{OrePolynomial[{{1 + s^2 + 2*t^2 + 2*s^2*t^2 + t^4 + s^2*t^4, {0, 0, 0, 1}}, 
   {-4*b*m11*s*s1 + 2*b*m21*s2 - 4*d*m22*s*s2 - 2*b*m21*s^2*s2 + 2*t + 
     2*s^2*t + 4*d*m11*s1*t - 4*d*m11*s^2*s1*t + 4*b*m22*s2*t + 
     8*d*m21*s*s2*t - 4*b*m22*s^2*s2*t + 4*b*m11*s*s1*t^2 - 2*b*m21*s2*t^2 + 
     4*d*m22*s*s2*t^2 + 2*b*m21*s^2*s2*t^2 + 2*t^3 + 2*s^2*t^3, 
    {0, 0, 0, 0}}}, OreAlgebraObject[{Der[d], Der[b], Der[s], Der[t]}, 
   Expand, #1 + #2 & , Expand[#1*#2] & , None], DegreeLexicographic], 
 OrePolynomial[{{1 + 3*s^2 + 3*s^4 + s^6 + t^2 + 3*s^2*t^2 + 3*s^4*t^2 + 
     s^6*t^2, {0, 0, 1, 0}}, {2*s + 4*s^3 + 2*s^5 + 4*b^2*s*s1 - 4*d^2*s*s1 + 
     4*d*m11*s*s1 - 4*b^2*s^3*s1 + 4*d^2*s^3*s1 + 4*d*m11*s^3*s1 - 
     2*d*m21*s2 - 4*b^2*s*s2 + 4*d^2*s*s2 + 4*b*m22*s*s2 + 4*b^2*s^3*s2 - 
     4*d^2*s^3*s2 + 4*b*m22*s^3*s2 + 2*d*m21*s^4*s2 - 4*b*m11*s1*t + 
     4*b*m11*s^4*s1*t - 4*d*m22*s2*t - 8*b*m21*s*s2*t - 8*b*m21*s^3*s2*t + 
     4*d*m22*s^4*s2*t + 2*s*t^2 + 4*s^3*t^2 + 2*s^5*t^2 + 4*b^2*s*s1*t^2 - 
     4*d^2*s*s1*t^2 - 4*d*m11*s*s1*t^2 - 4*b^2*s^3*s1*t^2 + 
     4*d^2*s^3*s1*t^2 - 4*d*m11*s^3*s1*t^2 + 2*d*m21*s2*t^2 - 
     4*b^2*s*s2*t^2 + 4*d^2*s*s2*t^2 - 4*b*m22*s*s2*t^2 + 4*b^2*s^3*s2*t^2 - 
     4*d^2*s^3*s2*t^2 - 4*b*m22*s^3*s2*t^2 - 2*d*m21*s^4*s2*t^2, 
    {0, 0, 0, 0}}}, OreAlgebraObject[{Der[d], Der[b], Der[s], Der[t]}, 
   Expand, #1 + #2 & , Expand[#1*#2] & , None], DegreeLexicographic], 
 OrePolynomial[{{b^2 - d^2 + 2*b^2*s^2 - 2*d^2*s^2 + b^2*s^4 - d^2*s^4 + 
     b^2*t^2 - d^2*t^2 + 2*b^2*s^2*t^2 - 2*d^2*s^2*t^2 + b^2*s^4*t^2 - 
     d^2*s^4*t^2, {0, 1, 0, 0}}, {-2*b - 4*b*s^2 - 2*b*s^4 + 4*b^3*s^2*s1 - 
     4*b*d^2*s^2*s1 + b^3*s2 - b*d^2*s2 - b^2*m22*s2 + d^2*m22*s2 - 
     2*b^3*s^2*s2 + 2*b*d^2*s^2*s2 + b^3*s^4*s2 - b*d^2*s^4*s2 + 
     b^2*m22*s^4*s2 - d^2*m22*s^4*s2 - 4*b^2*m11*s*s1*t + 4*d^2*m11*s*s1*t - 
     4*b^2*m11*s^3*s1*t + 4*d^2*m11*s^3*s1*t + 2*b^2*m21*s2*t - 
     2*d^2*m21*s2*t - 2*b^2*m21*s^4*s2*t + 2*d^2*m21*s^4*s2*t - 2*b*t^2 - 
     4*b*s^2*t^2 - 2*b*s^4*t^2 + 4*b^3*s^2*s1*t^2 - 4*b*d^2*s^2*s1*t^2 + 
     b^3*s2*t^2 - b*d^2*s2*t^2 + b^2*m22*s2*t^2 - d^2*m22*s2*t^2 - 
     2*b^3*s^2*s2*t^2 + 2*b*d^2*s^2*s2*t^2 + b^3*s^4*s2*t^2 - 
     b*d^2*s^4*s2*t^2 - b^2*m22*s^4*s2*t^2 + d^2*m22*s^4*s2*t^2, 
    {0, 0, 0, 0}}}, OreAlgebraObject[{Der[d], Der[b], Der[s], Der[t]}, 
   Expand, #1 + #2 & , Expand[#1*#2] & , None], DegreeLexicographic], 
 OrePolynomial[{{-b^2 + d^2 - 2*b^2*s^2 + 2*d^2*s^2 - b^2*s^4 + d^2*s^4 - 
     b^2*t^2 + d^2*t^2 - 2*b^2*s^2*t^2 + 2*d^2*s^2*t^2 - b^2*s^4*t^2 + 
     d^2*s^4*t^2, {1, 0, 0, 0}}, {-2*d - 4*d*s^2 - 2*d*s^4 - b^2*d*s1 + 
     d^3*s1 + b^2*m11*s1 - d^2*m11*s1 + 2*b^2*d*s^2*s1 - 2*d^3*s^2*s1 - 
     b^2*d*s^4*s1 + d^3*s^4*s1 - b^2*m11*s^4*s1 + d^2*m11*s^4*s1 + 
     2*b^2*m21*s*s2 - 2*d^2*m21*s*s2 - 4*b^2*d*s^2*s2 + 4*d^3*s^2*s2 + 
     2*b^2*m21*s^3*s2 - 2*d^2*m21*s^3*s2 + 4*b^2*m22*s*s2*t - 
     4*d^2*m22*s*s2*t + 4*b^2*m22*s^3*s2*t - 4*d^2*m22*s^3*s2*t - 2*d*t^2 - 
     4*d*s^2*t^2 - 2*d*s^4*t^2 - b^2*d*s1*t^2 + d^3*s1*t^2 - b^2*m11*s1*t^2 + 
     d^2*m11*s1*t^2 + 2*b^2*d*s^2*s1*t^2 - 2*d^3*s^2*s1*t^2 - 
     b^2*d*s^4*s1*t^2 + d^3*s^4*s1*t^2 + b^2*m11*s^4*s1*t^2 - 
     d^2*m11*s^4*s1*t^2 - 2*b^2*m21*s*s2*t^2 + 2*d^2*m21*s*s2*t^2 - 
     4*b^2*d*s^2*s2*t^2 + 4*d^3*s^2*s2*t^2 - 2*b^2*m21*s^3*s2*t^2 + 
     2*d^2*m21*s^3*s2*t^2, {0, 0, 0, 0}}}, 
  OreAlgebraObject[{Der[d], Der[b], Der[s], Der[t]}, Expand, #1 + #2 & , 
   Expand[#1*#2] & , None], DegreeLexicographic]}
