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100

101

Computer Algebra System (CAS) 14-59

Note that in step-by-step mode, synthetic division is

shown, with each polynomial represented as the list of its

coefficients in descending order of power.

REMAINDER Returns the remainder from the division of the two

polynomials, A(X) and B(X), divided in decreasing order

by exponent.

Example

Typing:

REMAINDER(X

– 1, X

– 1)

gives:

Note that in step-by-step mode, synthetic division is

shown, with each polynomial represented as the list of its

coefficients in descending order of power.

TCHEBYCHEFF For n > 0, TCHEBYCHEFF returns the polynomial T

such

that:

Tn(x) = cos(n·arccos(x))

For n ≥ 0, we have:

For n ≥ 0 we also have:

For n ≥ 1, we have:

If n < 0, TCHEBYCHEFF returns the 2nd-species

Tchebycheff polynomial:

x 1–

x() C

1–()

n 2k–

k 0=

---

[]

∑

1 x

–()T

″

x() xT

′

x()– n

x()+0=

n 1+

x() 2xT

x() T

n 1–

x()–=

x()

n arccos x()⋅()sin

arccos x()()sin

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