CortexJS Compute Engine Changelog
0.23.0 20240101
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 noncanonical expression. Previously,
ce.parse('\\frac{1}{2}', {canonical: false})
would returnHalf
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 nonexact numbers could fail. For
example:
2(13.1+3.1x)
and26.2+6.2x
would not be considered equal.
Improvements
 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 20231113
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 propertiesmatch
,replace
andcondition
. 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 }
 previous syntax:

CanonicalForm
The
CanonicalOrder
function has been replaced by the more flexibleCanonicalForm
function. TheCanonicalForm
function takes an expression and a list of transformations to apply. To apply the same transformations asCanonicalOrder
, use:['CanonicalForm', expr, 'Order']
These canonical forms can also be specified with
box()
andparse()
options:ce.box(expr, { 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 forconsole.log(expr.toString())
.  Added an
exact
option (false by default) to theexpr.match()
pattern matching method. Whentrue
some additional patterns are automatically recognized, for example,x
will match["Multiply", '_a', 'x']
whenexact
isfalse
, but not whenexact
istrue
.
Improvements
 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 20231102
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 toexpr.isSame()
. 
AddedCanonicalOrder
function, which sorts the arguments of commutative functions into canonical order. This is useful to compare two noncanonical expressions for equality.
ce.box(["CanonicalOrder", ["Add", 1, "x"]]).isSame(
ce.box(["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 20231031
Issues Resolved
 Fixed numerical evaluation of integrals and limits when parsed from LaTeX.
console.info(ce.parse('\\lim_{x \\to 0} \\frac{\\sin(x)}{x}').value);
// > 1
console.info(ce.parse('\\int_{0}^{2} x^2 dx').value);
// > 2.6666666666666665
0.20.1 20231031
Issues Resolved
 Fixed evaluation of functions with multiple arguments
 Fixed compilation of some function assignments
 Improved serialization of function assignment
0.20.0 20231030
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 examplef(x) := 2x
: previously, the lefthandside 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 theInvisibleOperator
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 tof := x > 2x+1
.  Implement the
Mod
andCongruent
function.  Correctly parse
11 \bmod 5
(Mod
) and26\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 thatf
is a function (and not a variablef
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 20231026
Issues Resolved
 Assigning a function to an indentifier works correctly now, i.e.
ce.parse("\\operatorname{f} := x \\mapsto 2x").evaluate();
0.19.0 20231025
Breaking Changes
 The
domain
property of the function definitionsignature
is deprecated and replaced with theparams
,optParams
,restParam
andresult
properties instead. Thedomain
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{2510\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
andIntersection
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
or1, 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
andLCM
functions
["GCD", 10, 5, 15]
// > 5
["LCM", 10, 5, 15]
// > 30

Added
Numerator
,Denominator
,NumeratorDenominator
functions. These functions can be used on noncanonical expressions. 
Added
Head
andTail
functions which can be used on noncanonical expressions. 
Added
displayquotient
andinlinequotient
style for formatting of division expressions in LaTeX.
Improvements
 Improved parsing of
\degree
command
ce.parse("30\\degree)
// > ["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 ofexpr.N().valueOf()
.
0.18.1 20231016
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
Improvements
 Speed up
NIntegrate
by temporarily switching the numeric mode tomachine
while computing the Monte Carlo approximation.
0.18.0 20231016
New Features
 Expanded LaTeX dictionary with
\max
,\min
,\sup
,\inf
and\lim
functions  Added
Supremum
andInfimum
functions  Compilation of
Block
expressions, local variables, return statements and conditionalsIf
.  Added numerical evaluation of limits with
Limit
functions andNLimit
functions, using a Richardson Extrapolation.
console.info(ce.parse("\\lim_{x\\to0} \\frac{\\sin x}{x}").N().json);
// > 1
console.info(
ce.box(["NLimit", ["Divide", ["Sin", "_"], "_"], 0]).evaluate().json
);
// > 1
console.info(ce.parse("\\lim_{x\\to \\infty} \\cos \\frac{1}{x}").N().json);
// > 1

Added
Assign
andDeclare
functions to assign values to symbols and declare symbols with a domain. 
Block
evaluations with local variables work now. For example:
ce.box(["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, setce.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.
Improvements
 LaTeX parser: empty superscripts are now ignored, e.g.
4^{}
is interpreted as4
.
0.17.0 20231012
Breaking Changes
 The
Nothing
domain has been renamed toNothingDomain
 The
Functions
,Maybe
,Sequence
,Dictionary
,List
andTuple
domain constructors have been renamed toFunctionOf
,OptArg
,VarArg
,DictionaryOf
,ListOf
andTupleOf
, respectively.  Domains no longer require a
["Domain"]
expression wrapper, so for examplece.box("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 thece.assume()
method. In some circumstances, the domain of a symbol can beundefined
.
New Features
 Symbolic derivatives of expressions can be calculated using the
D
function. For example,ce.box(["D", ce.parse("x^2 + 3x + 1"), "x"]).evaluate().latex
returns"2x + 3"
.
Improvements
 Some frequently used expressions are now available as predefined constants,
for example
ce.Pi
,ce.True
andce.Numbers
.  Improved type checking and inference, especially for functions with complicated or nonnumeric 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 20230929
Breaking Changes
 The methods
ce.let()
andce.set()
have been renamed toce.declare()
andce.assign()
respectively.  The method
ce.assume()
requires a predicate.  The signatures of
ce.assume()
andce.ask()
have been simplified.  The signature of
ce.pushScope()
has been simplified.  The
expr.freeVars
property has been renamed toexpr.unknowns
. It returns the identifiers used in the expression that do not have a value associated with them. Theexpr.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

Functions can now be defined:
 using
ce.assign()
orce.declare()
 evaluating LaTeX:
(x, y) \mapsto x^2 + y^2
 evaluating MathJSON:
["Function", ["Add", ["Power", "x", 2], ["Power", "y", 2]]], "x", "y"]
 using

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
andReturn
statements
Calculus
 Added numeric approximation of derivatives, using an 8th 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.
Collections
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
Improvements
 The documentation has been significantly rewritten with help from an AIpowered writing assistant.
Issues Resolved
 The LaTeX string returned in
["Error"]
expression was incorrectly tagged asLatex
instead ofLatexString
.
0.15.0 20230914
Improvements
 The
ce.serialize()
function now takes an optionalcanonical
argument. Set it tofalse
to prevent some transformations that are done to produce more readable LaTeX, but that may not match exactly the MathJSON. For example, by defaultce.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 ofx
.  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 20230913
Breaking Changes
 The entries in the LaTeX syntax dictionary can now have LaTeX triggers
(
latexTrigger
) or triggers based on identifiers (identifierTrigger
). The former replaces thetrigger
property. The latter is new. An entry with atriggerIdentifier
ofaverage
will match\operatorname{average}
,\mathrm{average}
and other variants.  The
ce.latexOptions
andce.jsonSerializationOptions
properties are more robust. They can be modified directly or one of their properties can be modified.
Improvements

Added more functions and symbols supported by
expr.compile()
:Factorial
postfix operator5!
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
constantCatalanConstant
constantEulerGamma
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 20230909
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
andi
.  Fixed serialization of
Half
.  Fixed serialization of
Which
 Improved serialization of
["Delimiter"]
expressions.
0.12.7 20230908
Improvements
 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 20230908
Breaking Changes
 New API for the
Parser
class.
Improvements and Bux Fixes
 The
ComputeEngine
now exports thebignum()
andcomplex()
methods that can be used to create bignum and complex numbers from strings or numbers. The methodsisBigNum()
andisComplex()
have also been added to check if a value is a bignum (Decimal
) or complex (Complex
) number, for example as returned byexpr.numericValue
.  #69
\leq
was incorrectly parsed asEquals
instead ofLessEqual
 #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
andProduct
 Support complex identifiers (i.e. nonlatin scripts, emojis).
 Fixed serialization of mixed numbers.
0.12.1 20221201
Work around unpckg.com issue with libraries using BigInt.
0.12.0 20221127
Breaking Changes
 The
expr.symbols
property return an array ofstring
. Previously it returned an array ofBoxedExpression
.
Improvements
 Rewrote the rational computation engine to use JavaScript
bigint
instead ofDecimal
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 nonlexicographic 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 20221118
Breaking Changes
 The signature of
ce.defineSymbol()
,ce.defineFunction()
andce.pushScope()
have changed
Improvements
 When a constant should be held or substituted with its value can now be more
precisely controlled. The
hold
symbol attribute is nowholdUntil
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()
orexpr.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 20221117
Breaking Changes
expr.isLiteral
has been removed. Useexpr.numericValue !== null
andexpr.string !== null
instead.
Issues Resolved
 Calling
ce.forget()
would not affect expressions that previously referenced the symbol.
Improvements
 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 tofalse
to bypass some domain and validity checks.
0.9.0 20221115
Breaking Changes
 The head of a number expression is always
Number
. Useexpr.domain
to be get more specific info about what kind of number this is.  By default,
ce.box()
andce.parse()
return a canonical expression. A flag can be used if a noncanonical expression is desired.  The API surface of
BoxedExpression
has been reduced. The propertiesmachineValue
,bignumValue
,asFloat
,asSmallInteger
,asRational
etc… have been replaced with a singlenumericValue
property. parseUnknownSymbol
is nowparseUnknownIdentifier
Improvements

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", "'expectedclosingdelimiter'", "')'"]]
is produced. 
["Expand"]
handles more cases 
The trig functions can now have a regular exponent, i.e.
\cos^2(x)
in addition to1
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 noninteger exponents and complex arguments and exponents. 
Added
Arccot
,Arcoth
,Arcsch
,Arcscc
,Arsech
andArccsc

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()
andce.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()
andN()
. 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
 APPROXIMATE
 2 + 2.1 > 4.1
 2 + √2.1 > 3.44914
 5/7 + √2.1 > 2.16342
 sin(2) + √2.1 > 2.35844
 EXACT

More consistent behavior of the
auto
numeric mode: calculations are done withbignum
andcomplex
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 float64:
// 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. withexpr.subs({})
) did not work.  #60 Correctly parse multichar 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 20221002
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 thatexpr.toJSON()
now returns anExpression
as an object literal, and not a string serialization of theExpression
. 
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 usesbignum
instead ofdecimal',
expr.decimalValue>
expr.bignumValue,
decimalValue()>
bignumValue()`
Bugs Fixed
 Numerical evaluation of expressions containing complex numbers when in
decimal
orauto
mode produced incorrect results. Example:e^{i\\pi}
0.7.0 20220930
Breaking Changes
 The
ce.latexOptions.preserveLatex
default value is nowfalse
 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.
Features
 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 (adhoc 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.
ce.box('Sin').domain
correctly returns["Domain", "Function"]
.  Correctly handle rational numbers with a numerator or denominator outside the range of a 64bit 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] (https://cortexjs.io/computeengine/reference/arithmetic/)
Bugs Fixed
 #43 If the input of
ce.parse()
is an empty string, return an empty string forexpr.latex
orexpr.json.latex
: that is, ensure verbatim LaTeX roundtripping  Evaluating some functions, such as
\arccos
would result in a crash  Correctly handle parsing of multitoken decimal markers, e.g.
{,}
0.6.0 20220418
Improvements
 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 multicharacter constants and variables, e.g.
\mathit{speed}
and\mathrm{radius}
 Parse/serialize some LaTeX styling commands:
\displaystyle
,\tiny
and more
0.5.0 20220405
Improvements
 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()
andN()
.  #41 Preserve the parsed LaTeX verbatim for toplevel expressions
 #40 Correctly calculate the synthetic LaTeX metadata for numbers
 Only require Node LTS (16.14.2)
 Improved documentation, including Dark Mode support
0.4.4
Release Date: 20220327
Improvements
 Added option to specify custom LaTeX dictionaries in
ComputeEngine
constructor expr.valueOf
returns rational numbers as[number, number]
when applicable The nonESM builds (
computeengine.min.js
) now targets vintage JavaScript for improved compatibility with outdated toolchains (e.g. Webpack 4) and environments. The ESM build (computeengine.min.esm.js
) targets evergreen JavaScript (currently ECMAScript 2020).
0.4.3
Release Date: 20220321
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 ce.box()
.
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 toplevel 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 ifexpr
andotherExpr
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 ifexpr
andotherExpr
are mathematically identical. For examplece.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(ce.box(["Equal", expr, 2]).evaluate().symbol);
// > "True"
console.log(expr.isEqual(ce.box(2)));
// > true
Before / After
Before  After 

expr = ["Add", 1, 2] 
expr = ce.box(["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 expr.simplify() 
0.3.0
Release Date: 20210618
Improvements
 In LaTeX, parse
\operatorname{foo}
as the MathJSON symbol"foo"
.