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 \ chProd.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) chProd.sng 2> chProd.sng 3. int N=12; chProd.sng 4> ring q=(0, r, R),( c(1..N), C(1..N)), dp; chProd.sng 5> chProd.sng 6. list l= c(1..N); chProd.sng 7> list L=C(1..N); chProd.sng 8> chProd.sng 9. chProd(r, l, R, L, N); [1]: (R)*c(1)+(r)*C(1) [2]: (R^2-R)/2*c(1)^2+(r*R-1)*c(1)*C(1)+(r^2-r)/2*C(1)^2+(R)*c(2)+(r)*C(2) [3]: (R^3-3*R^2+2*R)/6*c(1)^3+(r*R^2-r*R-2*R+2)/2*c(1)^2*C(1)+(r^2*R-r*R-2*r+2)/2*c(1)*C(1)^2+(r^3-3*r^2+2*r)/6*C(1)^3+(R^2-R)*c(1)*c(2)+(r*R-2)*c(2)*C(1)+(r*R-2)*c(1)*C(2)+(r^2-r)*C(1)*C(2)+(R)*c(3)+(r)*C(3) [4]: (R^4-6*R^3+11*R^2-6*R)/24*c(1)^4+(r*R^3-3*r*R^2+2*r*R-3*R^2+9*R-6)/6*c(1)^3*C(1)+(r^2*R^2-r^2*R-r*R^2-3*r*R+4*r+4*R-4)/4*c(1)^2*C(1)^2+(r^3*R-3*r^2*R-3*r^2+2*r*R+9*r-6)/6*c(1)*C(1)^3+(r^4-6*r^3+11*r^2-6*r)/24*C(1)^4+(R^3-3*R^2+2*R)/2*c(1)^2*c(2)+(r*R^2-r*R-3*R+3)*c(1)*c(2)*C(1)+(r^2*R-r*R-4*r+6)/2*c(2)*C(1)^2+(r*R^2-r*R-4*R+6)/2*c(1)^2*C(2)+(r^2*R-r*R-3*r+3)*c(1)*C(1)*C(2)+(r^3-3*r^2+2*r)/2*C(1)^2*C(2)+(R^2-R)/2*c(2)^2+(R^2-R)*c(1)*c(3)+(r*R-3)*c(3)*C(1)+(r*R-6)*c(2)*C(2)+(r^2-r)/2*C(2)^2+(r*R-3)*c(1)*C(3)+(r^2-r)*C(1)*C(3)+(R)*c(4)+(r)*C(4) [5]: (R^5-10*R^4+35*R^3-50*R^2+24*R)/120*c(1)^5+(r*R^4-6*r*R^3+11*r*R^2-6*r*R-4*R^3+24*R^2-44*R+24)/24*c(1)^4*C(1)+(r^2*R^3-3*r^2*R^2+2*r^2*R-r*R^3-3*r*R^2+16*r*R-12*r+6*R^2-18*R+12)/12*c(1)^3*C(1)^2+(r^3*R^2-r^3*R-3*r^2*R^2-3*r^2*R+6*r^2+2*r*R^2+16*r*R-18*r-12*R+12)/12*c(1)^2*C(1)^3+(r^4*R-6*r^3*R-4*r^3+11*r^2*R+24*r^2-6*r*R-44*r+24)/24*c(1)*C(1)^4+(r^5-10*r^4+35*r^3-50*r^2+24*r)/120*C(1)^5+(R^4-6*R^3+11*R^2-6*R)/6*c(1)^3*c(2)+(r*R^3-3*r*R^2+2*r*R-4*R^2+12*R-8)/2*c(1)^2*c(2)*C(1)+(r^2*R^2-r^2*R-r*R^2-5*r*R+6*r+8*R-8)/2*c(1)*c(2)*C(1)^2+(r^3*R-3*r^2*R-6*r^2+2*r*R+24*r-24)/6*c(2)*C(1)^3+(r*R^3-3*r*R^2+2*r*R-6*R^2+24*R-24)/6*c(1)^3*C(2)+(r^2*R^2-r^2*R-r*R^2-5*r*R+8*r+6*R-8)/2*c(1)^2*C(1)*C(2)+(r^3*R-3*r^2*R-4*r^2+2*r*R+12*r-8)/2*c(1)*C(1)^2*C(2)+(r^4-6*r^3+11*r^2-6*r)/6*C(1)^3*C(2)+(R^3-3*R^2+2*R)/2*c(1)*c(2)^2+(R^3-3*R^2+2*R)/2*c(1)^2*c(3)+(r*R^2-r*R-4*R+4)/2*c(2)^2*C(1)+(r*R^2-r*R-4*R+4)*c(1)*c(3)*C(1)+(r^2*R-r*R-6*r+12)/2*c(3)*C(1)^2+(r*R^2-r*R-8*R+12)*c(1)*c(2)*C(2)+(r^2*R-r*R-8*r+12)*c(2)*C(1)*C(2)+(r^2*R-r*R-4*r+4)/2*c(1)*C(2)^2+(r^3-3*r^2+2*r)/2*C(1)*C(2)^2+(r*R^2-r*R-6*R+12)/2*c(1)^2*C(3)+(r^2*R-r*R-4*r+4)*c(1)*C(1)*C(3)+(r^3-3*r^2+2*r)/2*C(1)^2*C(3)+(R^2-R)*c(2)*c(3)+(R^2-R)*c(1)*c(4)+(r*R-4)*c(4)*C(1)+(r*R-12)*c(3)*C(2)+(r*R-12)*c(2)*C(3)+(r^2-r)*C(2)*C(3)+(r*R-4)*c(1)*C(4)+(r^2-r)*C(1)*C(4)+(R)*c(5)+(r)*C(5) [6]: (R^6-15*R^5+85*R^4-225*R^3+274*R^2-120*R)/720*c(1)^6+(r*R^5-10*r*R^4+35*r*R^3-50*r*R^2+24*r*R-5*R^4+50*R^3-175*R^2+250*R-120)/120*c(1)^5*C(1)+(r^2*R^4-6*r^2*R^3+11*r^2*R^2-6*r^2*R-r*R^4-2*r*R^3+37*r*R^2-82*r*R+48*r+8*R^3-48*R^2+88*R-48)/48*c(1)^4*C(1)^2+(r^3*R^3-3*r^3*R^2+2*r^3*R-3*r^2*R^3+21*r^2*R-18*r^2+2*r*R^3+21*r*R^2-77*r*R+54*r-18*R^2+54*R-36)/36*c(1)^3*C(1)^3+(r^4*R^2-r^4*R-6*r^3*R^2-2*r^3*R+8*r^3+11*r^2*R^2+37*r^2*R-48*r^2-6*r*R^2-82*r*R+88*r+48*R-48)/48*c(1)^2*C(1)^4+(r^5*R-10*r^4*R-5*r^4+35*r^3*R+50*r^3-50*r^2*R-175*r^2+24*r*R+250*r-120)/120*c(1)*C(1)^5+(r^6-15*r^5+85*r^4-225*r^3+274*r^2-120*r)/720*C(1)^6+(R^5-10*R^4+35*R^3-50*R^2+24*R)/24*c(1)^4*c(2)+(r*R^4-6*r*R^3+11*r*R^2-6*r*R-5*R^3+30*R^2-55*R+30)/6*c(1)^3*c(2)*C(1)+(r^2*R^3-3*r^2*R^2+2*r^2*R-r*R^3-5*r*R^2+22*r*R-16*r+10*R^2-30*R+20)/4*c(1)^2*c(2)*C(1)^2+(r^3*R^2-r^3*R-3*r^2*R^2-6*r^2*R+9*r^2+2*r*R^2+31*r*R-33*r-30*R+30)/6*c(1)*c(2)*C(1)^3+(r^4*R-6*r^3*R-8*r^3+11*r^2*R+60*r^2-6*r*R-148*r+120)/24*c(2)*C(1)^4+(r*R^4-6*r*R^3+11*r*R^2-6*r*R-8*R^3+60*R^2-148*R+120)/24*c(1)^4*C(2)+(r^2*R^3-3*r^2*R^2+2*r^2*R-r*R^3-6*r*R^2+31*r*R-30*r+9*R^2-33*R+30)/6*c(1)^3*C(1)*C(2)+(r^3*R^2-r^3*R-3*r^2*R^2-5*r^2*R+10*r^2+2*r*R^2+22*r*R-30*r-16*R+20)/4*c(1)^2*C(1)^2*C(2)+(r^4*R-6*r^3*R-5*r^3+11*r^2*R+30*r^2-6*r*R-55*r+30)/6*c(1)*C(1)^3*C(2)+(r^5-10*r^4+35*r^3-50*r^2+24*r)/24*C(1)^4*C(2)+(R^4-6*R^3+11*R^2-6*R)/4*c(1)^2*c(2)^2+(R^4-6*R^3+11*R^2-6*R)/6*c(1)^3*c(3)+(r*R^3-3*r*R^2+2*r*R-5*R^2+15*R-10)/2*c(1)*c(2)^2*C(1)+(r*R^3-3*r*R^2+2*r*R-5*R^2+15*R-10)/2*c(1)^2*c(3)*C(1)+(r^2*R^2-r^2*R-r*R^2-7*r*R+8*r+12*R-12)/4*c(2)^2*C(1)^2+(r^2*R^2-r^2*R-r*R^2-7*r*R+8*r+14*R-14)/2*c(1)*c(3)*C(1)^2+(r^3*R-3*r^2*R-9*r^2+2*r*R+45*r-60)/6*c(3)*C(1)^3+(r*R^3-3*r*R^2+2*r*R-10*R^2+40*R-40)/2*c(1)^2*c(2)*C(2)+(r^2*R^2-r^2*R-r*R^2-10*r*R+15*r+15*R-20)*c(1)*c(2)*C(1)*C(2)+(r^3*R-3*r^2*R-10*r^2+2*r*R+40*r-40)/2*c(2)*C(1)^2*C(2)+(r^2*R^2-r^2*R-r*R^2-7*r*R+12*r+8*R-12)/4*c(1)^2*C(2)^2+(r^3*R-3*r^2*R-5*r^2+2*r*R+15*r-10)/2*c(1)*C(1)*C(2)^2+(r^4-6*r^3+11*r^2-6*r)/4*C(1)^2*C(2)^2+(r*R^3-3*r*R^2+2*r*R-9*R^2+45*R-60)/6*c(1)^3*C(3)+(r^2*R^2-r^2*R-r*R^2-7*r*R+14*r+8*R-14)/2*c(1)^2*C(1)*C(3)+(r^3*R-3*r^2*R-5*r^2+2*r*R+15*r-10)/2*c(1)*C(1)^2*C(3)+(r^4-6*r^3+11*r^2-6*r)/6*C(1)^3*C(3)+(R^3-3*R^2+2*R)/6*c(2)^3+(R^3-3*R^2+2*R)*c(1)*c(2)*c(3)+(R^3-3*R^2+2*R)/2*c(1)^2*c(4)+(r*R^2-r*R-5*R+5)*c(2)*c(3)*C(1)+(r*R^2-r*R-5*R+5)*c(1)*c(4)*C(1)+(r^2*R-r*R-8*r+20)/2*c(4)*C(1)^2+(r*R^2-r*R-12*R+20)/2*c(2)^2*C(2)+(r*R^2-r*R-14*R+20)*c(1)*c(3)*C(2)+(r^2*R-r*R-15*r+30)*c(3)*C(1)*C(2)+(r^2*R-r*R-12*r+20)/2*c(2)*C(2)^2+(r^3-3*r^2+2*r)/6*C(2)^3+(r*R^2-r*R-15*R+30)*c(1)*c(2)*C(3)+(r^2*R-r*R-14*r+20)*c(2)*C(1)*C(3)+(r^2*R-r*R-5*r+5)*c(1)*C(2)*C(3)+(r^3-3*r^2+2*r)*C(1)*C(2)*C(3)+(r*R^2-r*R-8*R+20)/2*c(1)^2*C(4)+(r^2*R-r*R-5*r+5)*c(1)*C(1)*C(4)+(r^3-3*r^2+2*r)/2*C(1)^2*C(4)+(R^2-R)/2*c(3)^2+(R^2-R)*c(2)*c(4)+(R^2-R)*c(1)*c(5)+(r*R-5)*c(5)*C(1)+(r*R-20)*c(4)*C(2)+(r*R-30)*c(3)*C(3)+(r^2-r)/2*C(3)^2+(r*R-20)*c(2)*C(4)+(r^2-r)*C(2)*C(4)+(r*R-5)*c(1)*C(5)+(r^2-r)*C(1)*C(5)+(R)*c(6)+(r)*C(6) [7]: 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^2-r^2*R-r*R^2-9*r*R+18*r+10*R-18)/2*c(1)^2*C(2)*C(3)+(r^3*R-3*r^2*R-6*r^2+2*r*R+18*r-12)*c(1)*C(1)*C(2)*C(3)+(r^4-6*r^3+11*r^2-6*r)/2*C(1)^2*C(2)*C(3)+(r*R^3-3*r*R^2+2*r*R-12*R^2+72*R-120)/6*c(1)^3*C(4)+(r^2*R^2-r^2*R-r*R^2-9*r*R+22*r+10*R-22)/2*c(1)^2*C(1)*C(4)+(r^3*R-3*r^2*R-6*r^2+2*r*R+18*r-12)/2*c(1)*C(1)^2*C(4)+(r^4-6*r^3+11*r^2-6*r)/6*C(1)^3*C(4)+(R^3-3*R^2+2*R)/2*c(2)^2*c(3)+(R^3-3*R^2+2*R)/2*c(1)*c(3)^2+(R^3-3*R^2+2*R)*c(1)*c(2)*c(4)+(R^3-3*R^2+2*R)/2*c(1)^2*c(5)+(r*R^2-r*R-6*R+6)/2*c(3)^2*C(1)+(r*R^2-r*R-6*R+6)*c(2)*c(4)*C(1)+(r*R^2-r*R-6*R+6)*c(1)*c(5)*C(1)+(r^2*R-r*R-10*r+30)/2*c(5)*C(1)^2+(r*R^2-r*R-18*R+30)*c(2)*c(3)*C(2)+(r*R^2-r*R-22*R+30)*c(1)*c(4)*C(2)+(r^2*R-r*R-24*r+60)*c(4)*C(1)*C(2)+(r^2*R-r*R-24*r+60)/2*c(3)*C(2)^2+(r*R^2-r*R-24*R+60)/2*c(2)^2*C(3)+(r*R^2-r*R-33*R+60)*c(1)*c(3)*C(3)+(r^2*R-r*R-33*r+60)*c(3)*C(1)*C(3)+(r^2*R-r*R-18*r+30)*c(2)*C(2)*C(3)+(r^3-3*r^2+2*r)/2*C(2)^2*C(3)+(r^2*R-r*R-6*r+6)/2*c(1)*C(3)^2+(r^3-3*r^2+2*r)/2*C(1)*C(3)^2+(r*R^2-r*R-24*R+60)*c(1)*c(2)*C(4)+(r^2*R-r*R-22*r+30)*c(2)*C(1)*C(4)+(r^2*R-r*R-6*r+6)*c(1)*C(2)*C(4)+(r^3-3*r^2+2*r)*C(1)*C(2)*C(4)+(r*R^2-r*R-10*R+30)/2*c(1)^2*C(5)+(r^2*R-r*R-6*r+6)*c(1)*C(1)*C(5)+(r^3-3*r^2+2*r)/2*C(1)^2*C(5)+(R^2-R)*c(3)*c(4)+(R^2-R)*c(2)*c(5)+(R^2-R)*c(1)*c(6)+(r*R-6)*c(6)*C(1)+(r*R-30)*c(5)*C(2)+(r*R-60)*c(4)*C(3)+(r*R-60)*c(3)*C(4)+(r^2-r)*C(3)*C(4)+(r*R-30)*c(2)*C(5)+(r^2-r)*C(2)*C(5)+(r*R-6)*c(1)*C(6)+(r^2-r)*C(1)*C(6)+(R)*c(7)+(r)*C(7) [8]: 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[9]: 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chProd.sng 10> chProd.sng 11. quit; Auf Wiedersehen.