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why I get huge number in H-representation in sage?

asked 2018-09-07 10:55:00 -0500

naghmeh_ms gravatar image

I have a set of vertices and I want to find a H-representation of them. I used sage to do that but I got weird number in the inequalities! here is my code:

vert2 = [[1,2,3,4,2,3,6,0,0,7,6,8,0,1,2,3,4,5,6,7,4,3,2,3,4,1,0,3,0,1],[1,1,2,3,4,2,3,6,0,0,7,6,8,0,1,2,3,4,5,6,7,4,3,2,3,4,1,0,3,0],[0,1,1,2,3,4,2,3,6,0,0,7,6,8,0,1,2,3,4,5,6,7,4,3,2,3,4,1,0,3],[3,0,1,1,2,3,4,2,3,6,0,0,7,6,8,0,1,2,3,4,5,6,7,4,3,2,3,4,1,0],[0,3,0,1,1,2,3,4,2,3,6,0,0,7,6,8,0,1,2,3,4,5,6,7,4,3,2,3,4,1],[1,0,3,0,1,1,2,3,4,2,3,6,0,0,7,6,8,0,1,2,3,4,5,6,7,4,3,2,3,4],[4,1,0,3,0,1,1,2,3,4,2,3,6,0,0,7,6,8,0,1,2,3,4,5,6,7,4,3,2,3],[3,4,1,0,3,0,1,1,2,3,4,2,3,6,0,0,7,6,8,0,1,2,3,4,5,6,7,4,3,2],[2,3,4,1,0,3,0,1,1,2,3,4,2,3,6,0,0,7,6,8,0,1,2,3,4,5,6,7,4,3],[3,2,3,4,1,0,3,0,1,1,2,3,4,2,3,6,0,0,7,6,8,0,1,2,3,4,5,6,7,4],
[4,3,2,3,4,1,0,3,0,1,1,2,3,4,2,3,6,0,0,7,6,8,0,1,2,3,4,5,6,7],[7,4,3,2,3,4,1,0,3,0,1,1,2,3,4,2,3,6,0,0,7,6,8,0,1,2,3,4,5,6],[6,7,4,3,2,3,4,1,0,3,0,1,1,2,3,4,2,3,6,0,0,7,6,8,0,1,2,3,4,5],[5,6,7,4,3,2,3,4,1,0,3,0,1,1,2,3,4,2,3,6,0,0,7,6,8,0,1,2,3,4],[4,5,6,7,4,3,2,3,4,1,0,3,0,1,1,2,3,4,2,3,6,0,0,7,6,8,0,1,2,3],[3,4,5,6,7,4,3,2,3,4,1,0,3,0,1,1,2,3,4,2,3,6,0,0,7,6,8,0,1,2],
[2,3,4,5,6,7,4,3,2,3,4,1,0,3,0,1,1,2,3,4,2,3,6,0,0,7,6,8,0,1],[1,2,3,4,5,6,7,4,3,2,3,4,1,0,3,0,1,1,2,3,4,2,3,6,0,0,7,6,8,0],
[0,1,2,3,4,5,6,7,4,3,2,3,4,1,0,3,0,1,1,2,3,4,2,3,6,0,0,7,6,8],[8,0,1,2,3,4,5,6,7,4,3,2,3,4,1,0,3,0,1,1,2,3,4,2,3,6,0,0,7,6],
[6,8,0,1,2,3,4,5,6,7,4,3,2,3,4,1,0,3,0,1,1,2,3,4,2,3,6,0,0,7],[7,6,8,0,1,2,3,4,5,6,7,4,3,2,3,4,1,0,3,0,1,1,2,3,4,2,3,6,0,0],
[0,7,6,8,0,1,2,3,4,5,6,7,4,3,2,3,4,1,0,3,0,1,1,2,3,4,2,3,6,0],[0,0,7,6,8,0,1,2,3,4,5,6,7,4,3,2,3,4,1,0,3,0,1,1,2,3,4,2,3,6],
[6,0,0,7,6,8,0,1,2,3,4,5,6,7,4,3,2,3,4,1,0,3,0,1,1,2,3,4,2,3],[3,6,0,0,7,6,8,0,1,2,3,4,5,6,7,4,3,2,3,4,1,0,3,0,1,1,2,3,4,2],
     [2,3,6,0,0,7,6,8,0,1,2,3,4,5,6,7,4,3,2,3,4,1,0,3,0,1,1,2,3,4],[4,2,3,6,0,0,7,6,8,0,1,2,3,4,5,6,7,4,3,2,3,4,1,0,3,0,1,1,2,3],
     [3,4,2,3,6,0,0,7,6,8,0,1,2,3,4,5,6,7,4,3,2,3,4,1,0,3,0,1,1,2],[2,3,4,2,3,6,0,0,7,6,8,0,1,2,3,4,5,6,7,4,3,2,3,4,1,0,3,0,1,1]]

p2=Polyhedron(vertices = vert2)
p2
p2.Hrepresentation()

And here is the part of my answer:

 A 29-dimensional polyhedron in ZZ^30 defined as the convex hull of 30 vertices
(An equation (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1) x - 91 == 0, An inequality (0, -6643755617445331037202609358, -1115451987061522518725310169, -4620824246361587837443723580, -3077838211630051976366550554, -2958690652672660811230373721, -974408181934402275593859480, -3250586099217454711737435326, -1999390120369594790625124513, -1415422103472822894852139772, -2534807215524130595973233650, -2780858391260346768723034201, -4072521014492760746645432088, -1331138469264064061646992630, -4722885096499104848736533209, -3180475210961898948969228316, -3851685143879995858104878858, -3228011163515660410829231425, -3072642994521821646580427696, -1374868705058151838371429430, -4889037447034222629220355689, -2510460065219895800789661380, -2297947035840486945050864530, -3657717103544642567050992273, -3458628241192993528820697768, -295584745844116667823309878, -3868958368255490017832885737, -6000440427999093271578675404, 853080186343081392188416198, -2835167870342318913892483281) x + 260907258623794816872847788563 >= 0, An inequality (0, -3688248056685400306080899479, -853080186343081392188416198, -7496835803788412429391025556, -1968532173404603910913726367, -5473904432704669229632139778, -3930918397973133368554966752, -3811770839015742203418789919, -1827488368277483667782275678, -4103666285560536103925851524, -2852470306712676182813540711, -2268502289815904287040555970, -3387887401867211988161649848, -3633938577603428160911450399, -4925601200835842138833848286, -2184218655607145453835408828, -5575965282842186240924949407, -4033555397304980341157644514, -4704765330223077250293295056, -4081091349858741803017647623, -3925723180864903038768843894, -2227948891401233230559845628, -5742117633377304021408771887, -3363540251562977192978077578, -3151027222183568337239280728, -4510797289887723959239408471, -4311708427536074921009113966, -1148664932187198060011726076, -4722038554598571410021301935, -6853520614342174663767091602) x + 338537555581015223561993662581 >= 0,
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answered 2018-09-09 10:08:28 -0500

vdelecroix gravatar image

What do you expect? The transformation from V-representation to H-representation is not a trivial one. This coefficient blowup might already seen when looking at solution to linear equations

sage: M = matrix(5, 6, [[2,1,0,0,0,0],
....:                   [0,2,1,0,0,0],
....:                   [0,0,2,1,0,0],
....:                   [0,0,0,2,1,0],
....:                   [0,0,0,0,2,1]])
sage: M
[2 1 0 0 0 0]
[0 2 1 0 0 0]
[0 0 2 1 0 0]
[0 0 0 2 1 0]
[0 0 0 0 2 1]
sage: M.right_kernel()
Free module of degree 6 and rank 1 over Integer Ring
Echelon basis matrix:
[  1  -2   4  -8  16 -32]
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Asked: 2018-09-07 10:55:00 -0500

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Last updated: Sep 09