i1 : R = QQ[a,b,c,d,e,f][x,y]; |
i2 : F = a*x^2+b*x*y+c*y^2 2 2 o2 = a*x + b*x*y + c*y o2 : R |
i3 : (M,C) = coefficients F o3 = (| x2 xy y2 |, {2, 0} | a |) {2, 0} | b | {2, 0} | c | o3 : Sequence |
i4 : M*C === matrix F o4 = true |
i5 : G = d*x^2+e*x*y+f*y^2 2 2 o5 = d*x + e*x*y + f*y o5 : R |
i6 : P = matrix{{x*F,y*F,x*G,y*G}} o6 = | ax3+bx2y+cxy2 ax2y+bxy2+cy3 dx3+ex2y+fxy2 dx2y+exy2+fy3 | 1 4 o6 : Matrix R <--- R |
i7 : (M,C) = coefficients P o7 = (| x3 x2y xy2 y3 |, {3, 0} | a 0 d 0 |) {3, 0} | b a e d | {3, 0} | c b f e | {3, 0} | 0 c 0 f | o7 : Sequence |
i8 : M*C === P o8 = true |
i9 : (M,C) = coefficients(P, Monomials=>{x^3,y^3,x^2*y,x*y^2}) o9 = (| x3 y3 x2y xy2 |, {3, 0} | a 0 d 0 |) {3, 0} | 0 c 0 f | {3, 0} | b a e d | {3, 0} | c b f e | o9 : Sequence |
i10 : (M,C) = coefficients(P, Monomials=>{x^3,y^3}) o10 = (| x3 y3 |, {3, 0} | a 0 d 0 |) {3, 0} | 0 c 0 f | o10 : Sequence |
i11 : M*C == P o11 = false |
The object coefficients is a method function with options.