miniapl

Ⓟ — Polynomial

J’s p. family. Ranks: 1 monadic, 1 0 dyadic.

Coefficients

CⓅX: evaluate constant-first coefficients at X. Decode uses the opposite order.

1x 2x 3xⓅ0x 1x 2x   ⍝ 1x 6x 17x

ⓅC: leading coefficient and numerical roots, as a nested pair. Ignores trailing zeros. Constants have no roots.

≢2⊃Ⓟ1 0 1           ⍝ 2x

Multiplier and roots

(M R)ⓅX: M××/X-R. ⊂R assumes M=1; use ⊂,R for one root. Monadic Ⓟ gives coefficients.

(2x (1x 3x))Ⓟ0x 1x 2x 3x  ⍝ 6x 0x ¯2x 0x
Ⓟ2x (1x 3x)                ⍝ 6x ¯8x 2x
Ⓟ⊂1x 3x                    ⍝ 3x ¯4x 1x

Coefficient/exponent tables

Enclosed matrix: one row per term, coefficient then exponents. Enclose multivariate coordinates; scalars extend.

(⊂2 3⍴1x 2x 0x 1x 0x 2x)Ⓟ⊂3x 4x  ⍝ 25x
(⊂2 2⍴2x 1r2 3x 1r4)Ⓟ16x           ⍝ 14
Ⓟ⊂2 2⍴1x 5x ¯1x 0x                 ⍝ ¯1x 0x 0x 0x 0x 1x

Evaluation accepts fractional/negative exponents. Conversion to coefficients requires one variable and nonnegative integral exponents; repeated degrees add.

Derivative coefficients: (1↓C)×⍳¯1+≢C. Integral: K,C÷⍳≢C. See Derivative.

LENGTH: wrong coordinate count. DOMAIN: nonnumeric data, invalid conversion exponents or failed root solve.

This site is open source. Improve this page.