Vocabulary/pdotdot
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p.. y Polynomial Derivative
Rank 1 -- operates on lists of y, producing a list for each one -- WHY IS THIS IMPORTANT?
The first derivative of a given polynomial y.
got from differentiating the individual terms of the polynomial
Polynomial y can be provided in coefficient form (list of ascending powers), multiplier-and-roots form (m;r), or exponent form (boxed table form). The result is always expressed in coefficient form.
Examples:
Series 1 y y² y³ y⁴ 1st derivative 1 2y 3y² 4y³
p.. 1 1 1 1 1 1 2 3 4
Series 1 2y 3y² 4y³ 5y⁴ 1st derivative 2 6y 12y² 20y³
p.. 1 2 3 4 5 2 6 12 20
Common uses
Work with finite approximations of infinite series.
Related Primitives
Ordinary Derivative (u d. n), Polynomial (x p. y)
x p.. y Polynomial Integral
Rank 0 1 -- operates on individual atoms of x, and lists of y -- WHY IS THIS IMPORTANT?
The integral of a given polynomial y.
got from integrating the individual terms of the series
The x-argument is the constant of integration that will be added to the result.
Polynomial y can be provided in coefficient form (list of ascending powers), multiplier-and-roots form (m;r), or exponent form (boxed table form). The result is always expressed in coefficient form.
Examples: (invert the examples in monadic p.. above)
Series 1 2y 3y² 4y³ Integral x y y² y³ y⁴
99 p.. 1 2 3 4 99 1 1 1 1
Series 2 6y 12y² 20y³ Integral x 2y 3y² 4y³ 5y⁴
1 p.. 2 6 12 20 1 2 3 4 5
Common uses
Work with finite approximations of infinite series.
More Information
1. Boolean x and y are always promoted to floating-point.
Related Primitives
Ordinary Derivative (u d. n), Polynomial (x p. y)