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Real embedded number field:
min_poly (a^2 - 5) embedding [2.236067977499789696409173668731 +/- 6.37e-31]
1 vertices of polyhedron
2 extreme rays of recession cone
3 support hyperplanes of polyhedron (homogenized)
embedding dimension = 4
affine dimension of the polyhedron = 2
rank of recession cone = 2
dehomogenization:
0 0 0 1
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1 vertices of polyhedron:
(15/151*a-81/151 ~ -0.31429788) (-27/151*a-126/151 ~ -1.2342638) (-4637/3020*a+7419/15100 ~ -2.9420024) 1
2 extreme rays of recession cone:
(-10000/49999*a+100/49999 ~ -0.44522250) (-22425/49999*a-37275/49999 ~ -1.7484115) -1 0
(10000/49999*a-100/49999 ~ 0.44522250) (-100/149997*a+50000/149997 ~ 0.33184926) 1 0
3 support hyperplanes of polyhedron (homogenized):
(-a+497/300 ~ -0.57940131) (-a ~ -2.2360680) 1 0
0 0 0 1
(3/4*a+9/4 ~ 3.9270510) -1 0 0
1 equations:
1 0 (-10000/49999*a+100/49999 ~ -0.44522250) (100/49999*a-50000/49999 ~ -0.99554778)
3 basis elements of generated space:
1 0 0 (1/500*a+1 ~ 1.0044721)
0 1 0 0
0 0 1 (-1/5*a ~ -0.44721360)
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