CoCalc Public Filestmp / 2015-10-28-big-tex.sagewsOpen in with one click!
Authors: Harald Schilly, ℏal Snyder, William A. Stein
() 20ed73b2-ea0b-422a-bdd7-f9d5f704011d a = matrix(3, 3, [1,pi,3, e,5,6, e^2,pi^2,1])^5
show(a)
(6(π+1)(π2e+2e2)+(πe+3e2+1)2+18(2π+π2)(e2+e)+3(2(π+1)(6π2+3e2+1)+2(π+1)(πe+3e2+1)+3(2π+π2)(e+12))e2+3(2(π+1)(6π2+πe2)+(2π+π2)(6π2+πe+25)+(2π+π2)(πe+3e2+1))e3π2(2(π+1)(6π2+3e2+1)+2(π+1)(πe+3e2+1)+3(2π+π2)(e+12))+30(π+1)(6π2+πe2)+15(2π+π2)(6π2+πe+25)+π(6(π+1)(π2e+2e2)+(πe+3e2+1)2+18(2π+π2)(e2+e))+15(2π+π2)(πe+3e2+1)18(π+1)(π2e+2e2)+36(π+1)(6π2+πe2)+18(2π+π2)(6π2+πe+25)+6(π+1)(6π2+3e2+1)+18(2π+π2)(πe+3e2+1)+6(π+1)(πe+3e2+1)+3(πe+3e2+1)2+54(2π+π2)(e2+e)+9(2π+π2)(e+12)6(6π2+πe+25)(e2+e)+6(πe+3e2+1)(e2+e)+3(π2e+2e2)(e+12)+3(12(π+1)(e2+e)+(6π2+πe+25)(e+12)+(6π2+3e2+1)(e+12))e2+((6π2+πe+25)2+18(2π+π2)(e2+e)+3(6π2+πe2)(e+12))e3π2(12(π+1)(e2+e)+(6π2+πe+25)(e+12)+(6π2+3e2+1)(e+12))+5(6π2+πe+25)2+3π(2(6π2+πe+25)(e2+e)+2(πe+3e2+1)(e2+e)+(π2e+2e2)(e+12))+90(2π+π2)(e2+e)+15(6π2+πe2)(e+12)6(6π2+πe+25)2+108(2π+π2)(e2+e)+36(π+1)(e2+e)+18(6π2+πe+25)(e2+e)+18(πe+3e2+1)(e2+e)+9(π2e+2e2)(e+12)+18(6π2+πe2)(e+12)+3(6π2+πe+25)(e+12)+3(6π2+3e2+1)(e+12)(π2e+2e2)(6π2+3e2+1)+(π2e+2e2)(πe+3e2+1)+6(6π2+πe2)(e2+e)+(6(π+1)(π2e+2e2)+(6π2+3e2+1)2+3(6π2+πe2)(e+12))e2+(3(2π+π2)(π2e+2e2)+(6π2+πe2)(6π2+πe+25)+(6π2+πe2)(6π2+3e2+1))eπ2(6(π+1)(π2e+2e2)+(6π2+3e2+1)2+3(6π2+πe2)(e+12))+15(2π+π2)(π2e+2e2)+5(6π2+πe2)(6π2+πe+25)+5(6π2+πe2)(6π2+3e2+1)+π((π2e+2e2)(6π2+3e2+1)+(π2e+2e2)(πe+3e2+1)+6(6π2+πe2)(e2+e))18(2π+π2)(π2e+2e2)+6(π+1)(π2e+2e2)+6(6π2+πe2)(6π2+πe+25)+3(π2e+2e2)(6π2+3e2+1)+6(6π2+πe2)(6π2+3e2+1)+(6π2+3e2+1)2+3(π2e+2e2)(πe+3e2+1)+18(6π2+πe2)(e2+e)+3(6π2+πe2)(e+12))\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)