CortexJS Compute Engine Changelog
0.12.1
Release Date: 20221201
Work around unpckg.com issue with libraries using BigInt.
0.12.0
Release Date: 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()
Bug Fixes
 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
Release Date: 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.
Bug Fixes
 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
Release Date: 20221117
Breaking Changes
expr.isLiteral
has been removed. Useexpr.numericValue !== null
andexpr.string !== null
instead.
Bug Fixes
 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
Release Date: 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\deg
,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
Release Date: 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
Release Date: 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
Release Date: 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
Release Date: 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"
.