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0,r(6469)),l=r(505),c=r(5884);e.DirectionVH=((r={})[1]="v",r[2]="h",r),e.CommonMoMixin=function(t){return o(e,n=t),e.prototype.computeBBox=function(t,e){void 0===e&&(e=!1),this.protoBBox(t),this.node.attributes.get("symmetric")&&2!==this.stretch.dir&&(e=this.getCenterOffset(t),t.h+=e,t.d-=e),this.node.getProperty("mathaccent")&&(0===this.stretch.dir||0<=this.size)&&(t.w=0)},e.prototype.protoBBox=function(t){var e=0!==this.stretch.dir;e&&null===this.size&&this.getStretchedVariant([0]),e&&this.size<0||(n.prototype.computeBBox.call(this,t),this.copySkewIC(t))},e.prototype.getAccentOffset=function(){var t=a.BBox.empty();return this.protoBBox(t),-t.w/2},e.prototype.getCenterOffset=function(t){return(t=void 0===t?null:t)||(t=a.BBox.empty(),n.prototype.computeBBox.call(this,t)),(t.h+t.d)/2+this.font.params.axis_height-t.h},e.prototype.getVariant=function(){this.node.attributes.get("largeop")?this.variant=this.node.attributes.get("displaystyle")?"-largeop":"-smallop":this.node.attributes.getExplicit("mathvariant")||!1!==this.node.getProperty("pseudoscript")?n.prototype.getVariant.call(this):this.variant="-tex-variant"},e.prototype.canStretch=function(t){if(0!==this.stretch.dir)return this.stretch.dir===t;if(!this.node.attributes.get("stretchy"))return!1;var e=this.getText();if(1!==Array.from(e).length)return!1;e=this.font.getDelimiter(e.codePointAt(0));return this.stretch=e&&e.dir===t?e:c.NOSTRETCH,0!==this.stretch.dir},e.prototype.getStretchedVariant=function(t,e){var r,n;if(void 0===e&&(e=!1),0!==this.stretch.dir){var o=this.getWH(t),i=this.getSize("minsize",0),a=this.getSize("maxsize",1/0),s=this.node.getProperty("mathaccent"),o=Math.max(i,Math.min(a,o)),a=this.font.params.delimiterfactor/1e3,l=this.font.params.delimitershortfall,c=i||e?o:s?Math.min(o/a,o+l):Math.max(o*a,o-l),u=this.stretch,p=u.c||this.getText().codePointAt(0),h=0;if(u.sizes)try{for(var d=y(u.sizes),f=d.next();!f.done;f=d.next()){if(f.value>=c)return s&&h&&h--,this.variant=this.font.getSizeVariant(p,h),this.size=h,void(u.schar&&u.schar[h]&&(this.stretch=m(m({},this.stretch),{c:u.schar[h]})));h++}}catch(t){r={error:t}}finally{try{f&&!f.done&&(n=d.return)&&n.call(d)}finally{if(r)throw r.error}}u.stretch?(this.size=-1,this.invalidateBBox(),this.getStretchBBox(t,this.checkExtendedHeight(o,u),u)):(this.variant=this.font.getSizeVariant(p,h-1),this.size=h-1)}},e.prototype.getSize=function(t,e){var r=this.node.attributes;return e=r.isSet(t)?this.length2em(r.get(t),1,1):e},e.prototype.getWH=function(t){if(0===t.length)return 0;if(1===t.length)return t[0];var t=s(t,2),e=t[0],t=t[1],r=this.font.params.axis_height;return this.node.attributes.get("symmetric")?2*Math.max(e-r,t+r):e+t},e.prototype.getStretchBBox=function(t,e,r){r.hasOwnProperty("min")&&r.min>e&&(e=r.min);var n=s(r.HDW,3),o=n[0],i=n[1],n=n[2];1===this.stretch.dir?(o=(t=s(this.getBaseline(t,e,r),2))[0],i=t[1]):n=e,this.bbox.h=o,this.bbox.d=i,this.bbox.w=n},e.prototype.getBaseline=function(t,e,r){var n=2===t.length&&t[0]+t[1]===e,o=this.node.attributes.get("symmetric"),t=s(n?t:[e,0],2),e=t[0],t=t[1],i=s([e+t,0],2),a=i[0],i=i[1];return i=o?(o=this.font.params.axis_height,(a=n?2*Math.max(e-o,t+o):a)/2-o):n?t:(o=(e=s(r.HDW||[.75,.25],2))[0],(n=e[1])*(a/(o+n))),[a-i,i]},e.prototype.checkExtendedHeight=function(t,e){var r;return e.fullExt&&(r=(e=s(e.fullExt,2))[0],t=(e=e[1])+Math.ceil(Math.max(0,t-e)/r)*r),t},e.prototype.remapChars=function(t){var e=this.node.getProperty("primes");return e?(0,l.unicodeChars)(e):(1===t.length&&(e=this.node.coreParent().parent,e=this.isAccent&&!e.isKind("mrow")?"accent":"mo",(e=this.font.getRemappedChar(e,t[0]))&&(t=this.unicodeChars(e,this.variant))),t)},e;function e(){for(var t=[],e=0;e=t.length?void 0:t)&&t[n++],done:!t}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")},u=(Object.defineProperty(e,"__esModule",{value:!0}),e.CommonInferredMrowMixin=e.CommonMrowMixin=void 0,r(6469));e.CommonMrowMixin=function(t){return o(e,s=t),Object.defineProperty(e.prototype,"fixesPWidth",{get:function(){return!1},enumerable:!1,configurable:!0}),e.prototype.stretchChildren=function(){var t,e,r,n,o,i,a=[];try{for(var s=x(this.childNodes),l=s.next();!l.done;l=s.next())(S=l.value).canStretch(1)&&a.push(S)}catch(e){t={error:e}}finally{try{l&&!l.done&&(e=s.return)&&e.call(s)}finally{if(t)throw t.error}}var c=a.length,u=this.childNodes.length;if(c&&1p&&(p=g),(b*=v)>h&&(h=b))}}catch(t){r={error:t}}finally{try{m&&!m.done&&(n=f.return)&&n.call(f)}finally{if(r)throw r.error}}try{for(var S,O=x(a),M=O.next();!M.done;M=O.next())(S=M.value).coreMO().getStretchedVariant([p,h])}catch(t){o={error:t}}finally{try{M&&!M.done&&(i=O.return)&&i.call(O)}finally{if(o)throw o.error}}}},e;function e(){for(var e,t,r=[],n=0;nthis.surdH?(t.h+t.d-(this.surdH-2*e-r/2))/2:e+r/4]},e.prototype.getRootDimens=function(t,e){return[0,0,0,0]},e;function e(){for(var t=[],e=0;e=t.length?void 0:t)&&t[n++],done:!t}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")},s=(Object.defineProperty(e,"__esModule",{value:!0}),e.CommonMtableMixin=void 0,r(6469)),l=r(505),u=r(7875);e.CommonMtableMixin=function(t){return i(e,o=t),Object.defineProperty(e.prototype,"tableRows",{get:function(){return this.childNodes},enumerable:!1,configurable:!0}),e.prototype.findContainer=function(){for(var t=this,e=t.parent;e&&(e.node.notParent||e.node.isKind("mrow"));)e=(t=e).parent;this.container=e,this.containerI=t.node.childPosition()},e.prototype.getPercentageWidth=function(){var t;this.hasLabels?this.bbox.pwidth=s.BBox.fullWidth:(t=this.node.attributes.get("width"),(0,l.isPercent)(t)&&(this.bbox.pwidth=t))},e.prototype.stretchRows=function(){for(var t=this.node.attributes.get("equalrows"),e=t?this.getEqualRowHeight():0,r=t?this.getTableData():{H:[0],D:[0]},n=r.H,o=r.D,i=this.tableRows,a=0;ao[r]&&(o[r]=c),u>i[r]&&(i[r]=u),sa[e]&&(a[e]=l),s},e.prototype.extendHD=function(t,e,r,n){n=(n-(e[t]+r[t]))/2;n<1e-5||(e[t]+=n,r[t]+=n)},e.prototype.recordPWidthCell=function(t,e){t.childNodes[0]&&t.childNodes[0].getBBox().pwidth&&this.pwidthCells.push([t,e])},e.prototype.computeBBox=function(t,e){void 0===e&&(e=!1);var e=this.getTableData(),r=e.H,e=e.D,r=(n=this.node.attributes.get("equalrows")?(n=this.getEqualRowHeight(),(0,u.sum)([].concat(this.rLines,this.rSpace))+n*this.numRows):(0,u.sum)(r.concat(e,this.rLines,this.rSpace)),n+=2*(this.fLine+this.fSpace[1]),this.getComputedWidths()),e=(0,u.sum)(r.concat(this.cLines,this.cSpace))+2*(this.fLine+this.fSpace[0]),r=this.node.attributes.get("width"),n=("auto"!==r&&(e=Math.max(this.length2em(r,0)+2*this.fLine,e)),p(this.getBBoxHD(n),2)),o=n[0],n=n[1],o=(t.h=o,t.d=n,t.w=e,p(this.getBBoxLR(),2)),n=o[0],e=o[1];t.L=n,t.R=e,(0,l.isPercent)(r)||this.setColumnPWidths()},e.prototype.setChildPWidths=function(t,e,r){var n=this.node.attributes.get("width");if(!(0,l.isPercent)(n))return!1;this.hasLabels||(this.bbox.pwidth="",this.container.bbox.pwidth="");var o=this.bbox,i=o.w,a=o.L,o=o.R,s=this.node.attributes.get("data-width-includes-label"),n=Math.max(i,this.length2em(n,Math.max(e,a+i+o)))-(s?a+o:0),e=this.node.attributes.get("equalcolumns")?Array(this.numCols).fill(this.percent(1/Math.max(1,this.numCols))):this.getColumnAttributes("columnwidth",0),s=(this.cWidths=this.getColumnWidthsFixed(e,n),this.getComputedWidths());return this.pWidth=(0,u.sum)(s.concat(this.cLines,this.cSpace))+2*(this.fLine+this.fSpace[0]),this.isTop&&(this.bbox.w=this.pWidth),this.setColumnPWidths(),this.pWidth!==i&&this.parent.invalidateBBox(),this.pWidth!==i},e.prototype.setColumnPWidths=function(){var t,e,r=this.cWidths;try{for(var n=_(this.pwidthCells),o=n.next();!o.done;o=n.next()){var i=p(o.value,2),a=i[0],s=i[1];a.setChildPWidths(!1,r[s])&&(a.invalidateBBox(),a.getBBox())}}catch(e){t={error:e}}finally{try{o&&!o.done&&(e=n.return)&&e.call(n)}finally{if(t)throw t.error}}},e.prototype.getBBoxHD=function(t){var e,r=p(this.getAlignmentRow(),2),n=r[0],r=r[1];if(null===r)return{top:[0,t],center:[e=t/2,e],bottom:[t,0],baseline:[e,e],axis:[e+(o=this.font.params.axis_height),e-o]}[n]||[e,e];var o=this.getVerticalPosition(r,n);return[o,t-o]},e.prototype.getBBoxLR=function(){var t,e,r,n;return this.hasLabels?(t=(n=this.node.attributes).get("side"),e=(r=p(this.getPadAlignShift(t),2))[0],r=r[1],(n=this.hasLabels&&!!n.get("data-width-includes-label"))&&this.frame&&this.fSpace[0]&&(e-=this.fSpace[0]),"center"!==r||n?"left"===t?[e,0]:[0,e]:[e,e]):[0,0]},e.prototype.getPadAlignShift=function(t){var e=this.getTableData().L+this.length2em(this.node.attributes.get("minlabelspacing")),r=p(null==this.styles?["",""]:[this.styles.get("padding-left"),this.styles.get("padding-right")],2),n=r[0],r=r[1],n=((n||r)&&(e=Math.max(e,this.length2em(n||"0"),this.length2em(r||"0"))),p(this.getAlignShift(),2)),r=n[0],n=n[1];return[e,r,n=r===t?"left"===t?Math.max(e,n)-e:Math.min(-e,n)+e:n]},e.prototype.getAlignShift=function(){return this.isTop?o.prototype.getAlignShift.call(this):[this.container.getChildAlign(this.containerI),0]},e.prototype.getWidth=function(){return this.pWidth||this.getBBox().w},e.prototype.getEqualRowHeight=function(){var t=this.getTableData(),e=t.H,r=t.D,t=Array.from(e.keys()).map(function(t){return e[t]+r[t]});return Math.max.apply(Math,t)},e.prototype.getComputedWidths=function(){var e=this,r=this.getTableData().W,t=Array.from(r.keys()).map(function(t){return("number"==typeof e.cWidths[t]?e.cWidths:r)[t]});return t=this.node.attributes.get("equalcolumns")?Array(t.length).fill((0,u.max)(t)):t},e.prototype.getColumnWidths=function(){var t=this.node.attributes.get("width");if(this.node.attributes.get("equalcolumns"))return this.getEqualColumns(t);var e=this.getColumnAttributes("columnwidth",0);return"auto"===t?this.getColumnWidthsAuto(e):(0,l.isPercent)(t)?this.getColumnWidthsPercent(e):this.getColumnWidthsFixed(e,this.length2em(t))},e.prototype.getEqualColumns=function(t){var e,r=Math.max(1,this.numCols);return t="auto"===t?(e=this.getTableData().W,(0,u.max)(e)):(0,l.isPercent)(t)?this.percent(1/r):(e=(0,u.sum)([].concat(this.cLines,this.cSpace))+2*this.fSpace[0],Math.max(0,this.length2em(t)-e)/r),Array(this.numCols).fill(t)},e.prototype.getColumnWidthsAuto=function(t){var e=this;return t.map(function(t){return"auto"===t||"fit"===t?null:(0,l.isPercent)(t)?t:e.length2em(t)})},e.prototype.getColumnWidthsPercent=function(r){var n=this,o=0<=r.indexOf("fit"),i=(o?this.getTableData():{W:null}).W;return Array.from(r.keys()).map(function(t){var e=r[t];return"fit"===e?null:"auto"===e?o?i[t]:null:(0,l.isPercent)(e)?e:n.length2em(e)})},e.prototype.getColumnWidthsFixed=function(r,t){var n=this,e=Array.from(r.keys()),o=e.filter(function(t){return"fit"===r[t]}),i=e.filter(function(t){return"auto"===r[t]}),i=o.length||i.length,a=(i?this.getTableData():{W:null}).W,s=t-(0,u.sum)([].concat(this.cLines,this.cSpace))-2*this.fSpace[0],l=s,c=(e.forEach(function(t){var e=r[t];l-="fit"===e||"auto"===e?a[t]:n.length2em(e,s)}),i&&0this.numRows?null:t-1]},e.prototype.getColumnAttributes=function(t,e){var r=this.numCols-(e=void 0===e?1:e),n=this.getAttributeArray(t);if(0===n.length)return null;for(;n.lengthr&&n.splice(r),n},e.prototype.getRowAttributes=function(t,e){var r=this.numRows-(e=void 0===e?1:e),n=this.getAttributeArray(t);if(0===n.length)return null;for(;n.lengthr&&n.splice(r),n},e.prototype.getAttributeArray=function(t){var e=this.node.attributes.get(t);return e?(0,l.split)(e):[this.node.attributes.getDefault(t)]},e.prototype.addEm=function(t,e){var r=this;return void 0===e&&(e=1),t?t.map(function(t){return r.em(t/e)}):null},e.prototype.convertLengths=function(t){var e=this;return t?t.map(function(t){return e.length2em(t)}):null},e;function e(){for(var t=[],e=0;e=t.length?void 0:t)&&t[n++],done:!t}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")};Object.defineProperty(e,"__esModule",{value:!0}),e.CommonMlabeledtrMixin=e.CommonMtrMixin=void 0,e.CommonMtrMixin=function(t){return o(e,r=t),Object.defineProperty(e.prototype,"fixesPWidth",{get:function(){return!1},enumerable:!1,configurable:!0}),Object.defineProperty(e.prototype,"numCells",{get:function(){return this.childNodes.length},enumerable:!1,configurable:!0}),Object.defineProperty(e.prototype,"labeled",{get:function(){return!1},enumerable:!1,configurable:!0}),Object.defineProperty(e.prototype,"tableCells",{get:function(){return this.childNodes},enumerable:!1,configurable:!0}),e.prototype.getChild=function(t){return this.childNodes[t]},e.prototype.getChildBBoxes=function(){return this.childNodes.map(function(t){return t.getBBox()})},e.prototype.stretchChildren=function(t){void 0===t&&(t=null);var e,r,n,o,i=[],a=this.labeled?this.childNodes.slice(1):this.childNodes;try{for(var s=M(a),l=s.next();!l.done;l=s.next())(_=l.value.childNodes[0]).canStretch(1)&&i.push(_)}catch(t){u={error:t}}finally{try{l&&!l.done&&(c=s.return)&&c.call(s)}finally{if(u)throw u.error}}var c=i.length,u=this.childNodes.length;if(c&&1=t.length?void 0:t)&&t[n++],done:!t}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")},a=(Object.defineProperty(e,"__esModule",{value:!0}),e.CommonScriptbaseMixin=void 0,r(9007));e.CommonScriptbaseMixin=function(t){var o;return i(e,o=t),Object.defineProperty(e.prototype,"baseChild",{get:function(){return this.childNodes[this.node.base]},enumerable:!1,configurable:!0}),Object.defineProperty(e.prototype,"scriptChild",{get:function(){return this.childNodes[1]},enumerable:!1,configurable:!0}),e.prototype.getBaseCore=function(){for(var t=this.getSemanticBase()||this.childNodes[0];t&&(1===t.childNodes.length&&(t.node.isKind("mrow")||t.node.isKind("TeXAtom")&&t.node.texClass!==a.TEXCLASS.VCENTER||t.node.isKind("mstyle")||t.node.isKind("mpadded")||t.node.isKind("mphantom")||t.node.isKind("semantics"))||t.node.isKind("munderover")&&t.isMathAccent);)this.setBaseAccentsFor(t),t=t.childNodes[0];return t||(this.baseHasAccentOver=this.baseHasAccentUnder=!1),t||this.childNodes[0]},e.prototype.setBaseAccentsFor=function(t){t.node.isKind("munderover")&&(null===this.baseHasAccentOver&&(this.baseHasAccentOver=!!t.node.attributes.get("accent")),null===this.baseHasAccentUnder&&(this.baseHasAccentUnder=!!t.node.attributes.get("accentunder")))},e.prototype.getSemanticBase=function(){var t=this.node.attributes.getExplicit("data-semantic-fencepointer");return this.getBaseFence(this.baseChild,t)},e.prototype.getBaseFence=function(t,e){var r,n;if(!t||!t.node.attributes||!e)return null;if(t.node.attributes.getExplicit("data-semantic-id")===e)return t;try{for(var o=O(t.childNodes),i=o.next();!i.done;i=o.next()){var a=i.value,s=this.getBaseFence(a,e);if(s)return s}}catch(t){r={error:t}}finally{try{i&&!i.done&&(n=o.return)&&n.call(o)}finally{if(r)throw r.error}}return null},e.prototype.getBaseScale=function(){for(var t=this.baseCore,e=1;t&&t!==this;)e*=t.getOuterBBox().rscale,t=t.parent;return e},e.prototype.getBaseIc=function(){return this.baseCore.getOuterBBox().ic*this.baseScale},e.prototype.getAdjustedIc=function(){var t=this.baseCore.getOuterBBox();return(t.ic?1.05*t.ic+.05:0)*this.baseScale},e.prototype.isCharBase=function(){var t=this.baseCore;return(t.node.isKind("mo")&&null===t.size||t.node.isKind("mi")||t.node.isKind("mn"))&&1===t.bbox.rscale&&1===Array.from(t.getText()).length},e.prototype.checkLineAccents=function(){this.node.isKind("munderover")&&(this.node.isKind("mover")?this.isLineAbove=this.isLineAccent(this.scriptChild):this.node.isKind("munder")?this.isLineBelow=this.isLineAccent(this.scriptChild):(this.isLineAbove=this.isLineAccent(this.overChild),this.isLineBelow=this.isLineAccent(this.underChild)))},e.prototype.isLineAccent=function(t){t=t.coreMO().node;return t.isToken&&"―"===t.getText()},e.prototype.getBaseWidth=function(){var t=this.baseChild.getOuterBBox();return t.w*t.rscale-(this.baseRemoveIc?this.baseIc:0)+this.font.params.extra_ic},e.prototype.computeBBox=function(t,e){void 0===e&&(e=!1);var r=this.getBaseWidth(),n=y(this.getOffset(),2),o=n[0],n=n[1];t.append(this.baseChild.getOuterBBox()),t.combine(this.scriptChild.getOuterBBox(),r+o,n),t.w+=this.font.params.scriptspace,t.clean(),this.setChildPWidths(e)},e.prototype.getOffset=function(){return[0,0]},e.prototype.baseCharZero=function(t){var e=!!this.baseCore.node.attributes.get("largeop"),r=this.baseScale;return this.baseIsChar&&!e&&1===r?0:t},e.prototype.getV=function(){var t=this.baseCore.getOuterBBox(),e=this.scriptChild.getOuterBBox(),r=this.font.params,n=this.length2em(this.node.attributes.get("subscriptshift"),r.sub1);return Math.max(this.baseCharZero(t.d*this.baseScale+r.sub_drop*e.rscale),n,e.h*e.rscale-.8*r.x_height)},e.prototype.getU=function(){var t=this.baseCore.getOuterBBox(),e=this.scriptChild.getOuterBBox(),r=this.font.params,n=this.node.attributes.getList("displaystyle","superscriptshift"),o=this.node.getProperty("texprimestyle")?r.sup3:n.displaystyle?r.sup1:r.sup2,n=this.length2em(n.superscriptshift,o);return Math.max(this.baseCharZero(t.h*this.baseScale-r.sup_drop*e.rscale),n,e.d*e.rscale+.25*r.x_height)},e.prototype.hasMovableLimits=function(){var t=this.node.attributes.get("displaystyle"),e=this.baseChild.coreMO().node;return!t&&!!e.attributes.get("movablelimits")},e.prototype.getOverKU=function(t,e){var r=this.node.attributes.get("accent"),n=this.font.params,e=e.d*e.rscale,o=n.rule_thickness*n.separation_factor,i=this.baseHasAccentOver?o:0,o=this.isLineAbove?3*n.rule_thickness:o,r=(r?o:Math.max(n.big_op_spacing1,n.big_op_spacing3-Math.max(0,e)))-i;return[r,t.h*t.rscale+r+e]},e.prototype.getUnderKV=function(t,e){var r=this.node.attributes.get("accentunder"),n=this.font.params,e=e.h*e.rscale,o=n.rule_thickness*n.separation_factor,i=this.baseHasAccentUnder?o:0,o=this.isLineBelow?3*n.rule_thickness:o,r=(r?o:Math.max(n.big_op_spacing2,n.big_op_spacing4-e))-i;return[r,-(t.d*t.rscale+r+e)]},e.prototype.getDeltaW=function(e,t){void 0===t&&(t=[0,0,0]);var r,n,o,i,a=this.node.attributes.get("align"),s=e.map(function(t){return t.w*t.rscale}),l=(s[0]-=this.baseRemoveIc&&!this.baseCore.node.attributes.get("largeop")?this.baseIc:0,Math.max.apply(Math,g([],y(s),!1))),c=[],u=0;try{for(var p=O(s.keys()),h=p.next();!h.done;h=p.next()){var d=h.value;c[d]=("center"===a?(l-s[d])/2:"right"===a?l-s[d]:0)+t[d],c[d]=t.length?void 0:t)&&t[n++],done:!t}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")},u=this&&this.__read||function(t,e){var r="function"==typeof Symbol&&t[Symbol.iterator];if(!r)return t;var n,o,i=r.call(t),a=[];try{for(;(void 0===e||0=t.length?void 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MathJax is a JavaScript library that allows page"," authors to include mathematics within their web pages."," As a reader, you don't need to do anything to make that happen.

","

Browsers: MathJax works with all modern browsers including"," Edge, Firefox, Chrome, Safari, Opera, and most mobile browsers.

","

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Show Math As: These options allow you to view the formula's"," source markup (as MathML or in its original format).

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Copy to Clipboard: These options copy the formula's source markup,"," as MathML or in its original format, to the clipboard"," (in browsers that support that).

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","

Accessibility: MathJax can work with screen"," readers to make mathematics accessible to the visually impaired."," Turn on the explorer to enable generation of speech strings"," and the ability to investigate expressions interactively.

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Language: This menu lets you select the language used by MathJax"," for its menus and warning messages. (Not yet implemented in version 3.)

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","

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","

Preferences: MathJax uses your browser's localStorage database"," to save the preferences set via this menu locally in your browser. These"," are not used to track you, and are not transferred or used remotely by"," MathJax in any way.

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r.copyOriginal()}),this.submenu("Annotation","Annotation")]),this.rule(),this.submenu("Settings","Math Settings",[this.submenu("Renderer","Math Renderer",this.radioGroup("renderer",[["CHTML"],["SVG"]])),this.rule(),this.submenu("ZoomTrigger","Zoom Trigger",[this.command("ZoomNow","Zoom Once Now",function(){return r.zoom(null,"",r.menu.mathItem)}),this.rule(),this.radioGroup("zoom",[["Click"],["DoubleClick","Double-Click"],["NoZoom","No Zoom"]]),this.rule(),this.label("TriggerRequires","Trigger Requires:"),this.checkbox(v?"Option":"Alt",v?"Option":"Alt","alt"),this.checkbox("Command","Command","cmd",{hidden:!v}),this.checkbox("Control","Control","ctrl",{hiddne:v}),this.checkbox("Shift","Shift","shift")]),this.submenu("ZoomFactor","Zoom Factor",this.radioGroup("zscale",[["150%"],["175%"],["200%"],["250%"],["300%"],["400%"]])),this.rule(),this.command("Scale","Scale All Math...",function(){return r.scaleAllMath()}),this.rule(),this.checkbox("texHints","Add TeX hints to MathML","texHints"),this.checkbox("semantics","Add original as annotation","semantics"),this.rule(),this.command("Reset","Reset to defaults",function(){return r.resetDefaults()})]),this.submenu("Accessibility","Accessibility",[this.checkbox("Activate","Activate","explorer"),this.submenu("Speech","Speech",[this.checkbox("Speech","Speech Output","speech"),this.checkbox("Subtitles","Speech Subtitles","subtitles"),this.checkbox("Braille","Braille Output","braille"),this.checkbox("View Braille","Braille Subtitles","viewBraille"),this.rule(),this.submenu("A11yLanguage","Language"),this.rule(),this.submenu("Mathspeak","Mathspeak Rules",this.radioGroup("speechRules",[["mathspeak-default","Verbose"],["mathspeak-brief","Brief"],["mathspeak-sbrief","Superbrief"]])),this.submenu("Clearspeak","Clearspeak Rules",this.radioGroup("speechRules",[["clearspeak-default","Auto"]])),this.submenu("ChromeVox","ChromeVox 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r.help.post()})]}),this.menu);this.about.attachMenu(t),this.help.attachMenu(t),this.originalText.attachMenu(t),this.annotationText.attachMenu(t),this.mathmlCode.attachMenu(t),this.zoomBox.attachMenu(t),this.checkLoadableItems(),this.enableExplorerItems(this.settings.explorer),t.showAnnotation=this.annotationText,t.copyAnnotation=this.copyAnnotation.bind(this),t.annotationTypes=this.options.annotationTypes,y.CssStyles.addInfoStyles(this.document.document),y.CssStyles.addMenuStyles(this.document.document)},_.prototype.checkLoadableItems=function(){var t,e;if(b&&b._&&b.loader&&b.startup)!this.settings.collapsible||b._.a11y&&b._.a11y.complexity||this.loadA11y("complexity"),!this.settings.explorer||b._.a11y&&b._.a11y.explorer||this.loadA11y("explorer"),!this.settings.assistiveMml||b._.a11y&&b._.a11y["assistive-mml"]||this.loadA11y("assistive-mml");else{var r=this.menu;try{for(var n=u(Object.keys(this.jax)),o=n.next();!o.done;o=n.next()){var 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n=u(Object.keys(this.settings)),o=n.next();!o.done;o=n.next()){var i=o.value;this.settings[i]!==this.defaultSettings[i]&&(r[i]=this.settings[i])}}catch(t){e={error:t}}finally{try{o&&!o.done&&(t=n.return)&&t.call(n)}finally{if(e)throw e.error}}try{Object.keys(r).length?localStorage.setItem(_.MENU_STORAGE,JSON.stringify(r)):localStorage.removeItem(_.MENU_STORAGE)}catch(t){console.log("MathJax localStorage error: "+t.message)}},_.prototype.setA11y=function(t){b._.a11y&&b._.a11y.explorer&&b._.a11y.explorer_ts.setA11yOptions(this.document,t)},_.prototype.getA11y=function(t){if(b._.a11y&&b._.a11y.explorer)return(void 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t.constructors&&(t.useOutput(r,!0),t.output=t.getOutputJax(),n.jax[e]=t.output,n.setOutputJax(e))}))},_.prototype.setOutputJax=function(t){this.jax[t].setAdaptor(this.document.adaptor),this.document.outputJax=this.jax[t],this.rerender()},_.prototype.setTabOrder=function(t){this.menu.store.inTaborder(t)},_.prototype.setAssistiveMml=function(t){!(this.document.options.enableAssistiveMml=t)||b._.a11y&&b._.a11y["assistive-mml"]?this.rerender():this.loadA11y("assistive-mml")},_.prototype.setExplorer=function(t){this.enableExplorerItems(t),!(this.document.options.enableExplorer=t)||b._.a11y&&b._.a11y.explorer?this.rerender(this.settings.collapsible?c.STATE.RERENDER:c.STATE.COMPILED):this.loadA11y("explorer")},_.prototype.setCollapsible=function(t){!(this.document.options.enableComplexity=t)||b._.a11y&&b._.a11y.complexity?this.rerender(c.STATE.COMPILED):this.loadA11y("complexity")},_.prototype.scaleAllMath=function(){var t=(100*parseFloat(this.settings.scale)).toFixed(1).replace(/.0$/,""),t=prompt("Scale all mathematics (compared to surrounding text) by",t+"%");t&&(t.match(/^\s*\d+(\.\d*)?\s*%?\s*$/)?(t=parseFloat(t)/100)?this.menu.pool.lookup("scale").setValue(String(t)):alert("The scale should not be zero"):alert("The scale should be a percentage (e.g., 120%)"))},_.prototype.resetDefaults=function(){_.loading++;var e,t,r=this.menu.pool,n=this.defaultSettings;try{for(var o=u(Object.keys(this.settings)),i=o.next();!i.done;i=o.next()){var a,s=i.value,l=r.lookup(s);l?(l.setValue(n[s]),(a=l.items[0])&&a.executeCallbacks_()):this.settings[s]=n[s]}}catch(t){e={error:t}}finally{try{i&&!i.done&&(t=o.return)&&t.call(o)}finally{if(e)throw e.error}}_.loading--,this.rerender(c.STATE.COMPILED)},_.prototype.checkComponent=function(t){t=_.loadingPromises.get(t);t&&i.mathjax.retryAfter(t)},_.prototype.loadComponent=function(t,e){var r;_.loadingPromises.has(t)||(r=b.loader)&&(_.loading++,r=r.load(t).then(function(){_.loading--,_.loadingPromises.delete(t),e(),0===_.loading&&_._loadingPromise&&(_._loadingPromise=null,_._loadingOK())}).catch(function(t){_._loadingPromise?(_._loadingPromise=null,_._loadingFailed(t)):console.log(t)}),_.loadingPromises.set(t,r))},_.prototype.loadA11y=function(r){var n=this,o=!c.STATE.ENRICHED;this.loadComponent("a11y/"+r,function(){var t=b.startup,e=(i.mathjax.handlers.unregister(t.handler),t.handler=t.getHandler(),i.mathjax.handlers.register(t.handler),n.document);n.document=t.document=t.getDocument(),(n.document.menu=n).document.outputJax.reset(),n.transferMathList(e),n.document.processed=e.processed,_._loadingPromise||(n.document.outputJax.reset(),n.rerender("complexity"===r||o?c.STATE.COMPILED:c.STATE.TYPESET))})},_.prototype.transferMathList=function(t){var e,r,n=this.document.options.MathItem;try{for(var o=u(t.math),i=o.next();!i.done;i=o.next()){var a=i.value,s=new n;Object.assign(s,a),this.document.math.push(s)}}catch(t){e={error:t}}finally{try{i&&!i.done&&(r=o.return)&&r.call(o)}finally{if(e)throw e.error}}},_.prototype.formatSource=function(t){return t.trim().replace(/&/g,"&").replace(//g,">")},_.prototype.toMML=function(t){return this.MmlVisitor.visitTree(t.root,t,{texHints:this.settings.texHints,semantics:this.settings.semantics&&"MathML"!==t.inputJax.name})},_.prototype.zoom=function(t,e,r){t&&!this.isZoomEvent(t,e)||(this.menu.mathItem=r,t&&this.menu.post(t),this.zoomBox.post())},_.prototype.isZoomEvent=function(t,e){return this.settings.zoom===e&&(!this.settings.alt||t.altKey)&&(!this.settings.ctrl||t.ctrlKey)&&(!this.settings.cmd||t.metaKey)&&(!this.settings.shift||t.shiftKey)},_.prototype.rerender=function(t){void 0===t&&(t=c.STATE.TYPESET),this.rerenderStart=Math.min(t,this.rerenderStart),_.loading||(this.rerenderStart<=c.STATE.COMPILED&&this.document.reset({inputJax:[]}),this.document.rerender(this.rerenderStart),this.rerenderStart=c.STATE.LAST)},_.prototype.copyMathML=function(){this.copyToClipboard(this.toMML(this.menu.mathItem))},_.prototype.copyOriginal=function(){this.copyToClipboard(this.menu.mathItem.math.trim())},_.prototype.copyAnnotation=function(){this.copyToClipboard(this.menu.annotation.trim())},_.prototype.copyToClipboard=function(t){var e=document.createElement("textarea");e.value=t,e.setAttribute("readonly",""),e.style.cssText="height: 1px; width: 1px; padding: 1px; position: absolute; left: -10px",document.body.appendChild(e),e.select();try{document.execCommand("copy")}catch(t){alert("Can't copy to clipboard: "+t.message)}document.body.removeChild(e)},_.prototype.addMenu=function(e){var r=this,t=e.typesetRoot;t.addEventListener("contextmenu",function(){return 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t,e=0;t=this.contentNodes[e];e++)n=n.concat(t.querySelectorAll(r));return r(this)&&n.unshift(this),n}xml(o,i){function t(t,e){const r=e.map(function(t){return t.xml(o,i)}),n=o.createElementNS("",t);for(let t,e=0;t=r[e];e++)n.appendChild(t);return n}const e=o.createElementNS("",this.type);return i||this.xmlAttributes(e),e.textContent=this.textContent,0");return n.serializeXml(this.xml(e,t))}allAttributes(){const t=[];return t.push(["role",this.role]),"unknown"!==this.font&&t.push(["font",this.font]),Object.keys(this.annotation).length&&t.push(["annotation",this.xmlAnnotation()]),this.embellished&&t.push(["embellished",this.embellished]),this.fencePointer&&t.push(["fencepointer",this.fencePointer]),t.push(["id",this.id.toString()]),t}xmlAnnotation(){const e=[];for(const r in this.annotation)this.annotation[r].forEach(function(t){e.push(r+":"+t)});return e.join(";")}toJson(){const r={};r.type=this.type;var n=this.allAttributes();for(let t,e=0;t=n[e];e++)r[t[0]]=t[1].toString();return this.textContent&&(r.$t=this.textContent),this.childNodes.length&&(r.children=this.childNodes.map(function(t){return t.toJson()})),this.contentNodes.length&&(r.content=this.contentNodes.map(function(t){return t.toJson()})),r}updateContent(t,e){var e=e?t.replace(/^[ \f\n\r\t\v\u200b]*/,"").replace(/[ \f\n\r\t\v\u200b]*$/,""):t.trim();this.textContent!==(t=t&&!e?t:e)&&(e=(0,o.lookupMeaning)(t),this.textContent=t,this.role=e.role,this.type=e.type,this.font=e.font)}addMathmlNodes(r){for(let t,e=0;t=r[e];e++)-1===this.mathml.indexOf(t)&&this.mathml.push(t)}appendChild(t){this.childNodes.push(t),this.addMathmlNodes(t.mathml),t.parent=this}replaceChild(e,r){var t,n=this.childNodes.indexOf(e);-1!==n&&(e.parent=null,(r.parent=this).childNodes[n]=r,n=e.mathml.filter(function(t){return-1===r.mathml.indexOf(t)}),t=r.mathml.filter(function(t){return-1===e.mathml.indexOf(t)}),this.removeMathmlNodes(n),this.addMathmlNodes(t))}appendContentNode(t){t&&(this.contentNodes.push(t),this.addMathmlNodes(t.mathml),t.parent=this)}removeContentNode(t){t&&-1!==(t=this.contentNodes.indexOf(t))&&this.contentNodes.slice(t,1)}equals(n){if(!n)return!1;if(this.type!==n.type||this.role!==n.role||this.textContent!==n.textContent||this.childNodes.length!==n.childNodes.length||this.contentNodes.length!==n.contentNodes.length)return!1;for(let t,e,r=0;t=this.childNodes[r],e=n.childNodes[r];r++)if(!t.equals(e))return!1;for(let t,e,r=0;t=this.contentNodes[r],e=n.contentNodes[r];r++)if(!t.equals(e))return!1;return!0}displayTree(){console.info(this.displayTree_(0))}addAnnotation(t,e){e&&this.addAnnotation_(t,e)}getAnnotation(t){return this.annotation[t]||[]}hasAnnotation(t,e){const r=this.annotation[t];return!!r&&-1!==r.indexOf(e)}parseAnnotation(t){const r=t.split(";");for(let t=0,e=r.length;ti(t,"infixop")))return!1}return!0},n.isPrefixFunctionBoundary=function(t){return c(t)&&!s(t,"division")||i(t,"appl")||l(t)},n.isBigOpBoundary=function(t){return c(t)||l(t)},n.isIntegralDxBoundary=function(t,e){return!!e&&i(e,"identifier")&&r.lookupSecondary("d",t.textContent)},n.isIntegralDxBoundarySingle=function(t){var e;return!!i(t,"identifier")&&((e=t.textContent[0])&&t.textContent[1]&&r.lookupSecondary("d",e))},n.isGeneralFunctionBoundary=l,n.isEmbellished=function(t){return t.embellished||(r.isEmbellishedType(t.type)?t.type:null)},n.isOperator=c,n.isRelation=u,n.isPunctuation=p,n.isFence=h,n.isElligibleEmbellishedFence=function(t){return!(!t||!h(t))&&(!t.embellished||function t(e){return!e.embellished||!(i(e,"tensor")&&(!i(e.childNodes[1],"empty")||!i(e.childNodes[2],"empty"))&&(!i(e.childNodes[3],"empty")||!i(e.childNodes[4],"empty")))&&(!s(e,"close")||!i(e,"tensor"))&&(!s(e,"open")||!i(e,"subscript")&&!i(e,"superscript"))&&t(e.childNodes[0])}(t))},n.isTableOrMultiline=d,n.tableIsMatrixOrVector=function(t){return!!t&&f(t)&&d(t.childNodes[0])},n.isFencedElement=f,n.tableIsCases=function(t,e){return 0=r)){const o=n.childNodes[0].role;"unknown"!==o&&t.childNodes.every(function(t){t=t.childNodes[0];return!t||t.role===o&&(c.isType(t,"relation")||c.isType(t,"relseq"))})&&(t.role=o)}}static classifyTable(t){var e=y.computeColumns_(t);y.classifyByColumns_(t,e,"equality")||y.classifyByColumns_(t,e,"inequality",["equality"])||y.classifyByColumns_(t,e,"arrow")||y.detectCaleyTable(t)}static detectCaleyTable(t){if(!t.mathmlTree)return!1;const e=t.mathmlTree,r=e.getAttribute("columnlines"),n=e.getAttribute("rowlines");return!(!r||!n||!y.cayleySpacing(r)||!y.cayleySpacing(n)||(t.role="cayley",0))}static cayleySpacing(t){const e=t.split(" ");return("solid"===e[0]||"dashed"===e[0])&&e.slice(1).every(t=>"none"===t)}static proof(t,e,r){e=y.separateSemantics(e);return y.getInstance().proof(t,e,r)}static findSemantics(t,e,r){r=null==r?null:r,t=y.getSemantics(t);return!(!t||!t[e]||null!=r&&t[e]!==r)}static getSemantics(t){t=t.getAttribute("semantics");return t?y.separateSemantics(t):null}static removePrefix(t){const[,...e]=t.split("_");return e.join("_")}static separateSemantics(t){const r={};return t.split(";").forEach(function(t){var[t,e]=t.split(":");r[y.removePrefix(t)]=e}),r}static matchSpaces_(r,n){for(let t,e=0;t=n[e];e++){const n=r[e].mathmlTree,i=r[e+1].mathmlTree;var o;n&&i&&((o=n.nextSibling)&&o!==i&&(o=y.getSpacer_(o))&&(t.mathml.push(o),t.mathmlTree=o,t.role="space"))}}static getSpacer_(t){if("MSPACE"===m.tagName(t))return t;for(;u.hasEmptyTag(t)&&1===t.childNodes.length;)if(t=t.childNodes[0],"MSPACE"===m.tagName(t))return t;return null}static fenceToPunct_(t){var e=y.FENCE_TO_PUNCT_[t.role];if(e){for(;t.embellished;)t.embellished="punctuation",c.isRole(t,"subsup")||c.isRole(t,"underover")||(t.role=e),t=t.childNodes[0];t.type="punctuation",t.role=e}}static classifyFunction_(e,r){if("appl"===e.type||"bigop"===e.type||"integral"===e.type)return"";if(r[0]&&r[0].textContent===s.functionApplication()){y.getInstance().funcAppls[e.id]=r.shift();let t="simple function";return o.run("simple2prefix",e),"prefix function"!==e.role&&"limit function"!==e.role||(t=e.role),y.propagateFunctionRole_(e,t),"prefix"}return y.CLASSIFY_FUNCTION_[e.role]||(c.isSimpleFunctionHead(e)?"simple":"")}static propagateFunctionRole_(t,e){t&&"infixop"!==t.type&&(c.isRole(t,"subsup")||c.isRole(t,"underover")||(t.role=e),y.propagateFunctionRole_(t.childNodes[0],e))}static getFunctionOp_(r,n){if(n(r))return r;for(let t,e=0;t=r.childNodes[e];e++){const r=y.getFunctionOp_(t,n);if(r)return r}return null}static tableToMatrixOrVector_(t){const r=t.childNodes[0];c.isType(r,"multiline")?y.tableToVector_(t):y.tableToMatrix_(t),t.contentNodes.forEach(r.appendContentNode.bind(r));for(let t,e=0;t=r.childNodes[e];e++)y.assignRoleToRow_(t,y.getComponentRoles_(r));return r.parent=null,r}static tableToVector_(t){const e=t.childNodes[0];e.type="vector",1!==e.childNodes.length?y.binomialForm_(e):y.tableToSquare_(t)}static binomialForm_(t){c.isBinomial(t)&&(t.role="binomial",t.childNodes[0].role="binomial",t.childNodes[1].role="binomial")}static tableToMatrix_(t){const e=t.childNodes[0];e.type="matrix",e.childNodes&&0t.match(/[^\s]/)),r=e.map(s.lookupMeaning);if(r.every(function(t){return"number"===t.type&&"integer"===t.role||"punctuation"===t.type&&"comma"===t.role}))return t.role="integer",void("0"===e[0]&&t.addAnnotation("general","basenumber"));r.every(function(t){return"number"===t.type&&"integer"===t.role||"punctuation"===t.type})?t.role="float":t.role="othernumber"}}static exprFont_(t){var e;"unknown"===t.font&&(e=[...t.textContent].map(s.lookupMeaning).reduce(function(t,e){return t&&e.font&&"unknown"!==e.font&&e.font!==t?"unknown"===t?e.font:null:t},"unknown"))&&(t.font=e)}static purgeFences_(e){const r=e.rel,n=e.comp,o=[],i=[];for(;0y.isPureRelation_(t,r))||2===e.length&&(y.testColumns_(e,1,t=>y.isEndRelation_(t,r)||y.isPureRelation_(t,r))||y.testColumns_(e,0,t=>y.isEndRelation_(t,r,!0)||y.isPureRelation_(t,r))))&&(t.role=r,!0)}static isEndRelation_(t,e,r){r=r?t.childNodes.length-1:0;return c.isType(t,"relseq")&&c.isRole(t,e)&&c.isType(t.childNodes[r],"empty")}static isPureRelation_(t,e){return c.isType(t,"relation")&&c.isRole(t,e)}static computeColumns_(e){const n=[];for(let r,t=0;r=e.childNodes[t];t++)for(let t,e=0;t=r.childNodes[e];e++)n[e]?n[e].push(t):n[e]=[t];return n}static testColumns_(t,e,r){const n=t[e];return!!n&&n.some(function(t){return t.childNodes.length&&r(t.childNodes[0])})&&n.every(function(t){return!t.childNodes.length||r(t.childNodes[0])})}setNodeFactory(t){y.getInstance().factory_=t,o.updateFactory(y.getInstance().factory_)}getNodeFactory(){return y.getInstance().factory_}identifierNode(t,e,r){if("MathML-Unit"===r)t.type="identifier",t.role="unit";else if(!e&&1===t.textContent.length&&("integer"===t.role||"latinletter"===t.role||"greekletter"===t.role)&&"normal"===t.font)return t.font="italic",o.run("simpleNamedFunction",t);return"unknown"===t.type&&(t.type="identifier"),y.exprFont_(t),o.run("simpleNamedFunction",t)}implicitNode(t){if(t=y.getInstance().getMixedNumbers_(t),1===(t=y.getInstance().combineUnits_(t)).length)return t[0];t=y.getInstance().implicitNode_(t);return o.run("combine_juxtaposition",t)}text(t,e){return y.exprFont_(t),t.type="text","MS"===e?t.role="string":"MSPACE"!==e&&!t.textContent.match(/^\s*$/)||(t.role="space"),t}row(t){return 0===(t=t.filter(function(t){return!c.isType(t,"empty")})).length?y.getInstance().factory_.makeEmptyNode():(t=y.getInstance().getFencesInRow_(t),t=y.getInstance().tablesInRow(t),t=y.getInstance().getPunctuationInRow_(t),t=y.getInstance().getTextInRow_(t),t=y.getInstance().getFunctionsInRow_(t),y.getInstance().relationsInRow_(t))}limitNode(t,e){if(!e.length)return y.getInstance().factory_.makeEmptyNode();let r,n=e[0],o="unknown";if(!e[1])return n;if(c.isLimitBase(n)){var i=(r=y.MML_TO_LIMIT_[t]).length;if(o=r.type,e=e.slice(0,r.length+1),1===i&&c.isAccent(e[1])||2===i&&c.isAccent(e[1])&&c.isAccent(e[2]))return r=y.MML_TO_BOUNDS_[t],y.getInstance().accentNode_(n,e,r.type,r.length,r.accent);if(2===i){if(c.isAccent(e[1]))return n=y.getInstance().accentNode_(n,[n,e[1]],{MSUBSUP:"subscript",MUNDEROVER:"underscore"}[t],1,!0),e[2]?y.getInstance().makeLimitNode_(n,[n,e[2]],null,"limupper"):n;if(e[2]&&c.isAccent(e[2]))return n=y.getInstance().accentNode_(n,[n,e[2]],{MSUBSUP:"superscript",MUNDEROVER:"overscore"}[t],1,!0),y.getInstance().makeLimitNode_(n,[n,e[1]],null,"limlower");e[i]||(o="limlower")}return y.getInstance().makeLimitNode_(n,e,null,o)}return r=y.MML_TO_BOUNDS_[t],y.getInstance().accentNode_(n,e,r.type,r.length,r.accent)}tablesInRow(t){let r=u.partitionNodes(t,c.tableIsMatrixOrVector),n=[];for(let t,e=0;t=r.rel[e];e++)(n=n.concat(r.comp.shift())).push(y.tableToMatrixOrVector_(t));n=n.concat(r.comp.shift()),r=u.partitionNodes(n,c.isTableOrMultiline),n=[];for(let t,e=0;t=r.rel[e];e++){const o=r.comp.shift();c.tableIsCases(t,o)&&y.tableToCases_(t,o.pop()),(n=n.concat(o)).push(t)}return n.concat(r.comp.shift())}mfenced(e,r,t,n){if(t&&0{r.push(y.getInstance().factory_.makeContentNode(e())),r.push(t)}),n=r}return e&&r?y.getInstance().horizontalFencedNode_(y.getInstance().factory_.makeContentNode(e),y.getInstance().factory_.makeContentNode(r),n):(e&&n.unshift(y.getInstance().factory_.makeContentNode(e)),r&&n.push(y.getInstance().factory_.makeContentNode(r)),y.getInstance().row(n))}fractionLikeNode(t,e,r,n){let o;if(n||!u.isZeroLength(r))return o=y.getInstance().fractionNode_(t,e),n&&o.addAnnotation("general","bevelled"),o;{const r=y.getInstance().factory_.makeBranchNode("line",[t],[]),n=y.getInstance().factory_.makeBranchNode("line",[e],[]);return o=y.getInstance().factory_.makeBranchNode("multiline",[r,n],[]),y.binomialForm_(o),y.classifyMultiline(o),o}}tensor(t,e,r,n,o){const i=y.getInstance().factory_.makeBranchNode("tensor",[t,y.getInstance().scriptNode_(e,"leftsub"),y.getInstance().scriptNode_(r,"leftsuper"),y.getInstance().scriptNode_(n,"rightsub"),y.getInstance().scriptNode_(o,"rightsuper")],[]);return i.role=t.role,i.embellished=c.isEmbellished(t),i}pseudoTensor(t,e,r){var n=t=>!c.isType(t,"empty"),o=e.filter(n).length,n=r.filter(n).length;if(!o&&!n)return t;const i=o?n?"MSUBSUP":"MSUB":"MSUP",a=[t];return o&&a.push(y.getInstance().scriptNode_(e,"rightsub",!0)),n&&a.push(y.getInstance().scriptNode_(r,"rightsuper",!0)),y.getInstance().limitNode(i,a)}font(t){return y.MATHJAX_FONTS[t]||t}proof(t,e,r){if(e.inference||e.axiom||console.log("Noise"),e.axiom){const e=y.getInstance().cleanInference(t.childNodes),n=e.length?y.getInstance().factory_.makeBranchNode("inference",r(e),[]):y.getInstance().factory_.makeEmptyNode();return n.role="axiom",n.mathmlTree=t,n}const n=y.getInstance().inference(t,e,r);return e.proof&&(n.role="proof",n.childNodes[0].role="final"),n}inference(t,e,r){if(e.inferenceRule){const e=y.getInstance().getFormulas(t,[],r);return y.getInstance().factory_.makeBranchNode("inference",[e.conclusion,e.premises],[])}const n=e.labelledRule,o=m.toArray(t.childNodes),i=[],a=("left"!==n&&"both"!==n||i.push(y.getInstance().getLabel(t,o,r,"left")),"right"!==n&&"both"!==n||i.push(y.getInstance().getLabel(t,o,r,"right")),y.getInstance().getFormulas(t,o,r)),s=y.getInstance().factory_.makeBranchNode("inference",[a.conclusion,a.premises],i);return s.mathmlTree=t,s}getLabel(t,e,r,n){const o=y.getInstance().findNestedRow(e,"prooflabel",n),i=y.getInstance().factory_.makeBranchNode("rulelabel",r(m.toArray(o.childNodes)),[]);return i.role=n,i.mathmlTree=o,i}getFormulas(t,e,r){const n=e.length?y.getInstance().findNestedRow(e,"inferenceRule"):t,o="up"===y.getSemantics(n).inferenceRule,i=o?n.childNodes[1]:n.childNodes[0],a=o?n.childNodes[0]:n.childNodes[1],s=i.childNodes[0].childNodes[0],l=m.toArray(s.childNodes[0].childNodes),c=[];let u=1;for(const t of l)u%2&&c.push(t.childNodes[0]),u++;const p=r(c),h=r(m.toArray(a.childNodes[0].childNodes))[0],d=y.getInstance().factory_.makeBranchNode("premises",p,[]),f=(d.mathmlTree=s,y.getInstance().factory_.makeBranchNode("conclusion",[h],[]));return f.mathmlTree=a.childNodes[0].childNodes[0],{conclusion:f,premises:d}}findNestedRow(t,e,r){return y.getInstance().findNestedRow_(t,e,0,r)}cleanInference(t){return m.toArray(t).filter(function(t){return"MSPACE"!==m.tagName(t)})}operatorNode(t){return"unknown"===t.type&&(t.type="operator"),o.run("multioperator",t)}implicitNode_(t){const e=y.getInstance().factory_.makeMultipleContentNodes(t.length-1,s.invisibleTimes()),r=(y.matchSpaces_(t,e),y.getInstance().infixNode_(t,e[0]));return r.role="implicit",e.forEach(function(t){t.parent=r}),r.contentNodes=e,r}infixNode_(t,e){const r=y.getInstance().factory_.makeBranchNode("infixop",t,[e],u.getEmbellishedInner(e).textContent);return r.role=e.role,o.run("propagateSimpleFunction",r)}explicitMixed_(r){var n=u.partitionNodes(r,function(t){return t.textContent===s.invisiblePlus()});if(!n.rel.length)return r;let o=[];for(let t,e=0;t=n.rel[e];e++){const s=n.comp[e],i=n.comp[e+1],a=s.length-1;if(s[a]&&i[0]&&c.isType(s[a],"number")&&!c.isRole(s[a],"mixed")&&c.isType(i[0],"fraction")){const r=y.getInstance().factory_.makeBranchNode("number",[s[a],i[0]],[]);r.role="mixed",(o=o.concat(s.slice(0,a))).push(r),i.shift()}else(o=o.concat(s)).push(t)}return o.concat(n.comp[n.comp.length-1])}concatNode_(t,e,r){if(0===e.length)return t;const n=e.map(function(t){return u.getEmbellishedInner(t).textContent}).join(" "),o=y.getInstance().factory_.makeBranchNode(r,[t],e,n);return 1c.isRole(t,"subtraction"));let n=y.getInstance().concatNode_(t,r.comp.pop(),"prefixop");for(1===n.contentNodes.length&&"addition"===n.contentNodes[0].role&&"+"===n.contentNodes[0].textContent&&(n.role="positive");0c.isType(t,"text"));if(0===r.rel.length)return t;const n=[];let o=r.comp[0];0c.isRole(t,"open");if(0===t.length){const t=n.shift();for(;0{t=t.type;return"punctuation"===t||"text"===t||"operator"===t||"relation"===t},t=u.partitionNodes(r,function(t){if(!c.isPunctuation(t))return!1;if(c.isPunctuation(t)&&!c.isRole(t,"ellipsis"))return!0;t=r.indexOf(t);if(0===t)return!r[1]||!n(r[1]);var e=r[t-1];if(t===r.length-1)return!n(e);t=r[t+1];return!n(e)||!n(t)});if(0===t.rel.length)return r;const e=[];let o=t.comp.shift(),i=(0c.isRole(t,"dummy"))?r.role="text":t.every(t=>c.isRole(t,"space"))?r.role="space":r.role="sequence",r}dummyNode_(t){const e=y.getInstance().factory_.makeMultipleContentNodes(t.length-1,s.invisibleComma());return e.forEach(function(t){t.role="dummy"}),y.getInstance().punctuatedNode_(t,e)}accentRole_(t,e){if(!c.isAccent(t))return!1;var r=t.textContent,r=s.lookupSecondary("bar",r)||s.lookupSecondary("tilde",r)||t.role;return t.role="underscore"===e?"underaccent":"overaccent",t.addAnnotation("accent",r),!0}accentNode_(t,e,r,n,o){var i=(e=e.slice(0,n+1))[1],a=e[2];let s;if(!o&&a&&((s=y.getInstance().factory_.makeBranchNode("subscript",[t,i],[])).role="subsup",e=[s,a],r="superscript"),o){const n=y.getInstance().accentRole_(i,r);a&&(r=y.getInstance().accentRole_(a,"overscore")&&!n?(e=[s=y.getInstance().factory_.makeBranchNode("overscore",[t,a],[]),i],"underscore"):(e=[s=y.getInstance().factory_.makeBranchNode("underscore",[t,i],[]),a],"overscore"),s.role="underover")}return y.getInstance().makeLimitNode_(t,e,s,r)}makeLimitNode_(t,e,r,n){if("limupper"===n&&"limlower"===t.type)return t.childNodes.push(e[1]),(e[1].parent=t).type="limboth",t;if("limlower"===n&&"limupper"===t.type)return t.childNodes.splice(1,-1,e[1]),(e[1].parent=t).type="limboth",t;const o=y.getInstance().factory_.makeBranchNode(n,e,[]),i=c.isEmbellished(t);return r&&(r.embellished=i),o.embellished=i,o.role=t.role,o}getFunctionsInRow_(t,e){const r=e||[];if(0===t.length)return r;var e=t.shift(),n=y.classifyFunction_(e,t);if(!n)return r.push(e),y.getInstance().getFunctionsInRow_(t,r);t=y.getInstance().getFunctionsInRow_(t,[]),e=y.getInstance().getFunctionArgs_(e,t,n);return r.concat(e)}getFunctionArgs_(t,e,r){let n,o,i;switch(r){case"integral":{const r=y.getInstance().getIntegralArgs_(e);if(!r.intvar&&!r.integrand.length)return r.rest.unshift(t),r.rest;const n=y.getInstance().row(r.integrand);return i=y.getInstance().integralNode_(t,n,r.intvar),r.rest.unshift(i),r.rest}case"prefix":if(e[0]&&"fenced"===e[0].type){const r=e.shift();return c.isNeutralFence(r)||(r.role="leftright"),i=y.getInstance().functionNode_(t,r),e.unshift(i),e}if((n=u.sliceNodes(e,c.isPrefixFunctionBoundary)).head.length)o=y.getInstance().row(n.head),n.div&&n.tail.unshift(n.div);else{if(!n.div||!c.isType(n.div,"appl"))return e.unshift(t),e;o=n.div}return i=y.getInstance().functionNode_(t,o),n.tail.unshift(i),n.tail;case"bigop":return(n=u.sliceNodes(e,c.isBigOpBoundary)).head.length?(o=y.getInstance().row(n.head),i=y.getInstance().bigOpNode_(t,o),n.div&&n.tail.unshift(n.div),n.tail.unshift(i),n.tail):(e.unshift(t),e);default:{if(0===e.length)return[t];const r=e[0];return"fenced"===r.type&&!c.isNeutralFence(r)&&c.isSimpleFunctionScope(r)?(r.role="leftright",y.propagateFunctionRole_(t,"simple function"),i=y.getInstance().functionNode_(t,e.shift()),e.unshift(i)):e.unshift(t),e}}}getIntegralArgs_(t,e=[]){if(0===t.length)return{integrand:e,intvar:null,rest:t};const 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r=i.tagName(t);-1!==o.IGNORETAGS.indexOf(r)||-1!==o.EMPTYTAGS.indexOf(r)&&0===t.childNodes.length||n.push(t)}return n},o.isZeroLength=function(t){if(!t)return!1;if(-1!==["negativeveryverythinmathspace","negativeverythinmathspace","negativethinmathspace","negativemediummathspace","negativethickmathspace","negativeverythickmathspace","negativeveryverythickmathspace"].indexOf(t))return!0;t=t.match(/[0-9.]+/);return!!t&&0===parseFloat(t[0])},o.addAttributes=function(e,t){if(t.hasAttributes()){var r=t.attributes;for(let t=r.length-1;0<=t;t--){const n=r[t].name;n.match(/^ext/)&&(e.attributes[n]=r[t].value,e.nobreaking=!0),-1!==o.directSpeechKeys.indexOf(n)&&(e.attributes["ext-speech"]=r[t].value,e.nobreaking=!0),n.match(/texclass$/)&&(e.attributes.texclass=r[t].value),"href"===n&&(e.attributes.href=r[t].value,e.nobreaking=!0)}}},o.getEmbellishedInner=function t(e){return 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e+"/"+t}));return[["ancestor::*/following-sibling::*",r,e(i.join(" | "))].join(" and ")]},s.removeParens=function(t){if(!t.childNodes.length||!t.childNodes[0].childNodes.length||!t.childNodes[0].childNodes[0].childNodes.length)return"";const e=t.childNodes[0].childNodes[0].childNodes[0].textContent;return e.match(/^\(.+\)$/)?e.slice(1,-1):e};const S=new Map([[3,"CSFleftsuperscript"],[4,"CSFleftsubscript"],[2,"CSFbaseline"],[1,"CSFrightsubscript"],[0,"CSFrightsuperscript"]]),O=new Map([[4,2],[3,3],[2,1],[1,4],[0,5]]);s.generateTensorRules=function(i,a=!0){var e=["11111","11110","11101","11100","10111","10110","10101","10100","01111","01110","01101","01100"];for(let o,t=0;o=e[t];t++){let t="tensor"+o,[e,r,n]=function(t){const e=[];let r="",n="",o=parseInt(t,2);for(let t=0;t<5;t++){var i="children/*["+O.get(t)+"]";if(1&o){const e=S.get(t%5);r="[t] "+e+"Verbose; [n] "+i+";"+r,n="[t] "+e+"Brief; [n] "+i+";"+n}else 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1i.generateTensorRules(t,!1),CTFrelationIterator:a.relationIterator,CTFimplicitIterator:a.implicitIterator})}},7599:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.init=e.INIT_=void 0;const n=r(5425),o=r(9577),i=r(9284);e.INIT_=!1,e.init=function(){e.INIT_||((0,o.MathspeakRules)(),(0,n.ClearspeakRules)(),(0,i.PrefixRules)(),(0,i.OtherRules)(),(0,i.BrailleRules)(),e.INIT_=!0)}},7283:function(t,o,e){Object.defineProperty(o,"__esModule",{value:!0}),o.getStore=o.addStore=o.funcStore=void 0;const n=e(1676);o.funcStore=new Map,o.addStore=function(t,e,r){var n={};if(e){const t=o.funcStore.get(e)||{};Object.assign(n,t)}o.funcStore.set(t,Object.assign(n,r))},o.getStore=function(t,e,r){return o.funcStore.get([t,e,r].join("."))||o.funcStore.get([n.DynamicCstr.DEFAULT_VALUES[n.Axis.LOCALE],e,r].join("."))||o.funcStore.get([n.DynamicCstr.BASE_LOCALE,e,r].join("."))||{}}},7598:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.oneLeft=e.leftMostUnit=e.rightMostUnit=e.unitMultipliers=void 0;const o=r(7052),n=r(5274),i=r(4356),a=(e.unitMultipliers=function(t,e){const r=t;let n=0;return function(){var t=o.AuditoryDescription.create({text:s(r[n])&&l(r[n+1])?i.LOCALE.MESSAGES.unitTimes:""},{});return n++,[t]}},["superscript","subscript","overscore","underscore"]);function s(t){for(;t;){if("unit"===t.getAttribute("role"))return!0;var e=t.tagName,r=n.evalXPath("children/*",t);t=-1!==a.indexOf(e)?r[0]:r[r.length-1]}return!1}function l(t){for(;t;){if("unit"===t.getAttribute("role"))return!0;t=n.evalXPath("children/*",t)[0]}return!1}e.rightMostUnit=s,e.leftMostUnit=l,e.oneLeft=function(t){for(;t;){if("number"===t.tagName&&"1"===t.textContent)return[t];if("infixop"!==t.tagName||"multiplication"!==t.getAttribute("role")&&"implicit"!==t.getAttribute("role"))return[];t=n.evalXPath("children/*",t)[0]}return[]}},3284:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.AbstractWalker=void 0;const o=r(7052),i=r(8290),a=r(5740),n=r(4440),s=r(6828),l=r(8496),c=r(2298),u=r(4356),p=r(2105),h=r(5656),d=r(9552),f=r(9543),m=r(8504),y=r(7730),g=r(1214),b=r(179),v=r(1204),_=r(5274);class S{constructor(t,e,r,n){this.node=t,this.generator=e,this.highlighter=r,this.modifier=!1,this.keyMapping=new Map([[l.KeyCode.UP,this.up.bind(this)],[l.KeyCode.DOWN,this.down.bind(this)],[l.KeyCode.RIGHT,this.right.bind(this)],[l.KeyCode.LEFT,this.left.bind(this)],[l.KeyCode.TAB,this.repeat.bind(this)],[l.KeyCode.DASH,this.expand.bind(this)],[l.KeyCode.SPACE,this.depth.bind(this)],[l.KeyCode.HOME,this.home.bind(this)],[l.KeyCode.X,this.summary.bind(this)],[l.KeyCode.Z,this.detail.bind(this)],[l.KeyCode.V,this.virtualize.bind(this)],[l.KeyCode.P,this.previous.bind(this)],[l.KeyCode.U,this.undo.bind(this)],[l.KeyCode.LESS,this.previousRules.bind(this)],[l.KeyCode.GREATER,this.nextRules.bind(this)]]),this.cursors=[],this.xml_=null,this.rebuilt_=null,this.focus_=null,this.active_=!1,this.node.id?this.id=this.node.id:this.node.hasAttribute(S.SRE_ID_ATTR)?this.id=this.node.getAttribute(S.SRE_ID_ATTR):(this.node.setAttribute(S.SRE_ID_ATTR,S.ID_COUNTER.toString()),this.id=S.ID_COUNTER++),this.rootNode=v.getSemanticRoot(t),this.rootId=this.rootNode.getAttribute(c.Attribute.ID),this.xmlString_=n,this.moved=b.WalkerMoves.ENTER}getXml(){return this.xml_||(this.xml_=a.parseInput(this.xmlString_)),this.xml_}getRebuilt(){return this.rebuilt_||this.rebuildStree(),this.rebuilt_}isActive(){return this.active_}activate(){this.isActive()||(this.generator.start(),this.toggleActive_())}deactivate(){this.isActive()&&(b.WalkerState.setState(this.id,this.primaryId()),this.generator.end(),this.toggleActive_())}getFocus(t=!1){return this.focus_||(this.focus_=this.singletonFocus(this.rootId)),t&&this.updateFocus(),this.focus_}setFocus(t){this.focus_=t}getDepth(){return this.levels.depth()-1}isSpeech(){return this.generator.modality===c.Attribute.SPEECH}focusDomNodes(){return this.getFocus().getDomNodes()}focusSemanticNodes(){return this.getFocus().getSemanticNodes()}speech(){var r=this.focusDomNodes();if(!r.length)return"";const n=this.specialMove();if(null!==n)return n;switch(this.moved){case b.WalkerMoves.DEPTH:return this.depth_();case b.WalkerMoves.SUMMARY:return this.summary_();case b.WalkerMoves.DETAIL:return this.detail_();default:{const n=[],a=this.focusSemanticNodes();for(let t=0,e=r.length;tt.id.toString()),this.getRebuilt(),this.node))}rebuildStree(){this.rebuilt_=new g.RebuildStree(this.getXml()),this.rootId=this.rebuilt_.stree.root.id.toString(),this.generator.setRebuilt(this.rebuilt_),this.skeleton=h.SemanticSkeleton.fromTree(this.rebuilt_.stree),this.skeleton.populate(),this.focus_=this.singletonFocus(this.rootId),this.levels=this.initLevels(),f.connectMactions(this.node,this.getXml(),this.rebuilt_.xml)}previousLevel(){var t=this.getFocus().getDomPrimary();return t?v.getAttribute(t,c.Attribute.PARENT):this.getFocus().getSemanticPrimary().parent.id.toString()}nextLevel(){var t=this.getFocus().getDomPrimary();let e,r;if(t){e=v.splitAttribute(v.getAttribute(t,c.Attribute.CHILDREN)),r=v.splitAttribute(v.getAttribute(t,c.Attribute.CONTENT));const n=v.getAttribute(t,c.Attribute.TYPE),o=v.getAttribute(t,c.Attribute.ROLE);return this.combineContentChildren(n,o,r,e)}const n=t=>t.id.toString(),o=this.getRebuilt().nodeDict[this.primaryId()];return e=o.childNodes.map(n),r=o.contentNodes.map(n),0===e.length?[]:this.combineContentChildren(o.type,o.role,r,e)}singletonFocus(t){this.getRebuilt();var e=this.retrieveVisuals(t);return this.focusFromId(t,e)}retrieveVisuals(t){if(!this.skeleton)return[t];const e=parseInt(t,10),r=this.skeleton.subtreeNodes(e);if(!r.length)return[t];r.unshift(e);const n={},o=[];_.updateEvaluator(this.getXml());for(const t of r)n[t]||(o.push(t.toString()),n[t]=!0,this.subtreeIds(t,n));return o}subtreeIds(t,e){t=_.evalXPath(`//*[@data-semantic-id="${t}"]`,this.getXml());_.evalXPath("*//@data-semantic-id",t[0]).forEach(t=>e[parseInt(t.textContent,10)]=!0)}focusFromId(t,e){return y.Focus.factory(t,e,this.getRebuilt(),this.node)}summary(){return this.moved=this.isSpeech()?b.WalkerMoves.SUMMARY:b.WalkerMoves.REPEAT,this.getFocus().clone()}detail(){return this.moved=this.isSpeech()?b.WalkerMoves.DETAIL:b.WalkerMoves.REPEAT,this.getFocus().clone()}specialMove(){return null}virtualize(t){return this.cursors.push({focus:this.getFocus(),levels:this.levels,undo:t||!this.cursors.length}),this.levels=this.levels.clone(),this.getFocus().clone()}previous(){var t=this.cursors.pop();return t?(this.levels=t.levels,t.focus):this.getFocus()}undo(){let t;for(;(t=this.cursors.pop())&&!t.undo;);return t?(this.levels=t.levels,t.focus):this.getFocus()}update(t){this.generator.setOptions(t),(0,s.setup)(t).then(()=>d.generator("Tree").getSpeech(this.node,this.getXml()))}nextRules(){const t=this.generator.getOptions();return"speech"!==t.modality?this.getFocus():(n.DOMAIN_TO_STYLES[t.domain]=t.style,t.domain="mathspeak"===t.domain?"clearspeak":"mathspeak",t.style=n.DOMAIN_TO_STYLES[t.domain],this.update(t),this.moved=b.WalkerMoves.REPEAT,this.getFocus().clone())}nextStyle(t,e){if("mathspeak"===t){const t=["default","brief","sbrief"],n=t.indexOf(e);return-1===n?e:n>=t.length-1?t[0]:t[n+1]}if("clearspeak"!==t)return e;{const t=m.ClearspeakPreferences.getLocalePreferences().en;if(!t)return"default";const o=m.ClearspeakPreferences.relevantPreferences(this.getFocus().getSemanticPrimary()),i=m.ClearspeakPreferences.findPreference(e,o),a=t[o].map(function(t){return t.split("_")[1]}),s=a.indexOf(i);if(-1===s)return e;var r=s>=a.length-1?a[0]:a[s+1];return m.ClearspeakPreferences.addPreference(e,o,r)}}previousRules(){const t=this.generator.getOptions();return"speech"!==t.modality?this.getFocus():(t.style=this.nextStyle(t.domain,t.style),this.update(t),this.moved=b.WalkerMoves.REPEAT,this.getFocus().clone())}refocus(){let t,e=this.getFocus();for(;!e.getNodes().length;){t=this.levels.peek();var r=this.up();if(!r)break;this.setFocus(r),e=this.getFocus(!0)}this.levels.push(t),this.setFocus(e)}toggleActive_(){this.active_=!this.active_}mergePrefix_(t,e=[]){var r=this.isSpeech()?this.prefix_():"",r=(r&&t.unshift(r),this.isSpeech()?this.postfix_():"");return r&&t.push(r),i.finalize(i.merge(e.concat(t)))}prefix_(){var t=this.getFocus().getDomNodes(),e=this.getFocus().getSemanticNodes();return t[0]?v.getAttribute(t[0],c.Attribute.PREFIX):f.retrievePrefix(e[0])}postfix_(){var t=this.getFocus().getDomNodes();return t[0]?v.getAttribute(t[0],c.Attribute.POSTFIX):""}depth_(){var t=p.Grammar.getInstance().getParameter("depth"),e=(p.Grammar.getInstance().setParameter("depth",!0),this.getFocus().getDomPrimary()),e=this.expandable(e)?u.LOCALE.MESSAGES.navigate.EXPANDABLE:this.collapsible(e)?u.LOCALE.MESSAGES.navigate.COLLAPSIBLE:"",r=u.LOCALE.MESSAGES.navigate.LEVEL+" "+this.getDepth(),n=this.getFocus().getSemanticNodes(),n=f.retrievePrefix(n[0]),r=[new o.AuditoryDescription({text:r,personality:{}}),new o.AuditoryDescription({text:n,personality:{}}),new o.AuditoryDescription({text:e,personality:{}})];return p.Grammar.getInstance().setParameter("depth",t),i.finalize(i.markup(r))}actionable_(t){t=null==t?void 0:t.parentNode;return t&&this.highlighter.isMactionNode(t)?t:null}summary_(){var t=this.getFocus().getSemanticPrimary().id.toString(),t=this.getRebuilt().xml.getAttribute("id")===t?this.getRebuilt().xml:a.querySelectorAllByAttrValue(this.getRebuilt().xml,"id",t)[0],t=f.retrieveSummary(t);return this.mergePrefix_([t])}detail_(){const t=this.getFocus().getSemanticPrimary().id.toString(),e=this.getRebuilt().xml.getAttribute("id")===t?this.getRebuilt().xml:a.querySelectorAllByAttrValue(this.getRebuilt().xml,"id",t)[0],r=e.getAttribute("alternative");e.removeAttribute("alternative");var n=f.computeMarkup(e),n=this.mergePrefix_([n]);return e.setAttribute("alternative",r),n}}(e.AbstractWalker=S).ID_COUNTER=0,S.SRE_ID_ATTR="sre-explorer-id"},162:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.DummyWalker=void 0;class n extends r(3284).AbstractWalker{up(){return null}down(){return null}left(){return null}right(){return null}repeat(){return null}depth(){return null}home(){return null}getDepth(){return 0}initLevels(){return null}combineContentChildren(t,e,r,n){return[]}findFocusOnLevel(t){return null}}e.DummyWalker=n},7730:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.Focus=void 0;const p=r(1204);class h{constructor(t,e){this.nodes=t,this.primary=e,this.domNodes=[],this.domPrimary_=null,this.allNodes=[]}static factory(t,e,r,n){const o=t=>p.getBySemanticId(n,t),i=r.nodeDict,a=o(t),s=e.map(o),l=e.map(function(t){return i[t]}),c=new h(l,i[t]);return c.domNodes=s,c.domPrimary_=a,c.allNodes=h.generateAllVisibleNodes_(e,s,i,n),c}static generateAllVisibleNodes_(r,n,o,i){var a=t=>p.getBySemanticId(i,t);let s=[];for(let t=0,e=r.length;t=e.length?null:e[t]}depth(){return this.level_.length}clone(){const t=new r;return t.level_=this.level_.slice(0),t}toString(){let r="";for(let t,e=0;t=this.level_[e];e++)r+="\n"+t.map(function(t){return t.toString()});return r}}},1214:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.RebuildStree=void 0;const n=r(5740),c=r(2298),o=r(3588),i=r(6537),a=r(3308),s=r(5656),l=r(7075),u=r(4795),p=r(1204);class h{constructor(t){this.mathml=t,this.factory=new i.SemanticNodeFactory,this.nodeDict={},this.mmlRoot=p.getSemanticRoot(t),this.streeRoot=this.assembleTree(this.mmlRoot),this.stree=l.SemanticTree.fromNode(this.streeRoot,this.mathml),this.xml=this.stree.xml(),a.default.getInstance().setNodeFactory(this.factory)}static addAttributes(t,e,r){r&&1===e.childNodes.length&&e.childNodes[0].nodeType!==n.NodeType.TEXT_NODE&&u.addAttributes(t,e.childNodes[0]),u.addAttributes(t,e)}static textContent(t,e,r){!r&&e.textContent?t.textContent=e.textContent:1<(r=p.splitAttribute(p.getAttribute(e,c.Attribute.OPERATOR))).length&&(t.textContent=r[1])}static isPunctuated(t){return!s.SemanticSkeleton.simpleCollapseStructure(t)&&t[1]&&s.SemanticSkeleton.contentCollapseStructure(t[1])}getTree(){return this.stree}assembleTree(t){const e=this.makeNode(t),r=p.splitAttribute(p.getAttribute(t,c.Attribute.CHILDREN)),n=p.splitAttribute(p.getAttribute(t,c.Attribute.CONTENT));if(h.addAttributes(e,t,!(r.length||n.length)),0===n.length&&0===r.length)return h.textContent(e,t),e;if(0this.setParent(t,e)),e.childNodes=r.map(t=>this.setParent(t,e));t=p.getAttribute(t,c.Attribute.COLLAPSED);return t?this.postProcess(e,t):e}makeNode(t){const e=p.getAttribute(t,c.Attribute.TYPE),r=p.getAttribute(t,c.Attribute.ROLE),n=p.getAttribute(t,c.Attribute.FONT),o=p.getAttribute(t,c.Attribute.ANNOTATION)||"",i=p.getAttribute(t,c.Attribute.ID),a=p.getAttribute(t,c.Attribute.EMBELLISHED),s=p.getAttribute(t,c.Attribute.FENCEPOINTER),l=this.createNode(parseInt(i,10));return l.type=e,l.role=r,l.font=n||"unknown",l.parseAnnotation(o),s&&(l.fencePointer=s),a&&(l.embellished=a),l}makePunctuation(t){const e=this.createNode(t);return e.updateContent((0,o.invisibleComma)()),e.role="dummy",e}makePunctuated(t,e,r){const n=this.createNode(e[0]),o=(n.type="punctuated",n.embellished=t.embellished,n.fencePointer=t.fencePointer,n.role=r,e.splice(1,1)[0].slice(1));n.contentNodes=o.map(this.makePunctuation.bind(this)),this.collapsedChildren_(e)}makeEmpty(t,e,r){const n=this.createNode(e);n.type="empty",n.embellished=t.embellished,n.fencePointer=t.fencePointer,n.role=r}makeIndex(t,e,r){if(h.isPunctuated(e))return this.makePunctuated(t,e,r),void e[0];s.SemanticSkeleton.simpleCollapseStructure(e)&&!this.nodeDict[e.toString()]&&this.makeEmpty(t,e,r)}postProcess(t,e){const r=s.SemanticSkeleton.fromString(e).array;if("subsup"===t.type){const e=this.createNode(r[1][0]);return e.type="subscript",e.role="subsup",t.type="superscript",e.embellished=t.embellished,e.fencePointer=t.fencePointer,this.makeIndex(t,r[1][2],"rightsub"),this.makeIndex(t,r[2],"rightsuper"),this.collapsedChildren_(r),t}if("subscript"===t.type)return this.makeIndex(t,r[2],"rightsub"),this.collapsedChildren_(r),t;if("superscript"===t.type)return this.makeIndex(t,r[2],"rightsuper"),this.collapsedChildren_(r),t;if("tensor"===t.type)return this.makeIndex(t,r[2],"leftsub"),this.makeIndex(t,r[3],"leftsuper"),this.makeIndex(t,r[4],"rightsub"),this.makeIndex(t,r[5],"rightsuper"),this.collapsedChildren_(r),t;if("punctuated"===t.type){if(h.isPunctuated(r)){const e=r.splice(1,1)[0].slice(1);t.contentNodes=e.map(this.makePunctuation.bind(this))}return t}if("underover"!==t.type)return t;{const e=this.createNode(r[1][0]);return"overaccent"===t.childNodes[1].role?(e.type="overscore",t.type="underscore"):(e.type="underscore",t.type="overscore"),e.role="underover",e.embellished=t.embellished,e.fencePointer=t.fencePointer,this.collapsedChildren_(r),t}}createNode(t){var e=this.factory.makeNode(t);return this.nodeDict[t.toString()]=e}collapsedChildren_(t){const i=r=>{const n=this.nodeDict[r[0]];n.childNodes=[];for(let t=1,e=r.length;tt.getSemanticPrimary().id===e)}}e.SemanticWalker=i},9806:function(t,e,r){Object.defineProperty(e,"__esModule",{value:!0}),e.SyntaxWalker=void 0;const o=r(707),n=r(3284),i=r(9797);class a extends n.AbstractWalker{constructor(t,e,r,n){super(t,e,r,n),this.node=t,this.generator=e,this.highlighter=r,this.levels=null,this.restoreState()}initLevels(){const t=new i.Levels;return t.push([this.primaryId()]),t}up(){super.up();var t=this.previousLevel();return t?(this.levels.pop(),this.singletonFocus(t)):null}down(){super.down();var t=this.nextLevel();if(0===t.length)return null;var e=this.singletonFocus(t[0]);return e&&this.levels.push(t),e}combineContentChildren(t,e,r,n){switch(t){case"relseq":case"infixop":case"multirel":return(0,o.interleaveLists)(n,r);case"prefixop":return r.concat(n);case"postfixop":return n.concat(r);case"matrix":case"vector":case"fenced":return n.unshift(r[0]),n.push(r[1]),n;case"cases":return n.unshift(r[0]),n;case"punctuated":return"text"===e?(0,o.interleaveLists)(n,r):n;case"appl":return[n[0],r[0],n[1]];case"root":return[n[1],n[0]];default:return n}}left(){super.left();var t=this.levels.indexOf(this.primaryId());if(null===t)return null;t=this.levels.get(t-1);return t?this.singletonFocus(t):null}right(){super.right();var t=this.levels.indexOf(this.primaryId());if(null===t)return null;t=this.levels.get(t+1);return t?this.singletonFocus(t):null}findFocusOnLevel(t){return 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index 5f7f54dc9..601fc5446 100644 --- a/index.html +++ b/index.html @@ -16,7 +16,7 @@ - + diff --git a/pkgdown.yml b/pkgdown.yml index 860758fe6..75d37e022 100644 --- a/pkgdown.yml +++ b/pkgdown.yml @@ -6,7 +6,7 @@ articles: ebola: ebola.html epidist: epidist.html faq: faq.html -last_built: 2024-09-18T16:35Z +last_built: 2024-09-19T13:20Z urls: reference: https://epidist.epinowcast.org/reference article: https://epidist.epinowcast.org/articles diff --git a/reference/add_mean_sd.default.html b/reference/add_mean_sd.default.html index c35a4ec94..ceea7cee4 100644 --- a/reference/add_mean_sd.default.html +++ b/reference/add_mean_sd.default.html @@ -1,5 +1,5 @@ -Default method for add natural scale parameters — add_mean_sd.default • epidist +Default method for add natural scale parameters — add_mean_sd.default • epidist Skip to contents diff --git a/reference/add_mean_sd.gamma_samples.html b/reference/add_mean_sd.gamma_samples.html index 23bf5f60f..ff91a9078 100644 --- a/reference/add_mean_sd.gamma_samples.html +++ b/reference/add_mean_sd.gamma_samples.html @@ -1,5 +1,5 @@ -Add natural scale mean and standard deviation parameters for a latent gamma model — add_mean_sd.gamma_samples • epidist +Add natural scale mean and standard deviation parameters for a latent gamma model — add_mean_sd.gamma_samples • epidist Skip to contents diff --git a/reference/add_mean_sd.html b/reference/add_mean_sd.html index 389d64f96..073936988 100644 --- a/reference/add_mean_sd.html +++ b/reference/add_mean_sd.html @@ -1,5 +1,5 @@ -Add natural scale mean and standard deviation parameters — add_mean_sd • epidist +Add natural scale mean and standard deviation parameters — add_mean_sd • epidist Skip to contents diff --git a/reference/add_mean_sd.lognormal_samples.html b/reference/add_mean_sd.lognormal_samples.html index dee37f9b9..a1b5cd4ae 100644 --- a/reference/add_mean_sd.lognormal_samples.html +++ b/reference/add_mean_sd.lognormal_samples.html @@ -1,5 +1,5 @@ -Add natural scale mean and standard deviation parameters for a latent lognormal model — add_mean_sd.lognormal_samples • epidistAdd natural scale mean and standard deviation parameters for a latent lognormal model — add_mean_sd.lognormal_samples • epidist Skip to contents diff --git a/reference/as_latent_individual.html b/reference/as_latent_individual.html index 824cddf98..8a9a3da4f 100644 --- a/reference/as_latent_individual.html +++ b/reference/as_latent_individual.html @@ -1,5 +1,5 @@ -Prepare latent individual model — as_latent_individual • epidistPrepare latent individual model — as_latent_individual • epidistRound to the nearest multiple — .floor_mult • epidistRound to the nearest multiple — .floor_mult • epidistReplace brms prior distributions — .replace_prior • epidistReplace brms prior distributions — .replace_prior • epidistRead in an epidist Stan code chunk — .stan_chunk • epidistRead in an epidist Stan code chunk — .stan_chunk • epidist Skip to contents diff --git a/reference/dot-version_stanvar.html b/reference/dot-version_stanvar.html index 752479b76..f5c3b65bd 100644 --- a/reference/dot-version_stanvar.html +++ b/reference/dot-version_stanvar.html @@ -1,5 +1,5 @@ -Label a epidist Stan model with a version indicator — .version_stanvar • epidistLabel a epidist Stan model with a version indicator — .version_stanvar • epidistepidist: Estimate epidemiological delay distributions for infectious diseases — epidist-package • epidistepidist: Estimate epidemiological delay distributions for infectious diseases — epidist-package • epidist Skip to contents diff --git a/reference/epidist.default.html b/reference/epidist.default.html index 556ad41bb..d8fa6c89a 100644 --- a/reference/epidist.default.html +++ b/reference/epidist.default.html @@ -1,5 +1,5 @@ -Default method used for interface using brms — epidist.default • epidist +Default method used for interface using brms — epidist.default • epidist Skip to contents diff --git a/reference/epidist.html b/reference/epidist.html index 305cba220..d784bd9e3 100644 --- a/reference/epidist.html +++ b/reference/epidist.html @@ -1,5 +1,5 @@ -Fit epidemiological delay distributions using a brms interface — epidist • epidist +Fit epidemiological delay distributions using a brms interface — epidist • epidist Skip to contents diff --git a/reference/epidist_diagnostics.html b/reference/epidist_diagnostics.html index a457d70c8..7b4692016 100644 --- a/reference/epidist_diagnostics.html +++ b/reference/epidist_diagnostics.html @@ -1,5 +1,5 @@ -Diagnostics for epidist_fit models — epidist_diagnostics • epidist -Default method for defining a model specific family — epidist_family.default • epidist +Default method for defining a model specific family — epidist_family.default • epidist Skip to contents diff --git a/reference/epidist_family.epidist_latent_individual.html b/reference/epidist_family.epidist_latent_individual.html index 3de905ba1..5b4d4571e 100644 --- a/reference/epidist_family.epidist_latent_individual.html +++ b/reference/epidist_family.epidist_latent_individual.html @@ -1,5 +1,5 @@ -Check if data has the epidist_latent_individual class — epidist_family.epidist_latent_individual • epidist +Check if data has the epidist_latent_individual class — epidist_family.epidist_latent_individual • epidist Skip to contents diff --git a/reference/epidist_family.html b/reference/epidist_family.html index f012a0e6e..2f5bf7474 100644 --- a/reference/epidist_family.html +++ b/reference/epidist_family.html @@ -1,5 +1,5 @@ -Define model specific family — epidist_family • epidistDefine model specific family — epidist_family • epidistDefault family specific prior distributions — epidist_family_prior.default • epidist +Default family specific prior distributions — epidist_family_prior.default • epidist Skip to contents diff --git a/reference/epidist_family_prior.html b/reference/epidist_family_prior.html index 95738f29e..a9e537bcf 100644 --- a/reference/epidist_family_prior.html +++ b/reference/epidist_family_prior.html @@ -1,5 +1,5 @@ -Family specific prior distributions — epidist_family_prior • epidistFamily specific prior distributions — epidist_family_prior • epidist Skip to contents diff --git a/reference/epidist_family_prior.lognormal.html b/reference/epidist_family_prior.lognormal.html index 08d433c33..ecae2fcd5 100644 --- a/reference/epidist_family_prior.lognormal.html +++ b/reference/epidist_family_prior.lognormal.html @@ -1,5 +1,5 @@ -Family specific prior distributions for the lognormal family — epidist_family_prior.lognormal • epidist +Family specific prior distributions for the lognormal family — epidist_family_prior.lognormal • epidist Skip to contents diff --git a/reference/epidist_formula.default.html b/reference/epidist_formula.default.html index d5307d415..e441f0976 100644 --- a/reference/epidist_formula.default.html +++ b/reference/epidist_formula.default.html @@ -1,5 +1,5 @@ -Default method for defining a model specific formula — epidist_formula.default • epidist +Default method for defining a model specific formula — epidist_formula.default • epidist Skip to contents diff --git a/reference/epidist_formula.epidist_latent_individual.html b/reference/epidist_formula.epidist_latent_individual.html index 670a7a4f8..c81c11306 100644 --- a/reference/epidist_formula.epidist_latent_individual.html +++ b/reference/epidist_formula.epidist_latent_individual.html @@ -1,5 +1,5 @@ -Define a formula for the latent_individual model — epidist_formula.epidist_latent_individual • epidist +Define a formula for the latent_individual model — epidist_formula.epidist_latent_individual • epidist Skip to contents diff --git a/reference/epidist_formula.html b/reference/epidist_formula.html index efa059418..b700816e2 100644 --- a/reference/epidist_formula.html +++ b/reference/epidist_formula.html @@ -1,5 +1,5 @@ -Define a model specific formula — epidist_formula • epidistDefine a model specific formula — epidist_formula • epidistDefault model specific prior distributions — epidist_model_prior.default • epidist +Default model specific prior distributions — epidist_model_prior.default • epidist Skip to contents diff --git a/reference/epidist_model_prior.html b/reference/epidist_model_prior.html index f967ec451..f0b3e9ede 100644 --- a/reference/epidist_model_prior.html +++ b/reference/epidist_model_prior.html @@ -1,5 +1,5 @@ -Model specific prior distributions — epidist_model_prior • epidistModel specific prior distributions — epidist_model_prior • epidist Skip to contents diff --git a/reference/epidist_prior.html b/reference/epidist_prior.html index ff55d9e78..9d4d3b313 100644 --- a/reference/epidist_prior.html +++ b/reference/epidist_prior.html @@ -1,5 +1,5 @@ -Define prior distributions using brms defaults, model specific priors, family specific priors, and user provided priors — epidist_prior • epidistDefine prior distributions using brms defaults, model specific priors, family specific priors, and user provided priors — epidist_prior • epidistDefault method for defining model specific Stan code — epidist_stancode.default • epidist +Default method for defining model specific Stan code — epidist_stancode.default • epidist Skip to contents diff --git a/reference/epidist_stancode.html b/reference/epidist_stancode.html index c4631eed6..57ff3511a 100644 --- a/reference/epidist_stancode.html +++ b/reference/epidist_stancode.html @@ -1,5 +1,5 @@ -Define model specific Stan code — epidist_stancode • epidistDefine model specific Stan code — epidist_stancode • epidistDefault method for data validation — epidist_validate.default • epidist +Default method for data validation — epidist_validate.default • epidist Skip to contents diff --git a/reference/epidist_validate.epidist_latent_individual.html b/reference/epidist_validate.epidist_latent_individual.html index c101d2146..7b8064593 100644 --- a/reference/epidist_validate.epidist_latent_individual.html +++ b/reference/epidist_validate.epidist_latent_individual.html @@ -1,5 +1,5 @@ -Validate latent individual model data — epidist_validate.epidist_latent_individual • epidistValidate latent individual model data — epidist_validate.epidist_latent_individual • epidistValidate a data object for use with epidist() — epidist_validate • epidistValidate a data object for use with epidist() — epidist_validate • epidistFilter observations based on a observation time of secondary events — filter_obs_by_obs_time • epidist +Filter observations based on a observation time of secondary events — filter_obs_by_obs_time • epidist Skip to contents diff --git a/reference/filter_obs_by_ptime.html b/reference/filter_obs_by_ptime.html index e9c083987..3330ad62c 100644 --- a/reference/filter_obs_by_ptime.html +++ b/reference/filter_obs_by_ptime.html @@ -1,5 +1,5 @@ -Filter observations based on the observation time of primary events — filter_obs_by_ptime • epidist +Filter observations based on the observation time of primary events — filter_obs_by_ptime • epidist Skip to contents diff --git a/reference/index.html b/reference/index.html index 40c6f1b45..709899ce6 100644 --- a/reference/index.html +++ b/reference/index.html @@ -1,5 +1,5 @@ -Package index • epidist +Package index • epidist Skip to contents diff --git a/reference/is_latent_individual.html b/reference/is_latent_individual.html index b693e92f3..b9f26d9cc 100644 --- a/reference/is_latent_individual.html +++ b/reference/is_latent_individual.html @@ -1,5 +1,5 @@ -Check if data has the epidist_latent_individual class — is_latent_individual • epidist +Check if data has the epidist_latent_individual class — is_latent_individual • epidist Skip to contents diff --git a/reference/log_lik_latent_gamma.html b/reference/log_lik_latent_gamma.html index a1915c2db..de00bab5c 100644 --- a/reference/log_lik_latent_gamma.html +++ b/reference/log_lik_latent_gamma.html @@ -1,5 +1,5 @@ -Calculate the pointwise log likelihood of the latent_gamma family — log_lik_latent_gamma • epidist +Calculate the pointwise log likelihood of the latent_gamma family — log_lik_latent_gamma • epidist Skip to contents diff --git a/reference/log_lik_latent_lognormal.html b/reference/log_lik_latent_lognormal.html index a8e58ce0b..6342c8e47 100644 --- a/reference/log_lik_latent_lognormal.html +++ b/reference/log_lik_latent_lognormal.html @@ -1,5 +1,5 @@ -Calculate the pointwise log likelihood of the latent_gamma family — log_lik_latent_lognormal • epidist +Calculate the pointwise log likelihood of the latent_gamma family — log_lik_latent_lognormal • epidist Skip to contents diff --git a/reference/observe_process.html b/reference/observe_process.html index dccdf80f9..88f540e66 100644 --- a/reference/observe_process.html +++ b/reference/observe_process.html @@ -1,5 +1,5 @@ -Observation process for primary and secondary events — observe_process • epidistObservation process for primary and secondary events — observe_process • epidistDraws from the expected value of the posterior predictive distribution of the latent_gamma family — posterior_epred_latent_gamma • epidist +Draws from the expected value of the posterior predictive distribution of the latent_gamma family — posterior_epred_latent_gamma • epidist Skip to contents diff --git a/reference/posterior_epred_latent_lognormal.html b/reference/posterior_epred_latent_lognormal.html index 1287cbcf5..6f78825fb 100644 --- a/reference/posterior_epred_latent_lognormal.html +++ b/reference/posterior_epred_latent_lognormal.html @@ -1,5 +1,5 @@ -Draws from the expected value of the posterior predictive distribution of the latent_gamma family — posterior_epred_latent_lognormal • epidist +Draws from the expected value of the posterior predictive distribution of the latent_gamma family — posterior_epred_latent_lognormal • epidist Skip to contents diff --git a/reference/posterior_predict_latent_gamma.html b/reference/posterior_predict_latent_gamma.html index 6e8407c62..456a60c30 100644 --- a/reference/posterior_predict_latent_gamma.html +++ b/reference/posterior_predict_latent_gamma.html @@ -1,5 +1,5 @@ -Draws from the posterior predictive distribution of the latent_gamma family — posterior_predict_latent_gamma • epidist +Draws from the posterior predictive distribution of the latent_gamma family — posterior_predict_latent_gamma • epidist Skip to contents diff --git a/reference/posterior_predict_latent_lognormal.html b/reference/posterior_predict_latent_lognormal.html index 838288f16..1a0d65a64 100644 --- a/reference/posterior_predict_latent_lognormal.html +++ b/reference/posterior_predict_latent_lognormal.html @@ -1,5 +1,5 @@ -Draws from the posterior predictive distribution of the latent_lognormal family — posterior_predict_latent_lognormal • epidist +Draws from the posterior predictive distribution of the latent_lognormal family — posterior_predict_latent_lognormal • epidist Skip to contents diff --git a/reference/predict_delay_parameters.html b/reference/predict_delay_parameters.html index 8af0c08da..655de58d7 100644 --- a/reference/predict_delay_parameters.html +++ b/reference/predict_delay_parameters.html @@ -1,5 +1,5 @@ -Extract samples of the delay distribution parameters — predict_delay_parameters • epidist +Extract samples of the delay distribution parameters — predict_delay_parameters • epidist Skip to contents diff --git a/reference/sierra_leone_ebola_data.html b/reference/sierra_leone_ebola_data.html index 44a431676..2fe1ddf5a 100644 --- a/reference/sierra_leone_ebola_data.html +++ b/reference/sierra_leone_ebola_data.html @@ -1,5 +1,5 @@ -Ebola linelist data from Fang et al. (2016) — sierra_leone_ebola_data • epidistEbola linelist data from Fang et al. (2016) — sierra_leone_ebola_data • epidist Skip to contents diff --git a/reference/simulate_exponential_cases.html b/reference/simulate_exponential_cases.html index 9c9161104..d4f2db2a1 100644 --- a/reference/simulate_exponential_cases.html +++ b/reference/simulate_exponential_cases.html @@ -1,5 +1,5 @@ -Simulate exponential cases — simulate_exponential_cases • epidistSimulate exponential cases — simulate_exponential_cases • epidistSimulate cases from a stochastic SIR model — simulate_gillespie • epidistSimulate cases from a stochastic SIR model — simulate_gillespie • epidistSimulate secondary events based on a delay distribution — simulate_secondary • epidistSimulate secondary events based on a delay distribution — simulate_secondary • epidistSimulate cases from a uniform distribution — simulate_uniform_cases • epidistSimulate cases from a uniform distribution — simulate_uniform_cases • epidist Skip to contents