1232.sagews

kmat = matrix(SR,[(4, 8, 4, 0, 8, 0), (5, 16, 4, 2, 12, 2), (1/3*sqrt(3) + 3, 8/3*sqrt(3) + 8, sqrt(3) + 1, 2, 4*sqrt(3) + 4, 10/9*sqrt(3)), (sqrt(2) + 2, 6*sqrt(2) + 4, 2*sqrt(2) + 2, 2, 6*sqrt(2) + 4, 2), (6, 24, 6, 4, 24, 4)])
kkernel = kmat.right_kernel().basis()[0]
k6 = kkernel[5]*(12*sqrt(2)+20)

show(k6)

-18 \, \frac{{(3 \, \sqrt{2} + 5)}}{{(\frac{{(4 \, \frac{{(\sqrt{3} - 2)}}{{(3 \, \sqrt{3} - 5)}} - 1)} {(5 \, \frac{{(2 \, \sqrt{3} - 3)} \sqrt{2}}{{(3 \, \sqrt{3} - 5)}} + 6 \, \sqrt{2} - 9)}}{{(5 \, \frac{{(\sqrt{3} - 2)} \sqrt{2}}{{(3 \, \sqrt{3} - 5)}} - 2 \, \sqrt{2} + 3)}} - \frac{{(\frac{{(\sqrt{3} - 2)} {(5 \, \frac{{(2 \, \sqrt{3} - 3)} \sqrt{2}}{{(3 \, \sqrt{3} - 5)}} + 6 \, \sqrt{2} - 9)}}{{(3 \, \sqrt{3} - 5)} {(5 \, \frac{{(\sqrt{3} - 2)} \sqrt{2}}{{(3 \, \sqrt{3} - 5)}} - 2 \, \sqrt{2} + 3)}} - \frac{{(2 \, \sqrt{3} - 3)}}{{(3 \, \sqrt{3} - 5)}})} {(2 \, \frac{{(4 \, \frac{{(\sqrt{3} - 2)}}{{(3 \, \sqrt{3} - 5)}} - 1)} {(5 \, \frac{{(\sqrt{3} - 1)} \sqrt{2}}{{(3 \, \sqrt{3} - 5)}} - \sqrt{2})}}{{(5 \, \frac{{(\sqrt{3} - 2)} \sqrt{2}}{{(3 \, \sqrt{3} - 5)}} - 2 \, \sqrt{2} + 3)}} - 8 \, \frac{{(\sqrt{3} - 1)}}{{(3 \, \sqrt{3} - 5)}} + 1)}}{{(2 \, \frac{{(\sqrt{3} - 2)} {(5 \, \frac{{(\sqrt{3} - 1)} \sqrt{2}}{{(3 \, \sqrt{3} - 5)}} - \sqrt{2})}}{{(3 \, \sqrt{3} - 5)} {(5 \, \frac{{(\sqrt{3} - 2)} \sqrt{2}}{{(3 \, \sqrt{3} - 5)}} - 2 \, \sqrt{2} + 3)}} - 2 \, \frac{{(\sqrt{3} - 1)}}{{(3 \, \sqrt{3} - 5)}} + 1)}} - 4 \, \frac{{(2 \, \sqrt{3} - 3)}}{{(3 \, \sqrt{3} - 5)}} - 3)}}

N(k6)

139.406088405362

N(k6.simplify_rational())

6.00000000000000

var('a,b')
k6sub = str(k6).replace('sqrt(2)','a').replace('sqrt(3)','b')
k6sub = SR(k6sub)
k6sub = k6sub.simplify_rational()

N(k6sub.subs({a:sqrt(2),b:sqrt(3)}))

139.406088405362

import sympy as S

k6sym = SR(str(S.simplify(k6)).replace('**','^'))
N(k6sym)

24.0000000000000