CortexJS Compute Engine Changelog

0.23.0 2024-01-01

New Features

  • Added ExpandAll function to expand an expression recursively.
  • Added Factor function to factor an expression.
  • Added Together function to combine rational expressions into a single fraction.

Issues Resolved

  • The expression \frac5 7 is now parsed correctly as \frac{5}{7} instead of \frac{5}{}7.
  • Do not sugar non-canonical expression. Previously, ce.parse('\\frac{1}{2}', {canonical: false}) would return Half instead of ['Divide', '1', '2'].
  • #132 Attempting to set a value to 0 with ce.defineSymbol("count", {value: 0}) would fail: the symbol would be undefined.
  • Correctly evaluate power expressions in some cases, for example (\sqrt2 + \sqrt2)^2.
  • Comparison of expressions containing non-exact numbers could fail. For example: 2(13.1+3.1x) and 26.2+6.2x would not be considered equal.


  • Significant improvements to symbolic computation. Now, boxing, canonicalization and evaluation are more consistent and produce more predictable results.
  • Adedd the \neg command, synonym for \lnot -> Not.
  • Relational expressions (inequalities, etc…) are now properly factored.
  • Integers are now factored when simplifying, i.e. 2x = 4x -> x = 2x.

0.22.0 2023-11-13

Breaking Changes

  • Rule Syntax

    The syntax to describe rules has changed. The syntax for a rule was previously a tuple [lhs, rhs, {condition} ]. The new syntax is an object with the properties match, replace and condition. For example:

    • previous syntax: [["Add", "_x", "_x"], ["Multiply", 2, "_x"]]
    • new syntax: {match: ["Add", "_x", "_x"], replace: ["Multiply", 2, "_x"]}

    The condition property is optional, and is either a boxed function or a JavaScript function. For example, to add a condition that cheks that _x is a number literal:

      match: ["Add", "_x", "_x"],
      replace: ["Multiply", 2, "_x"],
      condition: (_x) => _x.numericValue !== null
  • CanonicalForm

    The CanonicalOrder function has been replaced by the more flexible CanonicalForm function. The CanonicalForm function takes an expression and a list of transformations to apply. To apply the same transformations as CanonicalOrder, use:

    ['CanonicalForm', expr, 'Order']

    These canonical forms can also be specified with box() and parse() options:, { canonical: "Order" });
    ce.parse("x^2 + 2x + 1", { canonical: "Order" });

Work In Progress

  • Linear algebra functions: Rank, Shape,Reshape, Flatten, Determinant, Trace, Transpose, ConjugateTranspose, Inverse. See the Linear Algebra reference guide. Some of these function may not yet return correct result in all cases.

New Features

  • Added a expr.print() method as a synonym for console.log(expr.toString()).
  • Added an exact option (false by default) to the expr.match() pattern matching method. When true some additional patterns are automatically recognized, for example, x will match ["Multiply", '_a', 'x'] when exact is false, but not when exact is true.


  • The equation solver used by expr.solve() has been improved and can now solve more equations.
  • The pattern matching engine has been improved and can now match more expressions, including sequences for commutative functions.

0.21.0 2023-11-02

New Features

  • #125 Parse and serialize environemnts, i.e. \begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix} will be parsed as ["Matrix", ["List", ["List", 1, 2], ["List", 3, 4]]].

    A new section on Linear Algebra has some details on the supported formats.

    The linear algebra operations are limited at the moment, but will be expanded in the future.

  • Added IsSame function, which is the function expression corresponding to expr.isSame().

  • Added CanonicalOrder function, which sorts the arguments of commutative functions into canonical order. This is useful to compare two non-canonical expressions for equality.["CanonicalOrder", ["Add", 1, "x"]]).isSame(["CanonicalOrder", ["Add", "x", 1]])
// -> true

Issue Resolved

  • When evaluating a sum (\sum) with a bound that is not a number, return the sum expression instead of an error.

0.20.2 2023-10-31

Issues Resolved

  • Fixed numerical evaluation of integrals and limits when parsed from LaTeX.'\\lim_{x \\to 0} \\frac{\\sin(x)}{x}').value);
// -> 1'\\int_{0}^{2} x^2 dx').value);
// -> 2.6666666666666665

0.20.1 2023-10-31

Issues Resolved

  • Fixed evaluation of functions with multiple arguments
  • Fixed compilation of some function assignments
  • Improved serialization of function assignment

0.20.0 2023-10-30

Breaking Changes

  • Architectural changes: the invisible operator is used to represent the multiplication of two adjacent symbols, i.e. 2x. It was previously handled during parsing, but it is now handled during canonicalization. This allows more complex syntactic structures to be handled correctly, for example f(x) := 2x: previously, the left-hand-side argument would have been parsed as a function application, while in this case it should be interpreted as a function definition.

    A new InvisibleOperator function has been added to support this.

    The applyInvisibleOperator parsing option has been removed. To support custom invisible operators, use the InvisibleOperator function.

Issues Resolved

  • #25 Correctly parse chained relational operators, i.e. a < b <= c
  • #126 Logic operators only accepted up to two arguments.
  • #127 Correctly compile Log with bases other than 10.
  • Correctly parse numbers with repeating patterns but no fractional digits, i.e. 0.(1234)
  • Correctly parse |1+|a|+2|

New Features and Improvements

  • Function assignment can now be done with this syntax: f(x) := 2x+1. This syntax is equivalent to f := x -> 2x+1.
  • Implement the Mod and Congruent function.
  • Correctly parse 11 \bmod 5 (Mod) and 26\equiv 11 \pmod5 (Congruent)
  • Better handle empty argument lists, i.e. f()
  • When a function is used before being declared, infer that the symbol is a function, e.g. f(12) will infer that f is a function (and not a variable f multiplied by 12)
  • When a constant is followed by some parentheses, don’t assume this is a function application, e.g. \pi(3+n) is now parsed as ["Multiply", "Pi", ["Add", 3, "n"]] instead of ["Pi", ["Add", 3, "n"]]
  • Improved parsing of nested lists, sequences and sets.
  • Improved error messages when syntax errors are encountered during LaTeX parsing.
  • When parsing with the canonical option set to false, preserve more closely the original LaTeX syntax.
  • When parsing text strings, convert some LaTeX commands to Unicode, including spacing commands. As a result, ce.parse("\\text{dead\;beef}_{16}") correctly gets evaluated to 3,735,928,559.

0.19.1 2023-10-26

Issues Resolved

  • Assigning a function to an indentifier works correctly now, i.e.
ce.parse("\\operatorname{f} := x \\mapsto 2x").evaluate();

0.19.0 2023-10-25

Breaking Changes

  • The domain property of the function definition signature is deprecated and replaced with the params, optParams, restParam and result properties instead. The domain property is still supported for backward compatibility, but will be removed in a future version.

Issues Resolved

  • When invoking a declared function in a numeric operation, correctly infer the result type.
["Assign", "f", ["Add", "_", 1]]
["Add", ["f", 1], 1]
// -> 3

Previously a domain error was returned, now f is inferred to have a numeric return type.

  • Fixed a runtime error when inverting a fraction, i.e. \frac{3}{4}^{-1}
  • The tangent of π/2 now correctly returns ComplexInfinity.
  • The exact values of some constructible trigonometric operations (e.g. \tan 18\degree = \frac{\sqrt{25-10\sqrt5}}{5}) returned incorrect results. The unit test case was incorrect and did not detect the problem. The unit test case has been fixed and the returned values are now correct.

New Features

  • Implemented Union and Intersection of collections, for example:
["Intersection", ["List", 3, 5, 7], ["List", 2, 5, 9]]
// -> ["Set", 5]

["Union", ["List", 3, 5, 7], ["List", 2, 5, 9]]
// -> ["Set", 3, 5, 7, 2, 9]
  • Parse ranges, for example 1..5 or 1, 3..10. Ranges are collections and can be used anywhere collections can be used.

  • The functions Sum, Product, Min, Max, and the statistics functions (Mean, Median, Variance, etc…) now handle collection arguments: collections:

    • ["Range"], ["Interval"], ["Linspace"] expressions
    • ["List"] or ["Set"] expressions
    • ["Tuple"], ["Pair"], ["Pair"], ["Triple"] expressions
    • ["Sequence"] expressions
  • Most mathematical functions are now threadable, that is their arguments can be collections, for example:

["Sin", ["List", 0, 1, 5]]
// -> ["List", 0, 0.8414709848078965, -0.9589242746631385]

["Add", ["List", 1, 2], ["List", 3, 4]]
// -> ["List", 4, 6]
  • Added GCD and LCM functions
["GCD", 10, 5, 15]
// -> 5

["LCM", 10, 5, 15]
// -> 30
  • Added Numerator, Denominator, NumeratorDenominator functions. These functions can be used on non-canonical expressions.

  • Added Head and Tail functions which can be used on non-canonical expressions.

  • Added display-quotient and inline-quotient style for formatting of division expressions in LaTeX.


  • Improved parsing of \degree command
// -> ["Divide", "Pi", 6]
  • Improved interoperability with JavaScript: expr.value will return a JavaScript primitive (number, boolean, string, etc…) when possible. This is a more succinct version of expr.N().valueOf().

0.18.1 2023-10-16

Issues Resolved

  • Parsing of whole numbers while in rational mode would return incorrect results.
  • The ND function to evaluate derivatives numerically now return correct values.
ce.parse("\\mathrm{ND}(x \\mapsto 3x^2+5x+7, 2)").N();
// -> 17.000000000001


  • Speed up NIntegrate by temporarily switching the numeric mode to machine while computing the Monte Carlo approximation.

0.18.0 2023-10-16

New Features

  • Expanded LaTeX dictionary with \max, \min, \sup, \inf and \lim functions
  • Added Supremum and Infimum functions
  • Compilation of Block expressions, local variables, return statements and conditionals If.
  • Added numerical evaluation of limits with Limit functions and NLimit functions, using a Richardson Extrapolation."\\lim_{x\\to0} \\frac{\\sin x}{x}").N().json);
// -> 1["NLimit", ["Divide", ["Sin", "_"], "_"], 0]).evaluate().json
// -> 1"\\lim_{x\\to \\infty} \\cos \\frac{1}{x}").N().json);
// -> 1
  • Added Assign and Declare functions to assign values to symbols and declare symbols with a domain.

  • Block evaluations with local variables work now. For example:["Block", ["Assign", "c", 5], ["Multiply", "c", 2]]).evaluate().json;
// -> 10
  • When decimal numbers are parsed they are interpreted as inexact numbers by default, i.e. “1.2” -> {num: "1.2"}. To force the number to be interpreted as a rational number, set ce.latexOptions.parseNumbers = "rational". In that case, “1.2” -> ["Rational", 12, 10], an exact number.

    While regular decimals are considered “inexact” numbers (i.e. they are assumed to be an approximation), rationals are assumed to be exact. In most cases, the safest thing to do is to consider decimal numbers as inexact to avoid introducing errors in calculations. If you know that the decimal numbers you parse are exact, you can use this option to consider them as exact numbers.


  • LaTeX parser: empty superscripts are now ignored, e.g. 4^{} is interpreted as 4.

0.17.0 2023-10-12

Breaking Changes

  • The Nothing domain has been renamed to NothingDomain
  • The Functions, Maybe, Sequence, Dictionary, List and Tuple domain constructors have been renamed to FunctionOf, OptArg, VarArg, DictionaryOf, ListOf and TupleOf, respectively.
  • Domains no longer require a ["Domain"] expression wrapper, so for example"Pi").domain returns "TranscendentalNumbers" instead of ["Domain", "TranscendentalNumbers"].
  • The VarArg domain constructor now indicates the presence of 0 or more arguments, instead of 1 or more arguments.
  • The MaybeBooleans domain has been dropped. Use ["Union", "Booleans", "NothingDomain"] instead.
  • The ce.defaultDomain has been dropped. The domain of a symbol is now determined by the context in which it is used, or by the ce.assume() method. In some circumstances, the domain of a symbol can be undefined.

New Features

  • Symbolic derivatives of expressions can be calculated using the D function. For example,["D", ce.parse("x^2 + 3x + 1"), "x"]).evaluate().latex returns "2x + 3".


  • Some frequently used expressions are now available as predefined constants, for example ce.Pi, ce.True and ce.Numbers.
  • Improved type checking and inference, especially for functions with complicated or non-numeric signatures.

Bugs Fixed

  • Invoking a function repeatedly would invoke the function in the original scope rather than using a new scope for each invocation.

0.16.0 2023-09-29

Breaking Changes

  • The methods ce.let() and ce.set() have been renamed to ce.declare() and ce.assign() respectively.
  • The method ce.assume() requires a predicate.
  • The signatures of ce.assume() and ce.ask() have been simplified.
  • The signature of ce.pushScope() has been simplified.
  • The expr.freeVars property has been renamed to expr.unknowns. It returns the identifiers used in the expression that do not have a value associated with them. The expr.freeVariables property now return the identifiers used in the expression that are defined outside of the local scope and are not arguments of the function, if a function.

New Features

  • Domain Inference when the domain of a symbol is not set explicitly (for example with ce.declare()), the domain is inferred from the value of the symbol or from the context of its usage.

  • Added Assume, Identity, Which, Parse, N, Evaluate, Simplify, Domain.

  • Assignments in LaTeX: x \\coloneq 42 produce ["Assign", "x", 42]

  • Added ErfInv (inverse error function)

  • Added Factorial2 (double factorial)


  • Functions can now be defined:

    • using ce.assign() or ce.declare()
    • evaluating LaTeX: (x, y) \mapsto x^2 + y^2
    • evaluating MathJSON: ["Function", ["Add", ["Power", "x", 2], ["Power", "y", 2]]], "x", "y"]
  • Function can be applied using \operatorname{apply} or the operators \rhd and \lhd:

    • \operatorname{apply}(f, x)
    • f \rhd x
    • x \lhd f

See Adding New Definitions and Functions.

Control Structures

  • Added FixedPoint, Block, If, Loop
  • Added Break, Continue and Return statements

See Control Structures


  • Added numeric approximation of derivatives, using an 8-th order centered difference approximation, with the ND function.
  • Added numeric approximation of integrals, using a Monte Carlo method with rebasing for improper integrals, with the NIntegrate function
  • Added symbolic calculation of derivatives with the D function.


Added support for collections such as lists, tuples, ranges, etc…

See Collections

Collections can be used to represent various data structures, such as lists, vectors, matrixes and more.

They can be iterated, sliced, filtered, mapped, etc…

["Length", ["List", 19, 23, 5]]
// -> 3

["IsEmpty", ["Range", 1, 10]]
// -> "False"

["Take", ["Linspace", 0, 100, 50], 4]
// -> ["List", 0, 2, 4, 6]

["Map", ["List", 1, 2, 3], ["Function", "x", ["Power", "x", 2]]]
// -> ["List", 1, 4, 9]

["Exclude", ["List", 33, 45, 12, 89, 65], -2, 2]
// -> ["List", 33, 12, 65]

["First", ["List", 33, 45, 12, 89, 65]]
// -> 33


  • The documentation has been significantly rewritten with help from an AI-powered writing assistant.

Issues Resolved

  • The LaTeX string returned in ["Error"] expression was incorrectly tagged as Latex instead of LatexString.

0.15.0 2023-09-14


  • The ce.serialize() function now takes an optional canonical argument. Set it to false to prevent some transformations that are done to produce more readable LaTeX, but that may not match exactly the MathJSON. For example, by default ce.serialize(["Power", "x", -1]) returns \frac{1}{x} while ce.serialize([“Power”, “x”, -1], {canonical: false}) returnsx^{-1}.
  • Improved parsing of delimiters, i.e. \left(, \right], etc…
  • Added complex functions Real, Imaginary, Arg, Conjugate, AbsArg. See Complex
  • Added parsing and evaluation of \Re, \Im, \arg, ^\star (Conjugate).
  • #104 Added the ["ComplexRoots", x, n] function which returns the nthroot of x.
  • Added parsing and evaluation of statistics functions Mean, Median, StandardDeviation, Variance, Skewness, Kurtosis, Quantile, Quartiles, InterquartileRange, Mode, Count, Erf, Erfc. See Statistics

0.14.0 2023-09-13

Breaking Changes

  • The entries in the LaTeX syntax dictionary can now have LaTeX triggers (latexTrigger) or triggers based on identifiers (identifierTrigger). The former replaces the trigger property. The latter is new. An entry with a triggerIdentifier of average will match \operatorname{average}, \mathrm{average} and other variants.
  • The ce.latexOptions and ce.jsonSerializationOptions properties are more robust. They can be modified directly or one of their properties can be modified.


  • Added more functions and symbols supported by expr.compile():

    • Factorial postfix operator 5!
    • Gamma function \Gamma(2)
    • LogGamma function \operatorname{LogGamma}(2)
    • Gcd function \operatorname{gcd}(20, 5)
    • Lcm function \operatorname{lcm}(20, 5)
    • Chop function \operatorname{chop}(0.00000000001)
    • Half constant \frac{1}{2}
    • ‘MachineEpsilon’ constant
    • GoldenRatio constant
    • CatalanConstant constant
    • EulerGamma constant \gamma
    • Max function \operatorname{max}(1, 2, 3)
    • Min function \operatorname{min}(13, 5, 7)
    • Relational operators: Less, Greater, LessEqual, GreaterEqual, ‘Equal’, ‘NotEqual’
    • Some logical operators and constants: And, Or, Not, True, False
  • More complex identifiers syntax are recognized, including \mathbin{}, \mathord{}, etc… \operatorname{} is the recommended syntax, though: it will display the identifier in upright font and with the propert spacing, and is properly enclosing. Some commands, such as \mathrm{} are not properly enclosing: two adjacent \mathrm{} command could be merged into one.

  • Environments are now parsed and serialized correctly.

  • When parsing LaTeX, function application is properly handled in more cases, including custom functions, e.g. f(x)

  • When parsing LaTeX, multiple arguments are properly handled, e.g. f(x, y)

  • Add LaTeX syntax for logical operators:

    • And: \land, \operatorname{and} (infix or function)
    • Or: \lor, \operatorname{or} (infix or function)
    • Not: \lnot, \operatorname{not} (prefix or function)
    • Xor: \veebar (infix)
    • Nand: \barwedge (infix)
    • Nor: ^^^^22BD (infix)
    • Implies: \implies (infix)
    • Equivalent: \iff (infix)
  • When a postfix operator is defined in the LaTeX syntax dictionary of the form ^ plus a single token, a definition with braces is added automatically so that both forms will be recognized.

  • Extended the LaTeX dictionary with:

    • floor
    • ceil
    • round
    • sgn
    • exp
    • abs
    • gcd
    • lcm
    • apply
  • Properly handle inverse and derivate notations, e.g. \sin^{-1}(x), \sin'(x), \cos''(x), \cos^{(4)}(x)or even\sin^{-1}‘’(x)`

0.13.0 2023-09-09

New Features

  • Compilation Some expressions can be compiled to Javascript. This is useful to evaluate an expression many times, for example in a loop. The compiled expression is faster to evaluate than the original expression. To get the compiled expression, use expr.compile(). Read more at Compiling

Issues Resolved and Improvements

  • Fixed parsing and serialization of extended LaTeX synonyms for e and i.
  • Fixed serialization of Half.
  • Fixed serialization of Which
  • Improved serialization of ["Delimiter"] expressions.

0.12.7 2023-09-08


  • Made customization of the LaTeX dictionary simpler. The ce.latexDictionary property can be used to access and modify the dictionary. The documentation has been updated.

0.12.6 2023-09-08

Breaking Changes

  • New API for the Parser class.

Improvements and Bux Fixes

  • The ComputeEngine now exports the bignum() and complex() methods that can be used to create bignum and complex numbers from strings or numbers. The methods isBigNum() and isComplex() have also been added to check if a value is a bignum (Decimal) or complex (Complex) number, for example as returned by expr.numericValue.
  • #69 \leq was incorrectly parsed as Equals instead of LessEqual
  • #94 The \exp command was not parsed correctly.
  • Handle PlusMinus in infix and prefix position, i.e. a\pm b and \pm a.
  • Improved parsing, serialization
  • Improved simplification
  • Improved evaluation of Sum and Product
  • Support complex identifiers (i.e. non-latin scripts, emojis).
  • Fixed serialization of mixed numbers.

0.12.1 2022-12-01

Work around issue with libraries using BigInt.

0.12.0 2022-11-27

Breaking Changes

  • The expr.symbols property return an array of string. Previously it returned an array of BoxedExpression.


  • Rewrote the rational computation engine to use JavaScript bigint instead of Decimal instances. Performance improvements of up to 100x.
  • expr.freeVars provides the free variables in an expression.
  • Improved performance of prime factorization of big num by x100.
  • Added ["RandomExpression"]
  • Improved accuracy of some operations, for example expr.parse("1e999 + 1").simplify()

Issues Resolved

  • When ce.numericMode === "auto", square roots of negative numbers would return an expression instead of a complex number.
  • The formatting of LaTeX numbers when using ce.latexOptions.notation = "engineering" or "scientific" was incorrect.
  • The trig functions no longer “simplify” to the less simple exponential formulas.
  • The canonical order of polynomials now orders non-lexicographic terms of degree 1 last, i.e. “ax^2+ bx+ c” instead of “x + ax^2 + bx”.
  • Fixed evaluation of inverse functions
  • Fixed expr.isLess, expr.isGreater, expr.isLessEqual, expr.isGreaterEqual and ["Min"], ["Max"]

0.11.0 2022-11-18

Breaking Changes

  • The signature of ce.defineSymbol(), ce.defineFunction() and ce.pushScope() have changed


  • When a constant should be held or substituted with its value can now be more precisely controlled. The hold symbol attribute is now holdUntil and can specify at which stage the substitution should take place.

Issues Resolved

  • Some constants would return a value as bignum or complex even when the numericMode did not allow it.
  • Changing the value or domain of a symbol is now correctly taken into account. Changes can be made with ce.assume(), ce.set() or expr.value.
  • When a symbol does not have a value associated with it, assumptions about it (e.g. “x > 0”) are now correctly tracked and reflected.

0.10.0 2022-11-17

Breaking Changes

  • expr.isLiteral has been removed. Use expr.numericValue !== null and expr.string !== null instead.

Issues Resolved

  • Calling ce.forget() would not affect expressions that previously referenced the symbol.


  • More accurate calculations of some trig functions when using bignums.
  • Improved performance when changing a value with ce.set(). Up to 10x faster when evaluating a simple polynomial in a loop.
  • ce.strict can be set to false to bypass some domain and validity checks.

0.9.0 2022-11-15

Breaking Changes

  • The head of a number expression is always Number. Use expr.domain to be get more specific info about what kind of number this is.
  • By default, and ce.parse() return a canonical expression. A flag can be used if a non-canonical expression is desired.
  • The API surface of BoxedExpression has been reduced. The properties machineValue, bignumValue, asFloat, asSmallInteger, asRational etc… have been replaced with a single numericValue property.
  • parseUnknownSymbol is now parseUnknownIdentifier


  • Support angles in degrees with 30\degree, 30^\circ and \ang{30}.

  • More accurate error expressions, for example if there is a missing closing delimiter an ["Error", ["ErrorCode", "'expected-closing-delimiter'", "')'"]] is produced.

  • ["Expand"] handles more cases

  • The trig functions can now have a regular exponent, i.e.\cos^2(x) in addition to -1 for inverse, and a combination of \prime, \doubleprime and ' for derivatives.

  • ce.assume() handle more expressions and can be used to define new symbols by domain or value.

  • Better error message when parsing, e.g. \sqrt(2) (instead of \sqrt{2})

  • Better simplification for square root expressions:

    • \sqrt{25x^2} -> 5x
  • Improved evaluation of ["Power"] expressions, including for negative arguments and non-integer exponents and complex arguments and exponents.

  • Added Arccot, Arcoth, Arcsch, Arcscc, Arsech and Arccsc

  • expr.solve() returns result for polynomials of order up to 2.

  • The pattern.match() function now work correctly for commutative functions, i.e. ce.pattern(['Add', '_a', 'x']).match(ce.parse('x+y')) -> {"_a": "y"}

  • Added ce.let() and ce.set() to declare and assign values to identifiers.

  • Preserve exact calculations involving rationals or square root of rationals.

    • \sqrt{\frac{49}{25}} -> \frac{7}{5}
  • Addition and multiplication provide more consistent results for evaluate() and N(). Evaluate returns an exact result when possible.

    • EXACT
      • 2 + 5 -> 7
      • 2 + 5/7 -> 19/7
      • 2 + √2 -> 2 + √2
      • 2 + √(5/7) -> 2 + √(5/7)
      • 5/7 + 9/11 -> 118/77
      • 5/7 + √2 -> 5/7 + √2
      • 10/14 + √(18/9) -> 5/7 + √2
      • √2 + √5 -> √2 + √5
      • √2 + √2 -> 2√2
      • sin(2) -> sin(2)
      • sin(π/3) -> √3/2
      • 2 + 2.1 -> 4.1
      • 2 + √2.1 -> 3.44914
      • 5/7 + √2.1 -> 2.16342
      • sin(2) + √2.1 -> 2.35844
  • More consistent behavior of the auto numeric mode: calculations are done with bignum and complex in most cases.

  • JsonSerializationOptions has a new option to specify the numeric precision in the MathJSON serialization.

  • Shorthand numbers can now be strings if they do not fit in a float-64:

// Before
["Rational", { "num": "1234567890123456789"}, { "num": "2345678901234567889"}]

// Now
["Rational", "1234567890123456789", "2345678901234567889"]
  • \sum is now correctly parsed and evaluated. This includes creating a local scope with the index and expression value of the sum.

Bugs Fixed

  • The parsing and evaluation of log functions could produce unexpected results
  • The \gamma command now correctly maps to ["Gamma"]
  • Fixed numeric evaluation of the ["Gamma"] function when using bignum
  • #57 Substituting 0 (i.e. with expr.subs({})) did not work.
  • #60 Correctly parse multi-char symbols with underscore, i.e. \mathrm{V_a}
  • Parsing a number with repeating decimals and an exponent would drop the exponent.
  • Correct calculation of complex square roots
    • \sqrt{-49} -> 7i
  • Calculations were not always performed as bignum in "auto" numeric mode if the precision was less than 15. Now, if the numeric mode is "auto", calculations are done as bignum or complex numbers.
  • If an identifier contained multiple strings of digits, it would not be rendered to LaTeX correctly, e.g. V20_20.
  • Correctly return isReal for real numbers

0.8.0 2022-10-02

Breaking Changes

  • Corrected the implementation of expr.toJSON(), expr.valueOf() and added the esoteric [Symbol.toPrimitive]() method. These are used by JavaScript when interacting with other primitive types. A major change is that expr.toJSON() now returns an Expression as an object literal, and not a string serialization of the Expression.

  • Changed from “decimal” to “bignum”. “Decimal” is a confusing name, since it is used to represent both integers and floating point numbers. Its key characteristic is that it is an arbitrary precision number, aka “bignum”. This affects ce.numericMode which now uses bignum instead of decimal', expr.decimalValue->expr.bignumValue, decimalValue()-> bignumValue()`

Bugs Fixed

  • Numerical evaluation of expressions containing complex numbers when in decimal or auto mode produced incorrect results. Example: e^{i\\pi}

0.7.0 2022-09-30

Breaking Changes

  • The ce.latexOptions.preserveLatex default value is now false
  • The first argument of the ["Error"] expression (default value) has been dropped. The first argument is now an error code, either as a string or an ["ErrorCode"] expression.


  • Much improved LaTeX parser, in particular when parsing invalid LaTeX. The parser now avoids throwing, but will return a partial expression with ["Error"] subexpressions indicating where the problems were.
  • Implemented new domain computation system (similar to type systems in programming languages)
  • Added support for multiple signatures per function (ad-hoc polymorphism)
  • Added FixedPoint, Loop, Product, Sum, Break, Continue, Block, If, Let, Set, Function, Apply, Return
  • Added Min, Max, Clamp
  • Parsing of \sum, \prod, \int.
  • Added parsing of log functions, \lb, \ln, \ln_{10}, \ln_2, etc…
  • Added expr.subexpressions, expr.getSubexpressions(), expr.errors, expr.symbols, expr.isValid`.
  • Symbols can now be used to represent functions, i.e.'Sin').domain correctly returns ["Domain", "Function"].
  • Correctly handle rational numbers with a numerator or denominator outside the range of a 64-bit float.
  • Instead of a Missing symbol an ["Error", "'missing'"] expression is used.
  • Name binding is now done lazily
  • Correctly handle MathJSON numbers with repeating decimals, e.g. 1.(3).
  • Correctly evaluate inverse functions, e.g. ce.parse('\\sin^{-1}(.5)).N()
  • Fixed some LaTeX serialization issues

Read more at Core Reference and [Arithmetic Reference] (

Bugs Fixed

  • #43 If the input of ce.parse() is an empty string, return an empty string for expr.latex or expr.json.latex: that is, ensure verbatim LaTeX round-tripping
  • Evaluating some functions, such as \arccos would result in a crash
  • Correctly handle parsing of multi-token decimal markers, e.g. {,}

0.6.0 2022-04-18


  • Parse more cases of tabular environments
  • Handle simplify and evaluate of inert functions by default
  • Avoid unnecessary wrapping of functions when serializing LaTeX
  • Parse arguments of LaTeX commands (e.g. \vec{})
  • #42 Export static ComputeEngine.getLatexDictionary
  • Parse multi-character constants and variables, e.g. \mathit{speed} and \mathrm{radius}
  • Parse/serialize some LaTeX styling commands: \displaystyle, \tiny and more

0.5.0 2022-04-05


  • Correctly parse tabular content (for example in \begin{pmatrix}...\end{pmatrix}
  • Correctly parse LaTeX groups, i.e. {...}
  • Ensure constructible trigonometric values are canonical
  • Correct and simplify evaluation loop for simplify(), evaluate() and N().
  • #41 Preserve the parsed LaTeX verbatim for top-level expressions
  • #40 Correctly calculate the synthetic LaTeX metadata for numbers
  • Only require Node LTS (16.14.2)
  • Improved documentation, including Dark Mode support


Release Date: 2022-03-27


  • Added option to specify custom LaTeX dictionaries in ComputeEngine constructor
  • expr.valueOf returns rational numbers as [number, number] when applicable
  • The non-ESM builds (compute-engine.min.js) now targets vintage JavaScript for improved compatibility with outdated toolchains (e.g. Webpack 4) and environments. The ESM build (compute-engine.min.esm.js) targets evergreen JavaScript (currently ECMAScript 2020).


Release Date: 2022-03-21

Transition Guide from 0.4.2

The API has changed substantially between 0.4.2 and 0.4.3, however adapting code to the new API is very straightforward.

The two major changes are the introduction of the BoxedExpression class and the removal of top level functions.

Boxed Expression

The BoxedExpression class is a immutable box (wrapper) that encapsulates a MathJSON Expression. It provides some member functions that can be used to manipulate the expression, for example expr.simplify() or expr.evaluate().

The boxed expresson itself is immutable. For example, calling expr.simplify() will return a new, simplified, expression, without modifying expr.

To create a “boxed” expression from a “raw” MathJSON expression, use To create a boxed expression from a LaTeX string, use ce.parse().

To access the “raw” MathJSON expression, use the expr.json property. To serialize the expression to LaTeX, use the expr.latex property.

The top level functions such as parse() and evaluate() are now member functions of the ComputeEngine class or the BoxedExpression class.

There are additional member functions to examine the content of a boxed expression. For example, expr.symbol will return null if the expression is not a MathJSON symbol, otherwise it will return the name of the symbol as a string. Similarly, expr.ops return the arguments (operands) of a function, expr.asFloat return null if the expression does not have a numeric value that can be represented by a float, a number otherwise, etc…

Canonical Form

Use expr.canonical to obtain the canonical form of an expression rather than the ce.format() method.

The canonical form is less aggressive in its attempt to simplify than what was performed by ce.format().

The canonical form still accounts for distributive and associative functions, and will collapse some integer constants. However, in some cases it may be necessary to invoke expr.simplify() in order to get the same results as ce.format(expr).

Rational and Division

In addition to machine floating points, arbitrary precision numbers and complex numbers, the Compute Engine now also recognize and process rational numbers.

This is mostly an implementation detail, although you may see ["Rational", 3, 4], for example, in the value of a expr.json property.

If you do not want rational numbers represented in the value of the .json property, you can exclude the Rational function from the serialization of JSON (see below) in which case Divide will be used instead.

Note also that internally (as a result of boxing), Divide is represented as a product of a power with a negative exponent. This makes some pattern detection and simplifications easier. However, when the .json property is accessed, product of powers with a negative exponents are converted to a Divide, unless you have included Divide as an excluded function for serialization.

Similarly, Subtract is converted internally to Add, but may be serialized unless excluded.

Parsing and Serialization Customization

Rather than using a separate instance of the LatexSyntax class to customize the parsing or serialization, use a ComputeEngine instance and its ce.parse() method and the expr.latex property.

Custom dictionaries (to parse/serialize custom LaTeX syntax) can be passed as an argument to the ComputeEngine constructor.

For more advanced customizations, use ce.latexOptions = {...}. For example, to change the formatting options of numbers, how the invisible operator is interpreted, how unknown commands and symbols are interpreted, etc…

Note that there are also now options available for the “serialization” to MathJSON, i.e. when the expr.json property is used. It is possible to control for example if metadata should be included, if shorthand forms are allowed, or whether some functions should be avoided (Divide, Sqrt, Subtract, etc…). These options can be set using ce.jsonSerializationOptions = {...}.

Comparing Expressions

There are more options to compare two expressions.

Previously, match() could be used to check if one expression matched another as a pattern.

If match() returned null, the first expression could not be matched to the second. If it returned an object literal, the two expressions matched.

The top-level match() function is replaced by the expr.match() method. However, there are two other options that may offer better results:

  • expr.isSame(otherExpr) return true if expr and otherExpr are structurally identical. Structural identity is closely related to the concept of pattern matching, that is ["Add", 1, "x"] and ["Add", "x", 1] are not the same, since the order of the arguments is different. It is useful for example to compare some input to an answer that is expected to have a specific form.
  • expr.isEqual(otherExpr) return true if expr and otherExpr are mathematically identical. For example ce.parse("1+1").isEqual(ce.parse("2")) will return true. This is useful if the specific structure of the expression is not important.

It is also possible to evaluate a boolean expression with a relational operator, such as Equal:

console.log(["Equal", expr, 2]).evaluate().symbol);
// -> "True"

// -> true

Before / After

Before After
expr = ["Add", 1, 2] expr =["Add", 1, 2])
expr = ce.evaluate(expr) expr = expr.evaluate()
console.log(expr) console.log(expr.json)
expr = new LatexSyntax().parse("x^2+1") expr = ce.parse("x^2+1")
new LatexSyntax().serialize(expr) expr.latex
ce.simplify(expr) expr.simplify()
await ce.evaluate(expr) expr.evaluate()
ce.N(expr) expr.N()
ce.domain(expr) expr.domain
ce.format(expr...) expr.canonical


Release Date: 2021-06-18


  • In LaTeX, parse \operatorname{foo} as the MathJSON symbol "foo".