games202-hw/hw4/lib/math.js

/**
 * math.js
 * https://github.com/josdejong/mathjs
 *
 * Math.js is an extensive math library for JavaScript and Node.js,
 * It features real and complex numbers, units, matrices, a large set of
 * mathematical functions, and a flexible expression parser.
 *
 * @version 9.3.2
 * @date    2021-04-12
 *
 * @license
 * Copyright (C) 2013-2021 Jos de Jong <wjosdejong@gmail.com>
 *
 * Licensed under the Apache License, Version 2.0 (the "License"); you may not
 * use this file except in compliance with the License. You may obtain a copy
 * of the License at
 *
 * https://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
 * License for the specific language governing permissions and limitations under
 * the License.
 */
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    /**
     * @license Complex.js v2.0.11 11/02/2016
     *
     * Copyright (c) 2016, Robert Eisele (robert@xarg.org)
     * Dual licensed under the MIT or GPL Version 2 licenses.
     **/!function(r){"use strict";var i=function(e){return.5*(Math.exp(e)+Math.exp(-e))},a=function(e){return.5*(Math.exp(e)-Math.exp(-e))},o=function(){throw SyntaxError("Invalid Param")};function s(e,t){var r=Math.abs(e),n=Math.abs(t);return 0===e?Math.log(n):0===t?Math.log(r):r<3e3&&n<3e3?.5*Math.log(e*e+t*t):Math.log(e/Math.cos(Math.atan2(t,e)))}function u(e,t){if(!(this instanceof u))return new u(e,t);var r=function(e,t){var r={re:0,im:0};if(null==e)r.re=r.im=0;else if(void 0!==t)r.re=e,r.im=t;else switch(typeof e){case"object":if("im"in e&&"re"in e)r.re=e.re,r.im=e.im;else if("abs"in e&&"arg"in e){if(!Number.isFinite(e.abs)&&Number.isFinite(e.arg))return u.INFINITY;r.re=e.abs*Math.cos(e.arg),r.im=e.abs*Math.sin(e.arg)}else if("r"in e&&"phi"in e){if(!Number.isFinite(e.r)&&Number.isFinite(e.phi))return u.INFINITY;r.re=e.r*Math.cos(e.phi),r.im=e.r*Math.sin(e.phi)}else 2===e.length?(r.re=e[0],r.im=e[1]):o();break;case"string":r.im=r.re=0;var n=e.match(/\d+\.?\d*e[+-]?\d+|\d+\.?\d*|\.\d+|./g),i=1,a=0;null===n&&o();for(var s=0;s<n.length;s++){var c=n[s];" "===c||"\t"===c||"\n"===c||("+"===c?i++:"-"===c?a++:"i"===c||"I"===c?(i+a===0&&o()," "===n[s+1]||isNaN(n[s+1])?r.im+=parseFloat((a%2?"-":"")+"1"):(r.im+=parseFloat((a%2?"-":"")+n[s+1]),s++),i=a=0):((i+a===0||isNaN(c))&&o(),"i"===n[s+1]||"I"===n[s+1]?(r.im+=parseFloat((a%2?"-":"")+c),s++):r.re+=parseFloat((a%2?"-":"")+c),i=a=0))}i+a>0&&o();break;case"number":r.im=0,r.re=e;break;default:o()}return isNaN(r.re)||isNaN(r.im),r}(e,t);this.re=r.re,this.im=r.im}u.prototype={re:0,im:0,sign:function(){var e=this.abs();return new u(this.re/e,this.im/e)},add:function(e,t){var r=new u(e,t);return this.isInfinite()&&r.isInfinite()?u.NAN:this.isInfinite()||r.isInfinite()?u.INFINITY:new u(this.re+r.re,this.im+r.im)},sub:function(e,t){var r=new u(e,t);return this.isInfinite()&&r.isInfinite()?u.NAN:this.isInfinite()||r.isInfinite()?u.INFINITY:new u(this.re-r.re,this.im-r.im)},mul:function(e,t){var r=new u(e,t);return this.isInfinite()&&r.isZero()||this.isZero()&&r.isInfinite()?u.NAN:this.isInfinite()||r.isInfinite()?u.INFINITY:0===r.im&&0===this.im?new u(this.re*r.re,0):new u(this.re*r.re-this.im*r.im,this.re*r.im+this.im*r.re)},div:function(e,t){var r=new u(e,t);if(this.isZero()&&r.isZero()||this.isInfinite()&&r.isInfinite())return u.NAN;if(this.isInfinite()||r.isZero())return u.INFINITY;if(this.isZero()||r.isInfinite())return u.ZERO;e=this.re,t=this.im;var n,i,a=r.re,o=r.im;return 0===o?new u(e/a,t/a):Math.abs(a)<Math.abs(o)?new u((e*(i=a/o)+t)/(n=a*i+o),(t*i-e)/n):new u((e+t*(i=o/a))/(n=o*i+a),(t-e*i)/n)},pow:function(e,t){var r=new u(e,t);if(e=this.re,t=this.im,r.isZero())return u.ONE;if(0===r.im){if(0===t&&e>=0)return new u(Math.pow(e,r.re),0);if(0===e)switch((r.re%4+4)%4){case 0:return new u(Math.pow(t,r.re),0);case 1:return new u(0,Math.pow(t,r.re));case 2:return new u(-Math.pow(t,r.re),0);case 3:return new u(0,-Math.pow(t,r.re))}}if(0===e&&0===t&&r.re>0&&r.im>=0)return u.ZERO;var n=Math.atan2(t,e),i=s(e,t);return e=Math.exp(r.re*i-r.im*n),t=r.im*i+r.re*n,new u(e*Math.cos(t),e*Math.sin(t))},sqrt:function(){var e,t,r=this.re,n=this.im,i=this.abs();if(r>=0){if(0===n)return new u(Math.sqrt(r),0);e=.5*Math.sqrt(2*(i+r))}else e=Math.abs(n)/Math.sqrt(2*(i-r));return t=r<=0?.5*Math.sqrt(2*(i-r)):Math.abs(n)/Math.sqrt(2*(i+r)),new u(e,n<0?-t:t)},exp:function(){var e=Math.exp(this.re);return this.im,new u(e*Math.cos(this.im),e*Math.sin(this.im))},expm1:function(){var e=this.re,t=this.im;return new u(Math.expm1(e)*Math.cos(t)+function(e){var t=Math.PI/4;if(e<-t||e>t)return Math.cos(e)-1;var r=e*e;return r*(r*(1/24+r*(-1/720+r*(1/40320+r*(-1/3628800+r*(1/4790014600+r*(-1/87178291200+r*(1/20922789888e3)))))))-.5)}(t),Math.exp(e)*Math.sin(t))},log:function(){var e=this.re,t=this.im;return new u(s(e,t),Math.atan2(t,e))},abs:function(){return e=this.re,t=this.im,r=Math.abs(e),n=Math.abs(t),r<3e3&&n<3e3?Math.sqrt(r*r+n*n):(r<n?(r=n,n=e/t):n=t/e,r*Math.sqrt(1+n*n));var e,t,r,n},arg:function(){return Math.atan2(this.im,this.re)},sin:function(){var e=this.re,t=this.im;return new u(Math.sin(e)*i(t),
    /**
     * @license Fraction.js v4.0.12 09/09/2015
     * http://www.xarg.org/2014/03/rational-numbers-in-javascript/
     *
     * Copyright (c) 2015, Robert Eisele (robert@xarg.org)
     * Dual licensed under the MIT or GPL Version 2 licenses.
     **/!function(r){"use strict";var i={s:1,n:0,d:1};function a(e){function t(){var t=Error.apply(this,arguments);t.name=this.name=e,this.stack=t.stack,this.message=t.message}function r(){}return r.prototype=Error.prototype,t.prototype=new r,t}var o=p.DivisionByZero=a("DivisionByZero"),s=p.InvalidParameter=a("InvalidParameter");function u(e,t){return isNaN(e=parseInt(e,10))&&c(),e*t}function c(){throw new s}var f=function(e,t){var r,n=0,a=1,s=1,f=0,l=0,p=0,m=1,h=1,d=0,y=1,g=1,v=1,x=1e7;if(null==e);else if(void 0!==t)s=(n=e)*(a=t);else switch(typeof e){case"object":"d"in e&&"n"in e?(n=e.n,a=e.d,"s"in e&&(n*=e.s)):0 in e?(n=e[0],1 in e&&(a=e[1])):c(),s=n*a;break;case"number":if(e<0&&(s=e,e=-e),e%1==0)n=e;else if(e>0){for(e>=1&&(e/=h=Math.pow(10,Math.floor(1+Math.log(e)/Math.LN10)));y<=x&&v<=x;){if(e===(r=(d+g)/(y+v))){y+v<=x?(n=d+g,a=y+v):v>y?(n=g,a=v):(n=d,a=y);break}e>r?(d+=g,y+=v):(g+=d,v+=y),y>x?(n=g,a=v):(n=d,a=y)}n*=h}else(isNaN(e)||isNaN(t))&&(a=n=NaN);break;case"string":if(null===(y=e.match(/\d+|./g))&&c(),"-"===y[d]?(s=-1,d++):"+"===y[d]&&d++,y.length===d+1?l=u(y[d++],s):"."===y[d+1]||"."===y[d]?("."!==y[d]&&(f=u(y[d++],s)),(++d+1===y.length||"("===y[d+1]&&")"===y[d+3]||"'"===y[d+1]&&"'"===y[d+3])&&(l=u(y[d],s),m=Math.pow(10,y[d].length),d++),("("===y[d]&&")"===y[d+2]||"'"===y[d]&&"'"===y[d+2])&&(p=u(y[d+1],s),h=Math.pow(10,y[d+1].length)-1,d+=3)):"/"===y[d+1]||":"===y[d+1]?(l=u(y[d],s),m=u(y[d+2],1),d+=3):"/"===y[d+3]&&" "===y[d+1]&&(f=u(y[d],s),l=u(y[d+2],s),m=u(y[d+4],1),d+=5),y.length<=d){s=n=p+(a=m*h)*f+h*l;break}default:c()}if(0===a)throw new o;i.s=s<0?-1:1,i.n=Math.abs(n),i.d=Math.abs(a)};function l(e,t){if(!e)return t;if(!t)return e;for(;;){if(!(e%=t))return t;if(!(t%=e))return e}}function p(e,t){if(!(this instanceof p))return new p(e,t);f(e,t),e=p.REDUCE?l(i.d,i.n):1,this.s=i.s,this.n=i.n/e,this.d=i.d/e}p.REDUCE=1,p.prototype={s:1,n:0,d:1,abs:function(){return new p(this.n,this.d)},neg:function(){return new p(-this.s*this.n,this.d)},add:function(e,t){return f(e,t),new p(this.s*this.n*i.d+i.s*this.d*i.n,this.d*i.d)},sub:function(e,t){return f(e,t),new p(this.s*this.n*i.d-i.s*this.d*i.n,this.d*i.d)},mul:function(e,t){return f(e,t),new p(this.s*i.s*this.n*i.n,this.d*i.d)},div:function(e,t){return f(e,t),new p(this.s*i.s*this.n*i.d,this.d*i.n)},clone:function(){return new p(this)},mod:function(e,t){return isNaN(this.n)||isNaN(this.d)?new p(NaN):void 0===e?new p(this.s*this.n%this.d,1):(f(e,t),0===i.n&&0===this.d&&p(0,0),new p(this.s*(i.d*this.n)%(i.n*this.d),i.d*this.d))},gcd:function(e,t){return f(e,t),new p(l(i.n,this.n)*l(i.d,this.d),i.d*this.d)},lcm:function(e,t){return f(e,t),0===i.n&&0===this.n?new p:new p(i.n*this.n,l(i.n,this.n)*l(i.d,this.d))},ceil:function(e){return e=Math.pow(10,e||0),isNaN(this.n)||isNaN(this.d)?new p(NaN):new p(Math.ceil(e*this.s*this.n/this.d),e)},floor:function(e){return e=Math.pow(10,e||0),isNaN(this.n)||isNaN(this.d)?new p(NaN):new p(Math.floor(e*this.s*this.n/this.d),e)},round:function(e){return e=Math.pow(10,e||0),isNaN(this.n)||isNaN(this.d)?new p(NaN):new p(Math.round(e*this.s*this.n/this.d),e)},inverse:function(){return new p(this.s*this.d,this.n)},pow:function(e){return e<0?new p(Math.pow(this.s*this.d,-e),Math.pow(this.n,-e)):new p(Math.pow(this.s*this.n,e),Math.pow(this.d,e))},equals:function(e,t){return f(e,t),this.s*this.n*i.d==i.s*i.n*this.d},compare:function(e,t){f(e,t);var r=this.s*this.n*i.d-i.s*i.n*this.d;return(0<r)-(r<0)},simplify:function(e){if(isNaN(this.n)||isNaN(this.d))return this;var t=this.abs().toContinued();function r(e){return 1===e.length?new p(e[0]):r(e.slice(1)).inverse().add(e[0])}e=e||.001;for(var n=0;n<t.length;n++){var i=r(t.slice(0,n+1));if(i.sub(this.abs()).abs().valueOf()<e)return i.mul(this.s)}return this},divisible:function(e,t){return f(e,t),!(!(i.n*this.d)||this.n*i.d%(i.n*this.d))},valueOf:function(){return this.s*this.n/this.d},toFraction:function(e){var t,r="",n=this.n,i=this.d;return this.s<0&&(r+="-"),1===i?r+=n:(e&&(t=Math.floor(n/i))>0&&(r+=t,r+=" ",n%=i),r+=n,r+="/",r+=i),r},toLatex:function(e){var t,r="",n=this.n,i=this.d;re
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