CoCalc Public Filestmp / 2015-10-28-big-tex.sagews
Authors: Harald Schilly, ℏal Snyder, William A. Stein
()
︠20ed73b2-ea0b-422a-bdd7-f9d5f704011d︠
a = matrix(3, 3, [1,pi,3, e,5,6, e^2,pi^2,1])^5

show(a)

$\displaystyle \left(\begin{array}{rrr} 6 \, {\left(\pi + 1\right)} {\left(\pi^{2} e + 2 \, e^{2}\right)} + {\left(\pi e + 3 \, e^{2} + 1\right)}^{2} + 18 \, {\left(2 \, \pi + \pi^{2}\right)} {\left(e^{2} + e\right)} + 3 \, {\left(2 \, {\left(\pi + 1\right)} {\left(6 \, \pi^{2} + 3 \, e^{2} + 1\right)} + 2 \, {\left(\pi + 1\right)} {\left(\pi e + 3 \, e^{2} + 1\right)} + 3 \, {\left(2 \, \pi + \pi^{2}\right)} {\left(e + 12\right)}\right)} e^{2} + 3 \, {\left(2 \, {\left(\pi + 1\right)} {\left(6 \, \pi^{2} + \pi e^{2}\right)} + {\left(2 \, \pi + \pi^{2}\right)} {\left(6 \, \pi^{2} + \pi e + 25\right)} + {\left(2 \, \pi + \pi^{2}\right)} {\left(\pi e + 3 \, e^{2} + 1\right)}\right)} e & 3 \, \pi^{2} {\left(2 \, {\left(\pi + 1\right)} {\left(6 \, \pi^{2} + 3 \, e^{2} + 1\right)} + 2 \, {\left(\pi + 1\right)} {\left(\pi e + 3 \, e^{2} + 1\right)} + 3 \, {\left(2 \, \pi + \pi^{2}\right)} {\left(e + 12\right)}\right)} + 30 \, {\left(\pi + 1\right)} {\left(6 \, \pi^{2} + \pi e^{2}\right)} + 15 \, {\left(2 \, \pi + \pi^{2}\right)} {\left(6 \, \pi^{2} + \pi e + 25\right)} + \pi {\left(6 \, {\left(\pi + 1\right)} {\left(\pi^{2} e + 2 \, e^{2}\right)} + {\left(\pi e + 3 \, e^{2} + 1\right)}^{2} + 18 \, {\left(2 \, \pi + \pi^{2}\right)} {\left(e^{2} + e\right)}\right)} + 15 \, {\left(2 \, \pi + \pi^{2}\right)} {\left(\pi e + 3 \, e^{2} + 1\right)} & 18 \, {\left(\pi + 1\right)} {\left(\pi^{2} e + 2 \, e^{2}\right)} + 36 \, {\left(\pi + 1\right)} {\left(6 \, \pi^{2} + \pi e^{2}\right)} + 18 \, {\left(2 \, \pi + \pi^{2}\right)} {\left(6 \, \pi^{2} + \pi e + 25\right)} + 6 \, {\left(\pi + 1\right)} {\left(6 \, \pi^{2} + 3 \, e^{2} + 1\right)} + 18 \, {\left(2 \, \pi + \pi^{2}\right)} {\left(\pi e + 3 \, e^{2} + 1\right)} + 6 \, {\left(\pi + 1\right)} {\left(\pi e + 3 \, e^{2} + 1\right)} + 3 \, {\left(\pi e + 3 \, e^{2} + 1\right)}^{2} + 54 \, {\left(2 \, \pi + \pi^{2}\right)} {\left(e^{2} + e\right)} + 9 \, {\left(2 \, \pi + \pi^{2}\right)} {\left(e + 12\right)} \\ 6 \, {\left(6 \, \pi^{2} + \pi e + 25\right)} {\left(e^{2} + e\right)} + 6 \, {\left(\pi e + 3 \, e^{2} + 1\right)} {\left(e^{2} + e\right)} + 3 \, {\left(\pi^{2} e + 2 \, e^{2}\right)} {\left(e + 12\right)} + 3 \, {\left(12 \, {\left(\pi + 1\right)} {\left(e^{2} + e\right)} + {\left(6 \, \pi^{2} + \pi e + 25\right)} {\left(e + 12\right)} + {\left(6 \, \pi^{2} + 3 \, e^{2} + 1\right)} {\left(e + 12\right)}\right)} e^{2} + {\left({\left(6 \, \pi^{2} + \pi e + 25\right)}^{2} + 18 \, {\left(2 \, \pi + \pi^{2}\right)} {\left(e^{2} + e\right)} + 3 \, {\left(6 \, \pi^{2} + \pi e^{2}\right)} {\left(e + 12\right)}\right)} e & 3 \, \pi^{2} {\left(12 \, {\left(\pi + 1\right)} {\left(e^{2} + e\right)} + {\left(6 \, \pi^{2} + \pi e + 25\right)} {\left(e + 12\right)} + {\left(6 \, \pi^{2} + 3 \, e^{2} + 1\right)} {\left(e + 12\right)}\right)} + 5 \, {\left(6 \, \pi^{2} + \pi e + 25\right)}^{2} + 3 \, \pi {\left(2 \, {\left(6 \, \pi^{2} + \pi e + 25\right)} {\left(e^{2} + e\right)} + 2 \, {\left(\pi e + 3 \, e^{2} + 1\right)} {\left(e^{2} + e\right)} + {\left(\pi^{2} e + 2 \, e^{2}\right)} {\left(e + 12\right)}\right)} + 90 \, {\left(2 \, \pi + \pi^{2}\right)} {\left(e^{2} + e\right)} + 15 \, {\left(6 \, \pi^{2} + \pi e^{2}\right)} {\left(e + 12\right)} & 6 \, {\left(6 \, \pi^{2} + \pi e + 25\right)}^{2} + 108 \, {\left(2 \, \pi + \pi^{2}\right)} {\left(e^{2} + e\right)} + 36 \, {\left(\pi + 1\right)} {\left(e^{2} + e\right)} + 18 \, {\left(6 \, \pi^{2} + \pi e + 25\right)} {\left(e^{2} + e\right)} + 18 \, {\left(\pi e + 3 \, e^{2} + 1\right)} {\left(e^{2} + e\right)} + 9 \, {\left(\pi^{2} e + 2 \, e^{2}\right)} {\left(e + 12\right)} + 18 \, {\left(6 \, \pi^{2} + \pi e^{2}\right)} {\left(e + 12\right)} + 3 \, {\left(6 \, \pi^{2} + \pi e + 25\right)} {\left(e + 12\right)} + 3 \, {\left(6 \, \pi^{2} + 3 \, e^{2} + 1\right)} {\left(e + 12\right)} \\ {\left(\pi^{2} e + 2 \, e^{2}\right)} {\left(6 \, \pi^{2} + 3 \, e^{2} + 1\right)} + {\left(\pi^{2} e + 2 \, e^{2}\right)} {\left(\pi e + 3 \, e^{2} + 1\right)} + 6 \, {\left(6 \, \pi^{2} + \pi e^{2}\right)} {\left(e^{2} + e\right)} + {\left(6 \, {\left(\pi + 1\right)} {\left(\pi^{2} e + 2 \, e^{2}\right)} + {\left(6 \, \pi^{2} + 3 \, e^{2} + 1\right)}^{2} + 3 \, {\left(6 \, \pi^{2} + \pi e^{2}\right)} {\left(e + 12\right)}\right)} e^{2} + {\left(3 \, {\left(2 \, \pi + \pi^{2}\right)} {\left(\pi^{2} e + 2 \, e^{2}\right)} + {\left(6 \, \pi^{2} + \pi e^{2}\right)} {\left(6 \, \pi^{2} + \pi e + 25\right)} + {\left(6 \, \pi^{2} + \pi e^{2}\right)} {\left(6 \, \pi^{2} + 3 \, e^{2} + 1\right)}\right)} e & \pi^{2} {\left(6 \, {\left(\pi + 1\right)} {\left(\pi^{2} e + 2 \, e^{2}\right)} + {\left(6 \, \pi^{2} + 3 \, e^{2} + 1\right)}^{2} + 3 \, {\left(6 \, \pi^{2} + \pi e^{2}\right)} {\left(e + 12\right)}\right)} + 15 \, {\left(2 \, \pi + \pi^{2}\right)} {\left(\pi^{2} e + 2 \, e^{2}\right)} + 5 \, {\left(6 \, \pi^{2} + \pi e^{2}\right)} {\left(6 \, \pi^{2} + \pi e + 25\right)} + 5 \, {\left(6 \, \pi^{2} + \pi e^{2}\right)} {\left(6 \, \pi^{2} + 3 \, e^{2} + 1\right)} + \pi {\left({\left(\pi^{2} e + 2 \, e^{2}\right)} {\left(6 \, \pi^{2} + 3 \, e^{2} + 1\right)} + {\left(\pi^{2} e + 2 \, e^{2}\right)} {\left(\pi e + 3 \, e^{2} + 1\right)} + 6 \, {\left(6 \, \pi^{2} + \pi e^{2}\right)} {\left(e^{2} + e\right)}\right)} & 18 \, {\left(2 \, \pi + \pi^{2}\right)} {\left(\pi^{2} e + 2 \, e^{2}\right)} + 6 \, {\left(\pi + 1\right)} {\left(\pi^{2} e + 2 \, e^{2}\right)} + 6 \, {\left(6 \, \pi^{2} + \pi e^{2}\right)} {\left(6 \, \pi^{2} + \pi e + 25\right)} + 3 \, {\left(\pi^{2} e + 2 \, e^{2}\right)} {\left(6 \, \pi^{2} + 3 \, e^{2} + 1\right)} + 6 \, {\left(6 \, \pi^{2} + \pi e^{2}\right)} {\left(6 \, \pi^{2} + 3 \, e^{2} + 1\right)} + {\left(6 \, \pi^{2} + 3 \, e^{2} + 1\right)}^{2} + 3 \, {\left(\pi^{2} e + 2 \, e^{2}\right)} {\left(\pi e + 3 \, e^{2} + 1\right)} + 18 \, {\left(6 \, \pi^{2} + \pi e^{2}\right)} {\left(e^{2} + e\right)} + 3 \, {\left(6 \, \pi^{2} + \pi e^{2}\right)} {\left(e + 12\right)} \end{array}\right)$