#### Exercise 6.3: Polynomial Evaluation Program

Given: a two-dimensional array, `C`, of real valued polynomial coefficients, each row of which contains the coefficients of a single polynomial;

Given: for each row of `C`, the index of each coefficient's position is the exponent of x for that term;

Given: a one-dimensional array `X` of real valued polynomial unknowns, with each element corresponding to the unknown for the whole set of polynomials;

Compose: a function of `C` and `X` that evaluates each polynomial with each unknown, and returns the two-dimensional array containing in each row the value of each polynomial for one of the unknowns.

define multi_poly
%$entry = multi_poly
type Poly_Coeffs = array [ real ]; % Coefficients of one polynomial
type Many_Polys = array [ Poly_Coeffs ]; % Coefficients of many polynomials
type Unknowns = array [ real ]; % Values for X, the polynomial unknown
type Values = array [ real ]; % Values of all polys for one unknown
type Many_Values = array [ Values ]; % Values of all polys for all unknowns
function eval_poly( coeffs : Poly_Coeffs; x_val := real returns Values )
for c in coeffs at i
term := c * exp(x_val, real(i))
returns value of sum term
end for
end function % eval_poly
function multi_poly( C : Many_Polys; X : Unknowns returns Many_Values )
for x_val in X
row_of_poly_vals :=
for coeffs in C
poly_value := eval_poly(coeffs, x_val)
returns array of poly_value
end for % one row of result array - all polys for one x
returns array of row_of_poly_vals
end for
end function % multi_poly

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