From 6d7d172e2e706da44c2b30177a04648671aad69e Mon Sep 17 00:00:00 2001
From: Adrien Hopkins <adrien.p.hopkins@gmail.com>
Date: Wed, 26 Aug 2020 12:37:12 -0500
Subject: Added the prefix repetition rule, and the two basic rules.

---
 src/org/unitConverter/unit/SI.java | 472 ++++++++++++++++++++++++-------------
 1 file changed, 314 insertions(+), 158 deletions(-)

(limited to 'src/org/unitConverter/unit/SI.java')

diff --git a/src/org/unitConverter/unit/SI.java b/src/org/unitConverter/unit/SI.java
index 1a9eaf1..a4fbd5f 100644
--- a/src/org/unitConverter/unit/SI.java
+++ b/src/org/unitConverter/unit/SI.java
@@ -16,13 +16,19 @@
  */
 package org.unitConverter.unit;
 
+import java.util.Arrays;
+import java.util.HashSet;
+import java.util.Set;
+
 import org.unitConverter.math.ObjectProduct;
 
 /**
- * All of the units, prefixes and dimensions that are used by the SI, as well as some outside the SI.
+ * All of the units, prefixes and dimensions that are used by the SI, as well as
+ * some outside the SI.
  * 
  * <p>
- * This class does not include prefixed units. To obtain prefixed units, use {@link LinearUnit#withPrefix}:
+ * This class does not include prefixed units. To obtain prefixed units, use
+ * {@link LinearUnit#withPrefix}:
  * 
  * <pre>
  * LinearUnit KILOMETRE = SI.METRE.withPrefix(SI.KILO);
@@ -36,42 +42,61 @@ public final class SI {
 	/// dimensions used by SI units
 	// base dimensions, as BaseDimensions
 	public static final class BaseDimensions {
-		public static final BaseDimension LENGTH = BaseDimension.valueOf("Length", "L");
-		public static final BaseDimension MASS = BaseDimension.valueOf("Mass", "M");
-		public static final BaseDimension TIME = BaseDimension.valueOf("Time", "T");
-		public static final BaseDimension ELECTRIC_CURRENT = BaseDimension.valueOf("Electric Current", "I");
-		public static final BaseDimension TEMPERATURE = BaseDimension.valueOf("Temperature", "\u0398"); // theta symbol
-		public static final BaseDimension QUANTITY = BaseDimension.valueOf("Quantity", "N");
-		public static final BaseDimension LUMINOUS_INTENSITY = BaseDimension.valueOf("Luminous Intensity", "J");
-		public static final BaseDimension INFORMATION = BaseDimension.valueOf("Information", "Info"); // non-SI
-		public static final BaseDimension CURRENCY = BaseDimension.valueOf("Currency", "$$"); // non-SI
-
+		public static final BaseDimension LENGTH = BaseDimension.valueOf("Length",
+				"L");
+		public static final BaseDimension MASS = BaseDimension.valueOf("Mass",
+				"M");
+		public static final BaseDimension TIME = BaseDimension.valueOf("Time",
+				"T");
+		public static final BaseDimension ELECTRIC_CURRENT = BaseDimension
+				.valueOf("Electric Current", "I");
+		public static final BaseDimension TEMPERATURE = BaseDimension
+				.valueOf("Temperature", "\u0398"); // theta symbol
+		public static final BaseDimension QUANTITY = BaseDimension
+				.valueOf("Quantity", "N");
+		public static final BaseDimension LUMINOUS_INTENSITY = BaseDimension
+				.valueOf("Luminous Intensity", "J");
+		public static final BaseDimension INFORMATION = BaseDimension
+				.valueOf("Information", "Info"); // non-SI
+		public static final BaseDimension CURRENCY = BaseDimension
+				.valueOf("Currency", "$$"); // non-SI
+		
 		// You may NOT get SI.BaseDimensions instances!
 		private BaseDimensions() {
 			throw new AssertionError();
 		}
 	}
-
+	
 	/// base units of the SI
-	// suppressing warnings since these are the same object, but in a different form (class)
+	// suppressing warnings since these are the same object, but in a different
+	/// form (class)
 	@SuppressWarnings("hiding")
 	public static final class BaseUnits {
-		public static final BaseUnit METRE = BaseUnit.valueOf(BaseDimensions.LENGTH, "metre", "m");
-		public static final BaseUnit KILOGRAM = BaseUnit.valueOf(BaseDimensions.MASS, "kilogram", "kg");
-		public static final BaseUnit SECOND = BaseUnit.valueOf(BaseDimensions.TIME, "second", "s");
-		public static final BaseUnit AMPERE = BaseUnit.valueOf(BaseDimensions.ELECTRIC_CURRENT, "ampere", "A");
-		public static final BaseUnit KELVIN = BaseUnit.valueOf(BaseDimensions.TEMPERATURE, "kelvin", "K");
-		public static final BaseUnit MOLE = BaseUnit.valueOf(BaseDimensions.QUANTITY, "mole", "mol");
-		public static final BaseUnit CANDELA = BaseUnit.valueOf(BaseDimensions.LUMINOUS_INTENSITY, "candela", "cd");
-		public static final BaseUnit BIT = BaseUnit.valueOf(BaseDimensions.INFORMATION, "bit", "b");
-		public static final BaseUnit DOLLAR = BaseUnit.valueOf(BaseDimensions.CURRENCY, "dollar", "$");
-
+		public static final BaseUnit METRE = BaseUnit
+				.valueOf(BaseDimensions.LENGTH, "metre", "m");
+		public static final BaseUnit KILOGRAM = BaseUnit
+				.valueOf(BaseDimensions.MASS, "kilogram", "kg");
+		public static final BaseUnit SECOND = BaseUnit
+				.valueOf(BaseDimensions.TIME, "second", "s");
+		public static final BaseUnit AMPERE = BaseUnit
+				.valueOf(BaseDimensions.ELECTRIC_CURRENT, "ampere", "A");
+		public static final BaseUnit KELVIN = BaseUnit
+				.valueOf(BaseDimensions.TEMPERATURE, "kelvin", "K");
+		public static final BaseUnit MOLE = BaseUnit
+				.valueOf(BaseDimensions.QUANTITY, "mole", "mol");
+		public static final BaseUnit CANDELA = BaseUnit
+				.valueOf(BaseDimensions.LUMINOUS_INTENSITY, "candela", "cd");
+		public static final BaseUnit BIT = BaseUnit
+				.valueOf(BaseDimensions.INFORMATION, "bit", "b");
+		public static final BaseUnit DOLLAR = BaseUnit
+				.valueOf(BaseDimensions.CURRENCY, "dollar", "$");
+		
 		// You may NOT get SI.BaseUnits instances!
 		private BaseUnits() {
 			throw new AssertionError();
 		}
 	}
-
+	
 	/**
 	 * Constants that relate to the SI or other systems.
 	 * 
@@ -79,189 +104,320 @@ public final class SI {
 	 * @since 2019-11-08
 	 */
 	public static final class Constants {
-		public static final LinearUnit EARTH_GRAVITY = METRE.dividedBy(SECOND).dividedBy(SECOND).times(9.80665);
+		public static final LinearUnit EARTH_GRAVITY = METRE.dividedBy(SECOND)
+				.dividedBy(SECOND).times(9.80665);
 	}
-
+	
 	// dimensions used in the SI, as ObjectProducts
 	public static final class Dimensions {
-		public static final ObjectProduct<BaseDimension> EMPTY = ObjectProduct.empty();
-		public static final ObjectProduct<BaseDimension> LENGTH = ObjectProduct.oneOf(BaseDimensions.LENGTH);
-		public static final ObjectProduct<BaseDimension> MASS = ObjectProduct.oneOf(BaseDimensions.MASS);
-		public static final ObjectProduct<BaseDimension> TIME = ObjectProduct.oneOf(BaseDimensions.TIME);
+		public static final ObjectProduct<BaseDimension> EMPTY = ObjectProduct
+				.empty();
+		public static final ObjectProduct<BaseDimension> LENGTH = ObjectProduct
+				.oneOf(BaseDimensions.LENGTH);
+		public static final ObjectProduct<BaseDimension> MASS = ObjectProduct
+				.oneOf(BaseDimensions.MASS);
+		public static final ObjectProduct<BaseDimension> TIME = ObjectProduct
+				.oneOf(BaseDimensions.TIME);
 		public static final ObjectProduct<BaseDimension> ELECTRIC_CURRENT = ObjectProduct
 				.oneOf(BaseDimensions.ELECTRIC_CURRENT);
-		public static final ObjectProduct<BaseDimension> TEMPERATURE = ObjectProduct.oneOf(BaseDimensions.TEMPERATURE);
-		public static final ObjectProduct<BaseDimension> QUANTITY = ObjectProduct.oneOf(BaseDimensions.QUANTITY);
+		public static final ObjectProduct<BaseDimension> TEMPERATURE = ObjectProduct
+				.oneOf(BaseDimensions.TEMPERATURE);
+		public static final ObjectProduct<BaseDimension> QUANTITY = ObjectProduct
+				.oneOf(BaseDimensions.QUANTITY);
 		public static final ObjectProduct<BaseDimension> LUMINOUS_INTENSITY = ObjectProduct
 				.oneOf(BaseDimensions.LUMINOUS_INTENSITY);
-		public static final ObjectProduct<BaseDimension> INFORMATION = ObjectProduct.oneOf(BaseDimensions.INFORMATION);
-		public static final ObjectProduct<BaseDimension> CURRENCY = ObjectProduct.oneOf(BaseDimensions.CURRENCY);
+		public static final ObjectProduct<BaseDimension> INFORMATION = ObjectProduct
+				.oneOf(BaseDimensions.INFORMATION);
+		public static final ObjectProduct<BaseDimension> CURRENCY = ObjectProduct
+				.oneOf(BaseDimensions.CURRENCY);
 		// derived dimensions without named SI units
-		public static final ObjectProduct<BaseDimension> AREA = LENGTH.times(LENGTH);
-
-		public static final ObjectProduct<BaseDimension> VOLUME = AREA.times(LENGTH);
-		public static final ObjectProduct<BaseDimension> VELOCITY = LENGTH.dividedBy(TIME);
-		public static final ObjectProduct<BaseDimension> ACCELERATION = VELOCITY.dividedBy(TIME);
-		public static final ObjectProduct<BaseDimension> WAVENUMBER = EMPTY.dividedBy(LENGTH);
-		public static final ObjectProduct<BaseDimension> MASS_DENSITY = MASS.dividedBy(VOLUME);
-		public static final ObjectProduct<BaseDimension> SURFACE_DENSITY = MASS.dividedBy(AREA);
-		public static final ObjectProduct<BaseDimension> SPECIFIC_VOLUME = VOLUME.dividedBy(MASS);
-		public static final ObjectProduct<BaseDimension> CURRENT_DENSITY = ELECTRIC_CURRENT.dividedBy(AREA);
-		public static final ObjectProduct<BaseDimension> MAGNETIC_FIELD_STRENGTH = ELECTRIC_CURRENT.dividedBy(LENGTH);
-		public static final ObjectProduct<BaseDimension> CONCENTRATION = QUANTITY.dividedBy(VOLUME);
-		public static final ObjectProduct<BaseDimension> MASS_CONCENTRATION = CONCENTRATION.times(MASS);
-		public static final ObjectProduct<BaseDimension> LUMINANCE = LUMINOUS_INTENSITY.dividedBy(AREA);
-		public static final ObjectProduct<BaseDimension> REFRACTIVE_INDEX = VELOCITY.dividedBy(VELOCITY);
-		public static final ObjectProduct<BaseDimension> REFLACTIVE_PERMEABILITY = EMPTY.times(EMPTY);
-		public static final ObjectProduct<BaseDimension> ANGLE = LENGTH.dividedBy(LENGTH);
-		public static final ObjectProduct<BaseDimension> SOLID_ANGLE = AREA.dividedBy(AREA);
-
+		public static final ObjectProduct<BaseDimension> AREA = LENGTH
+				.times(LENGTH);
+		
+		public static final ObjectProduct<BaseDimension> VOLUME = AREA
+				.times(LENGTH);
+		public static final ObjectProduct<BaseDimension> VELOCITY = LENGTH
+				.dividedBy(TIME);
+		public static final ObjectProduct<BaseDimension> ACCELERATION = VELOCITY
+				.dividedBy(TIME);
+		public static final ObjectProduct<BaseDimension> WAVENUMBER = EMPTY
+				.dividedBy(LENGTH);
+		public static final ObjectProduct<BaseDimension> MASS_DENSITY = MASS
+				.dividedBy(VOLUME);
+		public static final ObjectProduct<BaseDimension> SURFACE_DENSITY = MASS
+				.dividedBy(AREA);
+		public static final ObjectProduct<BaseDimension> SPECIFIC_VOLUME = VOLUME
+				.dividedBy(MASS);
+		public static final ObjectProduct<BaseDimension> CURRENT_DENSITY = ELECTRIC_CURRENT
+				.dividedBy(AREA);
+		public static final ObjectProduct<BaseDimension> MAGNETIC_FIELD_STRENGTH = ELECTRIC_CURRENT
+				.dividedBy(LENGTH);
+		public static final ObjectProduct<BaseDimension> CONCENTRATION = QUANTITY
+				.dividedBy(VOLUME);
+		public static final ObjectProduct<BaseDimension> MASS_CONCENTRATION = CONCENTRATION
+				.times(MASS);
+		public static final ObjectProduct<BaseDimension> LUMINANCE = LUMINOUS_INTENSITY
+				.dividedBy(AREA);
+		public static final ObjectProduct<BaseDimension> REFRACTIVE_INDEX = VELOCITY
+				.dividedBy(VELOCITY);
+		public static final ObjectProduct<BaseDimension> REFLACTIVE_PERMEABILITY = EMPTY
+				.times(EMPTY);
+		public static final ObjectProduct<BaseDimension> ANGLE = LENGTH
+				.dividedBy(LENGTH);
+		public static final ObjectProduct<BaseDimension> SOLID_ANGLE = AREA
+				.dividedBy(AREA);
+		
 		// derived dimensions with named SI units
-		public static final ObjectProduct<BaseDimension> FREQUENCY = EMPTY.dividedBy(TIME);
-		public static final ObjectProduct<BaseDimension> FORCE = MASS.times(ACCELERATION);
-		public static final ObjectProduct<BaseDimension> ENERGY = FORCE.times(LENGTH);
-		public static final ObjectProduct<BaseDimension> POWER = ENERGY.dividedBy(TIME);
-		public static final ObjectProduct<BaseDimension> ELECTRIC_CHARGE = ELECTRIC_CURRENT.times(TIME);
-		public static final ObjectProduct<BaseDimension> VOLTAGE = ENERGY.dividedBy(ELECTRIC_CHARGE);
-		public static final ObjectProduct<BaseDimension> CAPACITANCE = ELECTRIC_CHARGE.dividedBy(VOLTAGE);
-		public static final ObjectProduct<BaseDimension> ELECTRIC_RESISTANCE = VOLTAGE.dividedBy(ELECTRIC_CURRENT);
-		public static final ObjectProduct<BaseDimension> ELECTRIC_CONDUCTANCE = ELECTRIC_CURRENT.dividedBy(VOLTAGE);
-		public static final ObjectProduct<BaseDimension> MAGNETIC_FLUX = VOLTAGE.times(TIME);
-		public static final ObjectProduct<BaseDimension> MAGNETIC_FLUX_DENSITY = MAGNETIC_FLUX.dividedBy(AREA);
-		public static final ObjectProduct<BaseDimension> INDUCTANCE = MAGNETIC_FLUX.dividedBy(ELECTRIC_CURRENT);
-		public static final ObjectProduct<BaseDimension> LUMINOUS_FLUX = LUMINOUS_INTENSITY.times(SOLID_ANGLE);
-		public static final ObjectProduct<BaseDimension> ILLUMINANCE = LUMINOUS_FLUX.dividedBy(AREA);
-		public static final ObjectProduct<BaseDimension> SPECIFIC_ENERGY = ENERGY.dividedBy(MASS);
-		public static final ObjectProduct<BaseDimension> CATALYTIC_ACTIVITY = QUANTITY.dividedBy(TIME);
-
+		public static final ObjectProduct<BaseDimension> FREQUENCY = EMPTY
+				.dividedBy(TIME);
+		public static final ObjectProduct<BaseDimension> FORCE = MASS
+				.times(ACCELERATION);
+		public static final ObjectProduct<BaseDimension> ENERGY = FORCE
+				.times(LENGTH);
+		public static final ObjectProduct<BaseDimension> POWER = ENERGY
+				.dividedBy(TIME);
+		public static final ObjectProduct<BaseDimension> ELECTRIC_CHARGE = ELECTRIC_CURRENT
+				.times(TIME);
+		public static final ObjectProduct<BaseDimension> VOLTAGE = ENERGY
+				.dividedBy(ELECTRIC_CHARGE);
+		public static final ObjectProduct<BaseDimension> CAPACITANCE = ELECTRIC_CHARGE
+				.dividedBy(VOLTAGE);
+		public static final ObjectProduct<BaseDimension> ELECTRIC_RESISTANCE = VOLTAGE
+				.dividedBy(ELECTRIC_CURRENT);
+		public static final ObjectProduct<BaseDimension> ELECTRIC_CONDUCTANCE = ELECTRIC_CURRENT
+				.dividedBy(VOLTAGE);
+		public static final ObjectProduct<BaseDimension> MAGNETIC_FLUX = VOLTAGE
+				.times(TIME);
+		public static final ObjectProduct<BaseDimension> MAGNETIC_FLUX_DENSITY = MAGNETIC_FLUX
+				.dividedBy(AREA);
+		public static final ObjectProduct<BaseDimension> INDUCTANCE = MAGNETIC_FLUX
+				.dividedBy(ELECTRIC_CURRENT);
+		public static final ObjectProduct<BaseDimension> LUMINOUS_FLUX = LUMINOUS_INTENSITY
+				.times(SOLID_ANGLE);
+		public static final ObjectProduct<BaseDimension> ILLUMINANCE = LUMINOUS_FLUX
+				.dividedBy(AREA);
+		public static final ObjectProduct<BaseDimension> SPECIFIC_ENERGY = ENERGY
+				.dividedBy(MASS);
+		public static final ObjectProduct<BaseDimension> CATALYTIC_ACTIVITY = QUANTITY
+				.dividedBy(TIME);
+		
 		// You may NOT get SI.Dimension instances!
 		private Dimensions() {
 			throw new AssertionError();
 		}
 	}
-
+	
 	/// The units of the SI
-	public static final LinearUnit ONE = LinearUnit.valueOf(ObjectProduct.empty(), 1);
+	public static final LinearUnit ONE = LinearUnit
+			.valueOf(ObjectProduct.empty(), 1);
 	public static final LinearUnit METRE = BaseUnits.METRE.asLinearUnit()
 			.withName(NameSymbol.of("metre", "m", "meter"));
 	public static final LinearUnit KILOGRAM = BaseUnits.KILOGRAM.asLinearUnit()
 			.withName(NameSymbol.of("kilogram", "kg"));
 	public static final LinearUnit SECOND = BaseUnits.SECOND.asLinearUnit()
 			.withName(NameSymbol.of("second", "s", "sec"));
-	public static final LinearUnit AMPERE = BaseUnits.AMPERE.asLinearUnit().withName(NameSymbol.of("ampere", "A"));
-	public static final LinearUnit KELVIN = BaseUnits.KELVIN.asLinearUnit().withName(NameSymbol.of("kelvin", "K"));
-	public static final LinearUnit MOLE = BaseUnits.MOLE.asLinearUnit().withName(NameSymbol.of("mole", "mol"));
-	public static final LinearUnit CANDELA = BaseUnits.CANDELA.asLinearUnit().withName(NameSymbol.of("candela", "cd"));
-	public static final LinearUnit BIT = BaseUnits.BIT.asLinearUnit().withName(NameSymbol.of("bit", "b"));
-	public static final LinearUnit DOLLAR = BaseUnits.DOLLAR.asLinearUnit().withName(NameSymbol.of("dollar", "$"));
-
+	public static final LinearUnit AMPERE = BaseUnits.AMPERE.asLinearUnit()
+			.withName(NameSymbol.of("ampere", "A"));
+	public static final LinearUnit KELVIN = BaseUnits.KELVIN.asLinearUnit()
+			.withName(NameSymbol.of("kelvin", "K"));
+	public static final LinearUnit MOLE = BaseUnits.MOLE.asLinearUnit()
+			.withName(NameSymbol.of("mole", "mol"));
+	public static final LinearUnit CANDELA = BaseUnits.CANDELA.asLinearUnit()
+			.withName(NameSymbol.of("candela", "cd"));
+	public static final LinearUnit BIT = BaseUnits.BIT.asLinearUnit()
+			.withName(NameSymbol.of("bit", "b"));
+	public static final LinearUnit DOLLAR = BaseUnits.DOLLAR.asLinearUnit()
+			.withName(NameSymbol.of("dollar", "$"));
+	
 	// Non-base units
-	public static final LinearUnit RADIAN = METRE.dividedBy(METRE).withName(NameSymbol.of("radian", "rad"));
-	public static final LinearUnit STERADIAN = RADIAN.times(RADIAN).withName(NameSymbol.of("steradian", "sr"));
-	public static final LinearUnit HERTZ = ONE.dividedBy(SECOND).withName(NameSymbol.of("hertz", "Hz"));
+	public static final LinearUnit RADIAN = METRE.dividedBy(METRE)
+			.withName(NameSymbol.of("radian", "rad"));
+	public static final LinearUnit STERADIAN = RADIAN.times(RADIAN)
+			.withName(NameSymbol.of("steradian", "sr"));
+	public static final LinearUnit HERTZ = ONE.dividedBy(SECOND)
+			.withName(NameSymbol.of("hertz", "Hz"));
 	// for periodic phenomena
-	public static final LinearUnit NEWTON = KILOGRAM.times(METRE).dividedBy(SECOND.times(SECOND))
+	public static final LinearUnit NEWTON = KILOGRAM.times(METRE)
+			.dividedBy(SECOND.times(SECOND))
 			.withName(NameSymbol.of("newton", "N"));
 	public static final LinearUnit PASCAL = NEWTON.dividedBy(METRE.times(METRE))
 			.withName(NameSymbol.of("pascal", "Pa"));
-	public static final LinearUnit JOULE = NEWTON.times(METRE).withName(NameSymbol.of("joule", "J"));
-	public static final LinearUnit WATT = JOULE.dividedBy(SECOND).withName(NameSymbol.of("watt", "W"));
-	public static final LinearUnit COULOMB = AMPERE.times(SECOND).withName(NameSymbol.of("coulomb", "C"));
-	public static final LinearUnit VOLT = JOULE.dividedBy(COULOMB).withName(NameSymbol.of("volt", "V"));
-	public static final LinearUnit FARAD = COULOMB.dividedBy(VOLT).withName(NameSymbol.of("farad", "F"));
-	public static final LinearUnit OHM = VOLT.dividedBy(AMPERE).withName(NameSymbol.of("ohm", "\u03A9")); // omega
-	public static final LinearUnit SIEMENS = ONE.dividedBy(OHM).withName(NameSymbol.of("siemens", "S"));
-	public static final LinearUnit WEBER = VOLT.times(SECOND).withName(NameSymbol.of("weber", "Wb"));
-	public static final LinearUnit TESLA = WEBER.dividedBy(METRE.times(METRE)).withName(NameSymbol.of("tesla", "T"));
-	public static final LinearUnit HENRY = WEBER.dividedBy(AMPERE).withName(NameSymbol.of("henry", "H"));
-	public static final LinearUnit LUMEN = CANDELA.times(STERADIAN).withName(NameSymbol.of("lumen", "lm"));
-	public static final LinearUnit LUX = LUMEN.dividedBy(METRE.times(METRE)).withName(NameSymbol.of("lux", "lx"));
-	public static final LinearUnit BEQUEREL = ONE.dividedBy(SECOND).withName(NameSymbol.of("bequerel", "Bq"));
+	public static final LinearUnit JOULE = NEWTON.times(METRE)
+			.withName(NameSymbol.of("joule", "J"));
+	public static final LinearUnit WATT = JOULE.dividedBy(SECOND)
+			.withName(NameSymbol.of("watt", "W"));
+	public static final LinearUnit COULOMB = AMPERE.times(SECOND)
+			.withName(NameSymbol.of("coulomb", "C"));
+	public static final LinearUnit VOLT = JOULE.dividedBy(COULOMB)
+			.withName(NameSymbol.of("volt", "V"));
+	public static final LinearUnit FARAD = COULOMB.dividedBy(VOLT)
+			.withName(NameSymbol.of("farad", "F"));
+	public static final LinearUnit OHM = VOLT.dividedBy(AMPERE)
+			.withName(NameSymbol.of("ohm", "\u03A9")); // omega
+	public static final LinearUnit SIEMENS = ONE.dividedBy(OHM)
+			.withName(NameSymbol.of("siemens", "S"));
+	public static final LinearUnit WEBER = VOLT.times(SECOND)
+			.withName(NameSymbol.of("weber", "Wb"));
+	public static final LinearUnit TESLA = WEBER.dividedBy(METRE.times(METRE))
+			.withName(NameSymbol.of("tesla", "T"));
+	public static final LinearUnit HENRY = WEBER.dividedBy(AMPERE)
+			.withName(NameSymbol.of("henry", "H"));
+	public static final LinearUnit LUMEN = CANDELA.times(STERADIAN)
+			.withName(NameSymbol.of("lumen", "lm"));
+	public static final LinearUnit LUX = LUMEN.dividedBy(METRE.times(METRE))
+			.withName(NameSymbol.of("lux", "lx"));
+	public static final LinearUnit BEQUEREL = ONE.dividedBy(SECOND)
+			.withName(NameSymbol.of("bequerel", "Bq"));
 	// for activity referred to a nucleotide
-	public static final LinearUnit GRAY = JOULE.dividedBy(KILOGRAM).withName(NameSymbol.of("grey", "Gy"));
+	public static final LinearUnit GRAY = JOULE.dividedBy(KILOGRAM)
+			.withName(NameSymbol.of("grey", "Gy"));
 	// for absorbed dose
-	public static final LinearUnit SIEVERT = JOULE.dividedBy(KILOGRAM).withName(NameSymbol.of("sievert", "Sv"));
+	public static final LinearUnit SIEVERT = JOULE.dividedBy(KILOGRAM)
+			.withName(NameSymbol.of("sievert", "Sv"));
 	// for dose equivalent
-	public static final LinearUnit KATAL = MOLE.dividedBy(SECOND).withName(NameSymbol.of("katal", "kat"));
-
+	public static final LinearUnit KATAL = MOLE.dividedBy(SECOND)
+			.withName(NameSymbol.of("katal", "kat"));
+	
 	// common derived units included for convenience
-	public static final LinearUnit GRAM = KILOGRAM.dividedBy(1000).withName(NameSymbol.of("gram", "g"));
+	public static final LinearUnit GRAM = KILOGRAM.dividedBy(1000)
+			.withName(NameSymbol.of("gram", "g"));
 	public static final LinearUnit SQUARE_METRE = METRE.toExponent(2)
-			.withName(NameSymbol.of("square metre", "m^2", "square meter", "metre squared", "meter squared"));
+			.withName(NameSymbol.of("square metre", "m^2", "square meter",
+					"metre squared", "meter squared"));
 	public static final LinearUnit CUBIC_METRE = METRE.toExponent(3)
-			.withName(NameSymbol.of("cubic metre", "m^3", "cubic meter", "metre cubed", "meter cubed"));
+			.withName(NameSymbol.of("cubic metre", "m^3", "cubic meter",
+					"metre cubed", "meter cubed"));
 	public static final LinearUnit METRE_PER_SECOND = METRE.dividedBy(SECOND)
-			.withName(NameSymbol.of("metre per second", "m/s", "meter per second"));
-
+			.withName(
+					NameSymbol.of("metre per second", "m/s", "meter per second"));
+	
 	// Non-SI units included for convenience
 	public static final Unit CELSIUS = Unit
-			.fromConversionFunctions(KELVIN.getBase(), tempK -> tempK - 273.15, tempC -> tempC + 273.15)
+			.fromConversionFunctions(KELVIN.getBase(), tempK -> tempK - 273.15,
+					tempC -> tempC + 273.15)
 			.withName(NameSymbol.of("degree Celsius", "\u00B0C"));
-	public static final LinearUnit MINUTE = SECOND.times(60).withName(NameSymbol.of("minute", "min"));
-	public static final LinearUnit HOUR = MINUTE.times(60).withName(NameSymbol.of("hour", "h", "hr"));
-	public static final LinearUnit DAY = HOUR.times(60).withName(NameSymbol.of("day", "d"));
-	public static final LinearUnit KILOMETRE_PER_HOUR = METRE.times(1000).dividedBy(HOUR)
-			.withName(NameSymbol.of("kilometre per hour", "km/h", "kilometer per hour"));
+	public static final LinearUnit MINUTE = SECOND.times(60)
+			.withName(NameSymbol.of("minute", "min"));
+	public static final LinearUnit HOUR = MINUTE.times(60)
+			.withName(NameSymbol.of("hour", "h", "hr"));
+	public static final LinearUnit DAY = HOUR.times(60)
+			.withName(NameSymbol.of("day", "d"));
+	public static final LinearUnit KILOMETRE_PER_HOUR = METRE.times(1000)
+			.dividedBy(HOUR).withName(NameSymbol.of("kilometre per hour", "km/h",
+					"kilometer per hour"));
 	public static final LinearUnit DEGREE = RADIAN.times(360 / (2 * Math.PI))
 			.withName(NameSymbol.of("degree", "\u00B0", "deg"));
-	public static final LinearUnit ARCMINUTE = DEGREE.dividedBy(60).withName(NameSymbol.of("arcminute", "arcmin"));
-	public static final LinearUnit ARCSECOND = ARCMINUTE.dividedBy(60).withName(NameSymbol.of("arcsecond", "arcsec"));
-	public static final LinearUnit ASTRONOMICAL_UNIT = METRE.times(149597870700.0)
+	public static final LinearUnit ARCMINUTE = DEGREE.dividedBy(60)
+			.withName(NameSymbol.of("arcminute", "arcmin"));
+	public static final LinearUnit ARCSECOND = ARCMINUTE.dividedBy(60)
+			.withName(NameSymbol.of("arcsecond", "arcsec"));
+	public static final LinearUnit ASTRONOMICAL_UNIT = METRE
+			.times(149597870700.0)
 			.withName(NameSymbol.of("astronomical unit", "au"));
-	public static final LinearUnit PARSEC = ASTRONOMICAL_UNIT.dividedBy(ARCSECOND)
-			.withName(NameSymbol.of("parsec", "pc"));
-	public static final LinearUnit HECTARE = METRE.times(METRE).times(10000.0).withName(NameSymbol.of("hectare", "ha"));
-	public static final LinearUnit LITRE = METRE.times(METRE).times(METRE).dividedBy(1000.0)
-			.withName(NameSymbol.of("litre", "L", "l", "liter"));
-	public static final LinearUnit TONNE = KILOGRAM.times(1000.0).withName(NameSymbol.of("tonne", "t", "metric ton"));
+	public static final LinearUnit PARSEC = ASTRONOMICAL_UNIT
+			.dividedBy(ARCSECOND).withName(NameSymbol.of("parsec", "pc"));
+	public static final LinearUnit HECTARE = METRE.times(METRE).times(10000.0)
+			.withName(NameSymbol.of("hectare", "ha"));
+	public static final LinearUnit LITRE = METRE.times(METRE).times(METRE)
+			.dividedBy(1000.0).withName(NameSymbol.of("litre", "L", "l", "liter"));
+	public static final LinearUnit TONNE = KILOGRAM.times(1000.0)
+			.withName(NameSymbol.of("tonne", "t", "metric ton"));
 	public static final LinearUnit DALTON = KILOGRAM.times(1.660539040e-27)
-			.withName(NameSymbol.of("dalton", "Da", "atomic unit", "u")); // approximate value
+			.withName(NameSymbol.of("dalton", "Da", "atomic unit", "u")); // approximate
+																								// value
 	public static final LinearUnit ELECTRONVOLT = JOULE.times(1.602176634e-19)
 			.withName(NameSymbol.of("electron volt", "eV"));
-	public static final LinearUnit BYTE = BIT.times(8).withName(NameSymbol.of("byte", "B"));
-	public static final Unit NEPER = Unit
-			.fromConversionFunctions(ONE.getBase(), pr -> 0.5 * Math.log(pr), Np -> Math.exp(2 * Np))
+	public static final LinearUnit BYTE = BIT.times(8)
+			.withName(NameSymbol.of("byte", "B"));
+	public static final Unit NEPER = Unit.fromConversionFunctions(ONE.getBase(),
+			pr -> 0.5 * Math.log(pr), Np -> Math.exp(2 * Np))
 			.withName(NameSymbol.of("neper", "Np"));
-	public static final Unit BEL = Unit
-			.fromConversionFunctions(ONE.getBase(), pr -> Math.log10(pr), dB -> Math.pow(10, dB))
+	public static final Unit BEL = Unit.fromConversionFunctions(ONE.getBase(),
+			pr -> Math.log10(pr), dB -> Math.pow(10, dB))
 			.withName(NameSymbol.of("bel", "B"));
 	public static final Unit DECIBEL = Unit
-			.fromConversionFunctions(ONE.getBase(), pr -> 10 * Math.log10(pr), dB -> Math.pow(10, dB / 10))
+			.fromConversionFunctions(ONE.getBase(), pr -> 10 * Math.log10(pr),
+					dB -> Math.pow(10, dB / 10))
 			.withName(NameSymbol.of("decibel", "dB"));
-
+	
 	/// The prefixes of the SI
 	// expanding decimal prefixes
-	public static final UnitPrefix KILO = UnitPrefix.valueOf(1e3).withName(NameSymbol.of("kilo", "k", "K"));
-	public static final UnitPrefix MEGA = UnitPrefix.valueOf(1e6).withName(NameSymbol.of("mega", "M"));
-	public static final UnitPrefix GIGA = UnitPrefix.valueOf(1e9).withName(NameSymbol.of("giga", "G"));
-	public static final UnitPrefix TERA = UnitPrefix.valueOf(1e12).withName(NameSymbol.of("tera", "T"));
-	public static final UnitPrefix PETA = UnitPrefix.valueOf(1e15).withName(NameSymbol.of("peta", "P"));
-	public static final UnitPrefix EXA = UnitPrefix.valueOf(1e18).withName(NameSymbol.of("exa", "E"));
-	public static final UnitPrefix ZETTA = UnitPrefix.valueOf(1e21).withName(NameSymbol.of("zetta", "Z"));
-	public static final UnitPrefix YOTTA = UnitPrefix.valueOf(1e24).withName(NameSymbol.of("yotta", "Y"));
-
+	public static final UnitPrefix KILO = UnitPrefix.valueOf(1e3)
+			.withName(NameSymbol.of("kilo", "k", "K"));
+	public static final UnitPrefix MEGA = UnitPrefix.valueOf(1e6)
+			.withName(NameSymbol.of("mega", "M"));
+	public static final UnitPrefix GIGA = UnitPrefix.valueOf(1e9)
+			.withName(NameSymbol.of("giga", "G"));
+	public static final UnitPrefix TERA = UnitPrefix.valueOf(1e12)
+			.withName(NameSymbol.of("tera", "T"));
+	public static final UnitPrefix PETA = UnitPrefix.valueOf(1e15)
+			.withName(NameSymbol.of("peta", "P"));
+	public static final UnitPrefix EXA = UnitPrefix.valueOf(1e18)
+			.withName(NameSymbol.of("exa", "E"));
+	public static final UnitPrefix ZETTA = UnitPrefix.valueOf(1e21)
+			.withName(NameSymbol.of("zetta", "Z"));
+	public static final UnitPrefix YOTTA = UnitPrefix.valueOf(1e24)
+			.withName(NameSymbol.of("yotta", "Y"));
+	
 	// contracting decimal prefixes
-	public static final UnitPrefix MILLI = UnitPrefix.valueOf(1e-3).withName(NameSymbol.of("milli", "m"));
-	public static final UnitPrefix MICRO = UnitPrefix.valueOf(1e-6).withName(NameSymbol.of("micro", "\u03BC", "u")); // mu
-	public static final UnitPrefix NANO = UnitPrefix.valueOf(1e-9).withName(NameSymbol.of("nano", "n"));
-	public static final UnitPrefix PICO = UnitPrefix.valueOf(1e-12).withName(NameSymbol.of("pico", "p"));
-	public static final UnitPrefix FEMTO = UnitPrefix.valueOf(1e-15).withName(NameSymbol.of("femto", "f"));
-	public static final UnitPrefix ATTO = UnitPrefix.valueOf(1e-18).withName(NameSymbol.of("atto", "a"));
-	public static final UnitPrefix ZEPTO = UnitPrefix.valueOf(1e-21).withName(NameSymbol.of("zepto", "z"));
-	public static final UnitPrefix YOCTO = UnitPrefix.valueOf(1e-24).withName(NameSymbol.of("yocto", "y"));
-
+	public static final UnitPrefix MILLI = UnitPrefix.valueOf(1e-3)
+			.withName(NameSymbol.of("milli", "m"));
+	public static final UnitPrefix MICRO = UnitPrefix.valueOf(1e-6)
+			.withName(NameSymbol.of("micro", "\u03BC", "u")); // mu
+	public static final UnitPrefix NANO = UnitPrefix.valueOf(1e-9)
+			.withName(NameSymbol.of("nano", "n"));
+	public static final UnitPrefix PICO = UnitPrefix.valueOf(1e-12)
+			.withName(NameSymbol.of("pico", "p"));
+	public static final UnitPrefix FEMTO = UnitPrefix.valueOf(1e-15)
+			.withName(NameSymbol.of("femto", "f"));
+	public static final UnitPrefix ATTO = UnitPrefix.valueOf(1e-18)
+			.withName(NameSymbol.of("atto", "a"));
+	public static final UnitPrefix ZEPTO = UnitPrefix.valueOf(1e-21)
+			.withName(NameSymbol.of("zepto", "z"));
+	public static final UnitPrefix YOCTO = UnitPrefix.valueOf(1e-24)
+			.withName(NameSymbol.of("yocto", "y"));
+	
 	// prefixes that don't match the pattern of thousands
-	public static final UnitPrefix DEKA = UnitPrefix.valueOf(1e1).withName(NameSymbol.of("deka", "da", "deca", "D"));
-	public static final UnitPrefix HECTO = UnitPrefix.valueOf(1e2).withName(NameSymbol.of("hecto", "h", "H", "hekto"));
-	public static final UnitPrefix DECI = UnitPrefix.valueOf(1e-1).withName(NameSymbol.of("deci", "d"));
-	public static final UnitPrefix CENTI = UnitPrefix.valueOf(1e-2).withName(NameSymbol.of("centi", "c"));
-	public static final UnitPrefix KIBI = UnitPrefix.valueOf(1024).withName(NameSymbol.of("kibi", "Ki"));
-	public static final UnitPrefix MEBI = KIBI.times(1024).withName(NameSymbol.of("mebi", "Mi"));
-	public static final UnitPrefix GIBI = MEBI.times(1024).withName(NameSymbol.of("gibi", "Gi"));
-	public static final UnitPrefix TEBI = GIBI.times(1024).withName(NameSymbol.of("tebi", "Ti"));
-	public static final UnitPrefix PEBI = TEBI.times(1024).withName(NameSymbol.of("pebi", "Pi"));
-	public static final UnitPrefix EXBI = PEBI.times(1024).withName(NameSymbol.of("exbi", "Ei"));
-
+	public static final UnitPrefix DEKA = UnitPrefix.valueOf(1e1)
+			.withName(NameSymbol.of("deka", "da", "deca", "D"));
+	public static final UnitPrefix HECTO = UnitPrefix.valueOf(1e2)
+			.withName(NameSymbol.of("hecto", "h", "H", "hekto"));
+	public static final UnitPrefix DECI = UnitPrefix.valueOf(1e-1)
+			.withName(NameSymbol.of("deci", "d"));
+	public static final UnitPrefix CENTI = UnitPrefix.valueOf(1e-2)
+			.withName(NameSymbol.of("centi", "c"));
+	public static final UnitPrefix KIBI = UnitPrefix.valueOf(1024)
+			.withName(NameSymbol.of("kibi", "Ki"));
+	public static final UnitPrefix MEBI = KIBI.times(1024)
+			.withName(NameSymbol.of("mebi", "Mi"));
+	public static final UnitPrefix GIBI = MEBI.times(1024)
+			.withName(NameSymbol.of("gibi", "Gi"));
+	public static final UnitPrefix TEBI = GIBI.times(1024)
+			.withName(NameSymbol.of("tebi", "Ti"));
+	public static final UnitPrefix PEBI = TEBI.times(1024)
+			.withName(NameSymbol.of("pebi", "Pi"));
+	public static final UnitPrefix EXBI = PEBI.times(1024)
+			.withName(NameSymbol.of("exbi", "Ei"));
+	
+	// sets of prefixes
+	public static final Set<UnitPrefix> ALL_PREFIXES = new HashSet<>(
+			Arrays.asList(DEKA, HECTO, KILO, MEGA, GIGA, TERA, PETA, EXA, ZETTA,
+					YOTTA, DECI, CENTI, MILLI, MICRO, NANO, PICO, FEMTO, ATTO, ZEPTO,
+					YOCTO, KIBI, MEBI, GIBI, TEBI, PEBI, EXBI));
+	public static final Set<UnitPrefix> DECIMAL_PREFIXES = new HashSet<>(
+			Arrays.asList(DEKA, HECTO, KILO, MEGA, GIGA, TERA, PETA, EXA, ZETTA,
+					YOTTA, DECI, CENTI, MILLI, MICRO, NANO, PICO, FEMTO, ATTO, ZEPTO,
+					YOCTO));
+	public static final Set<UnitPrefix> THOUSAND_PREFIXES = new HashSet<>(
+			Arrays.asList(KILO, MEGA, GIGA, TERA, PETA, EXA, ZETTA, YOTTA, MILLI,
+					MICRO, NANO, PICO, FEMTO, ATTO, ZEPTO, YOCTO));
+	public static final Set<UnitPrefix> MAGNIFYING_PREFIXES = new HashSet<>(
+			Arrays.asList(DEKA, HECTO, KILO, MEGA, GIGA, TERA, PETA, EXA, ZETTA,
+					YOTTA, KIBI, MEBI, GIBI, TEBI, PEBI, EXBI));
+	public static final Set<UnitPrefix> REDUCING_PREFIXES = new HashSet<>(
+			Arrays.asList(DECI, CENTI, MILLI, MICRO, NANO, PICO, FEMTO, ATTO,
+					ZEPTO, YOCTO));
+	
 	// You may NOT get SI instances!
 	private SI() {
 		throw new AssertionError();
-- 
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