SINGULAR / A Computer Algebra System for Polynomial Computations / version 4.0.3 0< by: W. Decker, G.-M. Greuel, G. Pfister, H. Schoenemann \ Jan 2016 FB Mathematik der Universitaet, D-67653 Kaiserslautern \ chSymm.sng 1> LIB "chern.lib"; // ** loaded chern.lib (0.615,Dec_2015") // ** loaded /usr/bin/../share/singular/LIB/lrcalc.lib (0.91,Dec_2015") // ** loaded /usr/bin/../share/singular/LIB/general.lib (4.0.0.1,Jan_2014) // ** loaded /usr/bin/../share/singular/LIB/matrix.lib (4.0.0.0,Jun_2013) // ** loaded /usr/bin/../share/singular/LIB/nctools.lib (4.0.0.0,Jun_2013) // ** loaded /usr/bin/../share/singular/LIB/random.lib (4.0.0.0,Jun_2013) // ** loaded /usr/bin/../share/singular/LIB/ring.lib (4.0.2.2,Jan_2016) // ** loaded /usr/bin/../share/singular/LIB/primdec.lib (4.0.2.0,Apr_2015) // ** loaded /usr/bin/../share/singular/LIB/absfact.lib (4.0.0.0,Jun_2013) // ** loaded /usr/bin/../share/singular/LIB/triang.lib (4.0.0.0,Jun_2013) // ** loaded /usr/bin/../share/singular/LIB/elim.lib (4.0.0.1,Jan_2014) // ** loaded /usr/bin/../share/singular/LIB/poly.lib (4.0.0.0,Jun_2013) // ** loaded /usr/bin/../share/singular/LIB/inout.lib (4.0.0.0,Jun_2013) chSymm.sng 2> chSymm.sng 3. int N=5; chSymm.sng 4> ring q=0,( c(1..4)), dp; chSymm.sng 5> chSymm.sng 6. list l = c(1..4); chSymm.sng 7> list pos=1,2,3, 4; chSymm.sng 8> chSymm.sng 9. chSymm(2,N,l, pos); [1]: 15 [2]: [1]: 6*c(1) [2]: -c(1)^2-1/2*c(2) [3]: -c(1)^3-31/16*c(1)*c(2)-9/16*c(3) [4]: -c(1)^4-17/3*c(1)^2*c(2)-5/3*c(2)^2-38/9*c(1)*c(3)-13/9*c(4) chSymm.sng 10> chSymm(3,N,l, pos); [1]: 35 [2]: [1]: 21*c(1) [2]: -c(1)^2-4/29*c(2) [3]: -c(1)^3-48/109*c(1)*c(2)-4/109*c(3) [4]: -c(1)^4-761/807*c(1)^2*c(2)-18/269*c(2)^2-406/2421*c(1)*c(3)-41/2421*c(4) chSymm.sng 11> chSymm(4,N,l, pos); [1]: 70 [2]: [1]: 56*c(1) [2]: -c(1)^2-1/18*c(2) [3]: -c(1)^3-1119/6556*c(1)*c(2)-39/6556*c(3) [4]: -c(1)^4-57459/164209*c(1)^2*c(2)-1608/164209*c(2)^2-4110/164209*c(1)*c(3)-177/164209*c(4) chSymm.sng 12> chSymm(5,N,l, pos); [1]: 126 [2]: [1]: 126*c(1) [2]: -c(1)^2-10/371*c(2) [3]: -c(1)^3-4295/52526*c(1)*c(2)-75/52526*c(3) [4]: -c(1)^4-517210/3126907*c(1)^2*c(2)-6985/3126907*c(2)^2-18290/3126907*c(1)*c(3)-400/3126907*c(4) chSymm.sng 13> chSymm(6,N,l, pos); [1]: 210 [2]: [1]: 252*c(1) [2]: -c(1)^2-1/68*c(2) [3]: -c(1)^3-1737/39140*c(1)*c(2)-17/39140*c(3) [4]: -c(1)^4-21322/238795*c(1)^2*c(2)-3137/4775900*c(2)^2-2101/1193975*c(1)*c(3)-26/1193975*c(4) chSymm.sng 14> chSymm(7,N,l, pos); [1]: 330 [2]: [1]: 462*c(1) [2]: -c(1)^2-4/459*c(2) [3]: -c(1)^3-9609/366290*c(1)*c(2)-57/366290*c(3) [4]: -c(1)^4-1456055/27656716*c(1)^2*c(2)-1586/6914179*c(2)^2-4336/6914179*c(1)*c(3)-131/27656716*c(4) chSymm.sng 15> chSymm(8,N,l, pos); [1]: 495 [2]: [1]: 792*c(1) [2]: -c(1)^2-1/182*c(2) [3]: -c(1)^3-787/47644*c(1)*c(2)-3/47644*c(3) [4]: -c(1)^4-616757/18629327*c(1)^2*c(2)-1694/18629327*c(2)^2-4714/18629327*c(1)*c(3)-23/18629327*c(4) chSymm.sng 16> chSymm(9,N,l, pos); [1]: 715 [2]: [1]: 1287*c(1) [2]: -c(1)^2-1/275*c(2) [3]: -c(1)^3-390/35701*c(1)*c(2)-1/35701*c(3) [4]: -c(1)^4-5730811/261941647*c(1)^2*c(2)-947/23812877*c(2)^2-29438/261941647*c(1)*c(3)-97/261941647*c(4) chSymm.sng 17> chSymm.sng 18. quit;Auf Wiedersehen.