Examples Gallery

This page provides a variety of snippets showing Zigma in action across different scientific and engineering domains.

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1. Projectile Motion (Kinematics)

This example calculates the trajectory of a projectile and demonstrates how Zigma derives complex units like Joules and Watts from base SI units.

g  = 9.81 m/s2
v0 = 50 m/s
angle = 45 // degrees (dimensionless)
mass = 2 kg

// Breaking velocity into components
vx = v0 * cos(angle)
vy = v0 * sin(angle)

// Calculate Kinetic Energy (Automatically becomes kg.m2/s2)
Ek = 0.5 * mass * v0^2
print "Initial Kinetic Energy: {Ek in J}"

// Calculate time of flight
t_total = (2 * vy) / g
print "Time of flight: {t_total}"

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2. Ideal Gas Law (Thermodynamics)

Using custom aliases to make equations look exactly like they do in a textbook.

alias Pa as N/m2
alias R_const as 8.314 J/(mol.K)

n = 1 mol
T = 300 K
V = 0.0224 m3

// P = nRT / V
P = (n * R_const * T) / V

print "Pressure: {P in Pa}"
print "Pressure in bar: {P in bar}"

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3. Stress and Strain (Structural Engineering)

This example uses a table to look up Material Properties (Young's Modulus) and calculates the deformation of a steel beam under load.

// material_data.csv: Material, E [GPa], Density [kg/m3]
materials = table("materials.csv")

E_steel = in materials get E as Material = "Steel"
area = 10 cm * 10 cm
length = 5 m
force = 5000 N

// Stress = Force / Area
stress = force / area

// Strain = Stress / Young's Modulus
strain = stress / E_steel

// Delta Length = Strain * Original Length
dl = strain * length

print "Total elongation: {dl in mm}"

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4. 3D Vector Rotation (Linear Algebra)

Zigma uses SIMD to accelerate matrix-vector multiplications.

// A 3D position vector
pos = [10, 0, 0] m

// A 3x3 Rotation Matrix (dimensionless)
R_z = [[ 0, -1,  0],
       [ 1,  0,  0],
       [ 0,  0,  1]]

// Rotate the vector using matrix multiplication operator (@)
new_pos = R_z @ pos

print "Original: {pos}"
print "Rotated:  {new_pos}" // [0, 10, 0] m

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5. Lab Measurement (Uncertainty Propagation)

Calculate the density of an object given measurements with sensor errors. Zigma propagates the uncertainty automatically.

mass   = 500.5 +/- 0.1 g
radius = 2.5 +/- 0.05 cm

// Volume of a sphere: 4/3 * pi * r^3
volume = (4/3) * 3.14159 * radius^3

// Density = Mass / Volume
density = mass / volume

print "Object Density: {density in kg/m3}"
// Output will include the +/- error margin automatically

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6. Financial Ledger (Custom Dimensions)

Zigma isn't just for physics; it can track any "dimension" you define.

dimension usd
alias eur as 1.08 * usd

price_eur = 50 eur
tax_rate = 0.20 // 20%

total_usd = (price_eur * (1 + tax_rate)) in usd

print "Total Price: {total_usd:.2} USD"

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7. High-Precision Orbital Mechanics

Using i128 fixed-point math to calculate the gravitational force between planets without floating-point drift.

as i128:
    G = 6.674e-11 m3/(kg.s2)
    m_earth = 5.972e24 kg
    m_moon  = 7.348e22 kg
    r = 384400 km

    // F = G * (m1 * m2) / r^2
    force = G * (m_earth * m_moon) / r^2

print "Gravitational Force: {force in PN}" // Peta-Newtons