@font-face {
    font-family: 'stixgeneralregular';
    src: url('stixgeneral-regular-webfont.woff2') format('woff2'),
         url('stixgeneral-regular-webfont.woff') format('woff');
    font-weight: normal;
    font-style: normal;
}


@font-face {
    font-family: 'stixgeneralregular';
    src: url('stix-italic-webfont.woff2') format('woff2'),
         url('stix-italic-webfont.woff') format('woff');
    font-weight: italic;
    font-style: italic;
}




/*
    Math is cool, CSS is cool, use for whatever you like!
    Made by Mathew Pregasen. MIT license.
    If you have any additions or questions, feel free to contact me
    at mathexl@gmail.com
*/


div[equation] {
    box-sizing: border-box;
    height: auto;
    margin: 0px auto 0;
    min-height: 100px;
    width: 80%;
    font-family:'stixgeneralregular';
}

*[absolute] {
    text-decoration: none;
    float:none;
    border-left:2px black solid;
    border-right:2px black solid;
    padding-left:2px;
    padding-right:2px;
}


*[absolute].white {
    border-left:2px white solid;
    border-right:2px white solid;
}

div[equation] u {
    text-decoration: none;
    float:none;
    border-left:2px black solid;
    border-right:2px black solid;
    padding-left:2px;
    padding-right:2px;
}


div[equation].white u {
    border-left:2px white solid;
    border-right:2px white solid;
}


div[equation].red {
    color:rgba(241,111,92,1);
}

div[equation].white {
    color:white;
}

div[equation]::after{
    clear: both;
    content: '';
    display: table;
}

div[equation] * {
    box-sizing: border-box;
    float: left;
}

div[equation] sup {
    float: none;
    font-size: 0.4em;
}

div[equation] sub {
    float: none;
    font-size: 0.4em;
    vertical-align: baseline;
}


/* equation Alias */

div[equation] {
    box-sizing: border-box;
    height: auto;
    margin: 50px auto 0;
    min-height: 100px;
    width: 80%;
}

div[equation]::after{
    clear: both;
    content: '';
    display: table;
}

div[equation] * {
    box-sizing: border-box;
    float: left;
}

div[equation] sup {
    float: none;
    font-size: 0.4em;
}


div[integral],
div[doubleintegral],
div[contourintegral],
div[surfaceintegral],
div[volumeintegral],
div[tripleintegral],
div[summation],
div[fraction],
div[choose],
div[contourintegral]{
    display: inline-block;
    height: 100px;
    margin-left: 0;
    margin-right: 0;
    padding-left: 9px;
    padding-right: 9px;
    position: relative;
    width: auto;
}


div[integral]::before {
    content: '\222b';
    float: left;
    font-size: 3em;
}

div[integral] > div[upperbound] {
    font-size: 0.8em;
    font-style: normal;
    height: 25%;
    padding-left: 59px;
    position: absolute;
    top: -2px;
    width: auto;
}

div[integral] > div[lowerbound] {
    font-size: 0.8em;
    font-style: normal;
    height: auto;
    padding-left: 52px;
    position: absolute;
    top: 36px;
    width: auto;
}

div[integral] > div[of] {
    display: inline-block;
    font-size: 1.5em;
    font-style: normal;
    height: 25px;
    margin-top: 0.4em;
    padding-left: 10px;
    width: auto;
}

div[contourintegral]::before {
    content: '\222E';
    float: left;
    font-size: 5em;
    margin-top: -8px;
}

div[root] {
    display: inline-block;
    height: 20px;
    margin-left: 20px;
    margin-right: 0;
    padding-left: 0px;
    padding-right: 2px;
    position: relative;
    width: auto;
    margin-top:2px;
    padding-top: 8px;
    border-top:1px black solid;
}

div[equation].white > div[root]{
    border-top:1px white solid;
}

div[equation].red > div[root]{
    border-top:2px rgba(241,111,92,1) solid;
}

div[root]::before {
    content: '\221A';
    float: left;
    font-size: 20px;
    margin-top: -8px;
    margin-left: -10px;
}

div[root] > div[of] {
    display: inline-block;
    font-size: 14px;
    font-style: italic;
    height: 25px;
    margin-top: -6px;
    padding-left: 0;
    width: auto;
}

div[root] > div[degree] {
    position:absolute;
	font-size: 10px;
    top: -4px; 
	left: -12px; 
}

div[BgRot] {
    display: inline-block;
    height: 20px;
    margin-left: 20px;
    margin-right: 0;
    padding-left: 0px;
    padding-right: 2px;
    position: relative;
    width: auto;
    margin-top:2px;
    padding-top: 8px;
    border-top:2px black solid;
}

div[equation].white > div[BgRot]{
    border-top:1px white solid;
}

div[equation].red > div[BgRot]{
    border-top:2px rgba(241,111,92,1) solid;
}

div[BgRot]::before {
    content: '\221A';
    float: left;
    font-size: 40px;
    margin-top: -8px;
    margin-left: -20px;
}

div[BgRot] > div[of] {
    display: inline-block;
    font-size: 14px;
    font-style: italic;
    height: 25px;
    margin-top: -6px;
    padding-left: 0;
    width: auto;
}

div[BgRot] > div[degree] {
    position:absolute;
	font-size: 10px;
    top: 1px; 
	left: -18px; 
}

div > div[upperbound] {
    min-width:70px;
}

div > div[lowerbound] {
    min-width:70px;
}


div[contourintegral] > div[upperbound] {
    font-size: 1em;
    font-style: italic;
    height: 25%;
    padding-left: 47px;
    position: absolute;
    top: 8px;
    width: auto;
    min-width:70px;
}

div[contourintegral] > div[lowerbound] {
    font-size: 1em;
    font-style: italic;
    height: auto;
    padding-left: 30px;
    position: absolute;
    top: 65px;
    width: auto;
    min-width:70px;
}

div[contourintegral] > div[of] {
    display: inline-block;
    font-size: 1.5em;
    font-style: italic;
    height: 25px;
    margin-top: 1.5em;
    padding-left: 0;
    width: auto;
}

div[term] {
    display: inline-block;
    float: left;
    font-size: 1.5em;
    font-style: italic;
    height: 30%;
    margin-bottom: 0;
    padding-left: 3px;
    position: relative;
    top: 35%;
    width: auto;
}


div[vector] {
    display: inline-block;
    float: left;
    font-size: 1.2em !important;;
    font-style: italic;
    height: 28% !important;
    margin-bottom: 10px !important;;
    padding-left: 3px;
    position: relative;
    top: 30% !important;
    width: auto;
}

div[vector]::before{
    content: '\2329';
    font-style:normal;
    margin-right:-6px;
}

div[vector]::after{
    content: '\232A';
    font-style:normal;
    margin-left:-4px;
}

div[doubleintegral]::before {
    content: '\222b \222b';
    float: left;
    font-size: 5em;
}

div[doubleintegral] > div[upperbound] {
    font-size: 1em;
    font-style: italic;
    height: 25%;
    padding-left: 62px;
    position: absolute;
    top: 8px;
    width: auto;
}

div[doubleintegral] > div[lowerbound] {
    font-size: 1em;
    font-style: italic;
    height: auto;
    padding-left: 50px;
    position: absolute;
    top: 75px;
    width: auto;
}

div[integral] > div[region] {
    font-size: 1.3em;
    font-style: italic;
    height: auto;
    padding-left: 2.5px;
    position: absolute;
    top: 85px;
    width: auto;
}


div[doubleintegral] > div[region] {
    font-size: 1.3em;
    font-style: italic;
    height: auto;
    padding-left: 12.5px;
    position: absolute;
    top: 85px;
    width: auto;
}

div[doubleintegral] > div[of] {
    display: inline-block;
    font-size: 1.5em;
    font-style: italic;
    height: 25%;
    margin-top: 1.5em;
    padding-left: 18px;
    width: auto;
}

div[surfaceintegral]::before {
    content: '\222F';
    float: left;
    font-size: 5em;
    margin-top: -8px;
}

div[surfaceintegral] > div[upperbound] {
    font-size: 1em;
    font-style: italic;
    height: 25%;
    padding-left: 72px;
    position: absolute;
    top: 3px;
    width: auto;
}

div[surfaceintegral] > div[lowerbound] {
    font-size: 1em;
    font-style: italic;
    height: auto;
    padding-left: 50px;
    position: absolute;
    top: 65px;
    width: auto;
}

div[surfaceintegral] > div[of] {
    display: inline-block;
    font-size: 1.5em;
    font-style: italic;
    height: 25%;
    margin-top: 1.5em;
    padding-left: 0;
    width: auto;
}

div[volumeintegral]::before {
    content: '\2230';
    float: left;
    font-size: 5em;
    margin-top: -8px;
}

div[volumeintegral] > div[upperbound] {
    font-size: 1em;
    font-style: italic;
    height: 25%;
    padding-left: 92px;
    position: absolute;
    top: 3px;
    width: auto;
}

div[volumeintegral] > div[lowerbound] {
    font-size: 1em;
    font-style: italic;
    height: auto;
    padding-left: 75px;
    position: absolute;
    top: 65px;
    width: auto;
}

div[volumeintegral] > div[of] {
    display: inline-block;
    font-size: 1.5em;
    font-style: italic;
    height: 25%;
    margin-top: 1.5em;
    padding-left: 0;
    width: auto;
}

div[tripleintegral]::before {
    content: '\222b \222b \222b';
    float: left;
    font-size: 5em;
}

div[tripleintegral] > div[upperbound] {
    font-size: 1em;
    font-style: italic;
    height: 25%;
    padding-left: 86px;
    position: absolute;
    top: 8px;
    width: auto;
}

div[tripleintegral] > div[lowerbound] {
    font-size: 1em;
    font-style: italic;
    height: auto;
    padding-left: 70px;
    position: absolute;
    top: 75px;
    width: auto;
}

div[tripleintegral] > div[region] {
    font-size: 1.3em;
    font-style: italic;
    height: auto;
    padding-left: 25px;
    position: absolute;
    top: 85px;
    width: auto;
}


div[tripleintegral] > div[of] {
    display: inline-block;
    font-size: 1.5em;
    font-style: italic;
    height: 25%;
    margin-top: 1.5em;
    padding-left: 18px;
    width: auto;
}

div[limit] {
    display: inline-block;
    height: 60px;
    margin-left: 0;
    margin-right: 0;
    padding-left: 9px;
    padding-right: 9px;
    position: relative;
    width: auto;
}

div[limit]::before {
    content: 'lim ';
    float: left;
    font-size: 18px;
    margin-top: 12px;
	padding-left: 2px;
}

div[limit] > div[variable] {
    font-size: 12px;
    font-style: italic;
    height: 25%;
    padding-left: -2px;
    position: absolute;
    top: 28px;
    width: auto;
}

div[limit] > div[variable]::after{
    content: ' \2192';
    margin-left: -6px;
	font-size: 14px;
}

div[limit] > div[goingto] {
    font-size: 12px;
    font-style: italic;
    height: 25%;
    padding-left: 18px;
	margin-left: -11px;
    position: absolute;
    text-align: right;
    top: 28px;
    width: 25px;
}  

div[limit] > div[of] {
    display: inline-block;
    font-size: 14px;
    font-style: italic;
    height: 25%;
    margin-left: 14px;
    margin-top: 10px;
    padding-left: 0;
    width: auto;
}

div[summation]::before {
    content: '\2211';
    float: left;
    font-size: 5em;
}

div[summation] > div[upperbound] {
    font-size: 1em;
    font-style: italic;
    height: 25%;
    position: absolute;
    text-align: center;
    top: 2px;
    width: 50px;
    left:0px;
}

div[summation] > div[lowerbound] {
    font-size: 1em;
    font-style: italic;
    height: auto;
    position: absolute;
    text-align: center;
    top: 82px;
    width: 45px;
    left:0px;
}

div[summation] > div[of] {
    display: inline-block;
    font-size: 1.5em;
    font-style: italic;
    height: 25%;
    margin-top: 1.5em;
    padding-left: 3px;
    width: auto;
}

div[product] {
    display: inline-block;
    float: left;
    height: 100px;
    margin-left: 0;
    padding-left: 9px;
    padding-right: 9px;
    position: relative;
    width: auto;
}

div[product]::before {
    content: '\03A0 ';
    float: left;
    font-size: 5em;
    padding-top: 5px;
}

div[product] > div[upperbound] {
    font-size: 1em;
    font-style: italic;
    height: 25%;
    position: absolute;
    text-align: center;
    top: 4px;
    width: 65px;
}

div[product] > div[lowerbound] {
    font-size: 1em;
    font-style: italic;
    height: auto;
    position: absolute;
    text-align: center;
    top: 80px;
    width: 65px;
}

div[product] > div[of] {
    display: inline-block;
    font-size: 1.5em;
    font-style: italic;
    height: 25%;
    margin-top: 1.5em;
    padding-left: 3px;
    width: auto;
}

div[fraction] {
    display: inline-block;
    float: left;
    height: 100px;
    margin-left: 0;
    padding-left: 9px;
    padding-right: 9px;
    position: relative;
    width: auto;
}

div[fraction] sup {
    float: none;
    font-size: 0.4em;
}

div[fraction] > div[top] {
    border-bottom: 2px solid #444;
    font-size: 1.3em;
    font-style: italic;
    height: 24px;
    min-width: 100%;
    padding-bottom: 3px;
    position: relative;
    text-align: center;
    top: 28px;
    width: 100%;
    clear:both;
        float:none;
}

div[equation].white div[fraction] > div[top]{
  border-bottom: 2px solid white !important;
}

div[equation].white div[derivative] > div[top]{
  border-bottom: 2px solid white !important;
}

div[equation].white div[fraction] > * > div[fraction] > div[top] {
  border-bottom: 0px solid white !important;
}

div[equation].white div[fraction] > * > div[fraction] > div[bottom] {
  border-top: 1px solid white !important;
}



div[fraction] > div[bottom] {
    font-size: 1.3em;
    font-style: italic;
    height: relative;
    min-width: 100%;
    position: relative;
    text-align: center;
    top: 26px;

}



div[fraction] > div[top] > div[fraction] {
    display: inline-block;
    float: none;
    height: 40px;
    margin-left: 0;
    padding-left: 4px;
    padding-right: 4px;
    position: relative;
    width: auto;
    margin-top:-11px;
    top:-20px;
    display:inline-block;
}

div[fraction] > div[top] > div[fraction] > div[top] {
    border-bottom: 0px solid #444;
    font-size: .5em;
    font-style: italic;
    height: 10px;
    min-width: 100%;
    padding-bottom: 3px;
    position: relative;
    text-align: center;
    top: 8px;
}



div[fraction] > div[top] > div[fraction] > div[bottom] {
    border-top: 1px solid #444;
    font-size: .5em;
    font-style: italic;
    height: relative;
    min-width: 100%;
    position: relative;
    text-align: center;
    top: 11px;
}



div[fraction] > div[bottom] > div[fraction] {
    float: none;
    height: 40px;
    margin-left: 0;
    padding-left: 4px;
    padding-right: 4px;
    position: relative;
    width: auto;
    margin-top:-9px;
    top:-14px;
    display:inline-block;
}

div[fraction] > div[bottom] > div[fraction] > div[top] {
    border-bottom: 0px solid #444;
    font-size: .5em;
    font-style: italic;
    height: 10px;
    min-width: 100%;
    padding-bottom: 3px;
    position: relative;
    text-align: center;
    top: 8px;
}

div[fraction] > div[bottom] > div[fraction] > div[bottom] {
    border-top: 1px solid #444;
    font-size: .5em;
    font-style: italic;
    height: relative;
    min-width: 100%;
    position: relative;
    text-align: center;
    top: 11px;
}



div[choose] {
    display: inline-block;
    float: left;
    height: 100px;
    margin-left: 10px;
    padding-left: 9px;
    padding-right: 9px;
    position: relative;
    width: auto;
    margin-right:10px;
}


div[choose] > div[top] {
    font-size: 1.3em;
    font-style: italic;
    height: 24px;
    min-width: 100%;
    padding-bottom: 3px;
    position: relative;
    text-align: center;
    top: 28px;
    width: 100%;
    clear:both;
    float:none;
}


div[choose] > div[bottom] {
    font-size: 1.3em;
    font-style: italic;
    height: relative;
    min-width: 100%;
    position: relative;
    text-align: center;
    top: 26px;

}

div[choose]::before{
  display: block;
    height: 100%;
    left: 0px;
    width: 10px;
    font-weight: 100;
    -webkit-margin-before: 0em;
    -webkit-margin-after: 0em;
    -webkit-margin-start: 0;
    -webkit-margin-end: 0;
    position: absolute;
    top: 21px;
    content: "(";
    font-size:3em;
    left: -7px;
    font-family:'stixgeneralregular', sans-serif;
}

div[choose]::after{
  display: block;
    height: 100%;
    width: 10px;
    font-weight: 100;
    -webkit-margin-before: 0em;
    -webkit-margin-after: 0em;
    -webkit-margin-start: 0;
    -webkit-margin-end: 0;
    position: absolute;
    top: 21px;
    content: ")";
    font-size:3em;
        font-family:'stixgeneralregular', sans-serif;
    right: -5px;
}

.white div[choose]::before{
    color:white;
}

.white div[choose]::after{
    color:white;
}






div[derivative] {
    display: inline-block;
    float: left;
    height: 100px;
    margin-left: 0;
    padding-left: 9px;
    padding-right: 9px;
    position: relative;
    width: 50px;
}

div[derivative] > div[top] {
    border-bottom: 2px solid #444;
    font-size: 1.3em;
    font-style: italic;
    height: 24px;
    min-width: 100%;
    padding-bottom: 3px;
    position: relative;
    text-align: center;
    top: 28px;
}

div[derivative] > div[bottom] {
    font-size: 1.3em;
    font-style: italic;
    height: relative;
    min-width: 100%;
    position: relative;
    text-align: center;
    top: 26px;
}

div[derivative] > div[top]::before,
div[derivative] > div[bottom]::before {
    content: 'd';
    font-style: normal;
    margin-right: -5px;
}


div[partial] > div[top]::before,
div[partial] > div[bottom]::before {
    content: '\2202';
    margin-right: -5px;
}

div[double] > div[top]::before{
    content: 'd\00B2';
    margin-right: -5px;
}

div[double] > div[bottom]{
  width:auto;
}

div[double] > div[bottom]::after{
    content: '\00B2';
    margin-left: -5px;
}

div[add],
div[subtract],
div[multiply],
div[divide] {
    display:inline-block;
    font-style: normal;
    float:left;
}

div[equation] > hr[multiply] {
    border: none;
    clear: none;
    display: inline-block;
    font-size: 1.5em;
    font-style: italic;
    height: 100px;
    margin: 0;
    padding-left: 3px;
    padding-top: 35px;
    position: relative;
    width: auto;
}

div[equation] > hr[multiply] {
    border: none;
    clear: none;
    display: inline-block;
    font-size: 1.5em;
    font-style: italic;
    height: 100px;
    margin: 0;
    padding-left: 3px;
    padding-top: 35px;
    position: relative;
    width: auto;
}

hr[divide] {
    display: inline-block;
}

hr[divide]::before {
    content: '\00F7';
    float: left;
    font-style: normal;
}

div[equation] > hr[divide] {
    border: none;
    clear: none;
    display: inline-block;
    font-size: 1.5em;
    font-style: italic;
    height: 100px;
    margin: 0;
    padding-left: 3px;
    padding-top: 35px;
    position: relative;
    width: auto;
}

div[equation] > hr[divide] {
    border: none;
    clear: none;
    display: inline-block;
    font-size: 1.5em;
    font-style: italic;
    height: 100px;
    margin: 0;
    padding-left: 3px;
    padding-top: 35px;
    position: relative;
    width: auto;
}

div[add]::before {
    content: '+';
}

div[subtract]::before {
    content: '-';
}

div[multiply]::before {
    content: '\00D7';
}

div[divide]::before {
    content: '\00F7';
}

div[equation] > div[add],
div[equation] > div[subtract],
div[equation] > div[multiply],
div[equation] > div[divide],
div[equation] > div[term],
div[equation] > div[vector]{
    display: inline-block;
    font-size: 1.5em;
    font-style: italic;
    height: 100px;
    margin-top: 0;
    padding-left: 3px;
    padding-top: 35px;
    position: relative;
    width: auto;
}

div[equation] > div[add],
div[equation] > div[subtract],
div[equation] > div[multiply],
div[equation] > div[divide],
div[equation] > div[term],
div[equation] > div[vector]{
    display: inline-block;
    font-size: 1.5em;
    font-style: italic;
    height: 100px;
    margin-top: 0;
    padding-left: 3px;
    padding-top: 35px;
    position: relative;
    width: auto;
}

div[equation] hr {
    border: none;
    clear: none;
    margin: 0;
    display:inline-block;
    float:none;
}

div[equation] hr[partial]::before {
    content: '\2202';
    font-style: normal;
}

div[equation] hr[null]::before{
    content: '\2205';
    font-style:normal;
}

div[equation] hr[real]::before{
    content: '\211D';
    font-style:normal;
}

div[equation] hr[integers]::before{
    content: '\2124';
    font-style:normal;
}

div[equation] hr[natural]::before{
    content: '\2115';
    font-style:normal;
}



div[equation] hr[rational]::before{
    content: '\211A';
    font-style:normal;
    font-family:'stixgeneralregular', Times;
}

div[equation] hr[pm]::before {
    content: '\2213';
    font-style: normal;
}

div[equation] hr[times] {
    -webkit-margin-after: -6px !important;
    -webkit-margin-before: 2px !important;
    display: inline-block !important;
    float: none !important;
}

div[equation] hr[times]::before {
    content: '\00D7';
    font-style: normal;
}

div[equation] hr[infty] {
    -webkit-margin-after: -6px !important;
    -webkit-margin-before: 2px !important;
    display: inline-block !important;
    float: none !important;
}

div[equation] hr[infty]::before {
    content: '\221e';
    font-style: normal;
}

div[equation] hr[nabla]::before {
    content: '\2207';
    font-style: normal;
}

div[equation] hr[lomega]::before {
    content: '\03C9';
    font-style: normal;
}

div[equation] hr[lambda]::before {
    content: '\03BB';
    font-style: normal;
}

div[equation] hr[proportional]::before {
    content: '\221D';
    font-style: normal;
}

div[equation] hr[dot]::before {
    content: '\00B7';
    font-style: normal;
}

div[equation] hr[approx]::before {
    content: '\2248';
    font-style: normal;
}




div[equation] hr[neq]::before {
    content: '\2260';
    font-style: normal;
}

div[equation] hr[leq]::before {
    content: '\2264';
    font-style: normal;
}

div[equation] hr[goesto]::before {
    content: '\2192';
    font-style: normal;
}

div[equation] hr[geq]::before {
    content: '\2265';
    font-style: normal;
}

div[equation] hr[forall]::before {
    content: '\2200';
    font-style: normal;
}

div[equation] hr[exists]::before {
    content: '\2203';
    font-style: normal;
}

div[equation] hr[nexists]::before {
    content: '\2204';
    font-style: normal;
}

div[equation] hr[in]::before {
    content: '\2208';
    font-style: normal;
}

div[equation] hr[notin]::before {
    content: '\2209';
    font-style: normal;
}

div[equation] hr[and]::before {
    content: '\2227';
    font-style: normal;
}

div[equation] hr[or]::before {
    content: '\2228';
    font-style: normal;
}

div[equation] hr[cap]::before {
    content: '\2229';
    font-style: normal;
}

div[equation] hr[cup]::before {
    content: '\222A';
    font-style: normal;
}

div[equation] hr[not]::before {
    content: '\00AC';
    font-style: normal;
}

div[equation] hr[therefore]::before {
    content: '\2234';
    font-style: normal;
}

div[equation] hr[because]::before {
    content: '\2235';
    font-style: normal;
}


/* Discrete Functionality */

div[equation] hr[congruent]::before {
    content: '\2261';
    font-style: normal;
}

div[equation] hr[subsetleft]::before {
    content: '\2282';
    font-style: normal;
}

div[equation] hr[subsetright]::before {
    content: '\2283';
    font-style: normal;
}

div[equation] hr[notsubsetleft]::before {
    content: '\2284';
    font-style: normal;
}

div[equation] hr[notsubsetright]::before {
    content: '\2285';
    font-style: normal;
}

div[equation] hr[subsetorequaltoleft]::before {
    content: '\2286';
    font-style: normal;
}

div[equation] hr[subsetorequaltoright]::before {
    content: '\2287';
    font-style: normal;
}

div[equation] hr[notsubsetorequaltoleft]::before {
    content: '\2288';
    font-style: normal;
}

div[equation] hr[notsubsetorequaltoright]::before {
    content: '\2289';
    font-style: normal;
}


/* Greek Functionality */

div[equation] hr[pi] {
    -webkit-margin-after: -4px !important;
    display: inline-block !important;
    float: none !important;
}

div[equation] hr[pi]::before {
    content: '\03C0';
    font-style: normal;
}

div[equation] hr[alpha]::before {
    content: '\03B1';
    font-style: normal;
}

div[equation] hr[chi]::before {
    content: '\03C7';
    font-style: normal;
}

div[equation] hr[flux]::before {
    content: '\03A6';
    font-style: normal;
}

div[equation] hr[dots]::before {
    content: '\2026';
    font-style: normal;
}

div[equation] hr[beta]::before {
    content: '\03B2';
    font-style: normal;
}

div[equation] hr[lambda]::before {
    content: '\03BB';
    font-style: normal;
}

div[equation] hr[delta]::before {
    content: '\2206';
    font-style: normal;
}

div[equation] hr[theta]::before {
    content: '\03B8';
    font-style: normal;
}

div[equation] hr[comega]::before {
    content: '\2126';
    font-style: normal;
}

hr[add] {
    display: inline-block;
}

hr[add]::before {
    content: '+';
    float: left;
    font-style: normal;
}

div[equation] > hr[add] {
    border: none;
    clear: none;
    display: inline-block;
    font-size: 1.5em;
    font-style: italic;
    height: 100px;
    margin: 0;
    padding-left: 3px;
    padding-top: 35px;
    position: relative;
    width: auto;
}

hr[subtract] {
    display: inline-block;
}

hr[subtract]::before {
    content: '-';
    float: left;
    font-style: normal;
}

div[equation] > hr[subtract] {
    border: none;
    clear: none;
    display: inline-block;
    font-size: 1.5em;
    font-style: italic;
    height: 100px;
    margin: 0;
    padding-left: 3px;
    padding-top: 35px;
    position: relative;
    width: auto;
}

hr[multiply] {
    display: inline-block;
}

hr[multiply]::before {
    content: '\00D7';
    float: left;
    font-style: normal;
}


div[equation] hr {
    border: none;
    clear: none;
    margin: 0;
}

div[equation] hr[partial]::before {
    content: '\2202';
    font-style: normal;
}

div[equation] hr[pm]::before {
    content: '\2213';
    font-style: normal;
}

div[equation] hr[times] {
    -webkit-margin-after: -6px !important;
    -webkit-margin-before: 2px !important;
    display: inline-block !important;
    float: none !important;
}

div[equation] hr[times]::before {
    content: '\00D7';
    font-style: normal;
}

div[equation] hr[infty] {
    -webkit-margin-after: -6px !important;
    -webkit-margin-before: 2px !important;
    display: inline-block !important;
    float: none !important;
}

div[equation] hr[infty]::before {
    content: '\221e';
    font-style: normal;
}

div[equation] hr[approx]::before {
    content: '\2248';
    font-style: normal;
}

div[equation] hr[neq]::before {
    content: '\2260';
    font-style: normal;
}

div[equation] hr[leq]::before {
    content: '\2264';
    font-style: normal;
}

div[equation] hr[geq]::before {
    content: '\2265';
    font-style: normal;
}

div[equation] hr[forall]::before {
    content: '\2200';
    font-style: normal;
}

div[equation] hr[exists]::before {
    content: '\2203';
    font-style: normal;
}

div[equation] hr[nexists]::before {
    content: '\2204';
    font-style: normal;
}

div[equation] hr[nor]::before{
    content: '\22BD';
    font-style:normal;
}

div[equation] hr[in]::before {
    content: '\2208';
    font-style: normal;
}

div[equation] hr[notin]::before {
    content: '\2209';
    font-style: normal;
}

div[equation] hr[and]::before {
    content: '\2227';
    font-style: normal;
}

div[equation] hr[or]::before {
    content: '\2228';
    font-style: normal;
}

div[equation] hr[cap]::before {
    content: '\2229';
    font-style: normal;
}

div[equation] hr[cup]::before {
    content: '\222A';
    font-style: normal;
}


/* Discrete Functionality */

div[equation] hr[congruent]::before {
    content: '\2261';
    font-style: normal;
}

div[equation] hr[subsetleft]::before {
    content: '\2282';
    font-style: normal;
}

div[equation] hr[subsetright]::before {
    content: '\2283';
    font-style: normal;
}

div[equation] hr[notsubsetleft]::before {
    content: '\2284';
    font-style: normal;
}

div[equation] hr[notsubsetright]::before {
    content: '\2285';
    font-style: normal;
}

div[equation] hr[subsetorequaltoleft]::before {
    content: '\2286';
    font-style: normal;
}

div[equation] hr[subsetorequaltoright]::before {
    content: '\2287';
    font-style: normal;
}

div[equation] hr[notsubsetorequaltoleft]::before {
    content: '\2288';
    font-style: normal;
}

div[equation] hr[notsubsetorequaltoright]::before {
    content: '\2289';
    font-style: normal;
}


/* Greek Functionality */

div[equation] hr[pi] {
    -webkit-margin-after: -4px !important;
    display: inline-block !important;
    float: none !important;
}

div[equation] hr[pi]::before {
    content: '\03C0';
    font-style: normal;
}

div[equation] hr[alpha]::before {
    content: '\03B1';
    font-style: normal;
}

div[equation] hr[beta]::before {
    content: '\03B2';
    font-style: normal;
}

div[equation] hr[lambda]::before {
    content: '\03BB';
    font-style: normal;
}

div[equation] hr[delta]::before {
    content: '\2206';
    font-style: normal;
}

hr[add] {
    display: inline-block;
}

hr[add]::before {
    content: '+';
    float: left;
    font-style: normal;
}

div[equation] > hr[add] {
    border: none;
    clear: none;
    display: inline-block;
    font-size: 1.5em;
    font-style: italic;
    height: 100px;
    margin: 0;
    padding-left: 3px;
    padding-top: 35px;
    position: relative;
    width: auto;
}

hr[subtract] {
    display: inline-block;
}

hr[subtract]::before {
    content: '-';
    float: left;
    font-style: normal;
}

div[equation] > hr[subtract] {
    border: none;
    clear: none;
    display: inline-block;
    font-size: 1.5em;
    font-style: italic;
    height: 100px;
    margin: 0;
    padding-left: 3px;
    padding-top: 35px;
    position: relative;
    width: auto;
}

div[matrix] {
    height: 100px;
    margin-left: 0;
    margin-right: 0;
    margin-left:10px;
    margin-right:5px;
    position: relative;
    width: auto;
        min-width: 30px;
}

div[piecewise] {
    height: 100px;
    margin-left: 0;
    margin-right: 0;
    margin-left:10px;
    margin-right:5px;
    position: relative;
    width: auto;
        min-width: 30px;
}

div[one]{
  height: 30px;
  margin-top:35px;
  margin-bottom:35px;
  display: inline-block;
  width:auto;
  position: relative;
  padding-top: 4px;
}


div[two]{
  height: 50px;
  margin-top:25px;
  margin-bottom:25px;
  display: inline-block;
  width:auto;
  position: relative;
}


div[three]{
  height: 75px;
  margin-top: 12.5px;
  margin-bottom:12.5px;
  display: inline-block;
  width:auto;
  position: relative;
}


div[four]{
  height: 100px;
  margin-top:0px;
  margin-bottom:0px;
  display: inline-block;
  width:auto;
  position: relative;
}

div[five]{
  height: 100px;
  margin-top:0px;
  margin-bottom:0px;
  display: inline-block;
  width:auto;
  position: relative;
}


div[matrix]::before{
  display: block;
    height: 100%;
    left: 0px;
    width: 10px;
    font-weight: 100;
    border: 3px black solid;
    border-right: none;
    -webkit-margin-before: 0em;
    -webkit-margin-after: 0em;
    -webkit-margin-start: 0;
    -webkit-margin-end: 0;
    position: absolute;
    top: -7px;
    content: "";
    left: 0px;
}

div[matrix]::after{
  display: block;
    height: 100%;
    width: 10px;
    font-weight: 100;
    border: 3px black solid;
    border-left: none;
    -webkit-margin-before: 0em;
    -webkit-margin-after: 0em;
    -webkit-margin-start: 0;
    -webkit-margin-end: 0;
    position: absolute;
    top: -7px;
    content: "";
    right: 0px;
}

div[equation].white div[matrix]::before{
  border: 3px white solid;
  border-right: none;
}

div[equation].white div[matrix]::after{
  border: 3px white solid;
  border-left: none;
}




div[piecewise]::before{
  display: block;
    height: 100%;
    left: 0px;
    width: 10px;
    font-weight: 100;
    border: 3px black solid;
    border-right: none;
    border-radius:10px;
    border-top-right-radius: 0px;
    border-bottom-right-radius:0px;
    -webkit-margin-before: 0em;
    -webkit-margin-after: 0em;
    -webkit-margin-start: 0;
    -webkit-margin-end: 0;
    position: absolute;
    top: -7px;
    content: "";
    left: 0px;
}

div[piecewise]::after{
  display: block;
    height: 100%;
    width: 10px;
    font-weight: 100;
    border: none;
    border-left: none;
    -webkit-margin-before: 0em;
    -webkit-margin-after: 0em;
    -webkit-margin-start: 0;
    -webkit-margin-end: 0;
    position: absolute;
    content: "";
    left: -5px;
    top:40%;
    width:5px;
    height:5px;
    background-color: black;

}

div[piecewise].white div[matrix]::before{
  border: 3px white solid;
  border-right: none;
}

div[piecewise].white div[matrix]::after{
  border: 3px white solid;
  border-left: none;
}


div[matrix]> b{
  min-width:25px;
  height: 100%;
  display:inline-block;
  float:left;
  font-weight:300;
  text-align: center;
    font-style: italic;
}

div[matrix] > b > a{
  clear: both;
      min-width: 100%;
      text-align: center;
      display: block;
      height: 25px;
      width: auto;
      padding-left: 8px;
      padding-right: 8px;
      box-sizing: border-box;
}

div[matrix] > b > hr{
  width: auto;
  clear: both;
  text-align: center;
  display: block;
  min-width: 25px;
  height: 1px;
  display: inline-block;
  float: none;
  display: block;
  top: -12px;
  margin-top: 0px;
  margin-bottom: 6px;
}


div[piecewise]> b{
  min-width:25px;
  height: 100%;
  display:inline-block;
  float:left;
  font-weight:300;
  text-align: center;
    font-style: italic;
}

div[piecewise] > b > a{
  clear: both;
      min-width: 100%;
      text-align: center;
      display: block;
      height: 25px;
      width: auto;
      padding-left: 8px;
      padding-right: 8px;
      box-sizing: border-box;
}

div[piecewise] > b > hr{
  width: auto;
  clear: both;
  text-align: center;
  display: block;
  min-width: 25px;
  height: 1px;
  display: inline-block;
  float: none;
  display: block;
  top: -12px;
  margin-top: 0px;
  margin-bottom: 6px;
}

div[five] > b > a{
  font-size:12px;
  height: 20px;
}

div[six] > b > a{
  font-size:10px;
  height: 16.666px;
  height: calc(100px / 6);
}

div[seven] > b > a{
  font-size:9.5px;
  height: 14.28px;
  height: calc(100px / 7);
}

div[eight] > b > a{
  font-size:9.5px;
  height: 12.5px;
  height: calc(100px / 8);
}


div[five] > b {
  font-size:12px;
}

div[six] > b {
  font-size:10px;
}

div[seven] > b {
  font-size:9.5px;
}

div[eight] > b {
  font-size:9.5px;
}


div[five] > b > hr{
  top: -12px;
  margin-top: 0px;
  margin-bottom: 5px;
}

div[six] > b > hr{
  top: -12px;
  margin-top: 0px;
  margin-bottom: 2.6px;
}

div[seven] > b > hr{
  top: -12px;
  margin-top: 0px;
  margin-bottom: 3px;
}

div[eight] > b > hr{
  top: -12px;
  margin-top: 0px;
  margin-bottom: 1.5px;
}

div[shaded] {
    background-color:white  !important;
}

div[venn] {
    display: inline-block;
    height: 150px;
    margin-left: 10px;
    margin-right: 10px;
    padding-left: 9px;
    padding-right: 9px;
    position: relative;
    border:1px white  solid;
    width:180px;
    margin-bottom:-50px;
    margin-top:-78px;
    background-color:rgba(241,111,92,1);
}

div[two]{

}

div[two]  > div[A]{
    margin-top:35px;
    margin-bottom:10px;
    margin-left:10px;
    width:80px;
    height: 80px;
    border-radius:100%;
    border:2px white  solid;
    float:left;
    box-sizing: border-box;
    overflow:hidden;
    z-index:2;
    background-color:rgba(241,111,92,1);
    position: relative;
}

div[two]  > div[B]{
    margin-top:35px;
    margin-bottom:10px;
    margin-left:10px;
    width:80px;
    float:left;
    margin-left:-20px;
    height: 80px;
    border-radius:100%;
    z-index:1;
    border:2px white  solid;
    box-sizing: border-box;
    background-color:rgba(241,111,92,1);
    position: relative;
}

div[two]  > div[A] > div[AB]{
    margin-bottom:10px;
    margin-left:58px;
    width:80px;
    margin-top:-2px;
    height: 80px;
    border-radius:100%;
    border:2px white  solid;
    float:left;
    box-sizing: border-box;
    background-color:rgba(241,111,92,1);

}


div[three]  > div[A]{
    margin-top:10px;
    margin-bottom:10px;
    margin-left:10px;
    width:80px;
    height: 80px;
    border-radius:100%;
    border:2px white  solid;
    float:left;
    box-sizing: border-box;
    overflow:hidden;
    z-index:3;
    background-color:rgba(241,111,92,1);
    position: relative;
}

div[three]  > div[B]{
    margin-top:10px;
    margin-bottom:10px;
    margin-left:10px;
    width:80px;
    float:left;
    margin-left:-20px;
    height: 80px;
    border-radius:100%;
    z-index:2;
    border:2px white  solid;
    box-sizing: border-box;
    background-color:rgba(241,111,92,1);
    overflow:hidden;
    position: relative;
}


div[three]  > div[C]{
    margin-top:10px;
    margin-bottom:10px;
    margin-left:10px;
    width:80px;
    float:left;
    margin-left:-20px;
    height: 80px;
    border-radius:100%;
    z-index:1;
    z-index:1;
    border:2px white  solid;
    box-sizing: border-box;
    background-color:rgba(241,111,92,1);
    margin-top:-40px;
    margin-left:39px;
    position: relative;
}

div[three]  > div[A] > div[AB]{
    margin-bottom:10px;
    margin-left:58px;
    width:80px;
    margin-top:-2px;
    height: 80px;
    border-radius:100%;
    border:2px white  solid;
    float:left;
    box-sizing: border-box;
    z-index:2;
    background-color:rgba(241,111,92,1);
    position:relative;
    overflow:hidden;
}

div[three]  > div[A] > div[AB] > div[ABC]{
    margin-bottom:10px;
    margin-left:-33px;
    width:80px;
    margin-top:49px;
    height: 80px;
    border-radius:100%;
    border:2px white  solid;
    float:left;
    box-sizing: border-box;
    z-index:2;
    background-color:rgba(241,111,92,1);
    position:relative;
}



div[three]  > div[A] > div[AC]{
    margin-bottom:10px;
    width:80px;
    height: 80px;
    border-radius:100%;
    z-index:1;
    position:relative;
    margin-top:-39px;
    margin-left:27px;
    border:2px white  solid;
    float:left;
    box-sizing: border-box;
    background-color:rgba(241,111,92,1);
}


div[three]  > div[B] > div[BC]{
    margin-bottom:10px;
    margin-left:-33px;
    width:80px;
    margin-top:49px;
    height: 80px;
    border-radius:100%;
    border:2px white  solid;
    float:left;
    box-sizing: border-box;
    z-index:2;
    background-color:rgba(241,111,92,1);
    position:relative;
}

div[four] * {
    background-color: rgba(241,111,92,1) !important;
    border-color: white !important;
}

div[four] div[shaded] {
    background-color: white !important;
}

div[four]  > div[A]{
    margin-top:15px;
    margin-bottom:10px;
    margin-left:15px;
    width:80px;
    height: 80px;
    border-radius:100%;
    border:2px black solid;
    float:left;
    box-sizing: border-box;
    overflow:hidden;
    z-index:4;
    background-color:transparent;
    position: relative;
}

div[four]  > div[B]{
    margin-top:15px;
    margin-bottom:10px;
    margin-left:15px;
    width:80px;
    float:left;
    margin-left:-30px;
    height: 80px;
    border-radius:100%;
    z-index:2;
    border:2px black solid;
    box-sizing: border-box;
    background-color:transparent;
    overflow:hidden;
    position: relative;
}

div[four]  > div[B] > div[BC]{
    margin-bottom:10px;
    margin-left:40px;
    width:80px;
    margin-top:-177px;
    height: 80px;
    border-radius:100%;
    border:2px black solid;
    float:left;
    box-sizing: border-box;
    z-index:2;
    background-color:white;
    position:relative;
    overflow:hidden;
}



div[four]  > div[C]{
    margin-top:10px;
    margin-bottom:10px;
    width:80px;
    float:left;
    height: 80px;
    border-radius:100%;
    z-index:3;
    border:2px black solid;
    box-sizing: border-box;
    background-color:transparent;
    margin-top:-50px;
    margin-left:15px;
    position: relative;
    overflow:hidden;
}

div[four]  > div[E]{
    margin-top:-50px;
    margin-bottom:10px;
    margin-left:10px;
    width:80px;
    float:left;
    margin-left:-30px;
    height: 80px;
    border-radius:100%;
    z-index:1;
    border:2px black solid;
    box-sizing: border-box;
    background-color:transparent;
    overflow:hidden;
    position: relative;
    background-color:white;

}

div[four]  > div[A] > div[AB]{
    margin-bottom:10px;
    margin-left:48px;
    width:80px;
    margin-top:-2px;
    height: 80px;
    border-radius:100%;
    border:2px black solid;
    float:left;
    box-sizing: border-box;
    z-index:2;
    background-color:white;
    position:relative;
    overflow:hidden;
}


div[four]  > div[A] > div[AE]{
    margin-bottom:10px;
    margin-left:-43px;
    width:80px;
    margin-top:-177px;
    height: 80px;
    border-radius:100%;
    border:2px black solid;
    float:left;
    box-sizing: border-box;
    z-index:2;
    background-color:white;
    position:relative;
    overflow:hidden;
}

div[four]  > div[E] > div[AE]{
    margin-bottom:10px;
    margin-left:38px;
    width:80px;
    margin-top:45px;
    height: 80px;
    border-radius:100%;
    border:2px black solid;
    float:left;
    box-sizing: border-box;
    z-index:2;
    background-color:white;
    position:relative;
    overflow:hidden;
}


div[four]  > div[A] > div[AB] > div[ABC]{
    margin-left:-52px;
    margin-top:38px;
    height: 80px;


    width:80px;
    border-radius:100%;
    border:2px black solid;
    float:left;
    box-sizing: border-box;
    z-index:2;
    background-color:white;
    position:relative;
    overflow:hidden;
}

div[four]  > div[A] > div[AB] > div[ABC] > div[ABCE]{
    margin-left:48px;
    margin-top:-2px;
    height: 80px;


    width:80px;
    border-radius:100%;
    border:2px black solid;
    float:left;
    box-sizing: border-box;
    z-index:2;
    background-color:white;
    position:relative;
    overflow:hidden;
}

div[four]  > div[A] > div[AB] > div[ABE]{
    margin-left:-2px;
    margin-top:-80px;


    height: 80px;
    width:80px;
    border-radius:100%;
    border:2px black solid;
    float:left;
    box-sizing: border-box;
    z-index:1;
    background-color:white;
    position:relative;
    overflow:hidden;
}




div[four]  > div[A] > div[AC]{
    margin-bottom:10px;
    width:80px;
    height: 80px;
    border-radius:100%;
    z-index:1;
    position:relative;
    margin-top:-50px;
    margin-left:-2px;
    border:2px black solid;
    float:left;
    box-sizing: border-box;
    background-color:white;
}


div[four]  > div[A] > div[AC] > div[ACE]{
    margin-left:48px;
    margin-top:-2px;
    height: 80px;
    width:80px;
    border-radius:100%;
    border:2px black solid;
    float:left;
    box-sizing: border-box;
    z-index:1;
    background-color:white;
    position:relative;
    overflow:hidden;
}

div[four]  > div[C] > div[CE]{
    margin-bottom:10px;
    margin-left:48px;
    width:80px;
    margin-top:-2px;
    height: 80px;
    border-radius:100%;
    border:2px black solid;
    float:left;
    box-sizing: border-box;
    z-index:2;
    background-color:white;
    position:relative;
    overflow:hidden;
}

div[four]  > div[C] > div[CE] > div[BCE]{
    margin-left:-2px;
    margin-top:-42px;
    height: 80px;
    width:80px;
    border-radius:100%;
    border:2px black solid;
    float:left;
    box-sizing: border-box;
    z-index:1;
    background-color:white;
    position:relative;
    overflow:hidden;
}


div[four]  > div[B] > div[BE]{
    margin-bottom:10px;
    width:80px;
    height: 80px;
    border-radius:100%;
    z-index:1;
    position:relative;
    margin-top:38px;
    margin-left:-2px;
    border:2px black solid;
    float:left;
    box-sizing: border-box;
    background-color:white;
}



div[four]  > div[C] > div[BC]{
    margin-bottom:10px;
    margin-left:-41px;
    width:80px;
    margin-top:-42px;
    height: 80px;
    border-radius:100%;
    border:2px black solid;
    float:left;
    box-sizing: border-box;
    z-index:2;
    background-color:white;
    position:relative;
    overflow:hidden;
}

span[hat]{
  float:none;
  position:relative;
}

span[hat]::before{
  content:'^';
  text-align: center;
  position:absolute;
  top:-7px;
  color:black;
  width:100%;
  border-bottom:0px black solid;
}

.white span[hat]::before{
  color:white;
}

span[vector]{
  float:none;
  position:relative;
}

span[vector]::before{
  content:'\2192';
  float:right;
  color:black;
  position:absolute;
  top:1px;
  width:100%;
  font-size:.5em;


}

div[modification]{
  height: 75px;
margin-top: 12.5px;
margin-bottom: 12.5px;
display: inline-block;
width: auto;
position: relative;
min-width: 20px;
}

.white span[vector]::before{
  color:white;
}

div[modification]> b{
  min-width:25px;
  height: 100%;
  display:inline-block;
  float:left;
  font-weight:300;
  text-align: center;
    font-style: italic;
}

div[modification] > b > a{
  clear: both;
      min-width: 100%;
      text-align: left;
      display: block;
      height: 25px;
      width: auto;
      padding-left: 8px;
      padding-right: 8px;
      box-sizing: border-box;
}

svg{
	width:400px;
	height:200px;
	border:1px solid #000000;
}
line{
	stroke:rgb(0,0,0);
	//stroke:rgb(255,0,0);
	stroke-width=2;
}