OrePolynomial[{{t^3 - t^5 - t^7 + t^9, {3}}, {2*(-t^4 - 4*t^6 + 5*t^8), {2}}, 
  {-3*t - 3*t^3 - 17*t^5 + 23*t^7, {1}}, {3 + 3*t^2 - 7*t^4 + 9*t^6, {0}}}, 
 OreAlgebraObject[{Der[t]}, Together, Together[#1 + #2] & , 
  Together[#1*#2] & , None], DegreeLexicographic]
