Text = {} Text.init = function(){ this.element = document.getElementById( "text" ) } Text.clear = function(){ this.element.value = "" } Text.get = function(){ return this.element.value } Text.put = function(){ if( arguments.length > 0 ) this.element.value += arguments[0] } Text.putln = function(){ this.put( ... arguments ) this.put( "\n" ) } Text.putN = function(){ if( arguments.length == 0 ) return var n = arguments[0] if( typeof n != "number" || isNaN( n ) ){ this.put( n ); return } var N = 7 if( typeof arguments[1] == "number" ){ N = Number( arguments[1] ) - 1 } if( Math.abs( n ) >= 1e-2 && Math.abs( n ) < 1e5 ){ this.put( Number( n.toExponential( N ) ) ) } else if( n == 0 ){ this.put( 0 ) } else { var s = n.toExponential( N ) var p, c while( true ){ p = s.indexOf( "e" ); if( p < 0 ) break c = s.substr( p - 1, 1 ) if( c == "0" || c == "." ){ s = s.substr( 0, p - 1 ) + s.substr( p ) continue } break } this.put( s ) } } Text.putlnN = function(){ this.putN( ... arguments ) this.put( "\n" ) } Coordinates = {} Coordinates.init = function(){ this.gra = document.getElementById( "canvas" ).getContext( "2d" ) this.x1 = -10; this.x2 = 10; this.y1 = -10; this.y2 = 10 this.gra.lineWidth = 2 this.gra.font = "32px sans-serif" } Coordinates.range = function(){ if( arguments.length == 2 ){ this.x1 = arguments[0]; this.x2 = arguments[1] this.y1 = arguments[0]; this.y2 = arguments[1] } if( arguments.length == 4 ){ this.x1 = arguments[0]; this.x2 = arguments[1] this.y1 = arguments[2]; this.y2 = arguments[3] } if( this.x1 == this.x2 || this.y1 == this.y2 ){ this.x1 = -10; this.x2 = 10 this.y1 = -10; this.y2 = 10 } this.clear() } Coordinates.xs = function( x ){ return ( x - this.x1 ) * 800 / ( this.x2 - this.x1 ) } Coordinates.ys = function( y ){ return 800 - ( y - this.y1 ) * 800 / ( this.y2 - this.y1 ) } Coordinates.clear = function(){ var fs = this.gra.fillStyle this.gra.fillStyle = "white" this.gra.fillRect( 0, 0, 800, 800 ) this.gra.fillStyle = fs } Coordinates.point = function( x, y ){ this.gra.lineWidth = 1 this.gra.beginPath() this.gra.arc( this.xs(x), this.ys(y), 1, 0, 2 * Math.PI ) this.gra.stroke() this.gra.lineWidth = 2 } Coordinates.circle = function( x, y, r ){ var i, x1, y1 var div = 50 var dth = 2 * Math.PI / div this.gra.beginPath() this.gra.moveTo( this.xs(x+r), this.ys(y) ) for( i = 1; i <= div; i++ ){ x1 = x + r * Math.cos( i * dth ) y1 = y + r * Math.sin( i * dth ) this.gra.lineTo( this.xs(x1), this.ys(y1) ) } this.gra.stroke() } /* Coordinates.circle = function( x, y, r ){ var rs = 800 / ( this.x2 - this.x1 ) * r this.gra.beginPath() this.gra.arc( this.xs(x), this.ys(y), rs, 0, 2 * Math.PI ) this.gra.stroke() } Coordinates.fillCircle = function( x, y, r ){ var rs = 800 / ( this.x2 - this.x1 ) * r this.gra.beginPath() this.gra.arc( this.xs(x), this.ys(y), rs, 0, 2 * Math.PI ) this.gra.fill() } */ Coordinates.line = function( x1, y1, x2, y2 ){ this.gra.beginPath() this.gra.moveTo( this.xs(x1), this.ys(y1) ) this.gra.lineTo( this.xs(x2), this.ys(y2) ) this.gra.stroke() } Coordinates.rect = function( x, y, width, height ){ var w = width / ( this.x2 - this.x1 ) * 800 var h = height / ( this.y1 - this.y2 ) * 800 this.gra.strokeRect( this.xs(x), this.ys(y), w, h ) } /* Coordinates.fillRect = function( x, y, width, height ){ var w = width / ( this.x2 - this.x1 ) * 800 var h = height / ( this.y1 - this.y2 ) * 800 this.gra.fillRect( this.xs(x), this.ys(y), w, h ) } */ Coordinates.axis = function(){ if( arguments.length == 1 ) var yg = arguments[0] if( arguments.length > 1 ) var yg = arguments[1] if( arguments.length > 0 ){ var xg = arguments[0] var fs = this.gra.strokeStyle this.gra.strokeStyle = "lightgray" for( var x = 0; x <= this.x2; x += xg ){ this.line( x, this.y1, x, this.y2 ) } for( var x = 0; x >= this.x1; x -= xg ){ this.line( x, this.y1, x, this.y2 ) } for( var y = 0; y <= this.y2; y += yg ){ this.line( this.x1, y, this.x2, y ) } for( var y = 0; y >= this.y1; y -= yg ){ this.line( this.x1, y, this.x2, y ) } this.gra.strokeStyle = fs } this.line( this.x1, 0, this.x2, 0 ) this.line( 0, this.y1, 0, this.y2 ) } Coordinates.text = function( s, x, y ){ this.gra.fillText( s, this.xs(x), this.ys(y) ) } Coordinates.graph = function( f, n ){ if( n == undefined ) n = 1 var dx = ( this.x2 - this.x1 ) / 400 / n for( var x = this.x1; x <= this.x2; x += dx ){ this.point( x, f( x ) ) } } Numerical = {} Numerical.summation = function( f, a, b ){ if( a > b ) return NaN var s = f( a ) for( var n = a + 1; n <= b; n++ ){ if( typeof s == "number" ) s += f( n ) if( typeof s != "number" ) s = s.add( f( n ) ) } return s } Numerical.product = function( f, a, b ){ if( a > b ) return NaN var s = f( a ) for( var n = a + 1; n <= b; n++ ){ if( typeof s == "number" ) s *= f( n ) if( typeof s != "number" ) s = s.times( f( n ) ) } return s } Numerical.permutation = function( n, m ){ if( m < 0 || m > n ) return NaN if( m == 0 ) return 1 var f = function( i ){ return i } return this.product( f, n - m + 1, n ) } Numerical.factorial = function( n ){ return this.permutation( n, n ) } Numerical.combination = function( n, m ){ return this.permutation( n, m ) / this.factorial( m ) } Numerical.integral = function( f, a, b, div ){ var n = 2 * div, h = ( b - a ) / n var x = function( i ){ return a + h * i } if( typeof f( a ) == "number" ){ var s = f( a ) + f( b ) for( var i = 1; i <= n/2; i++ ) s += 4 * f( x( 2 * i - 1 ) ) for( var i = 1; i <= n/2 - 1; i++ ) s += 2 * f( x( 2 * i ) ) return h / 3 * s } else{ var s = f( a ).add( f( b ) ) for( var i = 1; i <= n/2; i++ ) s = s.add( f( x( 2 * i - 1 ) ).times( 4 ) ) for( var i = 1; i <= n/2 - 1; i++ ) s = s.add( f( x( 2 * i ) ).times( 2 ) ) return s.times( h / 3 ) } } Numerical.zero = function( f, x1, x2, eps ){ if( x1 >= x2 ) return NaN if( x2 - x1 < eps ) return x1 var y1 = f(x1); if( y1 == 0 ) return x1 var y2 = f(x2); if( y2 == 0 ) return x2 if( y1 * y2 > 0 ) return NaN var xm = ( x1 + x2 ) / 2, ym = f(xm) if( y1 * ym <= 0 ) return this.zero( f, x1, xm, eps ) if( ym * y2 <= 0 ) return this.zero( f, xm, x2, eps ) } Numerical.evolution = function( x0, der, h, N ){ var D = x0.length - 1 var xd = []; for( j = 0; j <= D; j++ ) xd[j] = [] var x = []; for( j = 0; j <= D; j++ ) x[j] = x0[j] var y = [], a = [], b = [], c = [], d =[] for( i = 0; i <= N; i++ ){ for( j = 0; j <= D; j++ ) xd[j][i] = x[j] for( j = 0; j <= D; j++ ) a[j] = der( x, j ) for( j = 0; j <= D; j++ ) y[j] = x[j] + h * a[j] / 2 for( j = 0; j <= D; j++ ) b[j] = der( y, j ) for( j = 0; j <= D; j++ ) y[j] = x[j] + h * b[j] / 2 for( j = 0; j <= D; j++ ) c[j] = der( y, j ) for( j = 0; j <= D; j++ ) y[j] = x[j] + h * c[j] for( j = 0; j <= D; j++ ) d[j] = der( y, j ) for( j = 0; j <= D; j++ ){ x[j] += h * ( a[j] + 2*b[j] + 2*c[j] + d[j] ) / 6 } } return xd } Complex = function( re, im ){ this.re = re this.im = im if( re == undefined ) this.re = 0 if( im == undefined ) this.im = 0 } Complex.prototype.toString = function(){ var re = Number( this.re.toExponential( 7 ) ) var im = Number( this.im.toExponential( 7 ) ) return "(" + re + "," + im + ")" } Complex.prototype.isZero = function(){ if( this.re == 0 && this.im == 0 ) return true return false } Complex.prototype.abs = function(){ return ( this.re ** 2 + this.im ** 2 ) ** 0.5 } Complex.prototype.conj = function(){ return new this.constructor( this.re, -1 * this.im ) } Complex.prototype.add = function( a ){ if( typeof a == "number" ){ return new this.constructor( this.re + a, this.im ) } return new this.constructor( this.re + a.re, this.im + a.im ) } Complex.prototype.sub = function( a ){ if( typeof a == "number" ){ return new this.constructor( this.re - a, this.im ) } return new this.constructor( this.re - a.re, this.im - a.im ) } Complex.prototype.times = function( a ){ if( typeof a == "number" ){ return new this.constructor( this.re * a, this.im * a ) } var re = this.re * a.re - this.im * a.im var im = this.re * a.im + this.im * a.re return new this.constructor( re, im ) } Complex.prototype.div = function( a ){ if( typeof a == "number" ){ return new this.constructor( this.re / a, this.im / a ) } return this.times( a.conj() ).div( a.abs() ** 2 ) } Complex.prototype.inv = function(){ return new this.constructor( 1, 0 ).div( this ) } Complex.prototype.exp = function(){ var m = Math var re = m.exp( this.re ) * m.cos( this.im ) var im = m.exp( this.re ) * m.sin( this.im ) return new this.constructor( re, im ) } Complex.prototype.cos = function(){ var i = new Complex( 0, 1 ) var a = i.times( this ).exp() var b = i.times( -1 ).times( this ).exp() return a.add( b ).div( 2 ) } Complex.prototype.sin = function(){ var i = new Complex( 0, 1 ) var a = i.times( this ).exp() var b = i.times( -1 ).times( this ).exp() return a.sub( b ).div( 2 ).div( i ) } Complex.prototype.tan = function(){ return this.sin().div( this.cos() ) } Complex.prototype.cosh = function(){ var a = this.exp() var b = this.times( -1 ).exp() return a.add( b ).div( 2 ) } Complex.prototype.sinh = function(){ var a = this.exp() var b = this.times( -1 ).exp() return a.sub( b ).div( 2 ) } Complex.prototype.tanh = function(){ return this.sinh().div( this.cosh() ) } CMatrix = function( row, col ){ this.row = row if( col == undefined ) col = row this.col = col this.ele = [] for( var i = 1; i <= row; i++ ){ this.ele[ i ] = [] for( var j = 1; j <=col; j++ ){ this.ele[ i ][ j ] = new Complex() } } } CMatrix.byArray = function( a ){ var row = a.length var col = a[ 0 ].length var b = new this( row, col ) var n for( var i = 0; i < row; i++ ) for( var j = 0; j < col; j++ ){ n = a[ i ][ j ] if( typeof n == "number" ){ b.ele[ i + 1 ][ j + 1 ] = new Complex( n ) } else{ b.ele[ i + 1 ][ j + 1 ] = n } } return b } CMatrix.identity = function( n ){ var a = new CMatrix( n, n ) for( var i = 1; i <= n; i++ ){ a.ele[ i ][ i ] = new Complex( 1 ) } return a } CMatrix.prototype.toString = function(){ var s = "" for( var i = 1; i <= this.row; i++ ){ for( var j = 1; j <= this.col; j++ ){ s += this.ele[ i ][ j ].toString() + " " } if( i < this.row ) s += "\n" } return s } CMatrix.prototype.add = function( a ){ var b = new this.constructor( this.row, this.col ) for( var i = 1; i <= this.row; i++ ) for( var j = 1; j <= this.col; j++ ){ b.ele[ i ][ j ] = this.ele[ i ][ j ].add( a.ele[ i ][ j ] ) } return b } CMatrix.prototype.sub = function( a ){ var b = new this.constructor( this.row, this.col ) for( var i = 1; i <= this.row; i++ ) for( var j = 1; j <= this.col; j++ ){ b.ele[ i ][ j ] = this.ele[ i ][ j ].sub( a.ele[ i ][ j ] ) } return b } CMatrix.prototype.times = function( a ){ if( typeof a == "number" || a.constructor.name == "Complex" ){ var b = new this.constructor( this.row, this.col ) for( var i = 1; i <= this.row; i++ ) for( var j = 1; j <= this.col; j++ ){ b.ele[ i ][ j ] = this.ele[ i ][ j ].times( a ) } return b } var b = new this.constructor( this.row, a.col ) for( var i = 1; i <= this.row; i++ ) for( var j = 1; j <= a.col; j++ ) for( var k = 1; k <= this.col; k++ ){ b.ele[ i ][ j ] = b.ele[ i ][ j ].add( this.ele[ i ][ k ].times( a.ele[ k ][ j ] ) ) } return b } CMatrix.prototype.conj = function(){ var b = new this.constructor( this.row, this.col ) for( var i = 1; i <= this.row; i++ ) for( var j = 1; j <= this.col; j++ ){ b.ele[ i ][ j ] = this.ele[ i ][ j ].conj() } return b } CMatrix.prototype.trans = function(){ var b = new this.constructor( this.col, this.row ) for( var i = 1; i <= b.row; i++ ) for( var j = 1; j <= b.col; j++ ){ b.ele[ i ][ j ] = this.ele[ j ][ i ] } return b } CMatrix.prototype.hermit = function(){ return this.conj().trans() } CMatrix.prototype.trace = function(){ var a = new Complex( 0, 0 ) for( var i = 1; i <= this.row; i++ ){ a = a.add( this.ele[ i ][ i ] ) } return a } CMatrix.prototype.commute = function( a ){ return this.times( a ).sub( a.times( this ) ) } CMatrix.prototype.anticommute = function( a ){ return this.times( a ).add( a.times( this ) ) } CMatrix.prototype.det = function(){ if( this.row == 1 ) return this.ele[ 1 ][ 1 ] if( this.row == 2 ){ var a = this.ele[ 1 ][ 1 ].times( this.ele[ 2 ][ 2 ] ) var b = this.ele[ 1 ][ 2 ].times( this.ele[ 2 ][ 1 ] ) return a.sub( b ) } var k = new Complex( 0, 0 ) for( var j = 1; j <= this.col; j++ ){ if( this.ele[ 1 ][ j ].isZero() ) continue k = k.add( this.ele[ 1 ][ j ].times( this.cofactor( 1, j ) ) ) } return k } CMatrix.prototype.cofactor = function( i, j ){ if( this.row <= 1 ) return new Complex( 1 ) var a = new this.constructor( this.row - 1, this.col - 1 ) var x, y, xd, yd for( x = 1; x <= a.row; x++ ) for( y = 1; y <= a.col; y++ ){ xd = x; if( i <= x ) xd = x + 1 yd = y; if( j <= y ) yd = y + 1 a.ele[ x ][ y ] = this.ele[ xd ][ yd ] } return a.det().times( (-1) ** ( i + j ) ) } CMatrix.prototype.comatrix = function(){ var a = new this.constructor( this.row, this.col ) for( var i = 1; i <= a.row; i++ ) for( var j = 1; j <= a.col; j++ ){ a.ele[ i ][ j ] = this.cofactor( j, i ) } return a } CMatrix.prototype.inv = function(){ return this.comatrix().times( this.det().inv() ) } Phys = {} Phys.init = function( alpha ){ this.PI = Math.PI this.pi = Math.PI this.E = Math.E this.万 = 1e4 this.億 = 1e8 this.兆 = 1e12 this.京 = 1e16 this.thousand = 1e3 this.million = 1e6 this.billion = 1e9 this.trillion = 1e12 this.c = 1 this.k_0 = 1 / ( 4 * this.pi ) this.eps_0 = 1 this.mu_0 = 1 this.h = 2 * this.pi this.hbar = 1 this.k_B = 1 this.N_A = 1 this.R = 1 this.alpha = alpha this.e = ( 4 * this.pi * this.alpha )**0.5 this.G = 6.70883e-57 this.G_F = 1.16638e-23 this.kappa = 8 * this.pi * this.G this.J = 1 / 1.602176634e-19 this.s = 2 * this.pi / 6.62607015e-34 / this.J this.m = this.s / 2.99792458e8 this.C = this.e * this.J this.K = 1.380649e-23 * this.J this.mol = 6.02214076e23 this.Dnu_Cs = 9.19263177e9 / this.s this.Hz = this.s**(-1) this.kg = this.J * this.s**2 / this.m**2 this.N = this.J / this.m this.W = this.J / this.s this.Pa = this.N / this.m**2 this.A = this.C / this.s this.V = this.J / this.C this.Wb = this.V * this.s this.T = this.Wb / this.m**2 this.Ohm = this.V / this.A this.F = this.C / this.V this.H = this.Wb / this.A this.m_e = 0.51099895e6 this.m_p = 938.27209e6 this.m_n = 939.56542e6 this.m_mu = 105.6584e6 this.m_pi = 139.57e6 this.m_pi0 = 134.98e6 this.ms = 1e-3 * this.s this.msec = 1e-3 * this.s this.sec = this.s this.min = 60 * this.s this.hour = 60 * this.min this.day = 24 * this.hour this.year = 365.25 * this.day this.cm = 1e-2 * this.m this.mm = 1e-3 * this.m this.micron = 1e-6 * this.m this.km = 1e3 * this.m this.M = 1852 * this.m this.a = 1e2 * this.m**2 this.ha = 1e2 * this.a this.l = 1e-3 * this.m**3 this.dl = 1e-1 * this.l this.ml = 1e-3 * this.l this.cc = this.ml this.g = 1e-3 * this.kg this.mg = 1e-3 * this.g this.t = 1e3 * this.kg this.ct = 0.2 * this.g this.knot = this.M / this.hour this.g_n = 9.80665 * this.m / this.s**2 this.Gal = this.cm * this.s**(-2) this.kHz = 1e3 * this.Hz this.MHz = 1e6 * this.Hz this.GHz = 1e9 * this.Hz this.THz = 1e12 * this.Hz this.kgw = this.kg * this.g_n this.dyn = this.g * this.cm / this.s**2 this.erg = this.dyn * this.cm this.cal = 4.184 * this.J this.kcal = 1e3 * this.cal this.kW = 1e3 * this.W this.PS = 75 * this.kgw * this.m / this.s this.hPa = 1e2 * this.Pa this.atm = 101325 * this.Pa this.at = this.kgw / this.cm**2 this.mHg = this.atm / 0.76 this.mmHg = 1e-3 * this.mHg this.Torr = this.mmHg this.bar = 1e5 * this.Pa this.mbar = 1e-3 * this.bar this.mA = 1e-3 * this.A this.kA = 1e3 * this.A this.mV = 1e-3 * this.V this.kV = 1e3 * this.V this.mOhm = 1e-3 * this.Ohm this.kOhm = 1e3 * this.Ohm this.mF = 1e-3 * this.F this.mH = 1e-3 * this.H this.microF = 1e-6 * this.F this.microH = 1e-6 * this.H this.nF = 1e-9 * this.F this.nH = 1e-9 * this.H this.pF = 1e-12 * this.F this.pH = 1e-12 * this.H this.Fr = this.esu = this.statC = ( 4 * this.pi * this.dyn )**0.5 * this.cm this.statA = this.statC / this.s this.D = this.esu * this.cm * 1e-18 this.emu = this.esu * this.cm this.Gs = this.Oe = this.dyn / this.Fr this.statV = this.Gb = this.Gs * this.cm this.Mx = this.Gs * this.cm ** 2 this.statOhm = this.statV / this.statA this.statF = this.statC / this.statV this.statH = this.statV * this.s / this.statA this.AU = 1.495978707e11 * this.m this.au = this.AU this.ly = this.year this.pc = this.AU / Math.tan( this.pi / 180 / 3600 ) this.M_e = 5.972e24 * this.kg this.R_e = 6378 * this.km this.M_s = 1.9891e30 * this.kg this.R_s = 696000 * this.km this.L_s = 3.839e26 * this.W this.M_m = 7.3477e22 * this.kg this.R_m = 1738 * this.km this.r_m = 384400 * this.km this.nm = 1e-9 * this.m this.pm = 1e-12 * this.m this.fm = 1e-15 * this.m this.fermi = this.fm this.Ang = 1e-10 * this.m this.bn = 1e-28 * this.m**2 this.u = 9.3149410e8 this.eV = 1 this.meV = 1e-3 this.microeV = 1e-6 this.neV = 1e-9 this.peV = 1e-12 this.keV = 1e3 this.MeV = 1e6 this.GeV = 1e9 this.TeV = 1e12 this.lambda_C = 2 * this.pi / this.m_e this.a_B = 4 * this.pi / this.m_e / this.e**2 this.Ry = this.m_e * this.e**4 / 32 / this.pi**2 this.R_infty = this.Ry / 2 / this.pi this.mu_B = this.e / 2 / this.m_e this.inch = 2.54 * this.cm this.feet = 12 * this.inch this.yard = 3 * this.feet this.mile = 1760 * this.yard this.acre = 4840 * this.yard**2 this.lb = 453.59237 * this.g this.oz = this.lb / 16 this.dr = this.oz / 16 this.HP = 550 * this.lb * this.g_n * this.feet / this.s this.psi = this.lb * this.g_n / this.inch**2 this.寸 = this.m / 33 this.尺 = 10 * this.寸 this.間 = 6 * this.尺 this.丈 = 10 * this.尺 this.町 = 60 * this.間 this.里 = 36 * this.町 this.坪 = this.間**2 this.畝 = 30 * this.坪 this.反 = 10 * this.畝 this.町歩 = 10 * this.反 this.合 = 2401 / 13310 * this.l this.升 = 10 * this.合 this.斗 = 10 * this.升 this.石 = 10 * this.斗 this.匁 = 3.75 * this.g this.両 = 10 * this.匁 this.斤 = 16 * this.両 this.貫 = 100 * this.両 this.deg = function( d ){ return Math.PI / 180 * d } this.bdeg = function( r ){ return 180 / Math.PI * r } this.degC = function( d ){ return ( 273.15 + d ) * this.K } this.bdegC = function( T ){ return T / this.K - 273.15 } this.degF = function( d ){ return this.degC( 5 /9 * ( d - 32 ) ) } this.bdegF = function( T ){ return 32 + 9 / 5 * this.bdegC( T ) } } Phys.set = function(){ for( var i in this ){ if( typeof this[i] == "number" ){ window[i] = this[i] } } deg = function( a ){ return Phys.deg( a ) } bdeg = function( a ){ return Phys.bdeg( a ) } degC = function( a ){ return Phys.degC( a ) } bdegC = function( a ){ return Phys.bdegC( a ) } degF = function( a ){ return Phys.degF( a ) } bdegF = function( a ){ return Phys.bdegF( a ) } } Text.init() Coordinates.init() Phys.init( 1 / 137.035999084 )