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/** CortexJS Compute Engine 0.12.3 */
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0;const t=Vt(e);if(null!==t){const e=Vt(i);return null!==e?t-e:-1}if(e.numericValue instanceof He)return i.numericValue instanceof He?e.numericValue.re===i.numericValue.re?Math.abs(e.numericValue.im)===Math.abs(i.numericValue.im)?e.numericValue.im-i.numericValue.im:Math.abs(e.numericValue.im)-Math.abs(i.numericValue.im):e.numericValue.re-i.numericValue.re:null!==i.numericValue?1:-1;if(e.numericValue)return i.numericValue?1:-1;if("Sqrt"===e.head&&e.op1.numericValue)return"Sqrt"===i.head&&i.op1.numericValue?Qn(e.op1,i.op1):-1;if(e.symbol)return i.symbol?e.symbol===i.symbol?0:e.symbol>i.symbol?1:-1:null!==i.numericValue?1:-1;if(e.ops){if(i.ops){const t=e.functionDefinition?.complexity??jn,n=i.functionDefinition?.complexity??jn;return t===n?"string"==typeof e.head&&"string"==typeof i.head?e.head===i.head?Wn(e)-Wn(i):e.head<i.head?1:-1:Wn(e)-Wn(i):t-n}return null!==i.numericValue||i.symbol?1:-1}if(e.string)return i.string?e.string.length!==i.string.length?i.string.length-e.string.length:i.string<e.string?-1:e.string>i.string?1:0:i.keys?-1:1;if(e.keys&&i.keys){if(e.keysCount!==i.keysCount)return i.keysCount-e.keysCount;let t=0,n=0;for(const e of i.keys)t+=i.getKey(e).complexity??jn;for(const i of e.keys)n+=e.getKey(i).complexity??jn;return n-t}return(e.complexity??jn)-(i.complexity??jn)}function Wn(e){return null!==e.keys?1+e.keysCount:e.ops?("string"==typeof e.head?1:Wn(e.head))+[...e.ops].reduce(((e,i)=>e+Wn(i)),0):1}class Yn{constructor(e,i,t){if(this._terms=[],this._hasInfinity=!1,this._hasZero=!1,this._isCanonical=!0,t??(t={}),"canonical"in t||(t.canonical=!0),this._isCanonical=t.canonical,this.engine=e,this._sign=1,this._rational=Jt(e)?[BigInt(1),BigInt(1)]:[1,1],this._complex=He.ONE,this._bignum=e._BIGNUM_ONE,this._number=1,i)for(const e of i)this.addTerm(e)}get isEmpty(){return this._isCanonical?0===this._terms.length&&!1===this._hasInfinity&&!1===this._hasZero&&1===this._sign&&hn(this._rational)&&1===this._complex.re&&0===this._complex.im&&this._bignum.eq(this.engine._BIGNUM_ONE)&&1===this._number:0===this._terms.length}addTerm(e){if("Multiply"===e.head){for(const i of e.ops)this.addTerm(i);return}if(this._isCanonical){if(e.isNothing)return;if(null!==e.numericValue){if(e.isOne)return;if(e.isZero)return void(this._hasZero=!0);if(e.isNegativeOne)return void(this._sign*=-1);if(e.isInfinity)return this._hasInfinity=!0,void(e.isNegative&&(this._sign*=-1));let i=e.numericValue;if("number"==typeof i)return i<0&&(this._sign*=-1,i=-i),void(Number.isInteger(i)?this._rational=_n(this._rational,[i,1]):Jt(this.engine)?this._bignum=this._bignum.mul(i):this._number*=i);if(i instanceof Ze)return i.isNegative()&&(this._sign*=-1,i=i.neg()),void(i.isInteger()?this._rational=_n(this._rational,[Gt(i),BigInt(1)]):Jt(this.engine)?this._bignum=this._bignum.mul(i):this._number*=i.toNumber());if(i instanceof He)return void(this._complex=this._complex.mul(i));if(an(i))return this._rational=_n(this._rational,i),void(pn(this._rational)&&(this._sign*=-1,this._rational=dn(this._rational)))}}let i=e;if(this._isCanonical){let t;[t,i]=wn(e),this._rational=_n(this._rational,t),pn(this._rational)&&(this._sign*=-1,this._rational=dn(this._rational))}if(null!==i.numericValue&&i.isOne)return;let t=[1,1];if("Power"===i.head){const e=yn(i.op2);e&&(t=e,i=i.op1)}else"Divide"===i.head&&(this.addTerm(i.op1),t=[-1,1],i=i.op2);let n=!1;for(const e of this._terms)if(e.term.isSame(i)){e.exponent=Nn(e.exponent,t),n=!0;break}n||this._terms.push({term:i,exponent:t})}unitTerms(e){const i=this.engine;if("numeric"===e){if(!Xt(i)&&0!==this._complex.im)return null;if(Jt(i)){let e=i._BIGNUM_ONE;if(hn(this._rational)||(e=ln(this._rational)?i.bignum(this._rational[0].toString()).div(i.bignum(this._rational[1].toString())):i.bignum(this._rational[0]).div(this._rational[1])),e=e.mul(this._bignum).mul(this._sign*this._number),0!==this._complex.im){const t=this._complex.mul(e.toNumber());return t.equals(1)?[]:[{exponent:[1,1],terms:[i.number(t)]}]}return e=e.mul(this._complex.re),e.equals(1)?[]:[{exponent:[1,1],terms:[i.number(e)]}]}let e=1;if(hn(this._rational)||(e=ln(this._rational)?Number(this._rational[0])/Number(this._rational[1]):this._rational[0]/this._rational[1]),e*=this._sign*this._number*this._bignum.toNumber(),0!==this._complex.im){const t=this._complex.mul(e);return t.equals(1)?[]:[{exponent:[1,1],terms:[i.number(t)]}]}return e*=this._complex.re,1===e?[]:[{exponent:[1,1],terms:[i.number(e)]}]}const t=[],n=[];this._hasInfinity&&n.push(i._POSITIVE_INFINITY),this._rational=Sn(this._rational),1===this._complex.re&&0===this._complex.im||(0===this._complex.im&&(this._number*=Math.abs(this._complex.re)),this._complex.re<0?this._rational=dn(this._rational):n.push(i.number(this._complex)));let r=this._sign*this._number,s=this._bignum;return hn(this._rational)||("rational"===e?(1!==fn(this._rational)&&(ln(this._rational)?s=s.mul(i.bignum(this._rational[0])):r*=this._rational[0]),1!==gn(this._rational)&&t.push({exponent:[-1,1],terms:[i.number(this._rational[1])]})):-1===r?(n.push(i.number(dn(this._rational))),r=1):n.push(i.number(this._rational))),s.equals(i._BIGNUM_ONE)?1!==r&&n.push(i.number(r)):n.push(i.number(s.mul(r))),n.length>0&&t.push({exponent:[1,1],terms:n}),t}groupedByDegrees(e){e??(e={}),"mode"in e||(e.mode="expression");const i=this.engine;if("numeric"===e.mode){if(0!==this._complex.im&&!Xt(i))return null;if(this._hasInfinity)return[{exponent:[1,1],terms:[i._POSITIVE_INFINITY]}]}const t=this.unitTerms(e.mode??"expression");if(null===t)return null;for(const e of this._terms){const i=Sn(e.exponent);if(0===i[0])continue;let n=!1;for(const r of t)if(i[0]===r.exponent[0]&&i[1]===r.exponent[1]){r.terms.push(e.term),n=!0;break}n||t.push({exponent:i,terms:[e.term]})}return t}asExpression(e="evaluate"){const i=this.engine;if(this._hasInfinity){if(this._hasZero)return i._NAN;if(0===this._terms.length)return fn(this._rational)>0?i._POSITIVE_INFINITY:i._NEGATIVE_INFINITY}if(this._hasZero)return i._ZERO;const t=this.groupedByDegrees({mode:"N"===e?"numeric":"expression"});if(null===t)return i._NAN;const n=Xn(i,t);return 0===n.length?i._ONE:1===n.length?n[0]:this.engine._fn("Multiply",n)}asNumeratorDenominator(){const e=this.groupedByDegrees({mode:"rational"});if(null===e)return[this.engine._NAN,this.engine._NAN];const i=[],t=[];for(const n of e)n.exponent[0]>=0?i.push(n):t.push({exponent:dn(n.exponent),terms:n.terms});const n=this.engine,r=Xn(n,i);let s=n._ONE;1===r.length?s=r[0]:r.length>0&&(s=n._fn("Multiply",r));const o=Xn(n,t);let a=n._ONE;return 1===o.length?a=o[0]:o.length>0&&(a=n._fn("Multiply",o)),[s,a]}asRationalExpression(){const[e,i]=this.asNumeratorDenominator();if(null!==i.numericValue){if(i.isOne)return e;if(i.isNegativeOne)return this.engine.neg(e)}return this.engine._fn("Divide",[e,i])}}function Kn(e){if(hn(e))return 0;const[i,t]=[fn(e),gn(e)];return i>0&&Number.isInteger(i/t)?1:i>0?2:Number.isInteger(i/t)?3:4}function Jn(e,i){const t=Kn(e.exponent),n=Kn(i.exponent);if(t!==n)return t-n;const[r,s]=[fn(e.exponent),gn(e.exponent)],[o,a]=[fn(i.exponent),gn(i.exponent)];return r/s-o/a}function Xn(e,i){const t=i.sort(Jn).map((i=>{const t=En(i.terms,"Multiply"),n=t.length<=1?t[0]:e._fn("Multiply",t.sort(Qn));return hn(i.exponent)?n:e.pow(n,i.exponent)}));return En(t,"Multiply")??t}function er(e,i,t,n){if(null!==i.numericValue){if(an(i.numericValue))return fn(i.numericValue)<0?ir(e,"Subtract",[t,e.number(dn(i.numericValue))],n):null;const r=$t(i);if(null!==r&&r<0)return ir(e,"Subtract",[t,e.number(-r)],n)}return"Negate"===i.head?ir(e,"Subtract",[t,i.op1],n):null}function ir(e,i,t,n){const r=e.jsonSerializationOptions.exclude;if(("Rational"===i||"Divide"===i)&&2===t.length&&1===$t(t[0])&&2===$t(t[1])&&!r.includes("Half"))return tr(e,"Half",{...n,wikidata:"Q39373172"});if(1===t.length){const n=t[0].numericValue;if("Negate"===i&&null!==n){if("number"==typeof n)return nr(e,-n);if(n instanceof Ze)return nr(e,n.neg());if(n instanceof je.exports.Complex)return nr(e,n.neg());if(an(n))return nr(e,dn(n))}}if("string"==typeof i&&r.includes(i)){if("Rational"===i&&2===t.length)return ir(e,"Divide",t,n);if("Complex"===i&&2===t.length)return ir(e,"Add",[t[0],e._fn("Multiply",[t[1],e.symbol("ImaginaryUnit")])],n);if("Sqrt"===i&&1===t.length)return ir(e,"Power",[t[0],r.includes("Half")?e.number([1,2]):e._HALF],n);if("Root"===i&&2===t.length&&null!==t[1].numericValue){const i=$t(t[1]);if(2===i)return ir(e,"Sqrt",[t[0]]);if(null!==i)return i<0?ir(e,"Divide",[e._ONE,e._fn("Power",[t[0],e.number([1,-i])])],n):ir(e,"Power",[t[0],e.number([1,-i])],n)}if("Square"===i&&1===t.length)return ir(e,"Power",[t[0],e.number(2)],n);if("Exp"===i&&1===t.length)return ir(e,"Power",[e.symbol("ExponentialE"),t[0]],n);if("Subtract"===i&&2===t.length)return ir(e,"Add",[t[0],e._fn("Negate",[t[1]])],n);if("Subtract"===i&&1===t.length)return ir(e,"Negate",t,n)}if("Add"===i&&2===t.length&&!r.includes("Subtract")){if(null!==t[1].numericValue){const i=$t(t[1]);if(null!==i&&i<0)return ir(e,"Subtract",[t[0],e.number(-i)],n)}if("Negate"===t[1].head)return ir(e,"Subtract",[t[0],t[1].op1],n)}if("Tuple"===i){if(1===t.length&&!r.includes("Single"))return ir(e,"Single",t,n);if(2===t.length&&!r.includes("Pair"))return ir(e,"Pair",t,n);if(3===t.length&&!r.includes("Triple"))return ir(e,"Triple",t,n)}const s=["string"==typeof i?i:i.json,...t.map((e=>e.json))],o={...n??{}};return e.jsonSerializationOptions.metadata.includes("latex")?o.latex=o.latex??e.serialize({fn:s}):o.latex="",e.jsonSerializationOptions.metadata.includes("wikidata")||(o.wikidata=""),o.latex||o.wikidata||!e.jsonSerializationOptions.shorthands.includes("function")?o.latex&&o.wikidata?{fn:s,latex:o.latex,wikidata:o.wikidata}:o.latex?{fn:s,latex:o.latex}:o.wikidata?{fn:s,wikidata:o.wikidata}:{fn:s}:s}function tr(e,i,t){if("Half"===i&&e.jsonSerializationOptions.exclude.includes("Half"))return nr(e,[1,2],t);if(t={...t},e.jsonSerializationOptions.metadata.includes("latex")?(t.latex=t.latex??e.serialize({sym:i}),void 0!==t.latex&&(t.latex=t.latex)):t.latex=void 0,e.jsonSerializationOptions.metadata.includes("wikidata")){if(void 0===t.wikidata){const n=e.lookupSymbol(i)?.wikidata;void 0!==n&&(t.wikidata=n)}}else t.wikidata=void 0;return void 0===t.latex&&void 0===t.wikidata&&e.jsonSerializationOptions.shorthands.includes("symbol")?i:void 0!==t.latex&&void 0!==t.wikidata?{sym:i,latex:t.latex,wikidata:t.wikidata}:void 0!==t.latex?{sym:i,latex:t.latex}:void 0!==t.wikidata?{sym:i,wikidata:t.wikidata}:{sym:i}}function nr(e,i,t){t={...t},e.jsonSerializationOptions.metadata.includes("latex")||(t.latex=void 0);const n=void 0===t.latex&&void 0===t.wikidata&&!e.jsonSerializationOptions.metadata.includes("latex")&&e.jsonSerializationOptions.shorthands.includes("number");let r="";if(i instanceof Ze){if(i.isNaN())r="NaN";else if(i.isFinite()){if(n&&Bn(i))return i.toNumber();if(i.isInteger()&&i.e<i.precision()+4)r=i.toFixed(0);else{const t=e.jsonSerializationOptions.precision;if(r=rr(e,"max"===t?i.toString():i.toPrecision("auto"===t?e.precision:t)),n){const e=i.toNumber();if(e.toString()===r)return e}}}else r=i.isPositive()?"+Infinity":"-Infinity";return e.jsonSerializationOptions.metadata.includes("latex")&&(t.latex=t.latex??e.serialize({num:r})),void 0!==t.latex?{num:r,latex:t.latex}:n?r:{num:r}}if(i instanceof je.exports.Complex)return i.isInfinite()?tr(e,"ComplexInfinity",t):i.isNaN()?(r="NaN",e.jsonSerializationOptions.metadata.includes("latex")&&(t.latex=t.latex??e.serialize({num:r})),void 0!==t.latex?{num:r,latex:t.latex}:{num:r}):ir(e,"Complex",[e.number(i.re),e.number(i.im)],{...t,wikidata:"Q11567"});if(an(i))return n&&e.jsonSerializationOptions.shorthands.includes("function")&&un(i)?["Rational",i[0],i[1]]:ir(e,"Rational",[e.number(i[0]),e.number(i[1])],{...t});if(Number.isNaN(i))r="NaN";else if(Number.isFinite(i)){if(n)return i;r=rr(e,i.toString())}else r=i>0?"+Infinity":"-Infinity";return e.jsonSerializationOptions.metadata.includes("latex")&&(t.latex=t.latex??e.serialize({num:r})),void 0!==t.latex?{num:r,latex:t.latex}:{num:r}}function rr(e,i){if(!e.jsonSerializationOptions.repeatingDecimals)return i;let[t,n,r,s]=i.match(/^(.*)\.([0-9]+)([e|E][-+]?[0-9]+)?$/)??[];if(!r)return i.toLowerCase();const o=r[r.length-1];r=r.slice(0,-1);let a="";for(let e=0;e<r.length-16;e++){a=r.substring(0,e);for(let t=0;t<=16;t++){const u=r.substring(e,e+t+1),l=Math.floor((r.length-a.length)/u.length);if(l<3)break;if((a+u.repeat(l+1)).startsWith(r))return"0"===u?"0"===o?n+"."+a+(s??""):i:n+"."+a+"("+u+")"+(s??"")}}for(r+=o;r.endsWith("0");)r=r.slice(0,-1);return s?`${n}.${r}${s.toLowerCase()}`:`${n}.${r}`}class sr extends zn{constructor(e,i,t){t??(t={}),super(e,t.metadata),this._value=new Map;const n=t.canonical??!0;for(const t of Object.keys(i))this._value.set(t,e.box(i[t],{canonical:n}));e._register(this)}unbind(){for(const[e,i]of this._value)i.unbind()}get hash(){let e=en("Dictionary");for(const[i,t]of this._value)e^=en(i)^t.hash;return e}get complexity(){return 97}get head(){return"Dictionary"}get isPure(){return!1}getKey(e){return this._value.get(e)}hasKey(e){return this._value.has(e)}get keys(){return this._value.keys()}get keysCount(){return this._value.size}has(e){for(const[i,t]of this._value)if(t.has(e))return!0;return!1}get domain(){const e=["Dictionary"];for(const[i,t]of this._value)e.push(["Tuple",i,t.domain]);return this.engine.domain(e)}get json(){if(this.engine.jsonSerializationOptions.shorthands.includes("dictionary")){const e={};for(const i of this._value.keys())e[i]=this._value.get(i).json;return{dict:e}}const e=[];for(const i of this._value.keys())e.push(this.engine._fn("KeyValuePair",[this.engine.string(i),this._value.get(i)]));return ir(this.engine,"Dictionary",e,{latex:this._latex})}isSame(e){if(this===e)return!0;if(!(e instanceof sr))return!1;if(this._value.size!==e._value.size)return!1;for(const[i,t]of this._value){const n=e.getKey(i);if(!n||!t.isSame(n))return!1}return!0}match(e,i){if(!(e instanceof sr))return null;if(this._value.size!==e._value.size)return null;let t={};for(const[i,n]of this._value){const r=e.getKey(i);if(!r)return null;const s=n.match(r);if(null===s)return null;t={...t,...s}}return t}isEqual(e){if(this===e)return!0;if(!(e instanceof sr))return!1;if(!e.keys||this._value.size!==e._value.size)return!1;for(const[i,t]of this._value){const n=e.getKey(i);if(!n||!t.isEqual(n))return!1}return!0}apply(e,i){const t={};for(const i of this.keys)t[i]=this.engine.box(e(this.getKey(i)));return i?this.engine.fn(i,[{dict:t}]):new sr(this.engine,t)}evaluate(e){return this.apply((i=>i.evaluate(e)??i))}get isCanonical(){return this._isCanonical}set isCanonical(e){this._isCanonical=e}get canonical(){if(this.isCanonical)return this;const e=this.apply((e=>e.canonical));return e.isCanonical=!0,e}simplify(e){return e?.recursive??1?this.apply((i=>i.simplify(e)??i)):this}N(e){return this.apply((i=>i.N(e)))}replace(e,i){let t=0;const n={};for(const r of this.keys){const s=this.getKey(r),o=s.replace(e,i);null!==o&&(t+=1),n[r]=o??s}return 0===t?null:new sr(this.engine,n)}subs(e,i){const t={};for(const n of this.keys)t[n]=this.getKey(n).subs(e,i);return new sr(this.engine,t,i)}}const or=[];function ar(e,i,t){if(i.length===t)return i;const n=[...i.slice(0,t)];let r=Math.min(t,i.length);for(;r<t;)n.push(e.error("missing")),r+=1;for(;r<i.length;)n.push(e.error("unexpected-argument",i[r])),r+=1;return n}function ur(e,i,t){if(!e.strict)return i;let n;if(void 0===t)n=i;else{n=[];for(let r=0;r<=Math.max(t-1,i.length-1);r++)r>t-1?n.push(e.error("unexpected-argument",i[r])):n.push(void 0!==i[r]?e.box(i[r]):e.error(["missing","Number"]))}return n.map((i=>!i.isValid||i.isNumber?i:e.error(["incompatible-domain","Number",i.domain],i)))}function lr(e,i,t){return void 0===t?e.error("unexpected-argument",i):void 0===i?e.error(["missing",t]):i.isValid?i?.domain.isCompatible(t)?i:e.error(["incompatible-domain",t,i.domain],i):i}function cr(e,i,t,n){let r=n.shift();if(void 0===i)return[[...t,e.error("unexpected-argument",r)],n];if(!Array.isArray(i))return r?r.domain.isCompatible(i)?[[...t,r],n]:[[...t,e.error(["incompatible-domain",i,r.domain],r)],n]:[[...t,e.error(["missing",i])],n];const s=i[0];if(void 0===r){let r=!1;if("Union"===s){for(let e=1;e<=i.length-1;e++)if("Nothing"===i[e]){r=!0;break}}else"Maybe"===s&&(r=!0);return r?[[...t,e.symbol("Nothing")],n]:[[...t,e.error(["missing",i])],n]}if("Union"===s){let s=!1;for(let e=1;e<=i.length-1;e++)if(r.domain.isCompatible(i[e])){s=!0;break}return s?[[...t,r],n]:[[...t,e.error(["incompatible-domain",i,r.domain],r)],n]}if("Sequence"===s){const s=i[1];if(!r||!r.domain.isCompatible(s))return[[...t,e.error(["incompatible-domain",s,r.domain],r)],n];let o=!1;const a=[...t,r];for(;!o;)r=n.shift(),r?r.domain.isCompatible(s)?a.push(r):(n.unshift(r),o=!1):o=!1;return[a,n]}return"Maybe"===s?void 0===r||"Nothing"===r.symbol?[[...t,e.symbol("Nothing")],n]:cr(e,i[1],t,[r,...n]):[[...t,r],n]}function hr(e,i,t){if(i.length===t.length&&i.every(((e,i)=>e.domain.isCompatible(t[i]))))return i;const n=[];for(let r=0;r<=t.length-1;r++)n.push(lr(e,i[r],t[r]));for(let r=t.length;r<=i.length-1;r++)n.push(e.error("unexpected-argument",i[r]));return n}function mr(e,i){if(null==i)return e;if(e===i)return e;const t=e.engine,n=t.box(i);return t.costFunction(n)<=1.7*t.costFunction(e)?n:e}class fr extends zn{constructor(e,i,t,n){if(n??(n={}),n.canonical??(n.canonical=!1),super(e,n.metadata),this._scope=e.context,this._head=i,this._ops=t,this._def=n.def??null,n.canonical&&(this._def||(this._def=e.lookupFunction(i,e.context)),this._canonical=this),this._codomain=null,n.canonical){if("string"!=typeof this._head)this._codomain=this._head.domain.codomain;else if(this._def){const i=this._def.signature;"function"==typeof i.codomain?this._codomain=i.codomain(e,this._ops)??null:this._codomain=i.codomain??null}this._codomain||(this._codomain=e.defaultDomain??e.domain("Void"))}else this._codomain=e.domain("Anything");e._register(this)}get hash(){if(void 0!==this._hash)return this._hash;let e=0;for(const i of this._ops)e=e<<1^i.hash|0;return e="string"==typeof this._head?e^en(this._head)|0:e^this._head.hash|0,this._hash=e,e}get isCanonical(){return this._canonical===this}set isCanonical(e){this._canonical=e?this:void 0}get isPure(){if(void 0!==this._isPure)return this._isPure;if(!this.isCanonical)return this._isPure=!1,!1;let e;return void 0!==this.functionDefinition?.pure&&(e=this.functionDefinition.pure),!1!==e&&(e=this._ops.every((e=>e.isPure))),this._isPure=e,e}get json(){return this.isValid&&this._canonical===this?function(e,i,t,n){const r=e.jsonSerializationOptions.exclude;if("Add"===i&&2===t.length&&!r.includes("Subtract")){const i=er(e,t[0],t[1],n)??er(e,t[1],t[0],n);if(i)return i}if("Divide"===i&&2===t.length&&r.includes("Divide"))return ir(e,"Multiply",[t[0],e._fn("Power",[t[1],e._NEGATIVE_ONE])],n);if("Multiply"===i&&!r.includes("Negate")&&-1===Vt(t[0]))return ir(e,"Negate",[e._fn("Multiply",t.slice(1))],n);if("Multiply"===i&&!r.includes("Divide")){const i=new Yn(e,t,{canonical:!1}).asRationalExpression();if("Divide"===i.head)return ir(e,i.head,i.ops,n)}if("Power"===i){if(!r.includes("Exp")&&"ExponentialE"===t[0]?.symbol)return ir(e,"Exp",[t[1]],n);if(null!==t[1]?.numericValue){const i=$t(t[1]);if(2===i&&!r.includes("Square"))return ir(e,"Square",[t[0]],n);if(null!==i&&i<0&&!r.includes("Divide"))return ir(e,"Divide",[e._ONE,-1===i?t[0]:e.pow(t[0],-i)],n);const s=t[1].numericValue;if(!r.includes("Sqrt")&&.5===s)return ir(e,"Sqrt",[t[0]],n);if(!r.includes("Sqrt")&&-.5===s)return ir(e,"Divide",[e._ONE,e._fn("Sqrt",[t[0]])],n);if(an(s)){const i=fn(s),o=gn(s);if(1===i){if(!r.includes("Sqrt")&&2===o)return ir(e,"Sqrt",[t[0]],n);if(!r.includes("Root"))return ir(e,"Root",[t[0],e.number(s[1])],n)}if(-1===i){if(!r.includes("Sqrt")&&2===o)return ir(e,"Divide",[e._ONE,e._fn("Sqrt",[t[0]])],n);if(!r.includes("Root"))return ir(e,"Divide",[e._ONE,e._fn("Root",[t[0],e.number(s[1])])],n)}}}}return ir(e,i,t,n)}(this.engine,this._head,this._ops,{latex:this._latex,wikidata:this._wikidata}):ir(this.engine,this._head,this._ops,{latex:this._latex,wikidata:this._wikidata})}get scope(){return this._scope}get head(){return this._head}get ops(){return this._ops}get nops(){return this._ops.length}get op1(){return this._ops[0]??this.engine.symbol("Nothing")}get op2(){return this._ops[1]??this.engine.symbol("Nothing")}get op3(){return this._ops[2]??this.engine.symbol("Nothing")}get isValid(){return"Error"!==this._head&&!("string"!=typeof this._head&&!this._head.isValid)&&this._ops.every((e=>e.isValid))}get canonical(){return this._canonical||(this._canonical=this.isValid?gr(this.engine,this._head,this._ops):this),this._canonical}*map(e){let i=0;for(;i<this._ops.length;)yield e(this._ops[i++])}subs(e,i){i??(i={}),"canonical"in i||(i.canonical=!0);const t=this._ops.map((t=>t.subs(e,i)));return i.canonical&&t.every((e=>e.isValid))?gr(this.engine,this._head,t):new fr(this.engine,this._head,t,{canonical:!1})}replace(e,i){return on(this,e,i)}has(e){if("string"==typeof this._head)if("string"==typeof e){if(this._head===e)return!0}else if(e.includes(this._head))return!0;for(const i of this._ops)if(i.has(e))return!0;return!1}isSame(e){if(this===e)return!0;if(!(e instanceof fr))return!1;if(this.nops!==e.nops)return!1;if("string"==typeof this.head){if(this.head!==e.head)return!1}else{if("string"==typeof e.head)return!1;if(!e.head||!this.head.isSame(e.head))return!1}const i=this._ops,t=e._ops;for(let e=0;e<i.length;e++)if(!i[e].isSame(t[e]))return!1;return!0}match(e,i){if(!(e instanceof fr))return null;let t={};if("string"==typeof this.head){if(this.head!==e.head)return null}else{if("string"==typeof e.head)return null;{if(!e.head)return null;const n=this.head.match(e.head,i);if(null===n)return null;t={...t,...n}}}const n=this._ops,r=e._ops;for(let e=0;e<n.length;e++){const s=n[e].match(r[e],i);if(null===s)return null;t={...t,...s}}return t}unbind(){this._value=void 0,this._numericValue=void 0}get wikidata(){if(this.isCanonical)return this._wikidata??this.functionDefinition?.wikidata??void 0}get description(){if(!this.isCanonical)return;const e=this.functionDefinition;return e?e.description?"string"==typeof e.description?[e.description]:e.description:void 0:[]}get url(){return this.isCanonical?this.functionDefinition?.url??void 0:""}get complexity(){if(this.isCanonical)return this.functionDefinition?.complexity??jn}get functionDefinition(){if(this.isCanonical)return null!==this._def?this._def:void 0}bind(e){}get value(){if(this.isCanonical&&this.isPure)return this._value||(this._value=this.evaluate()),this._value}isEqual(e){const i=kn(this,e);return 0===i||void 0===i&&this.isSame(e)}isLess(e){const i=kn(this,e);if(void 0!==i)return i<0}isLessEqual(e){const i=kn(this,e);if(void 0!==i)return i<=0}isGreater(e){const i=kn(this,e);if(void 0!==i)return i>0}isGreaterEqual(e){const i=kn(this,e);if(void 0!==i)return i>=0}get isZero(){const e=this.sgn;return null!==e&&("number"==typeof e?0===e:void 0)}get isNotZero(){const e=this.sgn;return null!==e&&("number"==typeof e?0!==e:void 0)}get isOne(){return this.isEqual(this.engine._ONE)}get isNegativeOne(){return this.isEqual(this.engine._NEGATIVE_ONE)}get isPositive(){const e=this.sgn;return null!==e&&("number"==typeof e?e>0:void 0)}get isNonPositive(){const e=this.sgn;return null!==e&&("number"==typeof e?e<=0:void 0)}get isNegative(){const e=this.sgn;return null!==e&&("number"==typeof e?e<0:void 0)}get isNonNegative(){const e=this.sgn;return null!==e&&("number"==typeof e?e>=0:void 0)}get isNumber(){return this.domain.isCompatible("Number")}get isInteger(){return this.domain.isCompatible("Integer")}get isRational(){return this.domain.isCompatible("RationalNumber")}get isAlgebraic(){return this.domain.isCompatible("AlgebraicNumber")}get isReal(){return this.domain.isCompatible("RealNumber")}get isExtendedReal(){return this.domain.isCompatible("ExtendedRealNumber")}get isComplex(){return this.domain.isCompatible("ComplexNumber")}get isImaginary(){return this.domain.isCompatible("ImaginaryNumber")}get sgn(){if(!this.isCanonical)return;const e=this.head;if("Negate"===e){const e=this._ops[0]?.sgn;if(void 0===e)return;return null===e?null:0===e?0:e>0?-1:1}if("Multiply"===e){const e=this._ops.reduce(((e,i)=>e*(i.sgn??NaN)),1);return isNaN(e)?null:e>0?1:e<0?-1:0}if("Add"===e){let e=0,i=0,t=0;const n=this._ops.length;for(const n of this._ops){const r=n.sgn;if(null==r)break;0===r&&(t+=1),r>0&&(e+=1),r<0&&(i+=1)}return t===n?0:e===n?1:i===n?-1:null}if("Divide"===e){const e=this._ops[0]?.sgn,i=this._ops[1]?.sgn;return null===e||null===i||void 0===e||void 0===i?null:0===e?0:e>0&&i>0||e<0&&i<0?1:-1}if("Square"===e)return this._ops[0]?.isImaginary?-1:this._ops[0]?.isZero?0:1;if("Abs"===e)return this._ops[0]?.isZero?0:1;if("Sqrt"===e)return this._ops[0]?.isZero?0:this._ops[0]?.isImaginary?null:1;const i=Vt(this.N());return null!==i?0===i?0:i<0?-1:1:void 0}get domain(){return this._codomain}simplify(e){if(!this.isValid)return this;if(!this.isCanonical){const i=this.canonical;return i.isCanonical&&i.isValid?i.simplify(e):this}const i=this.functionDefinition,t=dr(this._ops,i?.hold??"none",i?.associative?i.name:"",(i=>i.simplify(e)));if("string"!=typeof this._head){const i=pr(this._head,t);return"string"!=typeof i.head?i:i.simplify(e)}let n;if(i)if(i.inert)n=t[0]?.canonical??this;else{const e=i.signature;e?.simplify&&(n=e.simplify(this.engine,t))}n=n?mr(this.engine.fn(this._head,t),n):this.engine.fn(this._head,t),n=mr(this,n);const r=e?.rules??this.engine.cache("standard-simplification-rules",(()=>rn(this.engine,or)),(e=>{for(const[i,t,n,r]of e)i.unbind(),t.unbind();return e}));let s=0,o=!1;do{const e=n.replace(r);null!==e?(n=mr(e,n),n===e&&(o=!0)):o=!0,s+=1}while(!o&&s<this.engine.iterationLimit);return mr(this,n)}evaluate(e){if(!this.isValid)return this;if(!this.isCanonical){const i=this.canonical;return i.isCanonical&&i.isValid?i.evaluate(e):this}const i=this.functionDefinition,t=dr(this._ops,i?.hold??"none",i?.associative?i.name:"",(i=>i.evaluate(e)));if("string"!=typeof this._head){const i=pr(this._head,t);return"string"!=typeof i.head?i:i.evaluate(e)}if(!i)return this.engine.fn(this._head,t);if(i.inert)return t[0]??this;const n=i.signature;return n&&n.evaluate?"function"!=typeof n.evaluate?pr(n.evaluate,t):n.evaluate(this.engine,t)??this.engine.fn(this._head,t):this.engine.fn(this._head,t)}N(e){if(this._numericValue)return this._numericValue;if(this.engine.strict&&!this.isValid)return this;if(!this.isCanonical){const i=this.canonical;return i.isCanonical&&i.isValid?i.N(e):this}const i=this.functionDefinition,t=dr(this._ops,i?.hold??"none",i?.associative?i.name:"",(i=>i.N(e)));if("string"!=typeof this._head){const i=pr(this._head,t);return"string"!=typeof i.head?i:i.N(e)}if(!i)return this.engine.fn(this._head,t);if(i.inert)return t[0]??this;const n=i.signature;let r=n?.N?.(this.engine,t)??this.engine.fn(this._head,t).evaluate();const s=r.numericValue;return null!==s&&(!Xt(this.engine)&&s instanceof He?r=this.engine._NAN:!Jt(this.engine)&&s instanceof Ze&&(r=this.engine.number(s.toNumber()))),this.isPure&&(this._numericValue=r),r}solve(e){return 1!==e.length?null:On(this.simplify(),e[0])}}function gr(e,i,t,n){if("string"!=typeof i&&(i=i.evaluate().symbol??i),"string"==typeof i){const r=function(e,i,t,n){let r=[];if("Add"===i||"Multiply"===i)r=ur(e,En(In(e.canonical(t)),i));else if("Negate"===i||"Square"===i||"Sqrt"===i)r=ur(e,In(e.canonical(t)),1);else{if("Divide"!==i&&"Power"!==i)return null;r=ur(e,In(e.canonical(t)),2)}if(!r.every((e=>e.isValid)))return new fr(e,i,r,{metadata:n,canonical:!1});if("Add"===i)return e.add(r,n);if("Negate"===i)return e.neg(r[0]??e.error("missing"),n);if("Multiply"===i)return e.mul(r,n);if("Divide"===i)return e.div(r[0],r[1],n);if("Power"===i)return e.pow(r[0],r[1],n);if("Square"===i)return e.pow(r[0],e.number(2),n);if("Sqrt"===i){const i=r[0].canonical;return an(i.numericValue)?new fr(e,"Sqrt",[i],{metadata:n,canonical:!0}):e.pow(i,e._HALF,n)}return null}(e,i,t,n);if(r)return r}else if(!i.isValid)return new fr(e,i,t.map((i=>e.box(i,{canonical:!1}))),{metadata:n,canonical:!1});const r=e.lookupFunction(i,e.context);if("string"!=typeof i||!r)return new fr(e,i,In(t.map((i=>e.box(i)))),{metadata:n,canonical:!0});let s=[];for(let i=0;i<t.length;i++)if(br(r.hold,t.length-1,i))s.push(e.box(t[i]));else{const n=e.box(t[i],{canonical:!1});"ReleaseHold"===n.head?s.push(n.op1.canonical):s.push(n)}const o=r.signature;if(o.canonical){try{const i=o.canonical(e,s);if(i)return i}catch(e){}return new fr(e,i,s,{metadata:n,canonical:!1})}if(s=In(s),r.associative&&(s=En(s,i)),!s.every((e=>e.isValid)))return new fr(e,i,s,{metadata:n,canonical:!1});if(s=function(e,i,t){const n=e.engine;if(!n.strict)return i;const r=i.map((e=>e.domain)),s=n.domain(["Function",...r,"Anything"]);if(e.isCompatible(s))return null;const o=e.domainArgs.slice(0,-1),a=Math.max(o.length,r.length);let u=[],l=[...i];for(let e=0;e<=a-1;e++)[u,l]=cr(n,o[e],u,l);for(;u.length>0&&"Nothing"===u[u.length-1].symbol;)u.pop();return u}(o.domain,s)??s,!s.every((e=>e.isValid)))return new fr(e,i,s,{metadata:n,canonical:!1});if(1===s.length&&s[0].head===i){if(r.involution)return s[0].op1;r.idempotent&&(s=s[0].ops)}return s.length>1&&!0===r.commutative&&(s=s.sort(Qn)),new fr(e,i,s,{metadata:n,def:r,canonical:!0})}function pr(e,i){if("Lambda"!==e.head)return e.engine._fn(e.evaluate(),i);const t={__:e.engine.tuple(i),"_#":e.engine.number(i.length)};let n=1;for(const e of i)t["_"+n++]=e;t._=t._1;const r=this.context;this.context=e.scope??null;const s=e.subs(t).evaluate();return this.context=r,s}function dr(e,i,t,n){if(0===e.length)return[];if(e=En(e,t),"all"===i)return e;if("none"===i){const i=[];for(const t of e){const e=t.head;if("Hold"===e)i.push(t);else{const r="ReleaseHold"===e?t.op1:t;if(r){const e=n(r);null!==e&&i.push(e)}}}return En(i,t)}const r=[];for(let t=0;t<e.length;t++)if("Hold"===e[t].head)r.push(e[t]);else{let s;if("ReleaseHold"===e[t].head?s=e[t].op1:br(i,e.length-1,t)?s=e[t]:r.push(e[t]),s){const e=n(s);null!==e&&r.push(e)}}return En(r,t)}function br(e,i,t){return"all"!==e&&("none"===e||("first"===e?0!==t:"rest"===e?0===t:"last"===e?t!==i:"most"===e&&t===i))}function yr(e){if(!Number.isInteger(e)||!Number.isFinite(e)||Number.isNaN(e)||e<=1)return!1;if(e<=7919)return qt.has(e);for(const i of qt)if(e%i==0)return!1;return e>=0x3ffffffffffe5?!!function(e,i){let t=0,n=e-1;for(;n%2==0;)n/=2,++t;e:do{let i=Math.pow(2+Math.floor(Math.random()*(e-3)),n)%e;if(1!==i&&i!==e-1){for(let n=t-1;n--;){if(i=i*i%e,1===i)return!1;if(i===e-1)continue e}return!1}}while(--i);return!0}(e,30)&&void 0:e===function(e){if(1===e)return 1;if(e%2==0)return 2;if(e%3==0)return 3;if(e%5==0)return 5;const i=Math.floor(Math.sqrt(e));let t=7;for(;t<=i;){if(e%t==0)return t;if(e%(t+4)==0)return t+4;if(e%(t+6)==0)return t+6;if(e%(t+10)==0)return t+10;if(e%(t+12)==0)return t+12;if(e%(t+16)==0)return t+16;if(e%(t+22)==0)return t+22;if(e%(t+24)==0)return t+24;t+=30}return e}(e)}class vr extends zn{constructor(e,i,t){if(super(e,t?.metadata),"number"==typeof i)return this._value=i,void(this._isCanonical=!0);if(an(i)){const[n,r]=i;t?.canonical??1?(this._value=Nr(e,i),this._isCanonical=!0):(this._value=i,this._isCanonical=!1)}else this._value=Nr(e,i),this._isCanonical=!0}get hash(){if(void 0!==this._hash)return this._hash;let e=0;return e="number"==typeof this._value?en(this._value.toString()):this._value instanceof je.exports.Complex?en(this._value.re.toString()+" +i "+this._value.im.toString()):this._value instanceof Ze?en(this._value.toString()):en(this._value[0].toString()+" / "+this._value[1].toString()),this._hash=e,e}get head(){return"Number"}get isPure(){return!0}get isExact(){return"number"==typeof this._value?Number.isInteger(this._value):this._value instanceof Ze?this._value.isInteger():this._value instanceof je.exports.Complex?Number.isInteger(this._value.re)&&Number.isInteger(this._value.im):an(this._value)}get isCanonical(){return this._isCanonical}set isCanonical(e){this._isCanonical=e}get complexity(){return 1}get value(){return this}get numericValue(){return this._value}get domain(){return void 0===this._domain&&(this._domain=this.engine.domain(function(e){if("number"==typeof e&&!isNaN(e))return isFinite(e)?Number.isInteger(e)?e>0?"PositiveInteger":e<0?"NegativeInteger":"Integer":e>0?"PositiveNumber":e<0?"NegativeNumber":"RealNumber":"ExtendedRealNumber";if(e instanceof Ze)return e.isNaN()?"Number":e.isFinite()?e.isInteger()?e.isPositive()?"PositiveInteger":e.isNegative()?"NegativeInteger":"Integer":e.isPositive()?"PositiveNumber":e.isNegative()?"NegativeNumber":"RealNumber":"ExtendedRealNumber";if(e instanceof je.exports.Complex)return 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this._value&&"number"==typeof e._value&&this._value===e._value}isEqual(e){if(this===e)return!0;const i=e.N();return i instanceof vr&&0===kn(this.N(),i)}match(e,i){return this.isEqualWithTolerance(e,i?.numericTolerance??0)?{}:null}isEqualWithTolerance(e,i){return e instanceof vr&&0===kn(this,e,i)}isLess(e){const i=kn(this,e);if(void 0!==i)return i<0}isLessEqual(e){const i=kn(this,e);if(void 0!==i)return i<=0}isGreater(e){return e.isLessEqual(this)}isGreaterEqual(e){return e.isLess(this)}get isPositive(){const e=this.sgn;if(null!=e)return e>0}get isNonNegative(){const e=this.sgn;if(null!=e)return e>=0}get isNegative(){const e=this.sgn;if(null!=e)return e<0}get isNonPositive(){const e=this.sgn;if(null!=e)return e<=0}get isZero(){return 0===this._value||(this._value instanceof Ze||this._value instanceof je.exports.Complex)&&this._value.isZero()}get isNotZero(){return"number"==typeof this._value&&0!==this._value||(this._value instanceof Ze?!this._value.isZero():!(this._value instanceof 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isPrime(){return!(!this.isInteger||!this.isFinite||this.isNonPositive||this.isOne||this.isZero)&&("number"==typeof this._value?yr(this._value):this._value instanceof Ze?yr(this._value.toNumber()):void 0)}get isComposite(){return!(!this.isInteger||!this.isFinite||this.isNonPositive||this.isOne||this.isZero)&&("number"==typeof this._value?!yr(this._value):this._value instanceof Ze?!yr(this._value.toNumber()):void 0)}get isInfinity(){return"number"==typeof this._value?!Number.isFinite(this._value)&&!Number.isNaN(this._value):(this._value instanceof Ze||this._value instanceof je.exports.Complex)&&!this._value.isFinite()&&!this._value.isNaN()}get isNaN(){return"number"==typeof this._value?Number.isNaN(this._value):(this._value instanceof Ze&&this._value.isNaN(),this._value instanceof je.exports.Complex&&this._value.isNaN(),!1)}get isFinite(){return!this.isInfinity&&!this.isNaN}get isNumber(){return!0}get isInteger(){return"number"==typeof this._value?Number.isInteger(this._value):this._value instanceof Ze&&this._value.isInteger()}get isRational(){return!!Array.isArray(this._value)||this.isInteger}get isAlgebraic(){if(this.isRational)return!0}get isReal(){return!(!this.isFinite||this._value instanceof je.exports.Complex&&0!==this.engine.chop(this._value.im))}get isExtendedReal(){return this.isInfinity||this.isReal}get isComplex(){return!this.isNaN}get isImaginary(){return this._value instanceof je.exports.Complex}get isExtendedComplex(){return this.isInfinity||!this.isNaN}get canonical(){return this._isCanonical?this:this.engine.number(Nr(this.engine,this._value))}simplify(e){return this.canonical}N(e){if(!Array.isArray(this._value))return this;const i=this.engine,[t,n]=this._value;return"number"!=typeof t||"number"!=typeof n||Jt(i)?i.number(i.bignum(t).div(i.bignum(n))):i.number(t/n)}}function Nr(e,i){if(i instanceof Ze&&Bn(i))return i.toNumber();if(!an(i))return i;if(ln(i=Sn(i))){let[t,n]=i;if(!(t>Number.MIN_SAFE_INTEGER&&t<Number.MAX_SAFE_INTEGER&&n>Number.MIN_SAFE_INTEGER&&n<Number.MAX_SAFE_INTEGER))return n<0&&([t,n]=[-t,-n]),n===BigInt(1)?e.bignum(t):n===BigInt(0)?t===n?NaN:t<0?-1/0:1/0:[t,n];i=[Number(t),Number(n)]}let[t,n]=i;return Number.isNaN(t)||Number.isNaN(n)?NaN:(n<0&&([t,n]=[-t,-n]),1===n?t:0===n?0!==t&&Number.isFinite(t)?t<0?-1/0:1/0:NaN:0===t?t:[t,n])}class _r extends zn{constructor(e,i,t){super(e,t),this._string=i.normalize(),e._register(this)}get hash(){return en("String"+this._string)}get json(){return e=this.engine,i=this._string,e.jsonSerializationOptions.shorthands.includes("string")?`'${i}'`:{str:i};var e,i}get head(){return"String"}get isPure(){return!0}get isCanonical(){return!0}set isCanonical(e){}get domain(){return this.engine.domain("String")}get complexity(){return 19}get string(){return this._string}isEqual(e){return e.string===this._string}isSame(e){return e.string===this._string}match(e,i){return e instanceof 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zn&&t[1]instanceof zn){const[i,r]=[nn(t[0]),nn(t[1])];if(i&&r)return e.number([i,r],n)}else{const[i,r]=[tn(e,t[0]),tn(e,t[1])];if(i&&r)return e.number([i,r],n)}i="Divide"}if("Complex"===i){if(1===t.length){const i=kr(e,t[0],n),r=Vt(i);return null!==r&&0!==r?e.number(e.complex(0,r),n):e.mul([i,e._I])}if(2===t.length){const i=kr(e,t[0],n),r=kr(e,t[1],n),s=Vt(i),o=Vt(r);return null!==o&&null!==s?0===o&&0===s?e._ZERO:null!==o&&0!==o?e.number(e.complex(s,o),n):i:e.add([i,e.mul([r,e._I])],n.metadata)}}if("Negate"===i&&1===t.length){const i=t[0];if("number"==typeof i)return e.number(-i,n);if(i instanceof Ze)return e.number(i.neg(),n);const r=e.box(i,n).numericValue;if(null!==r){if("number"==typeof r)return e.number(-r,n);if(r instanceof Ze)return e.number(r.neg(),n);if(r instanceof je.exports.Complex)return e.number(r.neg());if(an(r))return e.number(dn(r))}}if("Dictionary"===i){const i={};for(const n of t){const 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e.number(i);if("string"==typeof i)return i.startsWith("'")&&i.endsWith("'")?new _r(e,i.slice(1,-1)):/^[+-]?[0-9]/.test(i)?e.number(i):e.symbol(i,t);if("object"==typeof i){const n={latex:i.latex,wikidata:i.wikidata};if("dict"in i)return new sr(e,i.dict,{canonical:!0,metadata:n});if("fn"in i)return"string"==typeof i.fn[0]?wr(e,i.fn[0],i.fn.slice(1),t):new fr(e,kr(e,i.fn[0],t),i.fn.slice(1).map((i=>kr(e,i,t))),{metadata:n});if("str"in i)return new _r(e,i.str,n);if("sym"in i)return e.symbol(i.sym,t);if("num"in i)return e.number(i,t)}return e.symbol("Undefined")}function Er(e){if("string"==typeof e)return e;if(e instanceof zn)return e.string??e.symbol??e.toString();if("object"==typeof e){if("str"in e)return e.str;if("fn"in e&&"String"===e.fn[0]&&"string"==typeof e.fn[1])return e.fn[1]}return Array.isArray(e)&&"String"===e[0]&&"string"==typeof e[1]?e[1]:null}class 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r=0;r<this._terms.length;r++)if(null===this._terms[r].term.numericValue&&i===this._terms[r].term.hash&&e.isSame(this._terms[r].term)){this._terms[r].coef=Nn(this._terms[r].coef,t),n=!0;break}}else for(let i=0;i<this._terms.length;i++)if(null===this._terms[i].term.numericValue&&e.isSame(this._terms[i].term)){this._terms[i].coef=Nn(this._terms[i].coef,t),n=!0;break}n||this._terms.push({term:e,coef:t})}terms(e){const i=this.engine;if(this._naNCount>0)return[i._NAN];if(0!==this._imaginary&&!Xt(i))return[i._NAN];if(this._posInfinityCount>0&&this._negInfinityCount>0)return[i._NAN];if(this._posInfinityCount>0)return[i._POSITIVE_INFINITY];if(this._negInfinityCount>0)return[i._NEGATIVE_INFINITY];const t=[];for(const{coef:e,term:n}of this._terms)cn(e)||(hn(e)?t.push(n):mn(e)?t.push(i.neg(n)):1===gn(e)?t.push(i.mul([i.number(e[0]),n])):1===fn(e)?t.push(i.div(n,i.number(e[1]))):t.push(i.mul([i.number(e),n])));if("numeric"===e)if(Jt(this.engine)){let 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i;if(n.isExact)return}switch(t){case"Arccos":return Yr(n,Math.acos,(e=>e.acos()),(e=>e.acos()));case"Arccot":return Yr(n,(e=>Math.atan2(1,e)),(i=>Ze.atan2(e._BIGNUM_ONE,i)),(e=>e.inverse().atan()));case"Arccsc":return Yr(n,(e=>Math.asin(1/e)),(i=>e._BIGNUM_ONE.div(i).asin()),(e=>e.inverse().asin()));case"Arcosh":return Yr(n,Math.acosh,(e=>e.acosh()),(e=>e.acosh()));case"Arcoth":return Yr(n,(e=>e),(e=>e.acosh()),(e=>e.acosh()));case"Arcsch":return Yr(n,(e=>Math.log(1/e+Math.sqrt(1/(e*e)+1))),(i=>e._BIGNUM_ONE.div(i.mul(i)).add(e._BIGNUM_ONE).sqrt().add(e._BIGNUM_ONE.div(i)).log()),(e=>e.mul(e).inverse().add(1).sqrt().add(e.inverse()).log()));case"Arcsec":return Yr(n,(e=>Math.acos(1/e)),(i=>e._BIGNUM_ONE.div(i).acos()),(e=>e.inverse().acos()));case"Arcsin":return Yr(n,Math.asin,(e=>e.asin()),(e=>e.asin()));case"Arsech":return Yr(n,(e=>Math.log((1+Math.sqrt(1-e*e))/e)),(i=>e._BIGNUM_ONE.sub(i.mul(i).add(e._BIGNUM_ONE).div(i)).log()),(i=>e.complex(1).sub(i.mul(i)).add(1).div(i).log()));case"Arsinh":return Yr(n,Math.asinh,(e=>e.asinh()),(e=>e.asinh()));case"Arctan":return Yr(n,Math.atan,(e=>e.atan()),(e=>e.atan()));case"Artanh":return Yr(n,Math.atanh,(e=>e.atanh()),(e=>e.atanh()));case"Cos":return Yr(n,Math.cos,(i=>i.toSignificantDigits(e.precision+4).cos().toSignificantDigits(e.precision)),(e=>e.cos()));case"Cosh":return Yr(n,Math.cosh,(e=>e.cosh()),(e=>e.cosh()));case"Cot":return Yr(n,(e=>1/Math.tan(e)),(i=>e._BIGNUM_ONE.div(i.tan())),(e=>e.tan().inverse()));case"Coth":return Yr(n,(e=>1/Math.tanh(e)),(i=>e._BIGNUM_ONE.div(i.tanh())),(e=>e.tanh().inverse()));case"Csc":return Yr(n,(e=>1/Math.sin(e)),(i=>e._BIGNUM_ONE.div(i.sin())),(e=>e.sin().inverse()));case"Csch":return Yr(n,(e=>1/Math.sinh(e)),(i=>e._BIGNUM_ONE.div(i.sinh())),(e=>e.sinh().inverse()));case"Sec":return Yr(n,(e=>1/Math.cos(e)),(i=>e._BIGNUM_ONE.div(i.cos())),(e=>e.cos().inverse()));case"Sech":return Yr(n,(e=>1/Math.cosh(e)),(i=>e._BIGNUM_ONE.div(i.cosh())),(e=>e.cosh().inverse()));case"Sin":return Yr(n,Math.sin,(i=>i.toSignificantDigits(e.precision+4).sin().toSignificantDigits(e.precision)),(e=>e.sin()));case"Sinh":return Yr(n,Math.sinh,(e=>e.sinh()),(e=>e.sinh()));case"Tan":return Yr(n,Math.tan,(i=>i.toSignificantDigits(e.precision+4).tan().toSignificantDigits(e.precision)),(e=>e.tan()));case"Tanh":return Yr(n,Math.tanh,(e=>e.tanh()),(e=>e.tanh()))}}class Ps{constructor(e,i,t){if(!e.context)throw Error("No context available");this.name=i,this.wikidata=t.wikidata,this.description=t.description,this.url=t.url,this._engine=e,this.scope=e.context,this.name=i,this._flags=t.flags?Rs(t.flags):void 0,this._domain=t.domain?e.domain(t.domain):void 0,this.constant=t.constant??!1,this.holdUntil=t.holdUntil??"simplify",this.constant?(this._defValue=t.value,this._value=null):(t.value?jt(t.value)?this._value=e.parse(t.value)??e.symbol("Undefined"):"function"==typeof t.value?this._value=e.box(t.value(e)??"Undefined"):t.value instanceof zn?this._value=t.value:this._value=e.box(t.value):this._value=void 0,this._value||!this._domain||t.flags||(this._flags=zs(this._domain)))}reset(){this.constant&&(this._value=null)}get value(){if(null===this._value){const e=this._engine;if(jt(this._defValue)?this._value=e.parse(this._defValue)??e.symbol("Undefined"):"function"==typeof this._defValue?this._value=e.box(this._defValue(e)??"Undefined"):this._defValue?this._value=e.box(this._defValue):this._value=void 0,this._value?.numericValue){const i=this._value.numericValue;!Jt(e)&&i instanceof Ze?this._value=e.number(i.toNumber()):!Xt(e)&&i instanceof He&&(this._value=e._NAN)}}return this._value??void 0}set value(e){if(this.constant)throw Error(`The value of the constant "${this.name}" cannot be changed`);if("number"==typeof e)"number"==typeof this._value?.numericValue?this._value._value=e:this._value=this._engine.number(e);else if(e){const i=this._engine.box(e);!this._domain||i.domain.isCompatible(this._domain)?this._value=i:this._value=void 0}else this._value=void 0;void 0!==this._value?this._flags=void 0:this._flags=zs(this.domain)}get domain(){return this._domain??this._value?.domain??void 0}set domain(e){if(this.constant)throw Error(`The domain of the constant "${this.name}" cannot be changed`);if(!e)return this._defValue=void 0,this._value=void 0,this._flags=void 0,void(this._domain=void 0);if(e=this._engine.domain(e),this._domain?.isNumeric){if(!e.isNumeric)throw Error("Can't change from a numeric domain to a non-numeric one");return this._domain=e,void(this._value||(this._flags={...this._flags??{},...zs(e)}))}if(this._domain)throw Error("Can't change a non-numeric domain");this._flags=void 0,this._domain=e,!this._value&&e.isNumeric&&(this._flags={...this._flags??{},...zs(e)})}get number(){return this.value?.isNumber??this._flags?.number}set number(e){this.updateFlags({number:e})}get integer(){return this.value?.isInteger??this._flags?.integer}set integer(e){this.updateFlags({integer:e})}get rational(){return this.value?.isRational??this._flags?.rational}set rational(e){this.updateFlags({rational:e})}get algebraic(){return this.value?.isAlgebraic??this._flags?.algebraic}set algebraic(e){this.updateFlags({algebraic:e})}get real(){return this.value?.isReal??this._flags?.real}set real(e){this.updateFlags({real:e})}get extendedReal(){return this.value?.isExtendedReal??this._flags?.extendedReal}set extendedReal(e){this.updateFlags({extendedReal:e})}get complex(){return this.value?.isComplex??this._flags?.complex}set complex(e){this.updateFlags({complex:e})}get extendedComplex(){return this.value?.isExtendedComplex??this._flags?.extendedComplex}set extendedComplex(e){this.updateFlags({extendedComplex:e})}get imaginary(){return this.value?.isImaginary??this._flags?.imaginary}set imaginary(e){this.updateFlags({imaginary:e})}get positive(){return this.value?.isPositive??this._flags?.positive}set positive(e){this.updateFlags({positive:e})}get nonPositive(){return this.value?.isNonPositive??this._flags?.nonPositive}set nonPositive(e){this.updateFlags({nonPositive:e})}get negative(){return this.value?.isNegative??this._flags?.negative}set negative(e){this.updateFlags({negative:e})}get nonNegative(){return this.value?.isNonNegative??this._flags?.nonNegative}set nonNegative(e){this.updateFlags({nonNegative:e})}get zero(){return this.value?.isZero??this._flags?.zero}set zero(e){this.updateFlags({zero:e})}get notZero(){return this.value?.isNotZero??this._flags?.notZero}set notZero(e){this.updateFlags({notZero:e})}get one(){return this.value?.isOne??this._flags?.one}set one(e){this.updateFlags({one:e})}get negativeOne(){return this.value?.isNegativeOne??this._flags?.negativeOne}set negativeOne(e){this.updateFlags({negativeOne:e})}get infinity(){return this.value?.isInfinity??this._flags?.infinity}set infinity(e){this.updateFlags({infinity:e})}get finite(){return this.value?.isFinite??this._flags?.finite}set finite(e){this.updateFlags({finite:e})}get NaN(){return this.value?.isNaN??this._flags?.NaN}set NaN(e){this.updateFlags({NaN:e})}get even(){return this.value?.isEven??this._flags?.even}set even(e){this.updateFlags({even:e})}get odd(){return this.value?.isOdd??this._flags?.odd}set odd(e){this.updateFlags({odd:e})}get prime(){const e=this._value;return e?!(!e.isInteger||e.isNonPositive)&&yr(Vt(e)??NaN):this._flags?.prime}set prime(e){this.updateFlags({prime:e})}get composite(){const e=this._value;return e?!(!e.isInteger||e.isNonPositive||yr(Vt(e)??NaN)):this._flags?.composite}set composite(e){this.updateFlags({composite:e})}updateFlags(e){if(this.constant)throw Error("The flags of constant cannot be changed");if(!1===this.domain?.isNumeric)throw Error("Flags only apply to numeric domains");let i=0,t=!0;for(const n in Object.keys(e))if(i+=1,this._value&&void 0!==e[n])switch(n){case"number":t=this._value.isNumber===e.number;break;case"integer":t=this._value.isInteger===e.integer;break;case"rational":t=this._value.isRational===e.rational;break;case"algebraic":t=this._value.isAlgebraic===e.algebraic;break;case"real":t=this._value.isReal===e.real;break;case"extendedReal":t=this._value.isExtendedReal===e.extendedReal;break;case"complex":t=this._value.isComplex===e.complex;break;case"extendedComplex":t=this._value.isExtendedComplex===e.extendedComplex;break;case"imaginary":t=this._value.isImaginary===e.imaginary;break;case"positive":t=this._value.isPositive===e.positive;break;case"nonPositive":t=this._value.isNonPositive===e.nonPositive;break;case"negative":t=this._value.isNegative===e.negative;break;case"nonNegative":t=this._value.isNonNegative===e.nonNegative;break;case"zero":t=this._value.isZero===e.zero;break;case"notZero":t=this._value.isNotZero===e.notZero;break;case"one":t=this._value.isOne===e.one;break;case"negativeOne":t=this._value.isNegativeOne===e.negativeOne;break;case"infinity":t=this._value.isInfinity===e.infinity;break;case"NaN":t=this._value.isNaN===e.NaN;break;case"finite":t=this._value.isFinite===e.finite;break;case"even":t=this._value.isEven===e.even;break;case"odd":t=this._value.isOdd===e.odd;break;case"prime":t=this._value.isPrime===e.prime;break;case"composite":t=this._value.isComposite===e.composite}i>0&&(t||(this._defValue=void 0,this._value=void 0),this._domain=this._engine.domain("Number"),this._flags?this._flags={...this._flags,...Rs(e)}:this._flags=Rs(e))}}function Rs(e){const i={...e};return(e.zero||e.one||e.negativeOne)&&(i.zero=e.zero&&!e.one&&!e.negativeOne,i.notZero=!e.zero||e.one||e.negativeOne,i.one=e.one&&!e.zero&&!e.negativeOne,i.negativeOne=e.negativeOne&&!e.zero&&!e.one,i.infinity=!1,i.NaN=!1,i.finite=!0,i.integer=!0,i.finite=!0,i.infinity=!1,i.NaN=!1,i.even=e.one,i.odd=!e.one,i.prime=!1,i.composite=!1),i.zero&&(i.positive=!1,i.negative=!1,i.nonPositive=!0,i.nonNegative=!0),!0===i.notZero&&(i.imaginary||(i.real=!0),i.zero=!1),i.one&&(i.positive=!0),i.negativeOne&&(i.nonPositive=!0),(i.positive||i.nonNegative)&&(i.negativeOne=!1),i.positive?(i.nonPositive=!1,i.negative=!1,i.nonNegative=!0):i.nonPositive?(i.positive=!1,i.negative=i.notZero,i.nonNegative=!i.zero):i.negative?(i.positive=!1,i.nonPositive=i.notZero,i.nonNegative=!1):i.nonNegative&&(i.positive=i.notZero,i.nonPositive=!i.zero,i.negative=!1),(i.positive||i.negative||i.nonPositive||i.nonNegative)&&(i.number=!0,i.finite?i.real=!0:i.finite||(i.complex=!0),i.imaginary=!1),i.finite&&(i.number=!0,i.complex=!0,i.infinity=!1,i.NaN=!1),i.infinity&&(i.finite=!1,i.NaN=!1),!1===i.infinity&&(i.extendedComplex=!1,i.extendedReal=!1),e.even&&(i.odd=!1),e.odd&&(i.even=!1),i.integer&&(i.rational=!0),i.rational&&(i.algebraic=!0),i.algebraic&&(i.real=!0),i.real&&(i.complex=!0),i.imaginary&&(i.complex=!0),i.complex&&(i.number=!0),i.real&&!1!==i.infinity&&(i.extendedReal=!0),i.complex&&!1!==i.infinity&&(i.extendedComplex=!0),(i.even||i.infinity||i.NaN||i.negative||i.imaginary||!1===i.integer)&&(i.prime=!1),i.number&&i.prime&&(i.composite=!1),i}function zs(e){if(!e)return{};const i={};if(e.isNumeric){const t=e.literal;i.number=!0,"Integer"===t&&(i.integer=!0),"RationalNumber"===t&&(i.rational=!0),"AlgebraicNumber"===t&&(i.algebraic=!0),"TranscendentalNumber"===t&&(i.algebraic=!1,i.real=!0),"ExtendedRealNumber"===t&&(i.extendedReal=!0),"RealNumber"===t&&(i.real=!0),"ImaginaryNumber"===t&&(i.imaginary=!0),"ExtendedComplexNumber"===t&&(i.extendedComplex=!0),"ComplexNumber"===t&&(i.complex=!0),"PositiveNumber"===t&&(i.notZero=!0,i.real=!0,i.positive=!0),"NegativeNumber"===t&&(i.notZero=!0,i.real=!0,i.negative=!0),"NonNegativeNumber"===t&&(i.real=!0,i.positive=!0),"NonPositiveNumber"===t&&(i.real=!0,i.negative=!0),"PositiveInteger"===t&&(i.notZero=!0,i.integer=!0,i.positive=!0),"NegativeNumber"===t&&(i.notZero=!0,i.integer=!0,i.negative=!0),"NonNegativeNumber"===t&&(i.integer=!0,i.positive=!0),"NonPositiveNumber"===t&&(i.integer=!0,i.negative=!0)}else i.number=!1,i.integer=!1,i.rational=!1,i.algebraic=!1,i.real=!1,i.extendedReal=!1,i.complex=!1,i.extendedComplex=!1,i.imaginary=!1,i.positive=!1,i.nonPositive=!1,i.negative=!1,i.nonNegative=!1,i.zero=!1,i.notZero=!1,i.one=!1,i.negativeOne=!1,i.infinity=!1,i.NaN=!1,i.odd=!1,i.even=!1,i.prime=!1,i.composite=!1;return t=Rs(i),Object.fromEntries(Object.entries(t).filter((([e,i])=>void 0!==i)));var t}class Vs{constructor(e,i,t){if(!e.context)throw Error("No context available");this.engine=e,this.scope=e.context;const n=t.idempotent??!1,r=t.involution??!1;if(n&&r)throw Error(`Function Definition "${i}": the 'idempotent' and 'involution' flags are mutually exclusive`);if(this.name=i,this.description=t.description,this.wikidata=t.wikidata,this.threadable=t.threadable??!1,this.associative=t.associative??!1,this.commutative=t.commutative??!1,this.idempotent=n,this.involution=r,this.inert=t.inert??!1,this.numeric=t.numeric??!1,this.pure=t.pure??!0,this.complexity=t.complexity??jn,this.hold=t.hold??"none",this.inert){if(t.hold)throw Error(`Function Definition "${i}": an inert function should not have a hold`);if(this.hold="rest",t.signature){const e=t.signature;if("simplify"in e||"evaluate"in e||"N"in e||"evalDimension"in e||"sgn"in e||"compile"in e)throw Error(`Function Definition "${i}": an inert function should only have 'canonical' or 'codomain' handlers`)}if(this.threadable)throw Error(`Function Definition "${i}": an inert function should not be threadable`);if(this.associative)throw Error(`Function Definition "${i}": an inert function should not be associative`);if(this.commutative)throw Error(`Function Definition "${i}": an inert function should not be commutative`);if(this.idempotent)throw Error(`Function Definition "${i}": an inert function should not be idempotent`);if(this.involution)throw Error(`Function Definition "${i}": an inert function should not be involution`);if(!this.pure)throw Error(`Function Definition "${i}": an inert function should be pure`)}if(t.signature){const n=t.signature,r=n.domain?e.domain(n.domain):t.numeric?e.domain("NumericFunction"):e.domain("Function");if(!r.isValid)throw Error(`Function Definition "${i}": invalid domain ${JSON.stringify(n.domain)}`);const s=n.codomain??r.codomain??(t.numeric?e.domain("Number"):e.domain("Anything"));this.signature={domain:r,codomain:s,canonical:n.canonical,simplify:n.simplify,evaluate:n.evaluate?"function"==typeof n.evaluate?n.evaluate:e.box(n.evaluate,{canonical:!1}):void 0,N:n.N,evalDimension:n.evalDimension,sgn:n.sgn,compile:n.compile}}else t.numeric?this.signature={domain:e.domain("NumericFunction"),codomain:e.domain("Number")}:this.signature={domain:e.domain("Function"),codomain:e.domain("Anything")}}reset(){}}function Ls(e,i,t){return t instanceof Vs?t:new Vs(e,i,t)}function $s(e){return!!e&&"object"==typeof e&&("domain"in e||"value"in e||"constant"in e)}function Bs(e){return!!e&&"object"==typeof e&&("complexity"in e||"numeric"in e||"signature"in e)}function Gs(e){if("all"===e)return Gs(["domains","core","control-structures","logic","collections","relop","numeric","arithmetic","algebra","calculus","combinatorics","linear-algebra","other","physics","polynomials","statistics","trigonometry","dimensions","units"]);"string"==typeof e&&(e=[e]);const i=[];for(const t of e){const e=Zs[t];if(!e)throw Error("Unknown library category "+t);Array.isArray(e)?i.push(...e):i.push(e)}return i}const Zs={algebra:[],arithmetic:ls,calculus:hs,combinatorics:[],"control-structures":[],dimensions:[],domains:[],core:ps,collections:[ks,{Sequence:{signature:{domain:"Function"}}}],"linear-algebra":[],logic:ds,numeric:[],other:[],relop:ws,polynomials:Ss,physics:{"Mu-0":{description:"Vaccum permeability",constant:!0,wikidata:"Q1515261",domain:"RealNumber",value:125663706212e-17}},statistics:[],trigonometry:Es,units:[]};function Us(e){if(!oi(e=e.normalize()))throw Error("Invalid definition name "+e);return e}function js(e,i){var t;if(!e.context)throw Error("No context available");(t=e.context).idTable??(t.idTable=new Map);const n=e.context.idTable;for(let t of Object.keys(i)){const r=i[t];if(t=Us(t),Bs(r)){const i=Ls(e,t,r);if(n.has(t))throw Error(`Duplicate function definition ${t}:\n${JSON.stringify(n.get(t))}\n${JSON.stringify(r)}`);n.set(t,i)}else if($s(r)){const i=new Ps(e,t,r);if(e.strict&&r.wikidata)for(const[e,i]of n)if(i.wikidata===r.wikidata)throw Error(`Duplicate entries with wikidata "${r.wikidata}": "${t}" and "${i.name}"`);if(n.has(t))throw Error(`Duplicate symbol definition "${t}"`);n.set(t,i)}else{const i=new Ps(e,t,{value:e.box(r)});n.set(t,i)}}}function Hs(e){return Number.isInteger(e)&&0!==e?Math.floor(Math.log2(Math.abs(e))/Math.log2(10))+(e>0?1:2):2}const Qs=function e(i){if(i.symbol)return 1;const t=i.numericValue;if(null!==t){if(i.isZero)return 1;if(i.isInteger)return Hs(Vt(i));if(an(t))return un(t)?Hs(t[0])+Hs(t[1])+1:Hs(Number(t[0]))+Hs(Number(t[1]))+1;if(t instanceof He)return Hs(t.re)+Hs(t.im)+1;if(i.isNumber)return 2}const n=i.head;let r=2;return r="string"==typeof n?["Add","Divide"].includes(n)?3:["Subtract","Negate"].includes(n)?4:["Square","Sqrt","Multiply","Root"].includes(n)?5:["Power"].includes(n)?6:["Ln","Exp","Log"].includes(n)?7:8:e(n),r+(i.ops?.reduce(((i,t)=>i+e(t)),0)??0)};class Ws{constructor(e){this._items=e?e instanceof Ws?new Map(e._items):new Map(e):new Map}has(e){for(const i of this._items.keys())if(i.isSame(e))return!0;return!1}get(e){for(const[i,t]of this._items)if(i.isSame(e))return t}clear(){this._items.clear()}set(e,i){for(const t of this._items.keys())if(t.isSame(e))return void this._items.set(t,i);this._items.set(e,i)}delete(e){this._items.delete(e)}[Symbol.iterator](){return this._items.entries()}entries(){return this._items.entries()}}class Ys extends zn{constructor(e,i,t){super(e,t),this._pattern=jt(i)?e.parse(i,{canonical:!1}):e.box(i,{canonical:!1})}get hash(){return en("Pattern")^this._pattern.hash}unbind(){this._pattern.unbind()}get json(){return ir(this.engine,"Pattern",[this._pattern])}get head(){return"Pattern"}get domain(){return this.engine.domain("Pattern")}get isCanonical(){return!0}set isCanonical(e){}isSame(e){return this===e||e instanceof Ys&&this._pattern.isSame(e._pattern)}isEqual(e){return e instanceof Ys&&this._pattern.isEqual(e._pattern)}match(e,i){return function(e,i,t){return Xs(e,i,t.substitution??{},{numericTolerance:t?.numericTolerance??It})||null}(e,this._pattern,{recursive:i?.recursive??!1,numericTolerance:i?.numericTolerance??0,substitution:i?.substitution??{}})}test(e,i){return null!==this.match(e,i)}count(e,i){let t=0;for(const n of e)null!==this.match(n,i)&&(t+=1);return t}subs(e,i){return this._pattern.subs(e,i)}}function Ks(e){if("string"==typeof e)return e.startsWith("_");if(e.symbol?.startsWith("_"))return!0;if(e.ops)return Ks(e.head)||e.ops.some(Ks);if(e.keys)for(const i of e.keys)if(Ks(e.getKey(i)))return!0;return!1}function Js(e,i,t){const n=function(e){const i=e.match(/^(__?_?[a-zA-Z0-9]+)/);return null===i?"":i[1]}(e);return""===n?t:void 0!==t[n]?i.isSame(t[n])?t:null:Ks(i)?null:{...t,[n]:i}}function Xs(e,i,t,n){const r=e.engine;if("Pattern"===i.head)return i.match(e,{substitution:t,...n});if(i instanceof vr)return e instanceof vr?0===n.numericTolerance?i.isSame(e)?t:null:i.isEqualWithTolerance(e,n.numericTolerance)?t:null:null;const s=i.string;if(null!==s)return e.string===s?t:null;const o=i.symbol;if(null!==o)return o.startsWith("_")?Js(o,e,t):o===e.symbol?t:null;if(i.nops!==e.nops)return null;const a=i.keys;if(null!==a){const i=e.keys;if(null===i)return null;for(const e of a){const r=Xs(i[e],a[e],t,n);if(null===r)return null;t=r}return t}if(i.ops){const s=i.head;if("string"==typeof s&&s.startsWith("_"))return Js(s,r.box(e.head),t);let o;if("string"==typeof s&&"string"==typeof e.head){if(s!==e.head)return null;o=r.lookupFunction(s)}else{const i=Xs(r.box(e.head,{canonical:!1}),r.box(s,{canonical:!1}),t,n);if(null===i)return null;t=i}return o?.commutative?function(e,i,t,n){const r=function(e){const i=[],t=(e,n=[])=>{if(0===e.length)i.push(n);else for(let i=0;i<e.length;i++){const r=e.slice(),s=r.splice(i,1);t(r.slice(),n.concat(s))}};return t(e),i}(i.ops);for(const i of r){const r=eo(e.engine,e.ops,i,t,n);if(null!==r)return r}return null}(e,i,t,n):function(e,i,t,n){const r=e.engine,s=[...e.ops];let o={...t},a=0;const u=i.ops;for(;a<i.nops;){const e=u[a],i=e.symbol;if(null!==i)if(i.startsWith("__")){let e=0;if(void 0===u[a+1])e=s.length+1;else{let i=!1;for(;!i&&e<s.length;)i=null!==Xs(s[e],u[a+1],o,n),e+=1;if(!i)return null}if(!i.startsWith("___")&&e<=1)return null;o=Js(i,r.fn("Sequence",s.splice(0,e-1)),o)}else if(i.startsWith("_"))o=Js(i,s.shift(),o);else{const i=Xs(s.shift(),e,o,n);if(null===i)return null;o=i}else{const i=Xs(s.shift(),e,o,n);if(null===i)return null;o=i}if(null===o)return null;a+=1}return o}(e,i,t,n)}return null}function eo(e,i,t,n,r){let s={...n};i=[...i];let o=!1;for(const e of t)if("__"===e.symbol)o=!0;else{let t=null;if(e.symbol?.startsWith("_")){for(let n=0;n<=i.length-1;n++)if(t=Js(e.symbol,i[n],s),null!==t){i.splice(n,1);break}}else for(let n=0;n<=i.length-1;n++)if(t=Xs(i[n],e,s,r),null!==t){i.splice(n,1);break}if(null===t)return null;s=t}return!o&&i.length>0?null:(null!==s&&o&&(s.__=e._fn("Sequence",i)),s)}function io(e){return null!=e&&"constant"in e}class to extends zn{constructor(e,i,t){super(e,t?.metadata),this._name=i,this._scope=t?.canonical?e.context:null,this._def=t?.def??null}get hash(){return void 0===this._hash&&(this._hash=en(this._name)),this._hash}unbind(){this._def?.reset(),this._def=null}get isPure(){return(this.symbolDefinition?.constant&&this.symbolDefinition.value?.isPure)??this.functionDefinition?.pure??!1}get json(){return tr(this.engine,this._name,{latex:this._latex,wikidata:this._wikidata})}get scope(){return this._scope}get isFree(){const e=this._def??this.engine.lookupSymbol(this._name,this._wikidata);return!io(e)||void 0===e.value}get isConstant(){const e=this._def??this.engine.lookupSymbol(this._name,this._wikidata);return!io(e)||e.constant}get isCanonical(){return null!==this._scope}set isCanonical(e){this._scope=e?this.engine.context:null,this._def=null}get canonical(){return this._scope?this:this.engine.box(this._name)}get wikidata(){return this._wikidata??this.baseDefinition?.wikidata??void 0}get description(){if(this.baseDefinition&&this.baseDefinition.description)return"string"==typeof this.baseDefinition.description?[this.baseDefinition.description]:this.baseDefinition.description}get url(){return this.baseDefinition?.url??void 0}get complexity(){return 7}get head(){return"Symbol"}get symbol(){return this._name}get isNothing(){return"Nothing"===this._name}get baseDefinition(){return null===this._def&&this.bind(this._scope),this._def??void 0}get symbolDefinition(){return null===this._def&&this.bind(this._scope),io(this._def)?this._def:void 0}get functionDefinition(){return null===this._def&&this.bind(this._scope),null!=(e=this._def)&&"signature"in e?this._def:void 0;var e}bind(e){if(null===e)return void(this._def=void 0);let i;if(i=this.engine.lookupSymbol(this._name,this._wikidata,e),i?.wikidata&&this._wikidata&&i.wikidata!==this._wikidata&&(i=void 0),i)return this._name=i.name,void(this._def=i);i=this.engine.lookupFunction(this._name,e),i?this._def=i:null!==this.engine.defaultDomain&&(this._def=this.engine.defineSymbol(this._name,{wikidata:this._wikidata,domain:this.engine.defaultDomain}),this._name=this._def.name)}get value(){return this.symbolDefinition?.value}set value(e){if("_"===this._name[0])throw Error(`The value of the wildcard "${this._name}" cannot be changed`);let i;if(this.engine.forget(this._name),void 0!==e){const t=this.engine.box(e);i=t.value??t.evaluate()}if(i?.domain.isCompatible("Function"))this._def=this.engine.defineFunction(this._name,{signature:{domain:i.domain,evaluate:i}});else if(this._def&&io(this._def))this._def.value=i;else{let e=i?.domain;e?.isNumeric&&(e=this.engine.domain("Number")),this._def=this.engine.defineSymbol(this._name,{value:i,domain:e??void 0})}}get domain(){return this.functionDefinition?this.engine.domain("Function"):this.symbolDefinition?.domain??this.engine.defaultDomain??this.engine.domain("Value")}set domain(e){if("_"===this._name[0])throw Error(`The domain of the wildcard "${this._name}" cannot be changed`);const i=this.engine.domain(e);i.isCompatible("Function")?(this.engine.forget(this._name),this._def=this.engine.defineFunction(this._name,{signature:{domain:i}})):io(this._def)?this._def.domain=i:(this.engine.forget(this._name),this._def=this.engine.defineSymbol(this._name,{domain:i}))}get explicitDomain(){return this.functionDefinition?this.engine.domain("Function"):this.symbolDefinition?.domain??void 0}get sgn(){const e=this.value;if(e&&e!==this){const i=e.sgn;if(void 0!==i)return i}const i=this.symbolDefinition;return i?!0===i.zero?0:!0===i.positive?1:!0===i.negative?-1:void 0:null}has(e){return"string"==typeof e?this._name===e:e.includes(this._name)}isSame(e){return this===e||e instanceof to&&this._name===e._name}match(e,i){return e instanceof to&&this._name===e._name?{}:null}isEqual(e){if(!this.isCanonical)return this.canonical.isEqual(e);if(this===(e=e.canonical))return!0;if(null!==e.symbol)return e.symbol===this._name;const i=this.symbolDefinition?.value?.N();if(i)return i.isEqual(e.N());if(e.isZero){if(this.isZero)return!0;if(this.isNotZero)return!1}return!(this.isZero&&e.isNotZero||!(this.engine.ask(["Equal",this,e]).length>0)&&(this.engine.ask(["NotEqual",this,e]).length,1))}isLess(e){if(null!==e.symbol&&e.symbol===this._name)return!1;const i=this.symbolDefinition?.value?.N();if(i)return i.isLess(e.N());if(e.isZero){const e=this.sgn;if(null===e)return!1;if(void 0!==e)return e<0}}isLessEqual(e){if(null!==e.symbol&&e.symbol===this._name)return!0;const i=this.symbolDefinition?.value?.N();if(i)return i.isLessEqual(e.N());if(e.isZero){const e=this.sgn;if(null===e)return!1;if(void 0!==e)return e<=0}return this.isLess(e)||this.isEqual(e)}isGreater(e){if(null!==e.symbol&&e.symbol===this._name)return!1;const i=this.symbolDefinition?.value?.N();if(i)return i.isGreater(e.N());if(e.isZero){const e=this.sgn;if(null===e)return!1;if(void 0!==e)return e>0}}isGreaterEqual(e){if(null!==e.symbol&&e.symbol===this._name)return!0;const i=this.symbolDefinition?.value?.N();if(i)return i.isGreaterEqual(e.N());if(e.isZero){const e=this.sgn;if(null===e)return!1;if(void 0!==e)return e>=0}return this.isGreater(e)||this.isEqual(e)}get isFunction(){return!!this.functionDefinition}get isZero(){return this.symbolDefinition?.zero}get isNotZero(){return this.symbolDefinition?.notZero}get isOne(){return this.symbolDefinition?.one}get isNegativeOne(){return this.symbolDefinition?.negativeOne}get isOdd(){return this.symbolDefinition?.odd}get isEven(){return this.symbolDefinition?.even}get isPrime(){return this.symbolDefinition?.prime}get isComposite(){return this.symbolDefinition?.composite}get isInfinity(){return this.symbolDefinition?.infinity}get isNaN(){return this.symbolDefinition?.NaN}get isPositive(){return this.symbolDefinition?.positive}get isNonPositive(){return this.symbolDefinition?.nonPositive}get isNegative(){return this.symbolDefinition?.negative}get isNonNegative(){return this.symbolDefinition?.nonNegative}get isNumber(){return this.symbolDefinition?.number}get isInteger(){return this.symbolDefinition?.integer}get isRational(){return this.symbolDefinition?.rational}get isAlgebraic(){return this.symbolDefinition?.rational}get isReal(){return this.symbolDefinition?.real}get isExtendedReal(){return this.symbolDefinition?.extendedReal}get isComplex(){return this.symbolDefinition?.complex}get isImaginary(){return this.symbolDefinition?.imaginary}simplify(e){const i=this.symbolDefinition;return"never"!==i?.holdUntil&&"simplify"!==i?.holdUntil||!i.value?e?.rules?this.replace(e.rules)??this:this:i.value.simplify(e)}evaluate(e){const i=this.symbolDefinition;return"N"!==i?.holdUntil?i?.value?.evaluate(e)??this:this}N(e){return this.symbolDefinition?.value?.N(e)??this}replace(e,i){return on(this,e,i)}subs(e,i){return void 0===e[this._name]?i?.canonical?this.canonical:this:this.engine.box(e[this._name],i)}}function no(e,i){const t=e.lookupSymbol(i,void 0,e.context);return"never"===t?.holdUntil&&t.value?t.value:new to(e,i,{canonical:!0,def:t})}class ro{static getStandardLibrary(e="all"){return Gs(e)}constructor(e){if(this._cache={},this._commonSymbols={True:null,False:null,Maybe:null,All:null,Nothing:null,None:null,Undefined:null,Function:null,Pi:null,ImaginaryUnit:null},this._commonNumbers={"-5":null,"-4":null,"-3":null,"-2":null,2:null,3:null,4:null,5:null,6:null,7:null,8:null,9:null,10:null,11:null,12:null,36:null},this._commonDomains={Anything:null,Nothing:null,Boolean:null,MaybeBoolean:null,String:null,Domain:null,Symbol:null,Integer:null,RationalNumber:null,AlgebraicNumber:null,RealNumber:null,ExtendedRealNumber:null,ImaginaryNumber:null,ComplexNumber:null,ExtendedComplexNumber:null,Number:null,PositiveInteger:null,TranscendentalNumber:null,PositiveNumber:null,Function:null,NumericFunction:null,RealFunction:null,TrigonometricFunction:null,LogicOperator:null,Predicate:null,RelationalOperator:null},void 0!==e&&"object"!=typeof e)throw Error("Unexpected argument");this.strict=!0,this._latexDictionary=e?.latexDictionary,this._jsonSerializationOptions={exclude:[],shorthands:["function","symbol","string","dictionary","number"],metadata:[],precision:"max",repeatingDecimals:!0},this._useRawJsonSerializationOptions=!1,this._rawJsonSerializationOptions={exclude:[],shorthands:["function","symbol","string","dictionary","number"],metadata:[],precision:"max",repeatingDecimals:!1},this._stats={highwaterMark:0,symbols:new Set,expressions:new Set},this._defaultDomain=null,this._numericMode=e?.numericMode??"auto",this._precision=Math.max(e?.numericPrecision??100,Math.floor(Et)),this._bignum=Ze.clone({precision:this._precision}),this.tolerance=e?.tolerance??It,this._ZERO=new vr(this,0),this._ONE=new vr(this,1),this._HALF=new vr(this,[1,2]),this._NEGATIVE_ONE=new vr(this,-1),this._I=new vr(this,je.exports.Complex.I),this._NAN=new vr(this,NaN),this._POSITIVE_INFINITY=new vr(this,1/0),this._NEGATIVE_INFINITY=new vr(this,-1/0),this._COMPLEX_INFINITY=new vr(this,je.exports.Complex.INFINITY),this.reset(),this.context={assumptions:new Ws,timeLimit:2,memoryLimit:1,recursionLimit:1024,iterationLimit:1/0};const i=e?.ids??ro.getStandardLibrary();for(const e of i)js(this,e);for(const e of Object.keys(this._commonDomains))this._commonDomains[e]&&!this._commonDomains[e].symbolDefinition?this._commonDomains[e].bind(this.context):this._commonDomains[e]=Or(this,e);for(const e of Object.keys(this._commonSymbols))this._commonSymbols[e]=new to(this,e,{canonical:!0}),this._commonSymbols[e].bind(this.context);if(e?.defaultDomain){const i=this.domain(e.defaultDomain);i.isValid?this._defaultDomain=i:this._defaultDomain=this.domain("ExtendedRealNumber")}else this._defaultDomain=this.domain("ExtendedRealNumber");this.pushScope()}reset(){this._BIGNUM_NEGATIVE_ONE=this.bignum(-1),this._BIGNUM_NAN=this.bignum(NaN),this._BIGNUM_ZERO=this.bignum(0),this._BIGNUM_ONE=this.bignum(1),this._BIGNUM_TWO=this.bignum(2),this._BIGNUM_HALF=this._BIGNUM_ONE.div(this._BIGNUM_TWO),this._BIGNUM_PI=this._BIGNUM_NEGATIVE_ONE.acos();const e=this._stats.symbols.values(),i=this._stats.expressions.values();this._stats.symbols=new Set,this._stats.expressions=new Set;for(const i of e)i.unbind();for(const e of i)e.unbind();for(const e of Object.values(this._commonDomains))e?.unbind();for(const e of Object.values(this._commonSymbols))e?.unbind();let t=this.context;for(;t;){if(t.idTable)for(const[e,i]of t.idTable)i.reset();t=t.parentScope??null}for(const e of Object.keys(this._cache))this._cache[e].value&&(this._cache[e].purge?this._cache[e].value=this._cache[e].purge(this._cache[e].value):delete this._cache[e])}_register(e){this._stats.highwaterMark+=1}_unregister(e){}get stats(){const e=this._stats.expressions;return this._stats.expressions=null,this._stats.expressions=e,{...this._stats}}get precision(){return"machine"===this._numericMode||"complex"===this._numericMode?Math.floor(Et):this._precision}set precision(e){if("machine"===e&&(e=Math.floor(Et)),e!==this._precision){if("number"!=typeof e||e<=0)throw Error('Expected "machine" or a positive number');this._latexSyntax?.updateOptions({precision:e,avoidExponentsInRange:[-6,e]}),this._precision=Math.max(e,Math.floor(Et)),this.jsonSerializationOptions.precision>this._precision&&(this.jsonSerializationOptions={precision:this._precision}),"auto"!==this._numericMode&&"bignum"!==this._numericMode&&this._precision>Math.floor(Et)&&(this._numericMode="auto"),this._bignum=this._bignum.config({precision:this._precision}),this.reset()}}get numericMode(){return this._numericMode}set numericMode(e){if(e!==this._numericMode){if("string"!=typeof e)throw Error("Expected a string");this._numericMode=e,"complex"!==e&&"machine"!==e||(this._precision=Math.floor(Et)),this._latexSyntax&&this.latexSyntax.options.precision>this._precision&&this.latexSyntax.updateOptions({precision:this._precision}),this.jsonSerializationOptions.precision>this._precision&&(this.jsonSerializationOptions={precision:this._precision}),this.reset()}}get timeLimit(){let e=this.context;for(;e;){if(void 0!==e.timeLimit)return e.timeLimit;e=e.parentScope??null}return 2}get iterationLimit(){let e=this.context;for(;e;){if(void 0!==e.iterationLimit)return e.iterationLimit;e=e.parentScope??null}return 1024}get recursionLimit(){let e=this.context;for(;e;){if(void 0!==e.recursionLimit)return e.recursionLimit;e=e.parentScope??null}return 1024}get defaultDomain(){return this._defaultDomain}set defaultDomain(e){if(null===e)this._defaultDomain=null;else{const i=this.domain(e);if(!i.isValid)throw Error("Invalid domain "+e);this._defaultDomain=i}}get tolerance(){return this._tolerance}set tolerance(e){this._tolerance="number"==typeof e&&Number.isFinite(e)?Math.max(e,0):It,this._bignumTolerance=this.bignum(this._tolerance)}bignum(e){return"bigint"==typeof e?new this._bignum(e.toString()):new this._bignum(e)}complex(e,i){return new je.exports.Complex(e,i)}chop(e){return"number"==typeof e&&Math.abs(e)<=this._tolerance||e instanceof Ze&&e.abs().lte(this._bignumTolerance)||e instanceof je.exports.Complex&&Math.abs(e.re)<=this._tolerance&&Math.abs(e.im)<=this._tolerance?0:e}get latexSyntax(){return this._latexSyntax||(this._latexSyntax=new kt({computeEngine:this,dictionary:this._latexDictionary,precision:this.precision,avoidExponentsInRange:[-6,this.precision],onError:e=>{throw Error(e[0].message.toString())}})),this._latexSyntax}static getLatexDictionary(e="all"){return kt.getDictionary(e)}set costFunction(e){"function"!=typeof e&&(this._cost=Qs),this._cost=e}get costFunction(){return this._cost??Qs}lookupSymbol(e,i,t){if(!this.strict){for(t??(t=this.context??void 0);t;){const i=t.idTable?.get(e);if($s(i))return i;t=t.parentScope}return}if("string"!=typeof e)throw Error("Expected a string");if(0===e.length||!this.context)return;const n=t??this.context;if(i)for(t=n;t;){if(t.idTable)for(const[e,n]of t.idTable)if($s(n)&&n.wikidata===i)return n;t=t.parentScope}for(t=n;t;){const i=t.idTable?.get(e);if($s(i))return i;t=t.parentScope}}lookupFunction(e,i){if("string"==typeof e&&this.context)for(i??(i=this.context);i;){const t=i.idTable?.get(e);if(Bs(t))return t;i=i.parentScope}}defineSymbol(e,i){if(!this.context)throw Error("Symbol cannot be defined: no scope available");if(0===e.length||!oi(e))throw Error("Invalid identifier "+e);this.context.idTable||(this.context.idTable=new Map);const t=new Ps(this,e,i);return t.name&&this.context.idTable.set(t.name,t),t}defineFunction(e,i){if(!this.context)throw Error("Function cannot be defined: no scope 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