| Polynomial Derivative | p.. 1 0 1 | Polynomial Integral |
Applied to a polynomial (coefficients or boxed roots), p.. produces
the coefficients of the derivative of polynomial. For example:p.. 1 2 3 4 5 2 6 12 20 p.. 5 4 3 2 1 4 6 6 4 p.. 2; 1j1 1j_1 _4 4 p.. p. 2; 1j1 1j_1 _4 4 |
x p.. y produces the integral of polynomial y with a
constant term of x . Thus:
5 p.. 4 6 6 4 5 4 3 2 1 1 p.. 2 6 12 20 1 2 3 4 5 |
p.. 1&o. t. i. 11x NB. derivative of sine 1 0 _1r2 0 1r24 0 _1r720 0 1r40320 0 2&o. t. i.10x NB. cosine 1 0 _1r2 0 1r24 0 _1r720 0 1r40320 0 p.. 2&o. t. i. 11x NB. derivative of cosine 0 _1 0 1r6 0 _1r120 0 1r5040 0 _1r362880 -@(1&o.) t. i.10x NB. minus sine 0 _1 0 1r6 0 _1r120 0 1r5040 0 _1r362880 - (1&o. t. i.10x) 0 _1 0 1r6 0 _1r120 0 1r5040 0 _1r362880 p..^:(i.@#) 8 $ 1 1 1 1 1 1 1 1 1 1 2 3 4 5 6 7 0 2 6 12 20 30 42 0 0 6 24 60 120 210 0 0 0 24 120 360 840 0 0 0 0 120 720 2520 0 0 0 0 0 720 5040 0 0 0 0 0 0 5040 0 0 0 0 0 0 0