hp40g+.book Page 59 Friday, December 9, 2005 1:03 AM
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| 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. |
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| Example |
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| Typing: |
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| REMAINDER(X3 – 1, X2 – 1) | ||||||
| gives: |
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| x – 1 |
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| Note that in | ||||||
| shown, with each polynomial represented as the list of its | ||||||
| coefficients in descending order of power. | ||||||
TCHEBYCHEFF | For n > 0, TCHEBYCHEFF returns the polynomial Tn such | ||||||
| that: |
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| Tn(x) = cos(n·arccos(x)) |
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| For n ≥ 0, we have: |
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| [ | n |
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| Tn(x) = ∑ C2kn (x2 – 1)k xn | ||||||
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| k = 0 |
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| For n ≥ 0 we also have: |
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| (1 – x | 2 | ″ | ′ |
| 2 | Tn(x) = 0 |
| (x) – xTn(x) | + n | |||||
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| )Tn |
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For n ≥ 1, we have:
Tn + 1(x) = 2xTn(x) – Tn – 1(x)
If n < 0, TCHEBYCHEFF returns the
Tchebycheff polynomial:
( ) sin(n ⋅ arccos(x)) Tn x =
sin(arccos(x))
Computer Algebra System (CAS) |
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