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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
3
– 1, X
2
– 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
n
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–
T
n
x() C
2k
n
x
2
1–()
k
x
n 2k–
k 0=
n
2
---
[]
∑
=
1 x
2
–()T
″
n
x() xT
′
n
x()– n
2
T
n
x()+0=
T
n 1+
x() 2xT
n
x() T
n 1–
x()–=
T
n
x()
n arccos x()⋅()sin
arccos x()()sin
-------------------------------------------
=
hp40g+.book Page 59 Friday, December 9, 2005 1:03 AM