---------- ---------- ---------- ---------- ---------- ---------- ---------- ---------- # With divp you can divide a polynomial by a polynomial. Some examples: # # (x^4-1)/(x+1) A=c(1,0,0,0,-1); B=c(1,1); divp(A,B) # 1 0 0 0 -1 0 0 -1 # -1 0 0 1 0 -1 # 1 0 -1 -1 # -1 0 STOP # x^3 - x^2 + x -1 and remainder 0 # # Interpretation of the outputs: # 1 0 0 0 -> x^3 + 0*x^2 + 0*x + 0 # -1 0 0 -> -1*x^2 + 0*x + 0 # 1 0 -> 1*x + 0 # -1 -> -1 # # The parts on the right describe the algorithm: # x^4 - 1 : x + 1 # ---------------------- # x^4 + x^3 x^3 # ------------- # - x^3 - 1 -x^2 # - x^3 - x^2 # ------------- # x^2 - 1 x # x^2 + x # ------------- # - x - 1 -1 # - x - 1 # ------------- # 0 # # (x^3-3*x^2+x-1)/(2*x^2+1) divp( c(1,-3,1,-1), c(2,0,1) ) # 0.5 0 -3 0.5 -1 # -1.5 0.5 0.5 STOP # 0.5*x - 1.5 and remainder 0.5*x + 0.5 # # (x^5 + x^3 - 1) / (x^2 + x - 5) divp( c(1,0,1,0,0,-1), c(1,1,-5) ) # 1 0 0 0 -1 6 0 0 -1 # -1 0 0 7 -5 0 -1 # 7 0 -12 35 -1 # -12 47 -61 STOP # x^3 - x^2 + 7*x - 12 remainder: 47*x - 61 # # (2*x^8+7/4*x^7-33/4*x^6+3*x^5-41/4*x^4-3/4*x^3-7/4*x^2+ 41/4*x-5/4) / ( (x^2+x-5)*(2*x-1/4) ) divp(c(2,7/4,-33/4,3,-41/4,-3/4,-7/4,41/4,- 5/4), prodp( c(2,-1/4),c(1,1,-5) ) ) # 1 0 0 0 0 0 2 1.75 -10.25 -0.75 -1.75 10.25 -1.25 # 1 0 0 0 -2 -1.75 10.25 -1.25 # -1 0 STOP # x^5 + x^3 - 1 and remainder 0