epsilon is a package which allows numerical root finding directly in Typst. It currently supports the following methods:
- Newton
- bisection
- secant
The following example shows how to use epsilon to solve a non-linear equation and plot the result using lilaq:
#import "@preview/lilaq:0.3.0" as lq
#import "@preview/epsilon:0.1.0": find-root
#{
let prandtl-meyer-angle = M => (
calc.sqrt((1.4 + 1) / (1.4 - 1))
* calc.atan(calc.sqrt((1.4 - 1) / (1.4 + 1) * (calc.pow(M, 2) - 1)))
- calc.atan(calc.sqrt(calc.pow(M, 2) - 1))
)
let angle = 0.736810609185532rad
let prandtl-meyer-angle-root = M => prandtl-meyer-angle(M).rad() - angle.rad()
let root = find-root(prandtl-meyer-angle-root, 1, x1: 4)
let M = lq.linspace(1, 4)
lq.diagram(
width: 8cm,
height: 5cm,
title: [Calculating the Mach number for a given Prandtl-Meyer angle],
xlabel: [Mach number $M$],
ylabel: [Prandtl-Meyer angle $nu$ [°]],
lq.plot(
M, M.map(M => prandtl-meyer-angle(M).deg()), mark: none
),
lq.plot(
(root,),
(angle.deg(),),
mark-size: 6pt,
color: red
),
lq.hlines(angle.deg(), max: root, stroke: (dash: "dashed")),
lq.vlines(root, max: angle.deg(), stroke: (dash: "dashed")),
)
}
