// Basic arithmetic with proper order of operations val result = (5.num() + 3.num()) * 2.num() println(result.evaluate()) // 16.0 println(result.toLatex()) // "(5 + 3) \cdot 2" // Variables and equations with cached variables val x = Variable("x").setTo(5.0) val three = 3.num() val two = 2.num() val equation = x.squared() + three * x + two println(equation.evaluate()) // 42.0 (5² + 3×5 + 2 = 25 + 15 + 2 = 42) println(equation.toLatex()) // "x^{2} + 3 \cdot x + 2"

// Order of operations (multiplication before addition) val five = 5.num() val three = 3.num() val two = 2.num() val one = 1.num() val expr = five * three + two - one println(expr.evaluate()) // 16.0 (5×3 + 2 - 1 = 15 + 2 - 1 = 16) println(expr.toLatex()) // "5 \cdot 3 + 2 - 1" // Rational arithmetic with proper fractions val oneThird = 1.num() / 3.num() val oneFourth = 1.num() / 4.num() val fraction = oneThird + oneFourth println(fraction.toLatex()) // "\frac{1}{3} + \frac{1}{4}" println(fraction.evaluate()) // 0.5833333333333333

// Quadratic formula val a = Variable("a").setTo(1.0) val b = Variable("b").setTo(-5.0) val c = Variable("c").setTo(6.0) val x = Variable("x") val quadratic = a * x.squared() + b * x + c println(quadratic.toLatex()) // "a \cdot x^{2} + b \cdot x + c" // Simplification with proper order of operations val one = 1.num() val five = 5.num() val two = 2.num() val complex = one + five + five * x + two - one val simplified = simplify(complex) println(simplified.toLatex()) // "6 + 5 \cdot x + 1"

// Trigonometric derivatives with cached variables val x = Variable("x") val sinExpr = Sin(x) println(sinExpr.toLatex()) // "\sin(x)" // Exponential functions with proper multiplication val two = 2.num() val expExpr = Exp(two * x) println(expExpr.toLatex()) // "e^{2 \cdot x}"

// Summation with cached variables val k = Variable("k").setTo(1) val one = 1.num() val ten = 10.num() val sum = Sum(k, one, ten) { k -> k } println(sum.evaluate()) // 55.0 (1+2+3+...+10 = 55) println(sum.toLatex()) // "\sum_{k=1}^{10}{k}" // Product with cached variables val j = Variable("j") val five = 5.num() val product = Product(j, one, five) { j -> j } println(product.evaluate()) // 120.0 (1×2×3×4×5 = 120 = 5!) println(product.toLatex()) // "\prod_{j=1}^{5}{j}"

// Trigonometric expressions with cached values val ninety = 90.num() val zero = 0.num() val trigExpr = Sin(ninety) + Cos(zero) println(trigExpr.evaluate()) // ≈ 1.893 (sin(90) + cos(0) ≈ 0.893 + 1 = 1.893 in radians) println(trigExpr.toLatex()) // "\sin(90) + \cos(0)" // Inverse functions with cached values val three = 3.num() val arcExpr = ArcSin(Sin(three)) println(arcExpr.evaluate()) // 3.0 (arcsin(sin(3)) = 3)

// Boolean logic with cached propositions val p = PropositionalCalculus.Fact("p", name = "It is raining") val q = PropositionalCalculus.Fact("q", name = "It is cloudy") val implication = p implies q println(implication.toLatex()) // "p \implies q" // Logical operations with cached variables val andExpr = p and q val orExpr = p or q println(andExpr.toLatex()) // "p \land q" println(orExpr.toLatex()) // "p \lor q"

// Permutations and combinations with cached variables val n = Variable("n").setTo(5.0) val k = Variable("k").setTo(3.0) val perm = Permutation(n, k) val comb = Combination(n, k) println(perm.toLatex()) // "{}^{5}P_{3}" println(comb.toLatex()) // "{}^{5}C_{3}"

// Statistical functions with cached variables val i = Variable("i") val n = Variable("n") val one = 1.num() val mean = Sum(i, one, n) { i -> i } / n println(mean.toLatex()) // "\frac{\sum_{i=1}^{n}{i}}{n}" // Physical constants with cached values val c = Constant("c", 299792458.0) // Speed of light val e = Constant("e", 2.718281828459045)

import com.measures.distance.* import com.measures.volume.* import com.measures.area.* // Distance conversions val distance = Kilometer(5.0) val inMiles = distance.toMile() val inFeet = distance.toFoot() println("5 km = ${inMiles.value} miles = ${inFeet.value} feet") // Metric prefixes val length = Meter(1.0) val inKm = length.toKilometer() // 0.001 km val inCm = length.toCentimeter() // 100.0 cm val inMm = length.toMillimeter() // 1000.0 mm // Volume conversions val volume = Liter(1.0) val inGallons = volume.toUSFluidGallon() val inCups = volume.toUSCup() println("1 liter = ${inGallons.value} gallons = ${inCups.value} cups") // Area conversions val area = SquareMeter(100.0) val inAcres = area.toAcre() val inSquareFeet = area.toSquareFoot() println("100 m² = ${inAcres.value} acres = ${inSquareFeet.value} ft²")

// Type-safe unit arithmetic val speed = Kilometer(100.0) / Hour(1.0) // 100 km/h val acceleration = speed / Second(10.0) // 10 km/h/s // Automatic unit conversion val distance1 = Mile(1.0) val distance2 = Kilometer(1.0) val total = distance1 + distance2 // Automatically converts to common unit

// Survey measurements val surveyDistance = SurveyMile(1.0) val inMeters = surveyDistance.toMeter() println("1 survey mile = ${inMeters.value} meters") // Troy weights for precious metals val gold = TroyOunce(1.0) val inGrams = gold.toGram() println("1 troy ounce = ${inGrams.value} grams") // Nautical measurements val nauticalMile = NauticalMile(1.0) val inKilometers = nauticalMile.toKilometer() println("1 nautical mile = ${inKilometers.value} km")

// Complex expressions with cached variables val x = Variable("x") val y = Variable("y") val two = 2.num() val one = 1.num() val complexExpr = (x + two).squared() / (y - one) println(complexExpr.toLatex()) // Output: "\frac{(x + 2)^{2}}{y - 1}"

// Step-by-step equation solving with cached variables val x = Variable("x") val four = 4.num() val three = 3.num() val equation = x.squared() - four * x + three val explanation = equation.explain() println(explanation) // Shows step-by-step solution

// Complex scientific calculations with cached constants val e = Constant("e", 2.718281828459045) val pi = Constant("π", 3.141592653589793) val one = 1.num() val result = e.pow(pi * one) println(result.toLatex()) // "e^{\pi \cdot 1}"

// Generate LaTeX for papers with cached variables val a = Variable("a") val b = Variable("b") val formula = Sqrt(a.squared() + b.squared()) println(formula.toLatex()) // "\sqrt{a^{2} + b^{2}}"

// Unit conversions for engineering calculations val beamLength = Foot(20.0) val beamWidth = Inch(12.0) val beamHeight = Inch(8.0) val volume = beamLength * beamWidth * beamHeight val volumeInCubicMeters = volume.toCubicMeter() println("Beam volume: ${volumeInCubicMeters.value} m³") // Metric conversions for international projects val distance = Kilometer(5.0) val inMiles = distance.toMile() val inFeet = distance.toFoot() println("5 km = ${inMiles.value} miles = ${inFeet.value} feet")

// Precise measurements with appropriate units val wavelength = Nanometer(500.0) // Green light wavelength val frequency = wavelength.toMeter().let { Constant("c", 299792458.0) / it // c / λ } println("Green light frequency: ${frequency.evaluate()} Hz") // Temperature conversions for experiments val celsius = Celsius(25.0) val fahrenheit = celsius.toFahrenheit() val kelvin = celsius.toKelvin() println("25°C = ${fahrenheit.value}°F = ${kelvin.value}K")