content="text/html; charset=ISO-8859-1">
 <title>AboutHap</title>
</head>
<body
style="color: rgb(0, 0, 153); background-color: rgb(204, 255, 255);"
alink="#000066" link="#000066" vlink="#000066">
 
<table
style="text-align: left; margin-left: auto; margin-right: auto; color: rgb(0, 0, 102);"
border="0" cellpadding="20" cellspacing="10">
 <tbody>
 <tr align="center">
 <th style="vertical-align: top;">
 <table style="width: 100%; text-align: left;" cellpadding="2"
cellspacing="2">
 <tbody>
 <tr>
 <td style="vertical-align: top;"><a
href="aboutPoincareSeries.html">Previous</a> 
 </td>
 <td
style="text-align: center; vertical-align: top; color: rgb(0, 0, 102);"><big>About HAP: Poincare series for groups of
order 64 
 </big></td>
 <td style="text-align: right; vertical-align: top;"><a
href="aboutTorAndExt.html">next</a> 
 </td>
 </tr>
 </tbody>
 </table>
 <big></big> 
 </th>
 </tr>
 <tr>
 <td
style="vertical-align: top; background-color: rgb(255, 255, 255);">The
following commands compute Poincare functions for most of the groups of
order 64. A few groups are omitted from this general calculation as
they need too much RAM. Again, we
have no general proof that our algorithm produces a series which is
correct in
arbitrarily high degree. Proofs must be given case by case. 
 </td>
 </tr>
 <tr>
 <td
style="vertical-align: top; background-color: rgb(255, 255, 204);">gap>
L:=[60,67,73,80,88,99,199,206,213,215,216,224,227,232,241,242,266];; 
gap> for G in AllSmallGroups(64) do 
> if not IdSmallGroup(G)[2] in L then 
> Print("\n Small group ",IdSmallGroup(G), " has Poincare series \n", 
> PoincareSeries(G), "\n"); 
> fi; 
> od; 
 
Small group [ 64, 1 ] has Poincare series 
(1)/(-x+1) 
 
Small group [ 64, 2 ] has Poincare series 
(1)/(x^2-2*x+1) 
 
Small group [ 64, 3 ] has Poincare series 
(1)/(x^2-2*x+1) 
 
Small group [ 64, 4 ] has Poincare series 
(x^2-x+1)/(x^7-3*x^6+3*x^5-x^4-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 5 ] has Poincare series 
(1)/(-x^4+2*x^3-2*x+1) 
 
Small group [ 64, 6 ] has Poincare series 
(1)/(-x^4+2*x^3-2*x+1) 
 
Small group [ 64, 7 ] has Poincare series 
(1)/(x^2-2*x+1) 
 
Small group [ 64, 8 ] has Poincare series 
(x^4+x^3+x^2+x+1)/(-x^7+x^6+x^5-x^4+x^3-x^2-x+1) 
 
Small group [ 64, 9 ] has Poincare series 
(2*x^4+x^3+x^2+x+1)/(-x^9+x^8+2*x^5-2*x^4-x+1) 
 
Small group [ 64, 10 ] has Poincare series 
(1)/(-x^6+2*x^5-x^4+x^2-2*x+1) 
 
Small group [ 64, 11 ] has Poincare series 
(x^4+x^2+1)/(x^6-2*x^5+3*x^4-4*x^3+3*x^2-2*x+1) 
 
Small group [ 64, 12 ] has Poincare series 
(1)/(-x^4+2*x^3-2*x+1) 
 
Small group [ 64, 13 ] has Poincare series 
(1)/(x^2-2*x+1) 
 
Small group [ 64, 14 ] has Poincare series 
(1)/(x^2-2*x+1) 
 
Small group [ 64, 15 ] has Poincare series 
(1)/(x^2-2*x+1) 
 
Small group [ 64, 16 ] has Poincare series 
(1)/(x^2-2*x+1) 
 
Small group [ 64, 17 ] has Poincare series 
(x^2+x+1)/(-x^5+x^4+2*x^3-2*x^2-x+1) 
 
Small group [ 64, 18 ] has Poincare series 
(-x^6+x^5+x^4-2*x^3+2*x^2-x+1)/(-x^9+3*x^8-4*x^7+ 
4*x^6-4*x^5+4*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 19 ] has Poincare series 
(-x^6+x^5+x^4-2*x^3+2*x^2-x+1)/(-x^9+3*x^8-4*x^7+ 
4*x^6-4*x^5+4*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 20 ] has Poincare series 
(1)/(-x^4+2*x^3-2*x+1) 
 
Small group [ 64, 21 ] has Poincare series 
(x^2+x+1)/(-x^5+x^4+2*x^3-2*x^2-x+1) 
 
Small group [ 64, 22 ] has Poincare series 
(1)/(-x^4+2*x^3-2*x+1) 
 
Small group [ 64, 23 ] has Poincare series 
(-x^3+2*x^2-x+1)/(x^7-3*x^6+3*x^5-x^4-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 24 ] has Poincare series 
(1)/(-x^4+2*x^3-2*x+1) 
 
Small group [ 64, 25 ] has Poincare series 
(-x^6+x^5+x^4-2*x^3+2*x^2-x+1)/(-x^9+3*x^8-4*x^7+ 
4*x^6-4*x^5+4*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 26 ] has Poincare series 
(1)/(x^2-2*x+1) 
 
Small group [ 64, 27 ] has Poincare series 
(1)/(x^2-2*x+1) 
 
Small group [ 64, 28 ] has Poincare series 
(1)/(x^4-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 29 ] has Poincare series 
(1)/(-x^4+2*x^3-2*x+1) 
 
Small group [ 64, 30 ] has Poincare series 
(x^4-x^3+x^2-x+1)/(-x^9+3*x^8-4*x^7+4*x^6-4*x^5+4*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 31 ] has Poincare series 
(1)/(x^2-2*x+1) 
 
Small group [ 64, 32 ] has Poincare series 
(x^2-x+1)/(x^7-3*x^6+3*x^5-x^4-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 33 ] has Poincare series 
(x^6+x^3+1)/(-x^10+2*x^9-x^8+x^2-2*x+1) 
 
Small group [ 64, 34 ] has Poincare series 
(1)/(-x^4+2*x^3-2*x+1) 
 
Small group [ 64, 35 ] has Poincare series 
(-x^7+x^6+x^5-x^3+x^2+1)/(-x^10+2*x^9-x^8+x^2-2*x+1) 
 
Small group [ 64, 36 ] has Poincare series 
(x^5-x^4+x^2-x+1)/(-x^9+3*x^8-4*x^7+4*x^6-4*x^5+4*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 37 ] has Poincare series 
(x^5+x^2+1)/(x^8-2*x^7+2*x^6-2*x^5+2*x^4-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 38 ] has Poincare series 
(1)/(-x^4+2*x^3-2*x+1) 
 
Small group [ 64, 39 ] has Poincare series 
(1)/(x^2-2*x+1) 
 
Small group [ 64, 40 ] has Poincare series 
(1)/(x^2-2*x+1) 
 
Small group [ 64, 41 ] has Poincare series 
(1)/(x^2-2*x+1) 
 
Small group [ 64, 42 ] has Poincare series 
(x^2-x+1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 43 ] has Poincare series 
(x^5+x^2+1)/(x^8-2*x^7+2*x^6-2*x^5+2*x^4-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 44 ] has Poincare series 
(1)/(x^2-2*x+1) 
 
Small group [ 64, 45 ] has Poincare series 
(1)/(x^4-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 46 ] has Poincare series 
(1)/(x^4-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 47 ] has Poincare series 
(1)/(x^2-2*x+1) 
 
Small group [ 64, 48 ] has Poincare series 
(1)/(x^2-2*x+1) 
 
Small group [ 64, 49 ] has Poincare series 
(1)/(x^4-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 50 ] has Poincare series 
(1)/(x^2-2*x+1) 
 
Small group [ 64, 51 ] has Poincare series 
(1)/(x^4-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 52 ] has Poincare series 
(1)/(x^2-2*x+1) 
 
Small group [ 64, 53 ] has Poincare series 
(1)/(x^4-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 54 ] has Poincare series 
(x^2+x+1)/(-x^3+x^2-x+1) 
 
Small group [ 64, 55 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 56 ] has Poincare series 
(x^2+x+1)/(x^6-2*x^5-x^4+4*x^3-x^2-2*x+1) 
 
Small group [ 64, 57 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 58 ] has Poincare series 
(1)/(x^5-3*x^4+2*x^3+2*x^2-3*x+1) 
 
Small group [ 64, 59 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 61 ] has Poincare series 
(1)/(x^5-3*x^4+2*x^3+2*x^2-3*x+1) 
 
Small group [ 64, 62 ] has Poincare series 
(1)/(x^5-3*x^4+2*x^3+2*x^2-3*x+1) 
 
Small group [ 64, 63 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 64 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 65 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 66 ] has Poincare series 
(1)/(x^5-3*x^4+2*x^3+2*x^2-3*x+1) 
 
Small group [ 64, 68 ] has Poincare series 
(x^4+2*x^3+x^2+2*x+1)/(-x^7+x^6+x^5-x^4+x^3-x^2-x+1) 
 
Small group [ 64, 69 ] has Poincare series 
(-x^2+x+1)/(x^6-2*x^5-x^4+4*x^3-x^2-2*x+1) 
 
Small group [ 64, 70 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 71 ] has Poincare series 
(1)/(x^5-3*x^4+2*x^3+2*x^2-3*x+1) 
 
Small group [ 64, 72 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 74 ] has Poincare series 
(-x^3+x^2+1)/(x^7-3*x^6+3*x^5-x^4-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 75 ] has Poincare series 
(1)/(x^5-3*x^4+2*x^3+2*x^2-3*x+1) 
 
Small group [ 64, 76 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 77 ] has Poincare series 
(-x^2+x+1)/(x^6-2*x^5-x^4+4*x^3-x^2-2*x+1) 
 
Small group [ 64, 78 ] has Poincare series 
(-x^2+x+1)/(x^6-2*x^5-x^4+4*x^3-x^2-2*x+1) 
 
Small group [ 64, 79 ] has Poincare series 
(x^4+2*x^3+x^2+2*x+1)/(-x^7+x^6+x^5-x^4+x^3-x^2-x+1) 
 
Small group [ 64, 81 ] has Poincare series 
(x^4+2*x^3+x^2+2*x+1)/(-x^7+x^6+x^5-x^4+x^3-x^2-x+1) 
 
Small group [ 64, 82 ] has Poincare series 
(x^8+2*x^7+3*x^6+6*x^5+6*x^4+6*x^3+3*x^2+2*x+1)/(-x^11+ 
x^10-x^9+x^8+2*x^7-2*x^\6+2*x^5-2*x^4-x^3+x^2-x+1) 
 
Small group [ 64, 83 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 84 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 85 ] has Poincare series 
(1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 86 ] has Poincare series 
(1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 87 ] has Poincare series 
(1)/(x^5-3*x^4+2*x^3+2*x^2-3*x+1) 
 
Small group [ 64, 89 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
 Small group [ 64, 90 ] has Poincare series 
(1)/(x^5-3*x^4+2*x^3+2*x^2-3*x+1) 
 
 
Small group [ 64, 91 ] has Poincare series 
(x^5+x^2+1)/(-x^9+3*x^8-4*x^7+4*x^6-4*x^5+4*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 92 ] has Poincare series 
(x^2-x+1)/(x^6-4*x^5+7*x^4-8*x^3+7*x^2-4*x+1) 
 
Small group [ 64, 93 ] has Poincare series 
(x^5+x^2+1)/(-x^9+3*x^8-4*x^7+4*x^6-4*x^5+4*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 94 ] has Poincare series 
(x^5+x^2+1)/(-x^9+3*x^8-4*x^7+4*x^6-4*x^5+4*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 95 ] has Poincare series 
(1)/(x^5-3*x^4+2*x^3+2*x^2-3*x+1) 
 
Small group [ 64, 96 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 97 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 98 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 100 ] has Poincare series 
(x^5+x^2+1)/(-x^9+3*x^8-4*x^7+4*x^6-4*x^5+4*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 101 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 102 ] has Poincare series 
(x^5+x^2+1)/(-x^9+3*x^8-4*x^7+4*x^6-4*x^5+4*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 103 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 104 ] has Poincare series 
(1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 105 ] has Poincare series 
(1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 106 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 107 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 108 ] has Poincare series 
(1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 109 ] has Poincare series 
(1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 110 ] has Poincare series 
(1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 111 ] has Poincare series 
(-x^6+x^5+x^4-x^3+1)/(-x^9+3*x^8-4*x^7+4*x^6-4*x^5+4*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 112 ] has Poincare series 
(1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 113 ] has Poincare series 
(1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 114 ] has Poincare series 
(-x^4+x^3+1)/(-x^7+3*x^6-5*x^5+7*x^4-7*x^3+5*x^2-3*x+1) 
 
Small group [ 64, 115 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 116 ] has Poincare series 
(x^3+x+1)/(-x^6+2*x^5-x^4+x^2-2*x+1) 
 
Small group [ 64, 117 ] has Poincare series 
(1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 118 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 119 ] has Poincare series 
(1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 120 ] has Poincare series 
(x^2+x+1)/(x^4-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 121 ] has Poincare series 
(1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 122 ] has Poincare series 
(x^2+x+1)/(x^4-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 123 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 124 ] has Poincare series 
(x^2+x+1)/(x^4-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 125 ] has Poincare series 
(x^2+x+1)/(x^4-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 126 ] has Poincare series 
(x^2+x+1)/(x^4-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 127 ] has Poincare series 
(x^4+x^3+x^2+x+1)/(x^6-2*x^5+3*x^4-4*x^3+3*x^2-2*x+1) 
 
Small group [ 64, 128 ] has Poincare series 
(1)/(x^5-3*x^4+2*x^3+2*x^2-3*x+1) 
 
Small group [ 64, 129 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 130 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
 
Small group [ 64, 131 ] has Poincare series 
(x^2-x+1)/(x^6-4*x^5+7*x^4-8*x^3+7*x^2-4*x+1) 
 
Small group [ 64, 132 ] has Poincare series 
(x^2+x+1)/(-x^6+2*x^5-x^4+x^2-2*x+1) 
 
Small group [ 64, 133 ] has Poincare series 
(x^2+x+1)/(-x^6+2*x^5-x^4+x^2-2*x+1) 
 
Small group [ 64, 134 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 135 ] has Poincare series 
(-x^6+x^2+1)/(-x^9+3*x^8-4*x^7+4*x^6-4*x^5+4*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 136 ] has Poincare series 
(x^5+x^4-x^3+x^2+1)/(-x^9+3*x^8-4*x^7+4*x^6-4*x^5+4*x^4-4*x^3 
+4*x^2-3*x+1) 
 
Small group [ 64, 137 ] has Poincare series 
(x^6+x^5+2*x^4+x^3+2*x^2+x+1)/(x^8-2*x^7+2*x^6-2*x^5+2*x^4- 
2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 138 ] has Poincare series 
(-x^3+x^2+1)/(x^7-3*x^6+3*x^5-x^4-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 139 ] has Poincare series 
(x^7+2*x^5+x^3+x^2+x+1)/(-x^10+2*x^9-x^8+x^2-2*x+1) 
 
Small group [ 64, 140 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 141 ] has Poincare series 
(1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 142 ] has Poincare series 
(1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 143 ] has Poincare series 
(x^2+x+1)/(x^4-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 144 ] has Poincare series 
(x^3+x+1)/(-x^6+2*x^5-x^4+x^2-2*x+1) 
 
Small group [ 64, 145 ] has Poincare series 
(-x^3+x+1)/(-x^6+2*x^5-x^4+x^2-2*x+1) 
 
Small group [ 64, 146 ] has Poincare series 
(x^3+x+1)/(-x^6+2*x^5-x^4+x^2-2*x+1) 
 
Small group [ 64, 147 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 148 ] has Poincare series 
(1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 149 ] has Poincare series 
(1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 150 ] has Poincare series 
(x^3+x+1)/(-x^6+2*x^5-x^4+x^2-2*x+1) 
 
Small group [ 64, 151 ] has Poincare series 
(-x^3+x+1)/(-x^6+2*x^5-x^4+x^2-2*x+1) 
 
Small group [ 64, 152 ] has Poincare series 
(-x^6+x^5+x^4-x^3+1)/(-x^9+3*x^8-4*x^7+4*x^6-4*x^5+4*x^4-4*x^3 
+4*x^2-3*x+1) 
 
Small group [ 64, 153 ] has Poincare series 
(1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 154 ] has Poincare series 
(x^6+x^5+x^2+x+1)/(x^8-2*x^7+2*x^6-2*x^5+2*x^4-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 155 ] has Poincare series 
(1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 156 ] has Poincare series 
(x^4+x^3+x^2+x+1)/(x^6-2*x^5+3*x^4-4*x^3+3*x^2-2*x+1) 
 
Small group [ 64, 157 ] has Poincare series 
(1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 158 ] has Poincare series 
(x^4+x^3+x^2+x+1)/(x^6-2*x^5+3*x^4-4*x^3+3*x^2-2*x+1) 
 
Small group [ 64, 159 ] has Poincare series 
(2*x^3+x+1)/(-x^8+2*x^7-2*x^6+2*x^5-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 160 ] has Poincare series 
(x^4+x^3+x^2+x+1)/(x^6-2*x^5+3*x^4-4*x^3+3*x^2-2*x+1) 
 
Small group [ 64, 161 ] has Poincare series 
(x^3+x+1)/(-x^6+2*x^5-x^4+x^2-2*x+1) 
 
Small group [ 64, 162 ] has Poincare series 
(x^3+x+1)/(-x^6+2*x^5-x^4+x^2-2*x+1) 
 
Small group [ 64, 163 ] has Poincare series 
(2*x^3+x+1)/(-x^8+2*x^7-2*x^6+2*x^5-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 164 ] has Poincare series 
(2*x^3+x+1)/(-x^8+2*x^7-2*x^6+2*x^5-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 165 ] has Poincare series 
(2*x^3+x+1)/(-x^8+2*x^7-2*x^6+2*x^5-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 166 ] has Poincare series 
(-x^4+x^3+1)/(-x^7+3*x^6-5*x^5+7*x^4-7*x^3+5*x^2-3*x+1) 
 
Small group [ 64, 167 ] has Poincare series 
(1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 168 ] has Poincare series 
(x^4+x^3+x^2+x+1)/(x^6-2*x^5+3*x^4-4*x^3+3*x^2-2*x+1) 
 
Small group [ 64, 169 ] has Poincare series 
(-x^4+x^3+1)/(-x^7+3*x^6-5*x^5+7*x^4-7*x^3+5*x^2-3*x+1) 
 
Small group [ 64, 170 ] has Poincare series 
(-x^4+x^3+1)/(-x^7+3*x^6-5*x^5+7*x^4-7*x^3+5*x^2-3*x+1) 
 
Small group [ 64, 171 ] has Poincare series 
(2*x^3+x+1)/(-x^8+2*x^7-2*x^6+2*x^5-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 172 ] has Poincare series 
(x^4+x^3+x^2+x+1)/(x^6-2*x^5+3*x^4-4*x^3+3*x^2-2*x+1) 
 
Small group [ 64, 173 ] has Poincare series 
(1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 174 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 175 ] has Poincare series 
(x^2+x+1)/(x^4-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 176 ] has Poincare series 
(1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 177 ] has Poincare series 
(x^3+x+1)/(-x^6+2*x^5-x^4+x^2-2*x+1) 
 
Small group [ 64, 178 ] has Poincare series 
(-x^3+x+1)/(-x^6+2*x^5-x^4+x^2-2*x+1) 
 
Small group [ 64, 179 ] has Poincare series 
(x^4+x^3+x^2+x+1)/(x^6-2*x^5+3*x^4-4*x^3+3*x^2-2*x+1) 
 
Small group [ 64, 180 ] has Poincare series 
(x^4+x^3+x^2+x+1)/(x^6-2*x^5+3*x^4-4*x^3+3*x^2-2*x+1) 
 
Small group [ 64, 181 ] has Poincare series 
(x^2+x+1)/(x^4-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 182 ] has Poincare series 
(x^4+x^3+x^2+x+1)/(x^6-2*x^5+3*x^4-4*x^3+3*x^2-2*x+1) 
 
Small group [ 64, 183 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 184 ] has Poincare series 
(1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 185 ] has Poincare series 
(x^2+x+1)/(x^4-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 186 ] has Poincare series 
(1)/(-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 187 ] has Poincare series 
(1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 188 ] has Poincare series 
(x^2+x+1)/(x^4-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 189 ] has Poincare series 
(x^2+x+1)/(x^4-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 190 ] has Poincare series 
(1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 191 ] has Poincare series 
(x^6+x^5+x^2+x+1)/(x^8-2*x^7+2*x^6-2*x^5+2*x^4-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 192 ] has Poincare series 
(1)/(x^4-4*x^3+6*x^2-4*x+1) 
 
Small group [ 64, 193 ] has Poincare series 
(1)/(-x^6+4*x^5-5*x^4+5*x^2-4*x+1) 
 
Small group [ 64, 194 ] has Poincare series 
(1)/(x^4-4*x^3+6*x^2-4*x+1) 
 
Small group [ 64, 195 ] has Poincare series 
(1)/(x^6-4*x^5+7*x^4-8*x^3+7*x^2-4*x+1) 
 
Small group [ 64, 196 ] has Poincare series 
(1)/(x^4-4*x^3+6*x^2-4*x+1) 
 
Small group [ 64, 197 ] has Poincare series 
(x^2+x+1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 198 ] has Poincare series 
(x^2+x+1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 200 ] has Poincare series 
(x^2+x+1)/(-x^9+3*x^8-4*x^7+4*x^6-4*x^5+4*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 201 ] has Poincare series 
(x^2+x+1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 202 ] has Poincare series 
(1)/(-x^6+4*x^5-5*x^4+5*x^2-4*x+1) 
 
Small group [ 64, 203 ] has Poincare series 
(1)/(x^4-4*x^3+6*x^2-4*x+1) 
 
Small group [ 64, 204 ] has Poincare series 
(1)/(x^6-4*x^5+7*x^4-8*x^3+7*x^2-4*x+1) 
 
Small group [ 64, 205 ] has Poincare series 
(x^3+x+1)/(x^7-3*x^6+3*x^5-x^4-x^3+3*x^2-3*x+1) 
 
Small group [ 64, 207 ] has Poincare series 
(1)/(x^6-4*x^5+7*x^4-8*x^3+7*x^2-4*x+1) 
 
Small group [ 64, 208 ] has Poincare series 
(x^4+x^3+x^2+x+1)/(-x^7+3*x^6-5*x^5+7*x^4-7*x^3+5*x^2-3*x+1) 
 
Small group [ 64, 209 ] has Poincare series 
(-x^4+x^3+1)/(x^8-4*x^7+8*x^6-12*x^5+14*x^4-12*x^3+8*x^2-4*x+1) 
 
Small group [ 64, 210 ] has Poincare series 
(x^4+x^2+x+1)/(-x^7+3*x^6-5*x^5+7*x^4-7*x^3+5*x^2-3*x+1) 
 
Small group [ 64, 211 ] has Poincare series 
(1)/(x^4-4*x^3+6*x^2-4*x+1) 
 
Small group [ 64, 212 ] has Poincare series 
(x^2+x+1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 214 ] has Poincare series 
(-x^3+x^2+x+1)/(-x^7+3*x^6-5*x^5+7*x^4-7*x^3+5*x^2-3*x+1) 
 
Small group [ 64, 217 ] has Poincare series 
(x^6+x^5+x^2+x+1)/(-x^9+3*x^8-4*x^7+4*x^6-4*x^5+4*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 218 ] has Poincare series 
(x^2+x+1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 217 ] has Poincare series 
(x^6+x^5+x^2+x+1)/(-x^9+3*x^8-4*x^7+4*x^6-4*x^5+4*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 218 ] has Poincare series 
(x^2+x+1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 220 ] has Poincare series 
(x^5+2*x^4+2*x^2+2*x+1)/(-x^8+2*x^7-2*x^6+2*x^5-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 221 ] has Poincare series 
(x^4+x^3+x^2+x+1)/(-x^7+3*x^6-5*x^5+7*x^4-7*x^3+5*x^2-3*x+1) 
 
Small group [ 64, 222 ] has Poincare series 
(-x^4-x^3+x^2+x+1)/(-x^7+3*x^6-5*x^5+7*x^4-7*x^3+5*x^2-3*x+1) 
 
Small group [ 64, 223 ] has Poincare series 
(x^4-x^3+x^2+x+1)/(-x^7+3*x^6-5*x^5+7*x^4-7*x^3+5*x^2-3*x+1) 
 
Small group [ 64, 225 ] has Poincare series 
(-x^3+x^2+x+1)/(-x^7+3*x^6-5*x^5+7*x^4-7*x^3+5*x^2-3*x+1) 
 
Small group [ 64, 226 ] has Poincare series 
(1)/(x^4-4*x^3+6*x^2-4*x+1) 
 
Small group [ 64, 228 ] has Poincare series 
(x^2+x+1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 229 ] has Poincare series 
(x^2+x+1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 230 ] has Poincare series 
(x^2+x+1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 231 ] has Poincare series 
(x^2+x+1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 233 ] has Poincare series 
(x^4-x^3+x^2+x+1)/(-x^7+3*x^6-5*x^5+7*x^4-7*x^3+5*x^2-3*x+1) 
 
Small group [ 64, 234 ] has Poincare series 
(x^4+x^3+x^2+x+1)/(-x^7+3*x^6-5*x^5+7*x^4-7*x^3+5*x^2-3*x+1) 
 
Small group [ 64, 235 ] has Poincare series 
(x^4+x^2+x+1)/(-x^7+3*x^6-5*x^5+7*x^4-7*x^3+5*x^2-3*x+1) 
 
Small group [ 64, 236 ] has Poincare series 
(x^4+x^2+x+1)/(-x^7+3*x^6-5*x^5+7*x^4-7*x^3+5*x^2-3*x+1) 
 
Small group [ 64, 237 ] has Poincare series 
(-x^3+x^2+x+1)/(-x^7+3*x^6-5*x^5+7*x^4-7*x^3+5*x^2-3*x+1) 
 
Small group [ 64, 238 ] has Poincare series 
(x^4+2*x^3+3*x^2+2*x+1)/(x^6-2*x^5+3*x^4-4*x^3+3*x^2-2*x+1) 
 
Small group [ 64, 239 ] has Poincare series 
(x^4+2*x^3+3*x^2+2*x+1)/(x^6-2*x^5+3*x^4-4*x^3+3*x^2-2*x+1) 
 
Small group [ 64, 240 ] has Poincare series 
(x^4+x^2+x+1)/(-x^7+3*x^6-5*x^5+7*x^4-7*x^3+5*x^2-3*x+1) 
 
Small group [ 64, 243 ] has Poincare series 
(x^5+2*x^4+2*x^2+2*x+1)/(-x^8+2*x^7-2*x^6+2*x^5-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 244 ] has Poincare series 
(x^5-2*x^4+2*x^2+2*x+1)/(-x^8+2*x^7-2*x^6+2*x^5-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 245 ] has Poincare series 
(x^12+2*x^11+3*x^10+2*x^9+5*x^8+x^7+9*x^6+x^5+5*x^4+ 
2*x^3+3*x^2+2*x+1)/(x^14-2*x^13+3*x^12-4*x^11+5*x^10-6*x^9+ 
7*x^8-8*x^7+7*x^6-6*x^5+5*x^4-4*x^3+3*x^2-2*x\+1) 
 
Small group [ 64, 246 ] has Poincare series 
(1)/(x^4-4*x^3+6*x^2-4*x+1) 
 
Small group [ 64, 247 ] has Poincare series 
(1)/(x^6-4*x^5+7*x^4-8*x^3+7*x^2-4*x+1) 
 
Small group [ 64, 248 ] has Poincare series 
(x^2+x+1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 249 ] has Poincare series 
(x^2+x+1)/(-x^9+3*x^8-4*x^7+4*x^6-4*x^5+4*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 250 ] has Poincare series 
(1)/(x^4-4*x^3+6*x^2-4*x+1) 
 
Small group [ 64, 251 ] has Poincare series 
(1)/(x^6-4*x^5+7*x^4-8*x^3+7*x^2-4*x+1) 
 
Small group [ 64, 252 ] has Poincare series 
(x^2+x+1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 253 ] has Poincare series 
(x^2+x+1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 254 ] has Poincare series 
(1)/(x^6-4*x^5+7*x^4-8*x^3+7*x^2-4*x+1) 
 
Small group [ 64, 255 ] has Poincare series 
(x^6+x^5+x^2+x+1)/(-x^9+3*x^8-4*x^7+4*x^6-4*x^5+4*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 256 ] has Poincare series 
(x^6+x^5+x^2+x+1)/(-x^9+3*x^8-4*x^7+4*x^6-4*x^5+4*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 257 ] has Poincare series 
(x^2+x+1)/(-x^5+3*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 258 ] has Poincare series 
(x^2+x+1)/(-x^9+3*x^8-4*x^7+4*x^6-4*x^5+4*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 259 ] has Poincare series 
(x^6+2*x^5+3*x^4+3*x^3+3*x^2+2*x+1)/(x^8-2*x^7+2*x^6-2*x^5+ 
2*x^4-2*x^3+2*x^2-2*x+1) 
 
Small group [ 64, 260 ] has Poincare series 
(1)/(-x^5+5*x^4-10*x^3+10*x^2-5*x+1) 
 
Small group [ 64, 261 ] has Poincare series 
(1)/(-x^5+5*x^4-10*x^3+10*x^2-5*x+1) 
 
Small group [ 64, 262 ] has Poincare series 
(x^2+x+1)/(x^6-4*x^5+7*x^4-8*x^3+7*x^2-4*x+1) 
 
Small group [ 64, 263 ] has Poincare series 
(x^2+x+1)/(x^6-4*x^5+7*x^4-8*x^3+7*x^2-4*x+1) 
 
Small group [ 64, 264 ] has Poincare series 
(x^2+x+1)/(x^6-4*x^5+7*x^4-8*x^3+7*x^2-4*x+1) 
 
Small group [ 64, 265 ] has Poincare series 
(x^6+2*x^5+3*x^4+3*x^3+3*x^2+2*x+1)/(-x^9+3*x^8-4*x^7+ 
4*x^6-4*x^5+4*x^4-4*x^3+4*x^2-3*x+1) 
 
Small group [ 64, 267 ] has Poincare series 
(1)/(x^6-6*x^5+15*x^4-20*x^3+15*x^2-6*x+1) 
 </td>
 </tr>
 <tr>
 <td style="vertical-align: top;">
 <table
style="margin-left: auto; margin-right: auto; width: 100%; text-align: left;"
border="0" cellpadding="2" cellspacing="2">
 <tbody>
 <tr>
 <td style="vertical-align: top;"><a
style="color: rgb(0, 0, 102);" href="aboutPoincareSeries.html">Previous
Page</a> 
 </td>
 <td style="text-align: center; vertical-align: top;"><a
href="aboutContents.html">Contents</a> 
 </td>
 <td style="text-align: right; vertical-align: top;"><a
href="aboutTorAndExt.html">Next
page 
 </a> </td>
 </tr>
 </tbody>
 </table>
 <a href="aboutTopology.html"> 
 </a> </td>
 </tr>
 </tbody>
</table>
 
 
</body>
</html>

Messung V0.5 in Prozent

¤ Dauer der Verarbeitung: 0.25 Sekunden (vorverarbeitet am 2026-06-18) ¤

Wurzel

Suchen

PVS Prover

Isabelle Prover

NIST Cobol Testsuite

Cephes Mathematical Library

Vienna Development Method

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung und die Messung sind noch experimentell.