You can use the following functions from the SML Basis Library, but not any others.

http://sml-family.org/Basis/top-level-chapter.html http://sml-family.org/Basis/list.html http://sml-family.org/Basis/list-pair.html

4. Let us represent a polynom ao +aa22 +...+anz" (n 2 -1) by the list (ao, a1,a2,..., anl of its coefficents. (Notice that we list the coefficients in the ascending order of their degree; the head element of the list is the coefficient of degree 0 etc.) (i) Code a function evalPoly real list -> real -> real that returns the value of a given polynom for a given value of r - evalPoly [4.0,3.0,8.0] 10.0; val it-834.0: real; (ii) Code a function addPoly : real list ->real list -> real list that adds two polyno- mials. (This works like long addition of decimal representations natural numbers, except that you do not have to worry about carries.) addPoly [3.0,5.0,4.0] [40.0,30.0,80.0,90.0] val it -[43.0,53.0,84.0,90.0] : real list; (iii) Code a function multPoly : real list -> real list -> real list that multiplies two polynomials. (This works like long multiplication of decimal representations natural numbers, except that you do not have to worry about carries.) - multPoly [2.0,3.0,5.0] [7.0,9.0] - [14.0,39.0,62.0,45.0]; val it - [14.0,39.0,62.0,45.0]real list 4. Let us represent a polynom ao +aa22 +...+anz" (n 2 -1) by the list (ao, a1,a2,..., anl of its coefficents. (Notice that we list the coefficients in the ascending order of their degree; the head element of the list is the coefficient of degree 0 etc.) (i) Code a function evalPoly real list -> real -> real that returns the value of a given polynom for a given value of r - evalPoly [4.0,3.0,8.0] 10.0; val it-834.0: real; (ii) Code a function addPoly : real list ->real list -> real list that adds two polyno- mials. (This works like long addition of decimal representations natural numbers, except that you do not have to worry about carries.) addPoly [3.0,5.0,4.0] [40.0,30.0,80.0,90.0] val it -[43.0,53.0,84.0,90.0] : real list; (iii) Code a function multPoly : real list -> real list -> real list that multiplies two polynomials. (This works like long multiplication of decimal representations natural numbers, except that you do not have to worry about carries.) - multPoly [2.0,3.0,5.0] [7.0,9.0] - [14.0,39.0,62.0,45.0]; val it - [14.0,39.0,62.0,45.0]real list