#Density : 4121063416332321009068756828281/16000000000000000000000000000000

Program                      : VertexInducedHypercubeDensityChecker

Dimension of subcubes H      : 4
Number of induced hypercubes : 1
Induced hypercubes           :
4 : {5, 6, 9, 10, 13, 14}
Number of terms              : 19


--- Term 1 ---

Dimension of type  : 0
Dimension of flags : 2
Number of flags    : 6
Matrix dimension   : 6

Flags :
F1 : {0}
F2 : {0, 2}
F3 : {0, 3}
F4 : {0, 2, 3}
F5 : {0, 1, 2}
F6 : {0, 1, 2, 3}

Basis :
B1 : (F1)
B2 : (F2)
B3 : (F3)
B4 : (F4)
B5 : (F5)
B6 : (F6)

Matrix :
0/1 0/1 0/1 0/1 0/1 0/1
0/1 6904024205602755842637015483/500000000000000000000000000000 0/1 -2493768059562148510362297609/125000000000000000000000000000 -19950144479372046656083264209/500000000000000000000000000000 8386079243360123183544798951/250000000000000000000000000000
0/1 0/1 0/1 0/1 0/1 0/1
0/1 -2493768059562148510362297609/125000000000000000000000000000 0/1 900761490645646458755249507/31250000000000000000000000000 7206091926203584959460781307/125000000000000000000000000000 -3029093748697652636480251373/62500000000000000000000000000
0/1 -19950144479372046656083264209/500000000000000000000000000000 0/1 7206091926203584959460781307/125000000000000000000000000000 57648735417935985992233633107/500000000000000000000000000000 -24232749993073212297292431573/250000000000000000000000000000
0/1 8386079243360123183544798951/250000000000000000000000000000 0/1 -3029093748697652636480251373/62500000000000000000000000000 -24232749993073212297292431573/250000000000000000000000000000 10186280201457615870548586947/125000000000000000000000000000


--- Term 2 ---

Dimension of type  : 0
Dimension of flags : 2
Number of flags    : 6
Matrix dimension   : 6

Flags :
F1 : {}
F2 : {2}
F3 : {3}
F4 : {2, 3}
F5 : {1, 2}
F6 : {1, 2, 3}

Basis :
B1 : (F1)
B2 : (F2)
B3 : (F3)
B4 : (F4)
B5 : (F5)
B6 : (F6)

Matrix :
0/1 0/1 0/1 0/1 0/1 0/1
0/1 0/1 0/1 0/1 0/1 0/1
0/1 0/1 0/1 0/1 0/1 0/1
0/1 0/1 0/1 0/1 0/1 0/1
0/1 0/1 0/1 0/1 0/1 0/1
0/1 0/1 0/1 0/1 0/1 0/1


--- Term 3 ---

Dimension of type  : 1
Dimension of flags : 2
Number of flags    : 4
Matrix dimension   : 4

Flags :
F1 : {1}
F2 : {1, 2}
F3 : {1, 3}
F4 : {1, 2, 3}

Basis :
B1 : (F1)
B2 : (F2)
B3 : (F3)
B4 : (F4)

Matrix :
0/1 0/1 0/1 0/1
0/1 0/1 0/1 0/1
0/1 0/1 0/1 0/1
0/1 0/1 0/1 0/1


--- Term 4 ---

Dimension of type  : 1
Dimension of flags : 2
Number of flags    : 4
Matrix dimension   : 3

Flags :
F1 : {0, 1}
F2 : {0, 1, 2}
F3 : {0, 1, 3}
F4 : {0, 1, 2, 3}

Basis :
B1 : (F1)
B2 : (F2)+(F3)
B3 : (F4)

Matrix :
797821197045427071001292643/62500000000000000000000000000 -922166416058042076799793751/50000000000000000000000000000 3876343176054510792259603623/250000000000000000000000000000
-922166416058042076799793751/50000000000000000000000000000 1065891583295340335822960507/40000000000000000000000000000 -4480494510939523839185385611/200000000000000000000000000000
3876343176054510792259603623/250000000000000000000000000000 -4480494510939523839185385611/200000000000000000000000000000 18833839554765309005082037403/1000000000000000000000000000000


--- Term 5 ---

Dimension of type  : 1
Dimension of flags : 2
Number of flags    : 2
Matrix dimension   : 1

Flags :
F1 : {0, 1, 2}
F2 : {0, 1, 3}

Basis :
B1 : (F2)-(F1)

Matrix :
0/1


--- Term 6 ---

Dimension of type  : 1
Dimension of flags : 2
Number of flags    : 4
Matrix dimension   : 3

Flags :
F1 : {}
F2 : {2}
F3 : {3}
F4 : {2, 3}

Basis :
B1 : (F1)
B2 : (F2)+(F3)
B3 : (F4)

Matrix :
0/1 0/1 0/1
0/1 0/1 0/1
0/1 0/1 0/1


--- Term 7 ---

Dimension of type  : 1
Dimension of flags : 2
Number of flags    : 2
Matrix dimension   : 1

Flags :
F1 : {2}
F2 : {3}

Basis :
B1 : (F2)-(F1)

Matrix :
0/1


--- Term 8 ---

Dimension of type  : 2
Dimension of flags : 3
Number of flags    : 16
Matrix dimension   : 12

Flags :
F1  : {3}
F2  : {3, 4}
F3  : {3, 5}
F4  : {3, 4, 5}
F5  : {3, 6}
F6  : {3, 4, 6}
F7  : {3, 5, 6}
F8  : {3, 4, 5, 6}
F9  : {3, 7}
F10 : {3, 4, 7}
F11 : {3, 5, 7}
F12 : {3, 4, 5, 7}
F13 : {3, 6, 7}
F14 : {3, 4, 6, 7}
F15 : {3, 5, 6, 7}
F16 : {3, 4, 5, 6, 7}

Basis :
B1  : (F1)
B2  : (F2)
B3  : (F3)+(F5)
B4  : (F4)+(F6)
B5  : (F7)
B6  : (F8)
B7  : (F9)
B8  : (F10)
B9  : (F11)+(F13)
B10 : (F12)+(F14)
B11 : (F15)
B12 : (F16)

Matrix :
36627605274855546281665706329/40000000000000000000000000000 408809834340356258926006418597/500000000000000000000000000000 275479039145092059341693054241/250000000000000000000000000000 104079815546137804942700028299/125000000000000000000000000000 176806271169416250952284669009/500000000000000000000000000000 78514059550574755624514178573/250000000000000000000000000000 27503599582887771987776438143/250000000000000000000000000000 -177359359728843622295433004139/500000000000000000000000000000 -523688057661811763393786370997/200000000000000000000000000000 140659967061265738501938293213/1000000000000000000000000000000 -130001741503885970819949106057/62500000000000000000000000000 -602292997339156941008323843469/1000000000000000000000000000000
408809834340356258926006418597/500000000000000000000000000000 737165097031315105679801120923/1000000000000000000000000000000 98917124215100091077700546921/100000000000000000000000000000 746611513443047308039411714279/1000000000000000000000000000000 162714916964869138025893282593/500000000000000000000000000000 281497500193915982965890891513/1000000000000000000000000000000 97148715487233938011937648611/1000000000000000000000000000000 -319596275885340214791465764557/1000000000000000000000000000000 -1175490166403736856916468338933/500000000000000000000000000000 126274564404176587149599026571/1000000000000000000000000000000 -1873004137910292814649064574777/1000000000000000000000000000000 -269136525170091683905356653431/500000000000000000000000000000
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--- Term 9 ---

Dimension of type  : 2
Dimension of flags : 3
Number of flags    : 8
Matrix dimension   : 4

Flags :
F1 : {3, 5}
F2 : {3, 4, 5}
F3 : {3, 6}
F4 : {3, 4, 6}
F5 : {3, 5, 7}
F6 : {3, 4, 5, 7}
F7 : {3, 6, 7}
F8 : {3, 4, 6, 7}

Basis :
B1 : (F3)-(F1)
B2 : (F4)-(F2)
B3 : (F7)-(F5)
B4 : (F8)-(F6)

Matrix :
105678893574137781789456656711/200000000000000000000000000000 -308267654479602657248259204137/1000000000000000000000000000000 15850362921339779029535669539/25000000000000000000000000000 -74506673227816436492249596121/1000000000000000000000000000000
-308267654479602657248259204137/1000000000000000000000000000000 505699902792952481238842874407/250000000000000000000000000000 -92471713790225184649259068223/250000000000000000000000000000 26049293563915632601903100863/62500000000000000000000000000
15850362921339779029535669539/25000000000000000000000000000 -92471713790225184649259068223/250000000000000000000000000000 2377333791462650394159367667/3125000000000000000000000000 -22349927631681730241578380269/250000000000000000000000000000
-74506673227816436492249596121/1000000000000000000000000000000 26049293563915632601903100863/62500000000000000000000000000 -22349927631681730241578380269/250000000000000000000000000000 173130543185050357263342007357/62500000000000000000000000000


--- Term 10 ---

Dimension of type  : 2
Dimension of flags : 3
Number of flags    : 16
Matrix dimension   : 10

Flags :
F1  : {2, 3}
F2  : {2, 3, 4}
F3  : {2, 3, 5}
F4  : {2, 3, 4, 5}
F5  : {2, 3, 6}
F6  : {2, 3, 4, 6}
F7  : {2, 3, 5, 6}
F8  : {2, 3, 4, 5, 6}
F9  : {2, 3, 7}
F10 : {2, 3, 4, 7}
F11 : {2, 3, 5, 7}
F12 : {2, 3, 4, 5, 7}
F13 : {2, 3, 6, 7}
F14 : {2, 3, 4, 6, 7}
F15 : {2, 3, 5, 6, 7}
F16 : {2, 3, 4, 5, 6, 7}

Basis :
B1  : (F1)
B2  : (F2)+(F3)
B3  : (F4)
B4  : (F5)+(F9)
B5  : (F6)+(F11)
B6  : (F7)+(F10)
B7  : (F8)+(F12)
B8  : (F13)
B9  : (F14)+(F15)
B10 : (F16)

Matrix :
759351059783137551217791862711/500000000000000000000000000000 -23029001281769392000306705803/500000000000000000000000000000 -221249196080769952595308027479/250000000000000000000000000000 43993363662729649969459746429/40000000000000000000000000000 -49496554458939866990179598457/500000000000000000000000000000 -76264296314889518368213424851/1000000000000000000000000000000 -218619777597498380270000607467/1000000000000000000000000000000 -1855477838258299632046346289/10000000000000000000000000000 -313681605582936497880511947553/1000000000000000000000000000000 -86254163613756544233490090361/200000000000000000000000000000
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--- Term 11 ---

Dimension of type  : 2
Dimension of flags : 3
Number of flags    : 12
Matrix dimension   : 6

Flags :
F1  : {2, 3, 4}
F2  : {2, 3, 5}
F3  : {2, 3, 6}
F4  : {2, 3, 4, 6}
F5  : {2, 3, 5, 6}
F6  : {2, 3, 4, 5, 6}
F7  : {2, 3, 7}
F8  : {2, 3, 4, 7}
F9  : {2, 3, 5, 7}
F10 : {2, 3, 4, 5, 7}
F11 : {2, 3, 4, 6, 7}
F12 : {2, 3, 5, 6, 7}

Basis :
B1 : (F2)-(F1)
B2 : (F7)-(F3)
B3 : (F9)-(F4)
B4 : (F8)-(F5)
B5 : (F10)-(F6)
B6 : (F12)-(F11)

Matrix :
569760849662391318075804171923/1000000000000000000000000000000 214389669859511728836563492297/500000000000000000000000000000 145887310346020667360837834447/1000000000000000000000000000000 54445073504595639250265167473/250000000000000000000000000000 11189035341588689711619761069/200000000000000000000000000000 27297990991247000933137612381/200000000000000000000000000000
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--- Term 12 ---

Dimension of type  : 2
Dimension of flags : 3
Number of flags    : 16
Matrix dimension   : 9

Flags :
F1  : {1, 2}
F2  : {1, 2, 4}
F3  : {1, 2, 5}
F4  : {1, 2, 4, 5}
F5  : {1, 2, 6}
F6  : {1, 2, 4, 6}
F7  : {1, 2, 5, 6}
F8  : {1, 2, 4, 5, 6}
F9  : {1, 2, 7}
F10 : {1, 2, 4, 7}
F11 : {1, 2, 5, 7}
F12 : {1, 2, 4, 5, 7}
F13 : {1, 2, 6, 7}
F14 : {1, 2, 4, 6, 7}
F15 : {1, 2, 5, 6, 7}
F16 : {1, 2, 4, 5, 6, 7}

Basis :
B1 : (F1)
B2 : (F2)+(F9)
B3 : (F3)+(F5)
B4 : (F4)+(F6)+(F11)+(F13)
B5 : (F7)
B6 : (F8)+(F15)
B7 : (F10)
B8 : (F12)+(F14)
B9 : (F16)

Matrix :
123732751849023098841023100489/125000000000000000000000000000 1015558365332194537092492461741/1000000000000000000000000000000 100959393882585974554866445477/1000000000000000000000000000000 4206473126820435746032960009/50000000000000000000000000000 -29993442760754922372132932299/15625000000000000000000000000 -177495247778509904525547127763/1000000000000000000000000000000 708651058970966568959160869693/1000000000000000000000000000000 -161226684965699020375345999351/250000000000000000000000000000 -2355665493290261864568914803093/1000000000000000000000000000000
1015558365332194537092492461741/1000000000000000000000000000000 1043350848965636504027104324909/1000000000000000000000000000000 104160047803628334775751908461/1000000000000000000000000000000 86043872170257735255172846069/1000000000000000000000000000000 -767067526344833763144179413/390625000000000000000000000 -22877788680185867329363495597/125000000000000000000000000000 723707927171748443663530093341/1000000000000000000000000000000 -165392559683986441043902492527/250000000000000000000000000000 -2416276872944047488757419816679/1000000000000000000000000000000
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--- Term 13 ---

Dimension of type  : 2
Dimension of flags : 3
Number of flags    : 12
Matrix dimension   : 7

Flags :
F1  : {1, 2, 4}
F2  : {1, 2, 5}
F3  : {1, 2, 4, 5}
F4  : {1, 2, 6}
F5  : {1, 2, 4, 6}
F6  : {1, 2, 4, 5, 6}
F7  : {1, 2, 7}
F8  : {1, 2, 5, 7}
F9  : {1, 2, 4, 5, 7}
F10 : {1, 2, 6, 7}
F11 : {1, 2, 4, 6, 7}
F12 : {1, 2, 5, 6, 7}

Basis :
B1 : (F7)-(F1)
B2 : (F4)-(F2)
B3 : (F5)-(F3)
B4 : (F8)-(F3)
B5 : (F10)-(F3)
B6 : (F12)-(F6)
B7 : (F11)-(F9)

Matrix :
43981020118707067301881945227/500000000000000000000000000000 130432631785094824627/1000000000000000000000000000000 -196597174621714252745183757/1000000000000000000000000000000 49149330283160612824937003/250000000000000000000000000000 98298604141050743303177421/500000000000000000000000000000 -870746042150526162890839953/250000000000000000000000000000 123099439254241019341/1000000000000000000000000000000
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--- Term 14 ---

Dimension of type  : 2
Dimension of flags : 3
Number of flags    : 16
Matrix dimension   : 12

Flags :
F1  : {1, 2, 3}
F2  : {1, 2, 3, 4}
F3  : {1, 2, 3, 5}
F4  : {1, 2, 3, 4, 5}
F5  : {1, 2, 3, 6}
F6  : {1, 2, 3, 4, 6}
F7  : {1, 2, 3, 5, 6}
F8  : {1, 2, 3, 4, 5, 6}
F9  : {1, 2, 3, 7}
F10 : {1, 2, 3, 4, 7}
F11 : {1, 2, 3, 5, 7}
F12 : {1, 2, 3, 4, 5, 7}
F13 : {1, 2, 3, 6, 7}
F14 : {1, 2, 3, 4, 6, 7}
F15 : {1, 2, 3, 5, 6, 7}
F16 : {1, 2, 3, 4, 5, 6, 7}

Basis :
B1  : (F1)
B2  : (F2)
B3  : (F3)+(F5)
B4  : (F4)+(F6)
B5  : (F7)
B6  : (F8)
B7  : (F9)
B8  : (F10)
B9  : (F11)+(F13)
B10 : (F12)+(F14)
B11 : (F15)
B12 : (F16)

Matrix :
71498138734668576635413159287/100000000000000000000000000000 120058104582350240020975438537/250000000000000000000000000000 47194396409539212427453685891/100000000000000000000000000000 99193898036255688817217572929/250000000000000000000000000000 602415625628132404568485644019/500000000000000000000000000000 4516356489554162059007820153/50000000000000000000000000000 -21113740227456194003693311913/10000000000000000000000000000 -846015837193855288135423289601/500000000000000000000000000000 199875658912417613688088081763/500000000000000000000000000000 -87836145369436788815406164693/100000000000000000000000000000 694293605613537563599408394919/500000000000000000000000000000 25713782824269247855122911927/62500000000000000000000000000
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--- Term 15 ---

Dimension of type  : 2
Dimension of flags : 3
Number of flags    : 8
Matrix dimension   : 4

Flags :
F1 : {1, 2, 3, 5}
F2 : {1, 2, 3, 4, 5}
F3 : {1, 2, 3, 6}
F4 : {1, 2, 3, 4, 6}
F5 : {1, 2, 3, 5, 7}
F6 : {1, 2, 3, 4, 5, 7}
F7 : {1, 2, 3, 6, 7}
F8 : {1, 2, 3, 4, 6, 7}

Basis :
B1 : (F3)-(F1)
B2 : (F4)-(F2)
B3 : (F7)-(F5)
B4 : (F8)-(F6)

Matrix :
1372602381732701219950966710449/500000000000000000000000000000 -71382791471558573058793386003/1000000000000000000000000000000 229805930559956452842496059187/1000000000000000000000000000000 14610687394681766624553745343/62500000000000000000000000000
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229805930559956452842496059187/1000000000000000000000000000000 269987556251061874171101550163/1000000000000000000000000000000 2716184896652558915176936269289/1000000000000000000000000000000 2622737352550438826227031377633/1000000000000000000000000000000
14610687394681766624553745343/62500000000000000000000000000 286034566896057161647088745697/1000000000000000000000000000000 2622737352550438826227031377633/1000000000000000000000000000000 306794717397699958861417452087/100000000000000000000000000000


--- Term 16 ---

Dimension of type  : 2
Dimension of flags : 3
Number of flags    : 16
Matrix dimension   : 6

Flags :
F1  : {0, 1, 2, 3}
F2  : {0, 1, 2, 3, 4}
F3  : {0, 1, 2, 3, 5}
F4  : {0, 1, 2, 3, 4, 5}
F5  : {0, 1, 2, 3, 6}
F6  : {0, 1, 2, 3, 4, 6}
F7  : {0, 1, 2, 3, 5, 6}
F8  : {0, 1, 2, 3, 4, 5, 6}
F9  : {0, 1, 2, 3, 7}
F10 : {0, 1, 2, 3, 4, 7}
F11 : {0, 1, 2, 3, 5, 7}
F12 : {0, 1, 2, 3, 4, 5, 7}
F13 : {0, 1, 2, 3, 6, 7}
F14 : {0, 1, 2, 3, 4, 6, 7}
F15 : {0, 1, 2, 3, 5, 6, 7}
F16 : {0, 1, 2, 3, 4, 5, 6, 7}

Basis :
B1 : (F1)
B2 : (F2)+(F3)+(F5)+(F9)
B3 : (F4)+(F6)+(F11)+(F13)
B4 : (F7)+(F10)
B5 : (F8)+(F12)+(F14)+(F15)
B6 : (F16)

Matrix :
4965822171706837563342192669/15625000000000000000000000000 211146060929466378519249110727/1000000000000000000000000000000 11387653912365244237828963461/250000000000000000000000000000 -334003999194052706431535238087/1000000000000000000000000000000 -168831066367773500399386575597/500000000000000000000000000000 37668045164083816715444744889/500000000000000000000000000000
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--- Term 17 ---

Dimension of type  : 2
Dimension of flags : 3
Number of flags    : 14
Matrix dimension   : 10

Flags :
F1  : {0, 1, 2, 3, 4}
F2  : {0, 1, 2, 3, 5}
F3  : {0, 1, 2, 3, 4, 5}
F4  : {0, 1, 2, 3, 6}
F5  : {0, 1, 2, 3, 4, 6}
F6  : {0, 1, 2, 3, 5, 6}
F7  : {0, 1, 2, 3, 4, 5, 6}
F8  : {0, 1, 2, 3, 7}
F9  : {0, 1, 2, 3, 4, 7}
F10 : {0, 1, 2, 3, 5, 7}
F11 : {0, 1, 2, 3, 4, 5, 7}
F12 : {0, 1, 2, 3, 6, 7}
F13 : {0, 1, 2, 3, 4, 6, 7}
F14 : {0, 1, 2, 3, 5, 6, 7}

Basis :
B1  : (F2)-(F1)
B2  : (F4)-(F1)
B3  : (F8)-(F1)
B4  : (F5)-(F3)
B5  : (F10)-(F3)
B6  : (F12)-(F3)
B7  : (F9)-(F6)
B8  : (F11)-(F7)
B9  : (F13)-(F7)
B10 : (F14)-(F7)

Matrix :
423816868613422874771971052599/500000000000000000000000000000 -309695387644237855027693946087/500000000000000000000000000000 -5706074055845097099493249781/50000000000000000000000000000 -3688923334978165419345147889/500000000000000000000000000000 7377846678636834108949943919/1000000000000000000000000000000 -737784670829765611689220647/100000000000000000000000000000 0/1 -30296983758791676790592833687/200000000000000000000000000000 30296983758791676790592833687/200000000000000000000000000000 -10918747967392881/25000000000000000000000000000
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--- Term 18 ---

Dimension of type  : 2
Dimension of flags : 3
Number of flags    : 16
Matrix dimension   : 6

Flags :
F1  : {}
F2  : {4}
F3  : {5}
F4  : {4, 5}
F5  : {6}
F6  : {4, 6}
F7  : {5, 6}
F8  : {4, 5, 6}
F9  : {7}
F10 : {4, 7}
F11 : {5, 7}
F12 : {4, 5, 7}
F13 : {6, 7}
F14 : {4, 6, 7}
F15 : {5, 6, 7}
F16 : {4, 5, 6, 7}

Basis :
B1 : (F1)
B2 : (F2)+(F3)+(F5)+(F9)
B3 : (F4)+(F6)+(F11)+(F13)
B4 : (F7)+(F10)
B5 : (F8)+(F12)+(F14)+(F15)
B6 : (F16)

Matrix :
8048951978948060145494383341/31250000000000000000000000000 1359442142167199960015539791/5000000000000000000000000000 -6254024933727208572510318657/62500000000000000000000000000 -31652158906761572387285933487/125000000000000000000000000000 -32391414372304803959755960539/125000000000000000000000000000 -6441615108047352712886822631/25000000000000000000000000000
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--- Term 19 ---

Dimension of type  : 2
Dimension of flags : 3
Number of flags    : 14
Matrix dimension   : 10

Flags :
F1  : {4}
F2  : {5}
F3  : {4, 5}
F4  : {6}
F5  : {4, 6}
F6  : {5, 6}
F7  : {4, 5, 6}
F8  : {7}
F9  : {4, 7}
F10 : {5, 7}
F11 : {4, 5, 7}
F12 : {6, 7}
F13 : {4, 6, 7}
F14 : {5, 6, 7}

Basis :
B1  : (F2)-(F1)
B2  : (F4)-(F1)
B3  : (F8)-(F1)
B4  : (F5)-(F3)
B5  : (F10)-(F3)
B6  : (F12)-(F3)
B7  : (F9)-(F6)
B8  : (F11)-(F7)
B9  : (F13)-(F7)
B10 : (F14)-(F7)

Matrix :
24886619460449745535017317/31250000000000000000000000000 -24886619460449745535017317/31250000000000000000000000000 501452299470479/7812500000000000000000000000 -11237055235112034097761227/500000000000000000000000000000 5618528550547997966891429/250000000000000000000000000000 -11237041730615390348184051/500000000000000000000000000000 0/1 81556337810841033868617257/1000000000000000000000000000000 -81556337810841033868617257/1000000000000000000000000000000 -9913697267772637/1000000000000000000000000000000
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