/main/khan/static/latestKhan/utils/MathJax/1.1a/config/KAthJax-62e7a7b628ba168df6b9cd3de8feac38.js

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MathJax.Hub.Config({
messageStyle: "none",
skipStartupTypeset: !0,
jax: [ "input/TeX", "output/HTML-CSS" ],
extensions: [ "tex2jax.js", "MathZoom.js" ],
TeX: {
extensions: [ "AMSmath.js", "AMSsymbols.js", "noErrors.js", "noUndefined.js", "newcommand.js", "boldsymbol.js" ],
Macros: {
RR: "\\mathbb{R}",
blue: "\\color{#6495ED}",
orange: "\\color{#FFA500}",
pink: "\\color{#FF00AF}",
red: "\\color{red}",
green: "\\color{#28AE7B}",
gray: "\\color{gray}",
purple: "\\color{purple}"
},
Augment: {
Definitions: {
macros: {
lrsplit: "LRSplit",
cancel: "Cancel",
lcm: [ "NamedOp", 0 ]
}
},
Parse: {
prototype: {
LRSplit: function(e) {
var t = this.GetArgument(e), n = this.GetArgument(e), r = MathJax.ElementJax.mml.mfrac(MathJax.InputJax.TeX.Parse("\\strut\\textstyle{" + t + "\\qquad}", this.stack.env).mml(), MathJax.InputJax.TeX.Parse("\\strut\\textstyle{\\qquad " + n + "}", this.stack.env).mml());
r.numalign = MathJax.ElementJax.mml.ALIGN.LEFT, r.denomalign = MathJax.ElementJax.mml.ALIGN.RIGHT, r.linethickness = "0em", this.Push(r);
},
Cancel: function(e) {
this.Push(MathJax.ElementJax.mml.menclose(this.ParseArg(e)).With({
notation: MathJax.ElementJax.mml.NOTATION.UPDIAGONALSTRIKE
}));
}
}
}
}
},
"HTML-CSS": {
scale: 100,
showMathMenu: !1,
availableFonts: [ "TeX" ],
imageFont: null
}
}), MathJax.Hub.elementScripts = function(e) {
return e.nodeName.toLowerCase() === "code" ? [ e ] : e.getElementsByTagName("code");
}, MathJax.Hub.Browser.isKonqueror = !0, MathJax.Ajax.timeout = 6e4, MathJax.Ajax.loadError = function(e) {
return function(t) {
Khan.warnTimeout(), MathJax.Ajax.loadComplete = function(e) {}, e.call(this, t);
};
}(MathJax.Ajax.loadError), MathJax.Hub.Register.StartupHook("HTML-CSS Jax - disable web fonts", function() {
Khan.warnFont();
}), MathJax.Message.Init = function(e) {
return function(t) {
if (this.div && this.div.parentNode == null) {
var n = document.getElementById("MathJax_Message");
if (n && n.firstChild == null) {
var r = n.parentNode;
r && r.removeChild(n);
}
}
e.call(this, t);
};
}(MathJax.Message.Init), MathJax.Hub.Startup.onload(), MathJax.Ajax.Preloading("[MathJax]/extensions/MathZoom.js", "[MathJax]/extensions/TeX/AMSmath.js", "[MathJax]/extensions/TeX/AMSsymbols.js", "[MathJax]/extensions/TeX/noErrors.js", "[MathJax]/extensions/TeX/noUndefined.js", "[MathJax]/extensions/TeX/newcommand.js", "[MathJax]/extensions/TeX/boldsymbol.js", "[MathJax]/extensions/tex2jax.js", "[MathJax]/jax/element/mml/jax.js", "[MathJax]/jax/input/TeX/config.js", "[MathJax]/jax/input/TeX/jax.js", "[MathJax]/jax/output/HTML-CSS/config.js", "[MathJax]/jax/output/HTML-CSS/jax.js"), MathJax.Hub.Config({
"v1.0-compatible": !1
}), function(e, t, n, r, i) {
var s = "1.1", o = e.CombineConfig("MathZoom", {
delay: 400,
styles: {
"#MathJax_Zoom": {
position: "absolute",
"background-color": "#F0F0F0",
overflow: "auto",
display: "block",
"z-index": 301,
padding: ".5em",
border: "1px solid black",
margin: 0,
"font-family": "serif",
"font-size": "85%",
"font-weight": "normal",
"font-style": "normal",
"text-align": "left",
"text-indent": 0,
"text-transform": "none",
"line-height": "normal",
"letter-spacing": "normal",
"word-spacing": "normal",
"word-wrap": "normal",
"white-space": "nowrap",
"float": "none",
"box-shadow": "5px 5px 15px #AAAAAA",
"-webkit-box-shadow": "5px 5px 15px #AAAAAA",
"-moz-box-shadow": "5px 5px 15px #AAAAAA",
"-khtml-box-shadow": "5px 5px 15px #AAAAAA",
filter: "progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"
},
"#MathJax_ZoomOverlay": {
position: "absolute",
left: 0,
top: 0,
"z-index": 300,
display: "inline-block",
width: "100%",
height: "100%",
border: 0,
padding: 0,
margin: 0,
"background-color": "white",
opacity: 0,
filter: "alpha(opacity=0)"
}
}
}), u = function(e) {
return e || (e = window.event), e && (e.preventDefault && e.preventDefault(), e.stopPropagation && e.stopPropagation(), e.cancelBubble = !0, e.returnValue = !1), !1;
}, a = MathJax.Extension.MathZoom = {
version: s,
settings: e.config.menuSettings,
HandleEvent: function(e, t, n) {
return e || (e = window.event), a.settings.CTRL && !e.ctrlKey ? !0 : a.settings.ALT && !e.altKey ? !0 : a.settings.CMD && !e.metaKey ? !0 : a.settings.Shift && !e.shiftKey ? !0 : a[t](e, n);
},
Click: function(e, t) {
if (this.settings.zoom === "Click") return this.Zoom(t, e);
},
DblClick: function(e, t) {
if (this.settings.zoom === "Double-Click") return this.Zoom(t, e);
},
Mouseover: function(e, t) {
if (this.settings.zoom === "Hover") return a.oldMouseOver = t.onmouseover, t.onmouseover = null, t.onmousemove = this.Mousemove, t.onmouseout = this.Mouseout, a.Timer(e, t);
},
Mouseout: function(e) {
return this.onmouseover = a.oldMouseOver, delete a.oldMouseOver, this.onmousemove = this.onmouseout = null, a.ClearTimer(), u(e);
},
Mousemove: function(e) {
return a.Timer(e || window.event, this);
},
Timer: function(e, t) {
return this.ClearTimer(), this.timer = setTimeout(MathJax.Callback([ "Zoom", this, t, {} ]), o.delay), u(e);
},
ClearTimer: function() {
this.timer && (clearTimeout(this.timer), delete this.timer);
},
Zoom: function(n, s) {
this.ClearTimer(), this.Remove();
var a = n.parentNode;
a.className === "MathJax_MathContainer" && (a = a.parentNode), a.parentNode.className === "MathJax_MathContainer" && (a = a.parentNode.parentNode);
var f = (String(a.className).match(/^MathJax_(MathML|Display)$/) ? a : n).nextSibling, l = e.getJaxFor(f), p = l.root, v = r && l.outputJax.isa(r.constructor) ? "HTMLCSS" : i && l.outputJax.isa(i.constructor) ? "MathML" : null;
if (!v) return;
var m = Math.floor(.85 * document.body.clientWidth), y = Math.floor(.85 * document.body.clientHeight), w = t.Element("span", {
style: {
position: "relative",
display: "inline-block",
height: 0,
width: 0
},
id: "MathJax_ZoomFrame"
}, [ [ "span", {
id: "MathJax_ZoomOverlay",
onmousedown: this.Remove
} ], [ "span", {
id: "MathJax_Zoom",
onclick: this.Remove,
style: {
visibility: "hidden",
fontSize: this.settings.zscale,
"max-width": m + "px",
"max-height": y + "px"
}
}, [ [ "span" ] ] ] ]), E = w.lastChild, S = E.firstChild, x = w.firstChild;
n.parentNode.insertBefore(w, n);
if (this.msieZIndexBug) {
var T = t.Element("img", {
src: "about:blank",
id: "MathJax_ZoomTracker",
style: {
width: 0,
height: 0,
position: "relative"
}
});
document.body.appendChild(w), w.style.position = "absolute", w.style.zIndex = o.styles["#MathJax_ZoomOverlay"]["z-index"], w = T;
}
var N = this["Zoom" + v](p, S, n);
return this.msiePositionBug ? (this.msieIE8Bug && (S.style.position = "absolute", E.style.height = S.offsetHeight, S.style.position = "", E.offsetHeight <= y && E.offsetWidth <= m && (E.style.overflow = "visible")), this.msieWidthBug ? E.style.width = Math.min(m, N.w) : N.w > m && (E.style.width = m), E.offsetHeight > y && (E.style.Height = y + "px"), n.nextSibling ? n.parentNode.insertBefore(w, n.nextSibling) : a.appendChild(w)) : this.operaPositionBug && (E.style.width = Math.min(m, S.offsetWidth) + "px"), this.Position(E, N, v === "MathML" && a.nodeName.toLowerCase() === "div"), E.style.visibility = "", this.settings.zoom === "Hover" && (x.onmouseover = this.Remove), window.addEventListener ? addEventListener("resize", this.Resize, !1) : window.attachEvent ? attachEvent("onresize", this.Resize) : (this.onresize = window.onresize, window.onresize = this.Resize), u(s);
},
ZoomHTMLCSS: function(e, t, n) {
t.className = "MathJax", r.idPostfix = "-zoom", r.getScales(t, t), e.toHTML(t, t);
var i = e.HTMLspanElement().bbox;
r.idPostfix = "";
if (i.width && i.width !== "100%") {
var s = Math.floor(.85 * document.body.clientWidth);
t.style.width = s + "px", t.style.display = "inline-block";
var o = (e.id || "MathJax-Span-" + e.spanID) + "-zoom", u = document.getElementById(o).firstChild;
while (u && u.style.width !== i.width) u = u.nextSibling;
u && (u.style.width = "100%");
}
t.appendChild(this.topImg);
var a = this.topImg.offsetTop;
t.removeChild(this.topImg);
var f = this.msieWidthBug ? r.getW(n) * r.em : n.offsetWidth;
return {
w: i.w * r.em,
Y: -a,
W: f
};
},
ZoomMathML: function(e, t, n) {
e.toNativeMML(t, t);
var r;
t.appendChild(this.topImg), r = this.topImg.offsetTop, t.removeChild(this.topImg);
var i = (this.ffMMLwidthBug ? n.parentNode : n).offsetWidth;
return {
w: t.offsetWidth,
Y: -r,
W: i
};
},
Position: function(e, t, n) {
var r = this.Resize(), i = r.x, s = r.y, o = t.W;
this.msiePositionBug && (o = -o), n && this.ffMMLcenterBug && (o = 0);
var u = -Math.floor((e.offsetWidth - o) / 2), a = t.Y;
e.style.left = Math.max(u, 20 - i) + "px", e.style.top = Math.max(a, 20 - s) + "px";
},
Resize: function(e) {
a.onresize && a.onresize(e);
var t = 0, n = 0, r = document.getElementById("MathJax_ZoomFrame"), i = document.getElementById("MathJax_ZoomOverlay"), s = a.msieZIndexBug ? document.getElementById("MathJax_ZoomTracker") : r;
a.operaPositionBug && (r.style.border = "1px solid");
if (s.offsetParent) do t += s.offsetLeft, n += s.offsetTop; while (s = s.offsetParent);
return a.operaPositionBug && (r.style.border = ""), a.msieZIndexBug && (r.style.left = t + "px", r.style.top = n + "px"), i.style.left = -t + "px", i.style.top = -n + "px", a.msiePositionBug ? setTimeout(a.SetWH, 0) : a.SetWH(), {
x: t,
y: n
};
},
SetWH: function() {
var e = document.getElementById("MathJax_ZoomOverlay");
e.style.width = e.style.height = "1px", e.style.width = document.body.scrollWidth + "px", e.style.height = document.body.scrollHeight + "px";
},
Remove: function(e) {
var n = document.getElementById("MathJax_ZoomFrame");
if (n) {
n.parentNode.removeChild(n), n = document.getElementById("MathJax_ZoomTracker"), n && n.parentNode.removeChild(n);
if (a.operaRefreshBug) {
var r = t.addElement(document.body, "div", {
style: {
position: "fixed",
left: 0,
top: 0,
width: "100%",
height: "100%",
backgroundColor: "white",
opacity: 0
},
id: "MathJax_OperaDiv"
});
document.body.removeChild(r);
}
window.removeEventListener ? removeEventListener("resize", a.Resize, !1) : window.detachEvent ? detachEvent("onresize", a.Resize) : (window.onresize = a.onresize, delete a.onresize);
}
return u(e);
}
};
e.Register.StartupHook("HTML-CSS Jax Ready", function() {
r = MathJax.OutputJax["HTML-CSS"], r.Augment({
HandleEvent: a.HandleEvent
});
}), e.Register.StartupHook("NativeMML Jax Ready", function() {
i = MathJax.OutputJax.NativeMML, i.Augment({
HandleEvent: a.HandleEvent,
MSIEmouseup: function(e, t, n) {
return this.trapUp ? (delete this.trapUp, !0) : this.MSIEzoomKeys(e) ? !0 : !1;
},
MSIEclick: function(e, t, n) {
return this.trapClick ? (delete this.trapClick, !0) : this.MSIEzoomKeys(e) ? this.settings.zoom.match(/Click/) ? a.Click(e, t) === !1 : !1 : !1;
},
MSIEdblclick: function(e, t, n) {
return this.MSIEzoomKeys(e) ? a.DblClick(e, t) === !1 : !1;
},
MSIEmouseover: function(e, t, n) {
return this.settings.zoom !== "Hover" ? !1 : (a.Timer(e, t), !0);
},
MSIEmouseout: function(e, t, n) {
return this.settings.zoom !== "Hover" ? !1 : (a.ClearTimer(), !0);
},
MSIEmousemove: function(e, t, n) {
return this.settings.zoom !== "Hover" ? !1 : (a.Timer(e, t), !0);
},
MSIEzoomKeys: function(e) {
return this.settings.CTRL && !e.ctrlKey ? !1 : this.settings.CMD && !e.metaKey ? !1 : this.settings.ALT && !e.altKey ? !1 : this.settings.Shift && !e.shiftKey ? !1 : !0;
}
});
}), e.Browser.Select({
MSIE: function(e) {
var t = document.compatMode === "BackCompat", n = e.versionAtLeast("8.0") && document.documentMode > 7;
a.msiePositionBug = !0, a.msieWidthBug = !t, a.msieIE8Bug = n, a.msieZIndexBug = !n, a.msieInlineBlockAlignBug = !n || t, document.documentMode >= 9 && delete o.styles["#MathJax_Zoom"].filter;
},
Opera: function(e) {
a.operaPositionBug = !0, a.operaRefreshBug = !0;
},
Firefox: function(e) {
a.ffMMLwidthBug = !0, a.ffMMLcenterBug = !0;
}
}), a.topImg = a.msieInlineBlockAlignBug ? t.Element("img", {
style: {
width: 0,
height: 0
},
src: "about:blank"
}) : t.Element("span", {
style: {
width: 0,
height: 0,
display: "inline-block"
}
}), a.operaPositionBug && (a.topImg.style.border = "1px solid"), MathJax.Callback.Queue([ "Styles", n, o.styles ], [ "Post", e.Startup.signal, "MathZoom Ready" ], [ "loadComplete", n, "[MathJax]/extensions/MathZoom.js" ]);
}(MathJax.Hub, MathJax.HTML, MathJax.Ajax, MathJax.OutputJax["HTML-CSS"], MathJax.OutputJax.NativeMML), MathJax.Hub.Register.StartupHook("TeX Jax Ready", function() {
var e = "1.1", t = MathJax.ElementJax.mml, n = MathJax.InputJax.TeX, r = n.Definitions, i = n.Stack.Item, s = function(e) {
return e.join("em ") + "em";
};
MathJax.Hub.Insert(r, {
macros: {
mathring: [ "Accent", "2DA" ],
nobreakspace: "Tilde",
negmedspace: [ "Spacer", t.LENGTH.NEGATIVEMEDIUMMATHSPACE ],
negthickspace: [ "Spacer", t.LENGTH.NEGATIVETHICKMATHSPACE ],
intI: [ "Macro", "\\mathchoice{\\!}{}{}{}\\!\\!\\int" ],
iiiint: [ "MultiIntegral", "\\int\\intI\\intI\\intI" ],
idotsint: [ "MultiIntegral", "\\int\\cdots\\int" ],
dddot: [ "Macro", "\\mathop{#1}\\limits^{\\textstyle \\mathord{.}\\mathord{.}\\mathord{.}}", 1 ],
ddddot: [ "Macro", "\\mathop{#1}\\limits^{\\textstyle \\mathord{.}\\mathord{.}\\mathord{.}\\mathord{.}}", 1 ],
sideset: [ "Macro", "\\mathop{\\mathop{\\rlap{\\phantom{#3}}}\\nolimits#1\\!\\mathop{#3}\\nolimits#2}", 3 ],
boxed: [ "Macro", "\\fbox{$\\displaystyle{#1}$}", 1 ],
tag: "HandleTag",
notag: "HandleNoTag",
substack: [ "Macro", "\\begin{subarray}{c}#1\\end{subarray}", 1 ],
injlim: [ "Macro", "\\mathop{\\rm inj\\,lim}" ],
projlim: [ "Macro", "\\mathop{\\rm proj\\,lim}" ],
varliminf: [ "Macro", "\\mathop{\\underline{\\rm lim}}" ],
varlimsup: [ "Macro", "\\mathop{\\overline{\\rm lim}}" ],
varinjlim: [ "Macro", "\\mathop{\\underrightarrow{\\rm lim\\Rule{-1pt}{0pt}{1pt}}\\Rule{0pt}{0pt}{.45em}}" ],
varprojlim: [ "Macro", "\\mathop{\\underleftarrow{\\rm lim\\Rule{-1pt}{0pt}{1pt}}\\Rule{0pt}{0pt}{.45em}}" ],
DeclareMathOperator: "HandleDeclareOp",
operatorname: "HandleOperatorName",
genfrac: "Genfrac",
frac: [ "Genfrac", "", "", "", "" ],
tfrac: [ "Genfrac", "", "", "", 1 ],
dfrac: [ "Genfrac", "", "", "", 0 ],
binom: [ "Genfrac", "(", ")", "0em", "" ],
tbinom: [ "Genfrac", "(", ")", "0em", 1 ],
dbinom: [ "Genfrac", "(", ")", "0em", 0 ],
cfrac: "CFrac",
shoveleft: [ "HandleShove", t.ALIGN.LEFT ],
shoveright: [ "HandleShove", t.ALIGN.RIGHT ],
xrightarrow: [ "xArrow", 8594, 5, 6 ],
xleftarrow: [ "xArrow", 8592, 7, 3 ]
},
environment: {
align: [ "AMSarray", null, !0, !0, "rlrlrlrlrlrl", s([ 5 / 18, 2, 5 / 18, 2, 5 / 18, 2, 5 / 18, 2, 5 / 18, 2, 5 / 18 ]) ],
"align*": [ "AMSarray", null, !1, !0, "rlrlrlrlrlrl", s([ 5 / 18, 2, 5 / 18, 2, 5 / 18, 2, 5 / 18, 2, 5 / 18, 2, 5 / 18 ]) ],
multline: [ "Multline", null, !0 ],
"multline*": [ "Multline", null, !1 ],
split: [ "AMSarray", null, !1, !1, "rl", s([ 5 / 18 ]) ],
gather: [ "AMSarray", null, !0, !0, "c" ],
"gather*": [ "AMSarray", null, !1, !0, "c" ],
alignat: [ "AlignAt", null, !0, !0 ],
"alignat*": [ "AlignAt", null, !1, !0 ],
alignedat: [ "AlignAt", null, !1, !1 ],
aligned: [ "Array", null, null, null, "rlrlrlrlrlrl", s([ 5 / 18, 2, 5 / 18, 2, 5 / 18, 2, 5 / 18, 2, 5 / 18, 2, 5 / 18 ]), ".5em", "D" ],
gathered: [ "Array", null, null, null, "c", null, ".5em", "D" ],
subarray: [ "Array", null, null, null, null, s([ 0, 0, 0, 0 ]), "0.1em", "S", 1 ],
smallmatrix: [ "Array", null, null, null, "c", s([ 1 / 3 ]), ".2em", "S", 1 ]
},
delimiter: {
"\\lvert": [ "2223", {
texClass: t.TEXCLASS.OPEN
} ],
"\\rvert": [ "2223", {
texClass: t.TEXCLASS.CLOSE
} ],
"\\lVert": [ "2225", {
texClass: t.TEXCLASS.OPEN
} ],
"\\rVert": [ "2225", {
texClass: t.TEXCLASS.CLOSE
} ]
}
}), n.Parse.Augment({
HandleTag: function(e) {
var r = this.trimSpaces(this.GetArgument(e));
r === "*" ? r = this.GetArgument(e) : r = "(" + r + ")", this.stack.global.notag && n.Error(e + " not allowed in " + this.stack.global.notag + " environment"), this.stack.global.tag && n.Error("Multiple " + e), this.stack.global.tag = t.mtd.apply(t, this.InternalMath(r));
},
HandleNoTag: function(e) {
this.stack.global.tag && delete this.stack.global.tag;
},
HandleDeclareOp: function(e) {
var t = "", r = this.trimSpaces(this.GetArgument(e));
r == "*" && (t = "\\limits", r = this.trimSpaces(this.GetArgument(e))), r.charAt(0) == "\\" && (r = r.substr(1));
var i = this.GetArgument(e);
i = i.replace(/\*/g, "\\text{*}").replace(/-/g, "\\text{-}"), n.Definitions.macros[r] = [ "Macro", "\\mathop{\\rm " + i + "}" + t ];
},
HandleOperatorName: function(e) {
var t = "\\nolimits", n = this.trimSpaces(this.GetArgument(e));
n == "*" && (t = "\\limits", n = this.trimSpaces(this.GetArgument(e))), n = n.replace(/\*/g, "\\text{*}").replace(/-/g, "\\text{-}"), this.string = "\\mathop{\\rm " + n + "}" + t + " " + this.string.slice(this.i), this.i = 0;
},
HandleShove: function(e, t) {
var r = this.stack.Top();
(r.type !== "multline" || r.data.length) && n.Error(e + " must come at the beginning of the line"), r.data.shove = t;
},
CFrac: function(e) {
var r = this.trimSpaces(this.GetBrackets(e)), i = this.GetArgument(e), s = this.GetArgument(e), o = t.mfrac(n.Parse("\\strut\\textstyle{" + i + "}", this.stack.env).mml(), n.Parse("\\strut\\textstyle{" + s + "}", this.stack.env).mml());
r = {
l: t.ALIGN.LEFT,
r: t.ALIGN.RIGHT,
"": ""
}[r], r == null && n.Error("Illegal alignment specified in " + e), r && (o.numalign = o.denomalign = r), this.Push(o);
},
Genfrac: function(e, r, i, s, o) {
r == null ? r = this.GetDelimiterArg(e) : r = this.convertDelimiter(r), i == null ? i = this.GetDelimiterArg(e) : i = this.convertDelimiter(i), s == null && (s = this.GetArgument(e)), o == null && (o = this.trimSpaces(this.GetArgument(e)));
var u = this.ParseArg(e), l = this.ParseArg(e), c = t.mfrac(u, l);
s !== "" && (c.linethickness = s);
if (r || i) c = t.mfenced(c).With({
open: r,
close: i
});
if (o !== "") {
var h = [ "D", "T", "S", "SS" ][o];
h == null && n.Error("Bad math style for " + e), c = t.mstyle(c), h === "D" ? (c.displaystyle = !0, c.scriptlevel = 0) : (c.displaystyle = !1, c.scriptlevel = o - 1);
}
this.Push(c);
},
Multline: function(e, t) {
return this.Push(e), i.multline().With({
arraydef: {
displaystyle: !0,
rowspacing: ".5em",
width: n.config.MultLineWidth,
columnwidth: "100%",
side: n.config.TagSide,
minlabelspacing: n.config.TagIndent
}
});
},
AMSarray: function(e, t, r, s, o) {
return this.Push(e), s = s.replace(/[^clr]/g, "").split("").join(" "), s = s.replace(/l/g, "left").replace(/r/g, "right").replace(/c/g, "center"), i.AMSarray(e.name, t, r, this.stack).With({
arraydef: {
displaystyle: !0,
rowspacing: ".5em",
columnalign: s,
columnspacing: o || "1em",
rowspacing: "3pt",
side: n.config.TagSide,
minlabelspacing: n.config.TagIndent
}
});
},
AlignAt: function(e, t, r) {
var i = this.GetArgument("\\begin{" + e.name + "}");
i.match(/[^0-9]/) && n.Error("Argument to \\begin{" + e.name + "} must me a positive integer"), align = "", spacing = [];
while (i > 0) align += "rl", spacing.push("0em 0em"), i--;
return spacing = spacing.join(" "), r ? this.AMSarray(e, t, r, align, spacing) : this.Array(e, null, null, align, spacing, ".5em", "D");
},
MultiIntegral: function(e, t) {
var n = this.GetNext();
if (n === "\\") {
var r = this.i;
n = this.GetArgument(e), this.i = r, n === "\\limits" && (e === "\\idotsint" ? t = "\\!\\!\\mathop{\\,\\," + t + "}" : t = "\\!\\!\\!\\mathop{\\,\\,\\," + t + "}");
}
this.string = t + " " + this.string.slice(this.i), this.i = 0;
},
xArrow: function(e, r, i, s) {
var o = {
width: "+" + (i + s) + "mu",
lspace: i + "mu"
}, u = this.GetBrackets(e), l = this.ParseArg(e), c = t.mo(t.chars(String.fromCharCode(r))).With({
stretchy: !0,
texClass: t.TEXCLASS.REL
}), h = t.munderover(c);
h.SetData(h.over, t.mpadded(l).With(o).With({
voffset: ".15em"
})), u && (u = n.Parse(u, this.stack.env).mml(), h.SetData(h.under, t.mpadded(u).With(o).With({
voffset: "-.24em"
}))), this.Push(h);
},
GetDelimiterArg: function(e) {
var t = this.trimSpaces(this.GetArgument(e));
return t == "" ? null : (r.delimiter[t] || n.Error("Missing or unrecognized delimiter for " + e), this.convertDelimiter(t));
}
}), i.multline = i.array.Subclass({
type: "multline",
EndEntry: function() {
var e = t.mtd.apply(t, this.data);
this.data.shove && (e.columnalign = this.data.shove), this.row.push(e), this.data = [];
},
EndRow: function() {
this.row.length != 1 && n.Error("multline rows must have exactly one column"), this.table.push(this.row), this.row = [];
},
EndTable: function() {
this.SUPER(arguments).EndTable.call(this);
if (this.table.length) {
var e = this.table.length - 1, n;
this.table[0][0].columnalign || (this.table[0][0].columnalign = t.ALIGN.LEFT), this.table[e][0].columnalign || (this.table[e][0].columnalign = t.ALIGN.RIGHT);
var r = t.mtr;
this.global.tag && (this.table[0] = [ this.global.tag ].concat(this.table[0]), delete this.global.tag, r = t.mlabeledtr), this.table[0] = r.apply(t, this.table[0]);
for (n = 1, e = this.table.length; n < e; n++) this.table[n] = t.mtr.apply(t, this.table[n]);
}
}
}), i.AMSarray = i.array.Subclass({
type: "AMSarray",
Init: function(e, t, n, r) {
this.SUPER(arguments).Init.apply(this), this.numbered = t, this.save_notag = r.global.notag, r.global.notag = n ? null : e;
},
EndRow: function() {
var e = t.mtr;
this.global.tag && (this.row = [ this.global.tag ].concat(this.row), e = t.mlabeledtr, delete this.global.tag), this.table.push(e.apply(t, this.row)), this.row = [];
},
EndTable: function() {
this.SUPER(arguments).EndTable.call(this), this.global.notag = this.save_notag;
}
}), i.start.Augment({
oldCheckItem: i.start.prototype.checkItem,
checkItem: function(e) {
if (e.type === "stop") {
var r = this.mmlData();
if (this.global.tag) {
var s = [ this.global.tag, t.mtd(r) ];
delete this.global.tag;
var o = {
side: n.config.TagSide,
minlabelspacing: n.config.TagIndent,
columnalign: r.displayAlign
};
r.displayAlign === t.INDENTALIGN.LEFT ? (o.width = "100%", r.displayIndent && !String(r.displayIndent).match(/^0+(\.0*)?($|[a-z%])/) && (o.columnwidth = r.displayIndent + " fit", o.columnspacing = "0", s = [ s[0], t.mtd(), s[1] ])) : r.displayAlign === t.INDENTALIGN.RIGHT && (o.width = "100%", r.displayIndent && !String(r.displayIndent).match(/^0+(\.0*)?($|[a-z%])/) && (o.columnwidth = "fit " + r.displayIndent, o.columnspacing = "0", s[2] = t.mtd())), r = t.mtable(t.mlabeledtr.apply(t, s)).With(o);
}
return i.mml(r);
}
return this.SUPER(arguments).checkItem.call(this, e);
}
}), MathJax.Hub.Startup.signal.Post("TeX AMSmath Ready");
}), MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSmath.js"), MathJax.Hub.Register.StartupHook("TeX Jax Ready", function() {
var e = "1.1.2", t = MathJax.ElementJax.mml;
MathJax.Hub.Insert(MathJax.InputJax.TeX.Definitions, {
mathchar0mi: {
digamma: "03DD",
varkappa: "03F0",
varGamma: [ "0393", {
mathvariant: t.VARIANT.ITALIC
} ],
varDelta: [ "0394", {
mathvariant: t.VARIANT.ITALIC
} ],
varTheta: [ "0398", {
mathvariant: t.VARIANT.ITALIC
} ],
varLambda: [ "039B", {
mathvariant: t.VARIANT.ITALIC
} ],
varXi: [ "039E", {
mathvariant: t.VARIANT.ITALIC
} ],
varPi: [ "03A0", {
mathvariant: t.VARIANT.ITALIC
} ],
varSigma: [ "03A3", {
mathvariant: t.VARIANT.ITALIC
} ],
varUpsilon: [ "03A5", {
mathvariant: t.VARIANT.ITALIC
} ],
varPhi: [ "03A6", {
mathvariant: t.VARIANT.ITALIC
} ],
varPsi: [ "03A8", {
mathvariant: t.VARIANT.ITALIC
} ],
varOmega: [ "03A9", {
mathvariant: t.VARIANT.ITALIC
} ],
beth: "2136",
gimel: "2137",
daleth: "2138",
backprime: [ "2035", {
variantForm: !0
} ],
hslash: [ "210F", {
variantForm: !0
} ],
varnothing: [ "2205", {
variantForm: !0
} ],
blacktriangle: "25B2",
triangledown: "25BD",
blacktriangledown: "25BC",
square: "25A1",
Box: "25A1",
blacksquare: "25A0",
lozenge: "25CA",
Diamond: "25CA",
blacklozenge: "29EB",
circledS: [ "24C8", {
mathvariant: t.VARIANT.NORMAL
} ],
bigstar: "2605",
sphericalangle: "2222",
measuredangle: "2221",
nexists: "2204",
complement: "2201",
mho: "2127",
eth: [ "00F0", {
mathvariant: t.VARIANT.NORMAL
} ],
Finv: "2132",
diagup: "2571",
Game: "2141",
diagdown: "2572",
Bbbk: [ "006B", {
mathvariant: t.VARIANT.DOUBLESTRUCK
} ],
yen: "00A5",
circledR: "00AE",
checkmark: "2713",
maltese: "2720"
},
mathchar0mo: {
dotplus: "2214",
ltimes: "22C9",
smallsetminus: [ "2216", {
variantForm: !0
} ],
rtimes: "22CA",
Cap: "22D2",
doublecap: "22D2",
leftthreetimes: "22CB",
Cup: "22D3",
doublecup: "22D3",
rightthreetimes: "22CC",
barwedge: "22BC",
curlywedge: "22CF",
veebar: "22BB",
curlyvee: "22CE",
doublebarwedge: "2A5E",
boxminus: "229F",
circleddash: "229D",
boxtimes: "22A0",
circledast: "229B",
boxdot: "22A1",
circledcirc: "229A",
boxplus: "229E",
centerdot: "22C5",
divideontimes: "22C7",
intercal: "22BA",
leqq: "2266",
geqq: "2267",
leqslant: "2A7D",
geqslant: "2A7E",
eqslantless: "2A95",
eqslantgtr: "2A96",
lesssim: "2272",
gtrsim: "2273",
lessapprox: "2A85",
gtrapprox: "2A86",
approxeq: "224A",
lessdot: "22D6",
gtrdot: "22D7",
lll: "22D8",
llless: "22D8",
ggg: "22D9",
gggtr: "22D9",
lessgtr: "2276",
gtrless: "2277",
lesseqgtr: "22DA",
gtreqless: "22DB",
lesseqqgtr: "2A8B",
gtreqqless: "2A8C",
doteqdot: "2251",
Doteq: "2251",
eqcirc: "2256",
risingdotseq: "2253",
circeq: "2257",
fallingdotseq: "2252",
triangleq: "225C",
backsim: "223D",
thicksim: [ "223C", {
variantForm: !0
} ],
backsimeq: "22CD",
thickapprox: "2248",
subseteqq: "2AC5",
supseteqq: "2AC6",
Subset: "22D0",
Supset: "22D1",
sqsubset: "228F",
sqsupset: "2290",
preccurlyeq: "227C",
succcurlyeq: "227D",
curlyeqprec: "22DE",
curlyeqsucc: "22DF",
precsim: "227E",
succsim: "227F",
precapprox: "2AB7",
succapprox: "2AB8",
vartriangleleft: "22B2",
lhd: "22B2",
vartriangleright: "22B3",
rhd: "22B3",
trianglelefteq: "22B4",
unlhd: "22B4",
trianglerighteq: "22B5",
unrhd: "22B5",
vDash: "22A8",
Vdash: "22A9",
Vvdash: "22AA",
smallsmile: "2323",
shortmid: [ "2223", {
variantForm: !0
} ],
smallfrown: "2322",
shortparallel: [ "2225", {
variantForm: !0
} ],
bumpeq: "224F",
between: "226C",
Bumpeq: "224E",
pitchfork: "22D4",
varpropto: "221D",
backepsilon: "220D",
blacktriangleleft: "25C0",
blacktriangleright: "25B6",
therefore: "2234",
because: "2235",
eqsim: "2242",
vartriangle: [ "25B3", {
variantForm: !0
} ],
Join: "22C8",
nless: "226E",
ngtr: "226F",
nleq: "2270",
ngeq: "2271",
nleqslant: [ "2A87", {
variantForm: !0
} ],
ngeqslant: [ "2A88", {
variantForm: !0
} ],
nleqq: [ "2270", {
variantForm: !0
} ],
ngeqq: [ "2271", {
variantForm: !0
} ],
lneq: "2A87",
gneq: "2A88",
lneqq: "2268",
gneqq: "2269",
lvertneqq: [ "2268", {
variantForm: !0
} ],
gvertneqq: [ "2269", {
variantForm: !0
} ],
lnsim: "22E6",
gnsim: "22E7",
lnapprox: "2A89",
gnapprox: "2A8A",
nprec: "2280",
nsucc: "2281",
npreceq: [ "22E0", {
variantForm: !0
} ],
nsucceq: [ "22E1", {
variantForm: !0
} ],
precneqq: "2AB5",
succneqq: "2AB6",
precnsim: "22E8",
succnsim: "22E9",
precnapprox: "2AB9",
succnapprox: "2ABA",
nsim: "2241",
ncong: "2246",
nshortmid: [ "2224", {
variantForm: !0
} ],
nshortparallel: [ "2226", {
variantForm: !0
} ],
nmid: "2224",
nparallel: "2226",
nvdash: "22AC",
nvDash: "22AD",
nVdash: "22AE",
nVDash: "22AF",
ntriangleleft: "22EA",
ntriangleright: "22EB",
ntrianglelefteq: "22EC",
ntrianglerighteq: "22ED",
nsubseteq: "2288",
nsupseteq: "2289",
nsubseteqq: [ "2288", {
variantForm: !0
} ],
nsupseteqq: [ "2289", {
variantForm: !0
} ],
subsetneq: "228A",
supsetneq: "228B",
varsubsetneq: [ "228A", {
variantForm: !0
} ],
varsupsetneq: [ "228B", {
variantForm: !0
} ],
subsetneqq: "2ACB",
supsetneqq: "2ACC",
varsubsetneqq: [ "2ACB", {
variantForm: !0
} ],
varsupsetneqq: [ "2ACC", {
variantForm: !0
} ],
leftleftarrows: "21C7",
rightrightarrows: "21C9",
leftrightarrows: "21C6",
rightleftarrows: "21C4",
Lleftarrow: "21DA",
Rrightarrow: "21DB",
twoheadleftarrow: "219E",
twoheadrightarrow: "21A0",
leftarrowtail: "21A2",
rightarrowtail: "21A3",
looparrowleft: "21AB",
looparrowright: "21AC",
leftrightharpoons: "21CB",
rightleftharpoons: [ "21CC", {
variantForm: !0
} ],
curvearrowleft: "21B6",
curvearrowright: "21B7",
circlearrowleft: "21BA",
circlearrowright: "21BB",
Lsh: "21B0",
Rsh: "21B1",
upuparrows: "21C8",
downdownarrows: "21CA",
upharpoonleft: "21BF",
upharpoonright: "21BE",
downharpoonleft: "21C3",
restriction: "21BE",
multimap: "22B8",
downharpoonright: "21C2",
leftrightsquigarrow: "21AD",
rightsquigarrow: "21DD",
leadsto: "21DD",
dashrightarrow: "21E2",
dashleftarrow: "21E0",
nleftarrow: "219A",
nrightarrow: "219B",
nLeftarrow: "21CD",
nRightarrow: "21CF",
nleftrightarrow: "21AE",
nLeftrightarrow: "21CE"
},
delimiter: {
"\\ulcorner": "250C",
"\\urcorner": "2510",
"\\llcorner": "2514",
"\\lrcorner": "2518"
},
macros: {
implies: [ "Macro", "\\;\\Longrightarrow\\;" ],
impliedby: [ "Macro", "\\;\\Longleftarrow\\;" ]
}
});
var n = t.mo.OPTYPES.REL;
MathJax.Hub.Insert(t.mo.prototype, {
OPTABLE: {
infix: {
"\u2322": n,
"\u2323": n,
"\u25b3": n,
"\ue006": n,
"\ue007": n,
"\ue00c": n,
"\ue00d": n,
"\ue00e": n,
"\ue00f": n,
"\ue010": n,
"\ue011": n,
"\ue016": n,
"\ue017": n,
"\ue018": n,
"\ue019": n,
"\ue01a": n,
"\ue01b": n,
"\ue04b": n,
"\ue04f": n
}
}
});
}), MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready", function() {
var e = MathJax.OutputJax["HTML-CSS"], t = e.FONTDATA.VARIANT;
e.fontInUse === "TeX" && (t["-TeX-variant"] = {
fonts: [ "MathJax_AMS", "MathJax_Main", "MathJax_Size1" ],
remap: {
8808: 57356,
8809: 57357,
8816: 57361,
8817: 57358,
10887: 57360,
10888: 57359,
8740: 57350,
8742: 57351,
8840: 57366,
8841: 57368,
8842: 57370,
8843: 57371,
10955: 57367,
10956: 57369,
988: 57352,
1008: 57353
}
}, e.msieIE6 && MathJax.Hub.Insert(t["-TeX-variant"].remap, {
8592: [ 58049, "-WinIE6" ],
8594: [ 58048, "-WinIE6" ],
8739: [ 58050, "-WinIE6" ],
8741: [ 58051, "-WinIE6" ],
8764: [ 58052, "-WinIE6" ],
9651: [ 58067, "-WinIE6" ]
})), e.fontInUse === "STIX" && MathJax.Hub.Register.StartupHook("TeX Jax Ready", function() {
var e = MathJax.InputJax.TeX.Definitions;
e.mathchar0mi.varnothing = "2205", e.mathchar0mi.hslash = "210F", e.mathchar0mi.blacktriangle = "25B4", e.mathchar0mi.blacktriangledown = "25BE", e.mathchar0mi.square = "25FB", e.mathchar0mi.blacksquare = "25FC", e.mathchar0mi.vartriangle = [ "25B3", {
mathsize: "71%"
} ], e.mathchar0mi.triangledown = [ "25BD", {
mathsize: "71%"
} ], e.mathchar0mo.blacktriangleleft = "25C2", e.mathchar0mo.blacktriangleright = "25B8", e.mathchar0mo.smallsetminus = "2216", MathJax.Hub.Insert(t["-STIX-variant"], {
remap: {
10887: 57360,
10888: 57359,
8816: 57361,
8817: 57358,
8928: 57419,
8929: 57423,
8840: 57366,
8841: 57368
}
});
}), MathJax.Hub.Startup.signal.Post("TeX AMSsymbols Ready");
}), MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSsymbols.js"), function() {
var e = "1.1", t = MathJax.Hub.CombineConfig("TeX.noErrors", {
multiLine: !0,
inlineDelimiters: [ "", "" ],
style: {
"font-family": "serif",
"font-size": "80%",
"text-align": "left",
color: "black",
padding: "1px 3px",
border: "1px solid"
}
}), n = "\u00a0";
MathJax.Extension["TeX/noErrors"] = {
version: e,
config: t
}, MathJax.Hub.Register.StartupHook("TeX Jax Ready", function() {
MathJax.InputJax.TeX.Augment({
formatError: function(e, r, i, s) {
var o = t.inlineDelimiters, u = i || t.multiLine;
return i || (r = o[0] + r + o[1]), u ? r = r.replace(/ /g, n) : r = r.replace(/\n/g, " "), MathJax.ElementJax.mml.merror(r).With({
isError: !0,
multiLine: u
});
}
});
}), MathJax.Hub.Register.StartupHook("HTML-CSS Jax Config", function() {
MathJax.Hub.Config({
"HTML-CSS": {
styles: {
".MathJax .merror": MathJax.Hub.Insert({
"font-style": null,
"background-color": null,
"vertical-align": MathJax.Hub.Browser.isMSIE && t.multiLine ? "-2px" : ""
}, t.style)
}
}
});
});
}(), MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready", function() {
var e = MathJax.ElementJax.mml, t = MathJax.OutputJax["HTML-CSS"], n = e.math.prototype.toHTML;
e.math.Augment({
toHTML: function(e, t) {
return this.data[0] && this.data[0].data[0] && this.data[0].data[0].isError ? this.data[0].data[0].toHTML(e) : n.call(this, e, t);
}
}), e.merror.Augment({
toHTML: function(n) {
if (!this.isError) return e.mbase.prototype.toHTML.call(this, n);
n = this.HTMLcreateSpan(n), this.multiLine && (n.style.display = "inline-block");
var r = this.data[0].data[0].data.join("").split(/\n/);
for (var i = 0, s = r.length; i < s; i++) t.addText(n, r[i]), i !== s - 1 && t.addElement(n, "br");
var o = t.getHD(n.parentNode), u = t.getW(n.parentNode);
if (s > 1) {
var f = (o.h + o.d) / 2, l = t.TeX.x_height / 2, c = t.config.styles[".MathJax .merror"]["font-size"];
c && c.match(/%/) && (l *= parseInt(c) / 100), n.parentNode.style.verticalAlign = t.Em(o.d + (l - f)), o.h = l + f, o.d = f - l;
}
return n.bbox = {
h: o.h,
d: o.d,
w: u,
lw: 0,
rw: u
}, n;
}
}), MathJax.Hub.Startup.signal.Post("TeX noErrors Ready");
}), MathJax.Hub.Register.StartupHook("NativeMML Jax Ready", function() {
var e = MathJax.ElementJax.mml, t = MathJax.Extension["TeX/noErrors"].config, n = e.math.prototype.toNativeMML;
e.math.Augment({
toNativeMML: function(e) {
return this.data[0] && this.data[0].data[0] && this.data[0].data[0].isError ? this.data[0].data[0].toNativeMML(e) : n.call(this, e);
}
}), e.merror.Augment({
toNativeMML: function(n) {
if (!this.isError) return e.mbase.prototype.toNativeMML.call(this, n);
n = n.appendChild(document.createElement("span"));
var r = this.data[0].data[0].data.join("").split(/\n/);
for (var i = 0, s = r.length; i < s; i++) n.appendChild(document.createTextNode(r[i])), i !== s - 1 && n.appendChild(document.createElement("br"));
this.multiLine && (n.style.display = "inline-block", s > 1 && (n.style.verticalAlign = "middle"));
for (var o in t.style) if (t.style.hasOwnProperty(o)) {
var u = o.replace(/-./g, function(e) {
return e.charAt(1).toUpperCase();
});
n.style[u] = t.style[o];
}
return n;
}
}), MathJax.Hub.Startup.signal.Post("TeX noErrors Ready");
}), MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noErrors.js"), MathJax.Extension["TeX/noUndefined"] = {
version: "1.1",
config: MathJax.Hub.CombineConfig("TeX.noUndefined", {
attributes: {
mathcolor: "red"
}
})
}, MathJax.Hub.Register.StartupHook("TeX Jax Ready", function() {
var e = MathJax.Extension["TeX/noUndefined"].config, t = MathJax.ElementJax.mml;
MathJax.InputJax.TeX.Parse.Augment({
csUndefined: function(n) {
this.Push(t.mtext(n).With(e.attributes));
}
}), MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready");
}), MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"), MathJax.Hub.Register.StartupHook("TeX Jax Ready", function() {
var e = "1.1", t = MathJax.InputJax.TeX, n = t.Definitions;
MathJax.Hub.Insert(n, {
macros: {
newcommand: "NewCommand",
renewcommand: "NewCommand",
newenvironment: "NewEnvironment",
def: "MacroDef"
}
}), t.Parse.Augment({
NewCommand: function(e) {
var r = this.trimSpaces(this.GetArgument(e)), i = this.trimSpaces(this.GetBrackets(e)), s = this.GetArgument(e);
i === "" && (i = null), r.charAt(0) === "\\" && (r = r.substr(1)), r.match(/^(.|[a-z]+)$/i) || t.Error("Illegal control sequence name for " + e), i != null && !i.match(/^[0-9]+$/) && t.Error("Illegal number of parameters specified in " + e), n.macros[r] = [ "Macro", s, i ];
},
NewEnvironment: function(e) {
var r = this.trimSpaces(this.GetArgument(e)), i = this.trimSpaces(this.GetBrackets(e)), s = this.GetArgument(e), o = this.GetArgument(e);
i === "" && (i = null), i != null && !i.match(/^[0-9]+$/) && t.Error("Illegal number of parameters specified in " + e), n.environment[r] = [ "BeginEnv", "EndEnv", s, o, i ];
},
MacroDef: function(e) {
var t = this.GetCSname(e), r = this.GetTemplate(e, "\\" + t), i = this.GetArgument(e);
r instanceof Array ? n.macros[t] = [ "MacroWithTemplate", i, r[0], r[1] ] : n.macros[t] = [ "Macro", i, r ];
},
GetCSname: function(e) {
var n = this.GetNext();
n !== "\\" && t.Error("\\ must be followed by a control sequence");
var r = this.trimSpaces(this.GetArgument(e));
return r.substr(1);
},
GetTemplate: function(e, n) {
var r, i = [], s = 0;
r = this.GetNext();
var o = this.i;
while (this.i < this.string.length) {
r = this.GetNext();
if (r === "#") o !== this.i && (i[s] = this.string.substr(o, this.i - o)), r = this.string.charAt(++this.i), r.match(/^[1-9]$/) || t.Error("Illegal use of # in template for " + n), parseInt(r) != ++s && t.Error("Parameters for " + n + " must be numbered sequentially"), o = this.i + 1; else if (r === "{") return o !== this.i && (i[s] = this.string.substr(o, this.i - o)), i.length > 0 ? [ s, i ] : s;
this.i++;
}
t.Error("Missing replacement string for definition of " + e);
},
MacroWithTemplate: function(e, n, r, i) {
if (r) {
var s = [];
this.GetNext(), i[0] && !this.MatchParam(i[0]) && t.Error("Use of " + e + " doesn't match its definition");
for (var o = 0; o < r; o++) s.push(this.GetParameter(e, i[o + 1]));
n = this.SubstituteArgs(s, n);
}
this.string = this.AddArgs(n, this.string.slice(this.i)), this.i = 0, ++this.macroCount > t.config.MAXMACROS && t.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?");
},
BeginEnv: function(e, t, n, r) {
if (r) {
var i = [];
for (var s = 0; s < r; s++) i.push(this.GetArgument("\\begin{" + name + "}"));
t = this.SubstituteArgs(i, t), n = this.SubstituteArgs(i, n);
}
return e.edef = n, this.string = this.AddArgs(t, this.string.slice(this.i)), this.i = 0, e;
},
EndEnv: function(e, t) {
return this.string = this.AddArgs(e.edef, this.string.slice(this.i)), this.i = 0, t;
},
GetParameter: function(e, n) {
if (n == null) return this.GetArgument(e);
var r = this.i, i = 0, s = 0;
while (this.i < this.string.length) if (this.string.charAt(this.i) === "{") this.i === r && (s = 1), this.GetArgument(e), i = this.i - r; else {
if (this.MatchParam(n)) return s && (r++, i -= 2), this.string.substr(r, i);
this.i++, i++, s = 0;
}
t.Error("Runaway argument for " + e + "?");
},
MatchParam: function(e) {
return this.string.substr(this.i, e.length) !== e ? 0 : (this.i += e.length, 1);
}
}), t.Environment = function(e) {
n.environment[e] = [ "BeginEnv", "EndEnv" ].concat([].slice.call(arguments, 1));
}, MathJax.Hub.Startup.signal.Post("TeX newcommand Ready");
}), MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/newcommand.js"), MathJax.Hub.Register.StartupHook("TeX Jax Ready", function() {
var e = "1.1", t = MathJax.ElementJax.mml, n = MathJax.InputJax.TeX, r = n.Definitions, i = {};
i[t.VARIANT.NORMAL] = t.VARIANT.BOLD, i[t.VARIANT.ITALIC] = t.VARIANT.BOLDITALIC, i[t.VARIANT.FRAKTUR] = t.VARIANT.BOLDFRAKTUR, i[t.VARIANT.SCRIPT] = t.VARIANT.BOLDSCRIPT, i[t.VARIANT.SANSSERIF] = t.VARIANT.BOLDSANSSERIF, i["-tex-caligraphic"] = "-tex-caligraphic-bold", i["-tex-oldstyle"] = "-tex-oldstyle-bold", r.macros.boldsymbol = "Boldsymbol", n.Parse.Augment({
mmlToken: function(e) {
if (this.stack.env.boldsymbol) {
var n = e.Get("mathvariant");
n == null ? e.mathvariant = t.VARIANT.BOLD : e.mathvariant = i[n] || n;
}
return e;
},
Boldsymbol: function(e) {
var t = this.stack.env.boldsymbol, n = this.stack.env.font;
this.stack.env.boldsymbol = !0, this.stack.env.font = null;
var r = this.ParseArg(e);
this.stack.env.font = n, this.stack.env.boldsymbol = t, this.Push(r);
}
});
}), MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready", function() {
var e = MathJax.OutputJax["HTML-CSS"], t = e.FONTDATA.FONTS, n = e.FONTDATA.VARIANT;
e.fontInUse === "TeX" ? (t["MathJax_Caligraphic-bold"] = "Caligraphic/Bold/Main.js", n["-tex-caligraphic-bold"] = {
fonts: [ "MathJax_Caligraphic-bold", "MathJax_Main-bold", "MathJax_Main", "MathJax_Math", "MathJax_Size1" ],
offsetA: 65,
variantA: "bold-italic"
}, n["-tex-oldstyle-bold"] = {
fonts: [ "MathJax_Caligraphic-bold", "MathJax_Main-bold", "MathJax_Main", "MathJax_Math", "MathJax_Size1" ]
}, e.msieCheckGreek && e.Font.testFont({
family: "MathJax_Greek",
weight: "bold",
style: "italic",
testString: e.msieCheckGreek
}) && (n["bold-italic"].offsetG = 913, n["bold-italic"].variantG = "-Greek-Bold-Italic", n["-Greek-Bold-Italic"] = {
fonts: [ "MathJax_Greek-bold-italic" ]
}, t["MathJax_Greek-bold-italic"] = "Greek/BoldItalic/Main.js"), MathJax.Hub.Browser.isChrome && !MathJax.Hub.Browser.versionAtLeast("5.0") && (n["-tex-caligraphic-bold"].remap = {
84: [ 58096, "-WinChrome" ]
})) : e.fontInUse === "STIX" && (n["-tex-caligraphic-bold"] = {
fonts: [ "STIXGeneral-bold-italic", "STIXNonUnicode-bold-italic", "STIXNonUnicode", "STIXGeneral", "STIXSizeOneSym" ],
offsetA: 57927,
noLowerCase: 1
}, n["-tex-oldstyle-bold"] = {
fonts: [ "STIXGeneral-bold", "STIXNonUnicode-bold", "STIXGeneral", "STIXSizeOneSym" ],
offsetN: 57955,
remap: {
57956: 57959,
57957: 57963,
57958: 57967,
57959: 57971,
57960: 57975,
57961: 57979,
57962: 57983,
57963: 57987,
57964: 57991
}
}), MathJax.Hub.Startup.signal.Post("TeX boldsymbol Ready");
}), MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/boldsymbol.js"), MathJax.Extension.tex2jax = {
version: "1.1.3",
config: {
inlineMath: [ [ "\\(", "\\)" ] ],
displayMath: [ [ "$$", "$$" ], [ "\\[", "\\]" ] ],
skipTags: [ "script", "noscript", "style", "textarea", "pre", "code" ],
ignoreClass: "tex2jax_ignore",
processClass: "tex2jax_process",
processEscapes: !1,
processEnvironments: !0,
preview: "TeX"
},
PreProcess: function(e) {
this.configured || (this.config = MathJax.Hub.CombineConfig("tex2jax", this.config), this.config.Augment && MathJax.Hub.Insert(this, this.config.Augment), typeof this.config.previewTeX != "undefined" && !this.config.previewTeX && (this.config.preview = "none"), this.configured = !0), typeof e == "string" && (e = document.getElementById(e)), e || (e = document.body), this.createPatterns(), this.scanElement(e, e.nextSibling);
},
createPatterns: function() {
var e = [], t, n, r = this.config;
this.match = {};
for (t = 0, n = r.inlineMath.length; t < n; t++) e.push(this.patternQuote(r.inlineMath[t][0])), this.match[r.inlineMath[t][0]] = {
mode: "",
end: r.inlineMath[t][1],
pattern: this.endPattern(r.inlineMath[t][1])
};
for (t = 0, n = r.displayMath.length; t < n; t++) e.push(this.patternQuote(r.displayMath[t][0])), this.match[r.displayMath[t][0]] = {
mode: "; mode=display",
end: r.displayMath[t][1],
pattern: this.endPattern(r.displayMath[t][1])
};
this.start = new RegExp(e.sort(this.sortLength).join("|") + (r.processEnvironments ? "|\\\\begin\\{([^}]*)\\}" : "") + (r.processEscapes ? "|\\\\*\\\\\\$" : ""), "g"), this.skipTags = new RegExp("^(" + r.skipTags.join("|") + ")$", "i"), this.ignoreClass = new RegExp("(^| )(" + r.ignoreClass + ")( |$)"), this.processClass = new RegExp("(^| )(" + r.processClass + ")( |$)");
},
patternQuote: function(e) {
return e.replace(/([\^$(){}+*?\-|\[\]\:\\])/g, "\\$1");
},
endPattern: function(e) {
return new RegExp(this.patternQuote(e) + "|\\\\.", "g");
},
sortLength: function(e, t) {
return e.length !== t.length ? t.length - e.length : e == t ? 0 : e < t ? -1 : 1;
},
scanElement: function(e, t, n) {
var r, i, s;
while (e && e != t) e.nodeName.toLowerCase() === "#text" ? n || (e = this.scanText(e)) : (r = typeof e.className == "undefined" ? "" : e.className, i = typeof e.tagName == "undefined" ? "" : e.tagName, typeof r != "string" && (r = String(r)), e.firstChild && !r.match(/(^| )MathJax/) && !this.skipTags.exec(i) && (s = (n || this.ignoreClass.exec(r)) && !this.processClass.exec(r), this.scanElement(e.firstChild, t, s))), e && (e = e.nextSibling);
},
scanText: function(e) {
if (e.nodeValue.replace(/\s+/, "") == "") return e;
var t, n;
this.search = {
start: !0
}, this.pattern = this.start;
while (e) {
this.pattern.lastIndex = 0;
while (e && e.nodeName.toLowerCase() === "#text" && (t = this.pattern.exec(e.nodeValue))) this.search.start ? e = this.startMatch(t, e) : e = this.endMatch(t, e);
this.search.matched && (e = this.encloseMath(e));
if (e) {
do n = e, e = e.nextSibling; while (e && (e.nodeName.toLowerCase() === "br" || e.nodeName.toLowerCase() === "#comment"));
if (!e || e.nodeName !== "#text") return n;
}
}
return e;
},
startMatch: function(e, t) {
var n = this.match[e[0]];
if (n != null) this.search = {
end: n.end,
mode: n.mode,
open: t,
olen: e[0].length,
opos: this.pattern.lastIndex - e[0].length
}, this.switchPattern(n.pattern); else if (e[0].substr(0, 6) === "\\begin") this.search = {
end: "\\end{" + e[1] + "}",
mode: "; mode=display",
open: t,
olen: 0,
opos: this.pattern.lastIndex - e[0].length,
isBeginEnd: !0
}, this.switchPattern(this.endPattern(this.search.end)); else {
var r = e[0].substr(0, e[0].length - 1), i, s;
r.length % 2 === 0 ? (s = [ r.replace(/\\\\/g, "\\") ], i = 1) : (s = [ r.substr(1).replace(/\\\\/g, "\\"), "$" ], i = 0), s = MathJax.HTML.Element("span", null, s);
var o = MathJax.HTML.TextNode(t.nodeValue.substr(0, e.index));
t.nodeValue = t.nodeValue.substr(e.index + e[0].length - i), t.parentNode.insertBefore(s, t), t.parentNode.insertBefore(o, s), this.pattern.lastIndex = i;
}
return t;
},
endMatch: function(e, t) {
return e[0] == this.search.end && (this.search.close = t, this.search.cpos = this.pattern.lastIndex, this.search.clen = this.search.isBeginEnd ? 0 : e[0].length, this.search.matched = !0, t = this.encloseMath(t), this.switchPattern(this.start)), t;
},
switchPattern: function(e) {
e.lastIndex = this.pattern.lastIndex, this.pattern = e, this.search.start = e === this.start;
},
encloseMath: function(e) {
var t = this.search, n = t.close, r, i;
t.cpos === n.length ? n = n.nextSibling : n = n.splitText(t.cpos), n || (r = n = MathJax.HTML.addText(t.close.parentNode, "")), t.close = n, i = t.opos ? t.open.splitText(t.opos) : t.open;
while (i.nextSibling && i.nextSibling !== n) i.nextSibling.nodeValue !== null ? i.nextSibling.nodeName === "#comment" ? i.nodeValue += i.nextSibling.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/, "$1") : i.nodeValue += i.nextSibling.nodeValue : this.msieNewlineBug ? i.nodeValue += i.nextSibling.nodeName.toLowerCase() === "br" ? "\n" : " " : i.nodeValue += " ", i.parentNode.removeChild(i.nextSibling);
var s = i.nodeValue.substr(t.olen, i.nodeValue.length - t.olen - t.clen);
return i.parentNode.removeChild(i), this.config.preview !== "none" && this.createPreview(t.mode, s), i = this.createMathTag(t.mode, s), this.search = {}, this.pattern.lastIndex = 0, r && r.parentNode.removeChild(r), i;
},
insertNode: function(e) {
var t = this.search;
t.close.parentNode.insertBefore(e, t.close);
},
createPreview: function(e, t) {
var n;
this.config.preview === "TeX" ? n = [ this.filterTeX(t) ] : this.config.preview instanceof Array && (n = this.config.preview), n && (n = MathJax.HTML.Element("span", {
className: MathJax.Hub.config.preRemoveClass
}, n), this.insertNode(n));
},
createMathTag: function(e, t) {
var n = document.createElement("script");
return n.type = "math/tex" + e, MathJax.HTML.setScript(n, t), this.insertNode(n), n;
},
filterTeX: function(e) {
return e;
},
msieNewlineBug: MathJax.Hub.Browser.isMSIE && document.documentMode < 9
}, MathJax.Hub.Register.PreProcessor([ "PreProcess", MathJax.Extension.tex2jax ]), MathJax.Ajax.loadComplete("[MathJax]/extensions/tex2jax.js"), MathJax.ElementJax.mml = MathJax.ElementJax({
mimeType: "jax/mml"
}, {
id: "mml",
version: "1.1.1",
directory: MathJax.ElementJax.directory + "/mml",
extensionDir: MathJax.ElementJax.extensionDir + "/mml",
optableDir: MathJax.ElementJax.directory + "/mml/optable"
}), MathJax.ElementJax.mml.Augment({
Init: function() {
arguments.length === 1 && arguments[0].type === "math" ? this.root = arguments[0] : this.root = MathJax.ElementJax.mml.math.apply(this, arguments), this.root.mode && (!this.root.display && this.root.mode === "display" && (this.root.display = "block"), delete this.root.mode);
}
}, {
INHERIT: "_inherit_",
AUTO: "_auto_",
SIZE: {
INFINITY: "infinity",
SMALL: "small",
NORMAL: "normal",
BIG: "big"
},
COLOR: {
TRANSPARENT: "transparent"
},
VARIANT: {
NORMAL: "normal",
BOLD: "bold",
ITALIC: "italic",
BOLDITALIC: "bold-italic",
DOUBLESTRUCK: "double-struck",
FRAKTUR: "fraktur",
BOLDFRAKTUR: "bold-fraktur",
SCRIPT: "script",
BOLDSCRIPT: "bold-script",
SANSSERIF: "sans-serif",
BOLDSANSSERIF: "bold-sans-serif",
SANSSERIFITALIC: "sans-serif-italic",
SANSSERIFBOLDITALIC: "sans-serif-bold-italic",
MONOSPACE: "monospace",
INITIAL: "inital",
TAILED: "tailed",
LOOPED: "looped",
STRETCHED: "stretched",
CALIGRAPHIC: "-tex-caligraphic",
OLDSTYLE: "-tex-oldstyle"
},
FORM: {
PREFIX: "prefix",
INFIX: "infix",
POSTFIX: "postfix"
},
LINEBREAK: {
AUTO: "auto",
NEWLINE: "newline",
NOBREAK: "nobreak",
GOODBREAK: "goodbreak",
BADBREAK: "badbreak"
},
LINEBREAKSTYLE: {
BEFORE: "before",
AFTER: "after",
DUPLICATE: "duplicate",
INFIXLINBREAKSTYLE: "infixlinebreakstyle"
},
INDENTALIGN: {
LEFT: "left",
CENTER: "center",
RIGHT: "right",
AUTO: "auto",
ID: "id",
INDENTALIGN: "indentalign"
},
INDENTSHIFT: {
INDENTSHIFT: "indentshift"
},
LINETHICKNESS: {
THIN: "thin",
MEDIUM: "medium",
THICK: "thick"
},
NOTATION: {
LONGDIV: "longdiv",
ACTUARIAL: "actuarial",
RADICAL: "radical",
BOX: "box",
ROUNDEDBOX: "roundedbox",
CIRCLE: "circle",
LEFT: "left",
RIGHT: "right",
TOP: "top",
BOTTOM: "bottom",
UPDIAGONALSTRIKE: "updiagonalstrike",
DOWNDIAGONALSTRIKE: "downdiagonalstrike",
VERTICALSTRIKE: "verticalstrike",
HORIZONTALSTRIKE: "horizontalstrike",
MADRUWB: "madruwb"
},
ALIGN: {
TOP: "top",
BOTTOM: "bottom",
CENTER: "center",
BASELINE: "baseline",
AXIS: "axis",
LEFT: "left",
RIGHT: "right"
},
LINES: {
NONE: "none",
SOLID: "solid",
DASHED: "dashed"
},
SIDE: {
LEFT: "left",
RIGHT: "right",
LEFTOVERLAP: "leftoverlap",
RIGHTOVERLAP: "rightoverlap"
},
WIDTH: {
AUTO: "auto",
FIT: "fit"
},
ACTIONTYPE: {
TOGGLE: "toggle",
STATUSLINE: "statusline",
TOOLTIP: "tooltip",
INPUT: "input"
},
LENGTH: {
VERYVERYTHINMATHSPACE: "veryverythinmathspace",
VERYTHINMATHSPACE: "verythinmathspace",
THINMATHSPACE: "thinmathspace",
MEDIUMMATHSPACE: "mediummathspace",
THICKMATHSPACE: "thickmathspace",
VERYTHICKMATHSPACE: "verythickmathspace",
VERYVERYTHICKMATHSPACE: "veryverythickmathspace",
NEGATIVEVERYVERYTHINMATHSPACE: "negativeveryverythinmathspace",
NEGATIVEVERYTHINMATHSPACE: "negativeverythinmathspace",
NEGATIVETHINMATHSPACE: "negativethinmathspace",
NEGATIVEMEDIUMMATHSPACE: "negativemediummathspace",
NEGATIVETHICKMATHSPACE: "negativethickmathspace",
NEGATIVEVERYTHICKMATHSPACE: "negativeverythickmathspace",
NEGATIVEVERYVERYTHICKMATHSP…