f := 4*x^3+5*x^2+6*x+1;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJmR0YoLCoqJEkieEdGKCIiJCIiJSokRjAiIiMiIiZGMCIiJyIiIkY3NyNGLg==

g := 2*x^3-5*x+4;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJnR0YoLCgqJEkieEdGKCIiJCIiI0YwISImIiIlIiIiNyNGLg==

degree(f);

IiIk

coeff(f,x,2);

IiIm

SeriesMult := proc(f,g,x,n) # h = fg mod x^(n+1) local C,k,i; C := Array(0..n); for k from 0 to n do C[k] := 0; for i from 0 to k do C[k] := C[k] + coeff(f,x,i)*coeff(g,x,k-i); od; od; add( C[k]*x^k, k=0..n ); end : SeriesMult(f,g,x,3);

LCoqJEkieEc2IiIiJCEiKCokRiQiIiMhIzVGJCIjPiIiJSIiIg==

taylor(f*g,x=0,4);

Ky1JInhHNiIiIiUiIiEiIz4iIiIhIzUiIiMhIigiIiQtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGKEYl

add( x[i], i=1..4 );

LComSSJ4RzYiNiMiIiJGJyZGJDYjIiIjRicmRiQ2IyIiJEYnJkYkNiMiIiVGJw==

add( i*x^i, i=1..4 );

LCoqJEkieEc2IiIiJUYmKiRGJCIiJEYoKiRGJCIiI0YqRiQiIiI=

SeriesMult := proc(f,g,x,n) # h = fg mod x^(n+1) local C,k,i,A,B; A := Array(0..n); B := Array(0..n); for k from 0 to n do A[k] := coeff(f,x,k); B[k] := coeff(g,x,k); od; C := Array(0..n); for k from 0 to n do C[k] := 0; for i from 0 to k do C[k] += A[i]*B[k-i]; od; od; add( C[k]*x^k, k=0..n ); end : SeriesMult(f,g,x,3);

LCoqJEkieEc2IiIiJCEiKCokRiQiIiMhIzVGJCIjPiIiJSIiIg==

taylor(f*g,x=0,4);

Ky1JInhHNiIiIiUiIiEiIz4iIiIhIzUiIiMhIigiIiQtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGKEYl