3.24 One-variable polynomials

Procedures for one-variable polynomials.

Function: polynomial1 n …

creates a one-variable polynomial.

(polynomial1 1 2 3 4)

returns a polynomial x^3+2x^2+3x+4.

Function: polynomial1? obj

returns #t if the object is a one-variable polynomial.

Function: differenciate1 poly

differenciate the polynomial.

Function: integrate1 poly begin end

integrates the polynomial between begin to end.

Function: substitute1 poly x

substitutes variables in the polynomials to x.

Function: + n …

[R5RS+] adds all given arguments. This procedure extends for polynomials.

Function: - n …

[R5RS+] subtracts given arguments from the first argument. This procedure extends for polynomials.

Function: * n …

[R5RS+] multiplies all given arguments. This procedure extends for polynomials.

Function: quotient n m

[R5RS+] computes quotient of the polynomial. This procedure extends for polynomials.

Function: remainder n m

[R5RS+] computes remainder of the polynomial. This procedure extends for polynomials.

Function: degree-polynomial1 poly

gets degree of the polynomial. Degree of function 0 is -1.

Function: integrate-polynomial1 poly C

computes indefinite integral of the polynomial. Integral constant is given by C.

Function: polynomial1-ref poly n

gets coefficient of the nth order. This procedure return 0 if the order is greater than degree of the polynomial.

Function: solve-polynomial1 polynomial1

solves equation c_nx^n+c_{n-1}x^{n-1}+\dots+c_0=0 and returns a list of the real roots.
The roots are inexact value.

Function: solve-polynomial1-by-bairstow polynomial1

solves equation c_nx^n+c_{n-1}x^{n-1}+\dots+c_0=0 using Bairstow method and returns a list of the complex roots.
The roots are inexact value.

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