# hspray: Multivariate polynomials.

[ algebra, gpl, library, math ] [ Propose Tags ]

Manipulation of multivariate polynomials on a ring.

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Versions [RSS] 0.1.0.0, 0.1.1.0, 0.1.2.0 CHANGELOG.md base (>=4.7 && <5), containers (>=0.6.4.1), hashable (>=1.3.4.0), numeric-prelude (>=0.4.4), text (>=1.2.5.0), unordered-containers (>=0.2.17.0) [details] GPL-3.0-only 2022 Stéphane Laurent Stéphane Laurent laurent_step@outlook.fr Math, Algebra https://github.com/stla/hspray#readme head: git clone https://github.com/stla/hspray by stla at 2023-02-24T21:21:35Z NixOS:0.1.2.0 2 direct, 0 indirect [details] 65 total (24 in the last 30 days) (no votes yet) [estimated by Bayesian average] λ λ λ Docs available Last success reported on 2023-02-24

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# hspray

import Math.Algebra.Hspray
x = lone 1 :: Spray Double
y = lone 2 :: Spray Double
z = lone 3 :: Spray Double
poly = (2 *^ (x^**^3 ^*^ y ^*^ z) ^+^ x^**^2) ^*^ (4 *^ (x ^*^ y ^*^ z))
prettySpray show "X" poly
-- "(4.0) * X^(3, 1, 1) + (8.0) * X^(4, 2, 2)"


More generally, one can use the type Spray a as long as the type a has the instances Eq and Algebra.Ring (defined in the numeric-prelude library). For example a = Rational:

import Math.Algebra.Hspray
import Data.Ratio
x = lone 1 :: Spray Rational
y = lone 2 :: Spray Rational
z = lone 3 :: Spray Rational
poly = ((2%3) *^ (x^**^3 ^*^ y ^*^ z) ^+^ x^**^2) ^*^ ((7%4) *^ (x ^*^ y ^*^ z))
prettySpray show "X" poly
-- "(7 % 4) * X^(3, 1, 1) + (7 % 6) * X^(4, 2, 2)"


Or a = Spray Double:

import Math.Algebra.Hspray
p = lone 1 :: Spray Double
x = lone 1 :: Spray (Spray Double)
y = lone 2 :: Spray (Spray Double)
poly = ((p *^ x) ^+^ (p *^ y))^**^2
prettySpray (prettySpray show "a") "X" poly
-- "((1.0) * a^(2)) * X^(0, 2) + ((2.0) * a^(2)) * X^(1, 1) + ((1.0) * a^(2)) * X^(2)"


Evaluation:

import Math.Algebra.Hspray
x = lone 1 :: Spray Double
y = lone 2 :: Spray Double
z = lone 3 :: Spray Double
poly = 2 *^ (x ^*^ y ^*^ z)
-- evaluate poly at x=2, y=1, z=2
evalSpray poly [2, 1, 2]
-- 8.0


Differentiation:

import Math.Algebra.Hspray
x = lone 1 :: Spray Double
y = lone 2 :: Spray Double
z = lone 3 :: Spray Double
poly = 2 *^ (x ^*^ y ^*^ z) ^+^ (3 *^ x^**^2)
-- derivate with respect to x
prettySpray show "X" \$ derivSpray 1 poly
-- "(2.0) * X^(0, 1, 1) + (6.0) * X^(1)"