// <copyright file="Constants.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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//
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// Copyright (c) 2009-2010 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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namespace IStation.Numerics
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{
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/// <summary>
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/// A collection of frequently used mathematical constants.
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/// </summary>
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public static class Constants
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{
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#region Mathematical Constants
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/// <summary>The number e</summary>
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public const double E = 2.7182818284590452353602874713526624977572470937000d;
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/// <summary>The number log[2](e)</summary>
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public const double Log2E = 1.4426950408889634073599246810018921374266459541530d;
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/// <summary>The number log[10](e)</summary>
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public const double Log10E = 0.43429448190325182765112891891660508229439700580366d;
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/// <summary>The number log[e](2)</summary>
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public const double Ln2 = 0.69314718055994530941723212145817656807550013436026d;
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/// <summary>The number log[e](10)</summary>
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public const double Ln10 = 2.3025850929940456840179914546843642076011014886288d;
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/// <summary>The number log[e](pi)</summary>
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public const double LnPi = 1.1447298858494001741434273513530587116472948129153d;
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/// <summary>The number log[e](2*pi)/2</summary>
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public const double Ln2PiOver2 = 0.91893853320467274178032973640561763986139747363780d;
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/// <summary>The number 1/e</summary>
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public const double InvE = 0.36787944117144232159552377016146086744581113103176d;
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/// <summary>The number sqrt(e)</summary>
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public const double SqrtE = 1.6487212707001281468486507878141635716537761007101d;
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/// <summary>The number sqrt(2)</summary>
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public const double Sqrt2 = 1.4142135623730950488016887242096980785696718753769d;
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/// <summary>The number sqrt(3)</summary>
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public const double Sqrt3 = 1.7320508075688772935274463415058723669428052538104d;
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/// <summary>The number sqrt(1/2) = 1/sqrt(2) = sqrt(2)/2</summary>
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public const double Sqrt1Over2 = 0.70710678118654752440084436210484903928483593768845d;
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/// <summary>The number sqrt(3)/2</summary>
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public const double HalfSqrt3 = 0.86602540378443864676372317075293618347140262690520d;
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/// <summary>The number pi</summary>
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public const double Pi = 3.1415926535897932384626433832795028841971693993751d;
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/// <summary>The number pi*2</summary>
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public const double Pi2 = 6.2831853071795864769252867665590057683943387987502d;
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/// <summary>The number pi/2</summary>
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public const double PiOver2 = 1.5707963267948966192313216916397514420985846996876d;
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/// <summary>The number pi*3/2</summary>
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public const double Pi3Over2 = 4.71238898038468985769396507491925432629575409906266d;
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/// <summary>The number pi/4</summary>
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public const double PiOver4 = 0.78539816339744830961566084581987572104929234984378d;
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/// <summary>The number sqrt(pi)</summary>
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public const double SqrtPi = 1.7724538509055160272981674833411451827975494561224d;
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/// <summary>The number sqrt(2pi)</summary>
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public const double Sqrt2Pi = 2.5066282746310005024157652848110452530069867406099d;
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/// <summary>The number sqrt(pi/2)</summary>
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public const double SqrtPiOver2 = 1.2533141373155002512078826424055226265034933703050d;
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/// <summary>The number sqrt(2*pi*e)</summary>
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public const double Sqrt2PiE = 4.1327313541224929384693918842998526494455219169913d;
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/// <summary>The number log(sqrt(2*pi))</summary>
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public const double LogSqrt2Pi = 0.91893853320467274178032973640561763986139747363778;
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/// <summary>The number log(sqrt(2*pi*e))</summary>
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public const double LogSqrt2PiE = 1.4189385332046727417803297364056176398613974736378d;
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/// <summary>The number log(2 * sqrt(e / pi))</summary>
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public const double LogTwoSqrtEOverPi = 0.6207822376352452223455184457816472122518527279025978;
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/// <summary>The number 1/pi</summary>
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public const double InvPi = 0.31830988618379067153776752674502872406891929148091d;
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/// <summary>The number 2/pi</summary>
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public const double TwoInvPi = 0.63661977236758134307553505349005744813783858296182d;
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/// <summary>The number 1/sqrt(pi)</summary>
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public const double InvSqrtPi = 0.56418958354775628694807945156077258584405062932899d;
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/// <summary>The number 1/sqrt(2pi)</summary>
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public const double InvSqrt2Pi = 0.39894228040143267793994605993438186847585863116492d;
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/// <summary>The number 2/sqrt(pi)</summary>
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public const double TwoInvSqrtPi = 1.1283791670955125738961589031215451716881012586580d;
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/// <summary>The number 2 * sqrt(e / pi)</summary>
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public const double TwoSqrtEOverPi = 1.8603827342052657173362492472666631120594218414085755;
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/// <summary>The number (pi)/180 - factor to convert from Degree (deg) to Radians (rad).</summary>
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/// <seealso cref="Trig.DegreeToRadian"/>
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/// <seealso cref="Trig.RadianToDegree"/>
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public const double Degree = 0.017453292519943295769236907684886127134428718885417d;
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/// <summary>The number (pi)/200 - factor to convert from NewGrad (grad) to Radians (rad).</summary>
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/// <seealso cref="Trig.GradToRadian"/>
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/// <seealso cref="Trig.RadianToGrad"/>
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public const double Grad = 0.015707963267948966192313216916397514420985846996876d;
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/// <summary>The number ln(10)/20 - factor to convert from Power Decibel (dB) to Neper (Np). Use this version when the Decibel represent a power gain but the compared values are not powers (e.g. amplitude, current, voltage).</summary>
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public const double PowerDecibel = 0.11512925464970228420089957273421821038005507443144d;
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/// <summary>The number ln(10)/10 - factor to convert from Neutral Decibel (dB) to Neper (Np). Use this version when either both or neither of the Decibel and the compared values represent powers.</summary>
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public const double NeutralDecibel = 0.23025850929940456840179914546843642076011014886288d;
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/// <summary>The Catalan constant</summary>
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/// <remarks>Sum(k=0 -> inf){ (-1)^k/(2*k + 1)2 }</remarks>
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public const double Catalan = 0.9159655941772190150546035149323841107741493742816721342664981196217630197762547694794d;
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/// <summary>The Euler-Mascheroni constant</summary>
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/// <remarks>lim(n -> inf){ Sum(k=1 -> n) { 1/k - log(n) } }</remarks>
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public const double EulerMascheroni = 0.5772156649015328606065120900824024310421593359399235988057672348849d;
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/// <summary>The number (1+sqrt(5))/2, also known as the golden ratio</summary>
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public const double GoldenRatio = 1.6180339887498948482045868343656381177203091798057628621354486227052604628189024497072d;
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/// <summary>The Glaisher constant</summary>
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/// <remarks>e^(1/12 - Zeta(-1))</remarks>
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public const double Glaisher = 1.2824271291006226368753425688697917277676889273250011920637400217404063088588264611297d;
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/// <summary>The Khinchin constant</summary>
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/// <remarks>prod(k=1 -> inf){1+1/(k*(k+2))^log(k,2)}</remarks>
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public const double Khinchin = 2.6854520010653064453097148354817956938203822939944629530511523455572188595371520028011d;
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/// <summary>
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/// The size of a double in bytes.
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/// </summary>
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public const int SizeOfDouble = sizeof(double);
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/// <summary>
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/// The size of an int in bytes.
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/// </summary>
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public const int SizeOfInt = sizeof(int);
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/// <summary>
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/// The size of a float in bytes.
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/// </summary>
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public const int SizeOfFloat = sizeof(float);
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/// <summary>
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/// The size of a Complex in bytes.
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/// </summary>
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public const int SizeOfComplex = 2 * SizeOfDouble;
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/// <summary>
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/// The size of a Complex in bytes.
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/// </summary>
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public const int SizeOfComplex32 = 2 * SizeOfFloat;
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#endregion
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#region UNIVERSAL CONSTANTS
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/// <summary>Speed of Light in Vacuum: c_0 = 2.99792458e8 [m s^-1] (defined, exact; 2007 CODATA)</summary>
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public const double SpeedOfLight = 2.99792458e8;
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/// <summary>Magnetic Permeability in Vacuum: mu_0 = 4*Pi * 10^-7 [N A^-2 = kg m A^-2 s^-2] (defined, exact; 2007 CODATA)</summary>
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public const double MagneticPermeability = 1.2566370614359172953850573533118011536788677597500e-6;
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/// <summary>Electric Permittivity in Vacuum: epsilon_0 = 1/(mu_0*c_0^2) [F m^-1 = A^2 s^4 kg^-1 m^-3] (defined, exact; 2007 CODATA)</summary>
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public const double ElectricPermittivity = 8.8541878171937079244693661186959426889222899381429e-12;
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/// <summary>Characteristic Impedance of Vacuum: Z_0 = mu_0*c_0 [Ohm = m^2 kg s^-3 A^-2] (defined, exact; 2007 CODATA)</summary>
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public const double CharacteristicImpedanceVacuum = 376.73031346177065546819840042031930826862350835242;
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/// <summary>Newtonian Constant of Gravitation: G = 6.67429e-11 [m^3 kg^-1 s^-2] (2007 CODATA)</summary>
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public const double GravitationalConstant = 6.67429e-11;
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/// <summary>Planck's constant: h = 6.62606896e-34 [J s = m^2 kg s^-1] (2007 CODATA)</summary>
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public const double PlancksConstant = 6.62606896e-34;
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/// <summary>Reduced Planck's constant: h_bar = h / (2*Pi) [J s = m^2 kg s^-1] (2007 CODATA)</summary>
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public const double DiracsConstant = 1.054571629e-34;
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/// <summary>Planck mass: m_p = (h_bar*c_0/G)^(1/2) [kg] (2007 CODATA)</summary>
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public const double PlancksMass = 2.17644e-8;
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/// <summary>Planck temperature: T_p = (h_bar*c_0^5/G)^(1/2)/k [K] (2007 CODATA)</summary>
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public const double PlancksTemperature = 1.416786e32;
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/// <summary>Planck length: l_p = h_bar/(m_p*c_0) [m] (2007 CODATA)</summary>
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public const double PlancksLength = 1.616253e-35;
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/// <summary>Planck time: t_p = l_p/c_0 [s] (2007 CODATA)</summary>
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public const double PlancksTime = 5.39124e-44;
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#endregion
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#region ELECTROMAGNETIC CONSTANTS
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/// <summary>Elementary Electron Charge: e = 1.602176487e-19 [C = A s] (2007 CODATA)</summary>
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public const double ElementaryCharge = 1.602176487e-19;
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/// <summary>Magnetic Flux Quantum: theta_0 = h/(2*e) [Wb = m^2 kg s^-2 A^-1] (2007 CODATA)</summary>
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public const double MagneticFluxQuantum = 2.067833668e-15;
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/// <summary>Conductance Quantum: G_0 = 2*e^2/h [S = m^-2 kg^-1 s^3 A^2] (2007 CODATA)</summary>
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public const double ConductanceQuantum = 7.7480917005e-5;
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/// <summary>Josephson Constant: K_J = 2*e/h [Hz V^-1] (2007 CODATA)</summary>
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public const double JosephsonConstant = 483597.891e9;
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/// <summary>Von Klitzing Constant: R_K = h/e^2 [Ohm = m^2 kg s^-3 A^-2] (2007 CODATA)</summary>
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public const double VonKlitzingConstant = 25812.807557;
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/// <summary>Bohr Magneton: mu_B = e*h_bar/2*m_e [J T^-1] (2007 CODATA)</summary>
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public const double BohrMagneton = 927.400915e-26;
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/// <summary>Nuclear Magneton: mu_N = e*h_bar/2*m_p [J T^-1] (2007 CODATA)</summary>
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public const double NuclearMagneton = 5.05078324e-27;
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#endregion
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#region ATOMIC AND NUCLEAR CONSTANTS
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/// <summary>Fine Structure Constant: alpha = e^2/4*Pi*e_0*h_bar*c_0 [1] (2007 CODATA)</summary>
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public const double FineStructureConstant = 7.2973525376e-3;
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/// <summary>Rydberg Constant: R_infty = alpha^2*m_e*c_0/2*h [m^-1] (2007 CODATA)</summary>
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public const double RydbergConstant = 10973731.568528;
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/// <summary>Bor Radius: a_0 = alpha/4*Pi*R_infty [m] (2007 CODATA)</summary>
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public const double BohrRadius = 0.52917720859e-10;
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/// <summary>Hartree Energy: E_h = 2*R_infty*h*c_0 [J] (2007 CODATA)</summary>
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public const double HartreeEnergy = 4.35974394e-18;
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/// <summary>Quantum of Circulation: h/2*m_e [m^2 s^-1] (2007 CODATA)</summary>
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public const double QuantumOfCirculation = 3.6369475199e-4;
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/// <summary>Fermi Coupling Constant: G_F/(h_bar*c_0)^3 [GeV^-2] (2007 CODATA)</summary>
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public const double FermiCouplingConstant = 1.16637e-5;
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/// <summary>Weak Mixin Angle: sin^2(theta_W) [1] (2007 CODATA)</summary>
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public const double WeakMixingAngle = 0.22256;
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/// <summary>Electron Mass: [kg] (2007 CODATA)</summary>
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public const double ElectronMass = 9.10938215e-31;
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/// <summary>Electron Mass Energy Equivalent: [J] (2007 CODATA)</summary>
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public const double ElectronMassEnergyEquivalent = 8.18710438e-14;
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/// <summary>Electron Molar Mass: [kg mol^-1] (2007 CODATA)</summary>
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public const double ElectronMolarMass = 5.4857990943e-7;
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/// <summary>Electron Compton Wavelength: [m] (2007 CODATA)</summary>
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public const double ComptonWavelength = 2.4263102175e-12;
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/// <summary>Classical Electron Radius: [m] (2007 CODATA)</summary>
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public const double ClassicalElectronRadius = 2.8179402894e-15;
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/// <summary>Thomson Cross Section: [m^2] (2002 CODATA)</summary>
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public const double ThomsonCrossSection = 0.6652458558e-28;
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/// <summary>Electron Magnetic Moment: [J T^-1] (2007 CODATA)</summary>
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public const double ElectronMagneticMoment = -928.476377e-26;
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/// <summary>Electon G-Factor: [1] (2007 CODATA)</summary>
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public const double ElectronGFactor = -2.0023193043622;
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/// <summary>Muon Mass: [kg] (2007 CODATA)</summary>
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public const double MuonMass = 1.88353130e-28;
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/// <summary>Muon Mass Energy Equivalent: [J] (2007 CODATA)</summary>
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public const double MuonMassEnegryEquivalent = 1.692833511e-11;
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/// <summary>Muon Molar Mass: [kg mol^-1] (2007 CODATA)</summary>
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public const double MuonMolarMass = 0.1134289256e-3;
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/// <summary>Muon Compton Wavelength: [m] (2007 CODATA)</summary>
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public const double MuonComptonWavelength = 11.73444104e-15;
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/// <summary>Muon Magnetic Moment: [J T^-1] (2007 CODATA)</summary>
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public const double MuonMagneticMoment = -4.49044786e-26;
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/// <summary>Muon G-Factor: [1] (2007 CODATA)</summary>
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public const double MuonGFactor = -2.0023318414;
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/// <summary>Tau Mass: [kg] (2007 CODATA)</summary>
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public const double TauMass = 3.16777e-27;
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/// <summary>Tau Mass Energy Equivalent: [J] (2007 CODATA)</summary>
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public const double TauMassEnergyEquivalent = 2.84705e-10;
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/// <summary>Tau Molar Mass: [kg mol^-1] (2007 CODATA)</summary>
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public const double TauMolarMass = 1.90768e-3;
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/// <summary>Tau Compton Wavelength: [m] (2007 CODATA)</summary>
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public const double TauComptonWavelength = 0.69772e-15;
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/// <summary>Proton Mass: [kg] (2007 CODATA)</summary>
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public const double ProtonMass = 1.672621637e-27;
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/// <summary>Proton Mass Energy Equivalent: [J] (2007 CODATA)</summary>
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public const double ProtonMassEnergyEquivalent = 1.503277359e-10;
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/// <summary>Proton Molar Mass: [kg mol^-1] (2007 CODATA)</summary>
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public const double ProtonMolarMass = 1.00727646677e-3;
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/// <summary>Proton Compton Wavelength: [m] (2007 CODATA)</summary>
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public const double ProtonComptonWavelength = 1.3214098446e-15;
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/// <summary>Proton Magnetic Moment: [J T^-1] (2007 CODATA)</summary>
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public const double ProtonMagneticMoment = 1.410606662e-26;
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/// <summary>Proton G-Factor: [1] (2007 CODATA)</summary>
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public const double ProtonGFactor = 5.585694713;
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/// <summary>Proton Shielded Magnetic Moment: [J T^-1] (2007 CODATA)</summary>
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public const double ShieldedProtonMagneticMoment = 1.410570419e-26;
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/// <summary>Proton Gyro-Magnetic Ratio: [s^-1 T^-1] (2007 CODATA)</summary>
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public const double ProtonGyromagneticRatio = 2.675222099e8;
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/// <summary>Proton Shielded Gyro-Magnetic Ratio: [s^-1 T^-1] (2007 CODATA)</summary>
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public const double ShieldedProtonGyromagneticRatio = 2.675153362e8;
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/// <summary>Neutron Mass: [kg] (2007 CODATA)</summary>
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public const double NeutronMass = 1.674927212e-27;
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/// <summary>Neutron Mass Energy Equivalent: [J] (2007 CODATA)</summary>
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public const double NeutronMassEnegryEquivalent = 1.505349506e-10;
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/// <summary>Neutron Molar Mass: [kg mol^-1] (2007 CODATA)</summary>
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public const double NeutronMolarMass = 1.00866491597e-3;
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/// <summary>Neuron Compton Wavelength: [m] (2007 CODATA)</summary>
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public const double NeutronComptonWavelength = 1.3195908951e-1;
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/// <summary>Neutron Magnetic Moment: [J T^-1] (2007 CODATA)</summary>
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public const double NeutronMagneticMoment = -0.96623641e-26;
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/// <summary>Neutron G-Factor: [1] (2007 CODATA)</summary>
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public const double NeutronGFactor = -3.82608545;
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/// <summary>Neutron Gyro-Magnetic Ratio: [s^-1 T^-1] (2007 CODATA)</summary>
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public const double NeutronGyromagneticRatio = 1.83247185e8;
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/// <summary>Deuteron Mass: [kg] (2007 CODATA)</summary>
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public const double DeuteronMass = 3.34358320e-27;
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/// <summary>Deuteron Mass Energy Equivalent: [J] (2007 CODATA)</summary>
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public const double DeuteronMassEnegryEquivalent = 3.00506272e-10;
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/// <summary>Deuteron Molar Mass: [kg mol^-1] (2007 CODATA)</summary>
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public const double DeuteronMolarMass = 2.013553212725e-3;
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/// <summary>Deuteron Magnetic Moment: [J T^-1] (2007 CODATA)</summary>
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public const double DeuteronMagneticMoment = 0.433073465e-26;
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/// <summary>Helion Mass: [kg] (2007 CODATA)</summary>
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public const double HelionMass = 5.00641192e-27;
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/// <summary>Helion Mass Energy Equivalent: [J] (2007 CODATA)</summary>
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public const double HelionMassEnegryEquivalent = 4.49953864e-10;
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/// <summary>Helion Molar Mass: [kg mol^-1] (2007 CODATA)</summary>
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public const double HelionMolarMass = 3.0149322473e-3;
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/// <summary>Avogadro constant: [mol^-1] (2010 CODATA)</summary>
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public const double Avogadro = 6.0221412927e23;
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#endregion
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#region Scientific Prefixes
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/// <summary>The SI prefix factor corresponding to 1 000 000 000 000 000 000 000 000</summary>
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public const double Yotta = 1e24;
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/// <summary>The SI prefix factor corresponding to 1 000 000 000 000 000 000 000</summary>
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public const double Zetta = 1e21;
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/// <summary>The SI prefix factor corresponding to 1 000 000 000 000 000 000</summary>
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public const double Exa = 1e18;
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/// <summary>The SI prefix factor corresponding to 1 000 000 000 000 000</summary>
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public const double Peta = 1e15;
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/// <summary>The SI prefix factor corresponding to 1 000 000 000 000</summary>
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public const double Tera = 1e12;
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/// <summary>The SI prefix factor corresponding to 1 000 000 000</summary>
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public const double Giga = 1e9;
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/// <summary>The SI prefix factor corresponding to 1 000 000</summary>
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public const double Mega = 1e6;
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/// <summary>The SI prefix factor corresponding to 1 000</summary>
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public const double Kilo = 1e3;
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/// <summary>The SI prefix factor corresponding to 100</summary>
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public const double Hecto = 1e2;
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/// <summary>The SI prefix factor corresponding to 10</summary>
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public const double Deca = 1e1;
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/// <summary>The SI prefix factor corresponding to 0.1</summary>
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public const double Deci = 1e-1;
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/// <summary>The SI prefix factor corresponding to 0.01</summary>
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public const double Centi = 1e-2;
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/// <summary>The SI prefix factor corresponding to 0.001</summary>
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public const double Milli = 1e-3;
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/// <summary>The SI prefix factor corresponding to 0.000 001</summary>
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public const double Micro = 1e-6;
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/// <summary>The SI prefix factor corresponding to 0.000 000 001</summary>
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public const double Nano = 1e-9;
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/// <summary>The SI prefix factor corresponding to 0.000 000 000 001</summary>
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public const double Pico = 1e-12;
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/// <summary>The SI prefix factor corresponding to 0.000 000 000 000 001</summary>
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public const double Femto = 1e-15;
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/// <summary>The SI prefix factor corresponding to 0.000 000 000 000 000 001</summary>
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public const double Atto = 1e-18;
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/// <summary>The SI prefix factor corresponding to 0.000 000 000 000 000 000 001</summary>
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public const double Zepto = 1e-21;
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/// <summary>The SI prefix factor corresponding to 0.000 000 000 000 000 000 000 001</summary>
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public const double Yocto = 1e-24;
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#endregion
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}
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}
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