interface(quiet=true): proposition21 := { a = d1*d3*d2*d4*(d1+d3-d2-d4)+d2*d4*d5*d6*(d2+d4-d5-d6)+d5*d6*d1*d3*(d5+d6-d1-d3)+d5*d6*(d5+d6)*(d1^2-d2^2+d3^2-d4^2)+d1*d3*(d1+d3)*(d2^2+d4^2-d5^2-d6^2)+d2*d4*(d2+d4)*(-d1^2-d3^2+d5^2+d6^2), b = d1*d2*d3*d5*(d1+d2-d3-d5)+d3*d5*d4*d6*(d3+d5-d4-d6)+d4*d6*d1*d2*(d4+d6-d1-d2)+d4*d6*(d4+d6)*(d1^2+d2^2-d3^2-d5^2)+d1*d2*(d1+d2)*(d3^2-d4^2+d5^2-d6^2)+d3*d5*(d3+d5)*(-d1^2-d2^2+d4^2+d6^2), c = d1*d3*d2*d5*(d1+d3-d2-d5)+d2*d5*d4*d6*(d2+d5-d4-d6)+d4*d6*d1*d3*(d4+d6-d1-d3)+d4*d6*(d4+d6)*(d1^2-d2^2+d3^2-d5^2)+d1*d3*(d1+d3)*(d2^2-d4^2+d5^2-d6^2)+d2*d5*(d2+d5)*(-d1^2-d3^2+d4^2+d6^2), d = d1*d2*d3*d4*(d1+d2-d3-d4)+d3*d4*d5*d6*(d3+d4-d5-d6)+d5*d6*d1*d2*(d5+d6-d1-d2)+d5*d6*(d5+d6)*(d1^2+d2^2-d3^2-d4^2)+d1*d2*(d1+d2)*(d3^2+d4^2-d5^2-d6^2)+d3*d4*(d3+d4)*(-d1^2-d2^2+d5^2+d6^2), e = - (d1+d3+d5)*(d2+d4+d6)*(d1-d5)*(d2-d6)*(d3-d4), f = - (d1+d2+d4)*(d3+d5+d6)*(d1-d4)*(d2-d5)*(d3-d6), g = - (d1+d3+d4)*(d2+d5+d6)*(d1-d4)*(d2-d6)*(d3-d5), h = - (d1+d2+d5)*(d3+d4+d6)*(d1-d5)*(d3-d6)*(d2-d4)}: remark22 := {a+b+c+d+e+f+g+h, 4*a^3*b+4*a^3*e+4*a^3*f+9*a^2*b^2+4*a^2*b*c+4*a^2*b*d+20*a^2*b*e+20*a^2*b*f+2*a^2*b*g+4*a^2*c*e+4*a^2*c*f+4*a^2*d*e+4*a^2*d*f+12*a^2*e^2+20*a^2*e*f+4*a^2*e*g+12*a^2*f^2+4*a^2*f*g+a^2*g^2+6*a*b^3+6*a*b^2*c+6*a*b^2*d+22*a*b^2*e+22*a*b^2*f+4*a*b^2*g+4*a*b*c*d+14*a*b*c*e+12*a*b*c*f+2*a*b*c*g+12*a*b*d*e+14*a*b*d*f+2*a*b*d*g+28*a*b*e^2+48*a*b*e*f+10*a*b*e*g+28*a*b*f^2+10*a*b*f*g+2*a*b*g^2+4*a*c*d*e+4*a*c*d*f+8*a*c*e^2+12*a*c*e*f+2*a*c*e*g+8*a*c*f^2+4*a*c*f*g+8*a*d*e^2+12*a*d*e*f+4*a*d*e*g+8*a*d*f^2+2*a*d*f*g+12*a*e^3+28*a*e^2*f+8*a*e^2*g+28*a*e*f^2+12*a*e*f*g+4*a*e*g^2+12*a*f^3+8*a*f^2*g+4*a*f*g^2+b^4+2*b^3*c+2*b^3*d+6*b^3*e+6*b^3*f+2*b^3*g+b^2*c^2+2*b^2*c*d+8*b^2*c*e+6*b^2*c*f+2*b^2*c*g+b^2*d^2+6*b^2*d*e+8*b^2*d*f+2*b^2*d*g+13*b^2*e^2+22*b^2*e*f+6*b^2*e*g+13*b^2*f^2+6*b^2*f*g+b^2*g^2+2*b*c^2*e+6*b*c*d*e+6*b*c*d*f+10*b*c*e^2+14*b*c*e*f+6*b*c*e*g+8*b*c*f^2+4*b*c*f*g+2*b*d^2*f+8*b*d*e^2+14*b*d*e*f+4*b*d*e*g+10*b*d*f^2+6*b*d*f*g+12*b*e^3+28*b*e^2*f+8*b*e^2*g+28*b*e*f^2+12*b*e*f*g+4*b*e*g^2+12*b*f^3+8*b*f^2*g+4*b*f*g^2+c^2*e^2+4*c*d*e^2+6*c*d*e*f+4*c*d*f^2+4*c*e^3+8*c*e^2*f+4*c*e^2*g+8*c*e*f^2+4*c*e*f*g+4*c*f^3+4*c*f^2*g+d^2*f^2+4*d*e^3+8*d*e^2*f+4*d*e^2*g+8*d*e*f^2+4*d*e*f*g+4*d*f^3+4*d*f^2*g+4*e^4+12*e^3*f+4*e^3*g+16*e^2*f^2+8*e^2*f*g+4*e^2*g^2+12*e*f^3+8*e*f^2*g+4*e*f*g^2+4*f^4+4*f^3*g+4*f^2*g^2}: for nn in remark22 do print(factor(subs(proposition21,nn))); od: