OrePolynomial[{{t^2 - 2*t^6 + t^10, {3}}, 
  {t - 6*t^3 - 12*t^5 + 6*t^7 + 11*t^9, {2}}, 
  {-1 - 6*t^2 - 20*t^4 + 30*t^6 + 29*t^8, {1}}, 
  {8*(-t^3 + 3*t^5 + 2*t^7), {0}}}, OreAlgebraObject[{Der[t]}, Together, 
  Together[#1 + #2] & , Together[#1*#2] & , None], DegreeLexicographic]
