math-parser

A math expressions parser. We mean by mathematical that, e.g., arithmetic operations is considered for example if you pass 1+2, the result will be a node with type operator and name + with two children nodes of type number in its args property. Just play with expressions, log the result and see the different situations.

See also: math-latex-parser

Install

npm install @scicave/math-parser

Usage

Browser

<script src="https://cdn.jsdelivr.net/npm/@scicave/math-parser/lib/bundle.js"></script>
<!-- or -->
<script src="https://cdn.jsdelivr.net/npm/@scicave/math-parser/lib/bundle.min.js"></script>

Require, import

const mathParser = require('@scicave/math-parser'); /*
  {
    parse: function(math:string [,options: object]),
    Node: constructor,
    SyntaxError: constructor
  }
*/

Examples:

console.log(mathParser.parse(' 1.5 * 5  ^x !'));
console.log(mathParser.parse(' 5^2x !'));
console.log(mathParser.parse('2xy'));

// matrix,,, see: options.extra
console.log(mathParser.parse('[1,2; 3, 4]'));

// absolute values
console.log(mathParser.parse('||x - y| - |y - z||'));

// multi-char variables
console.log(mathParser.parse('2long_var_name', { singleCharName: false, }));
// xlong_var_name is considered as one var not automult
console.log(mathParser.parse('xlong_var_name', { singleCharName: false, }));

// member expressions and matrices, nonsense expression, but it can be parsed
console.log(mathParser.parse('f(x).someProperty ^ 2 >= [1,2,3; 5,6,7]', { functions: ['f'] }));

// will throw error, member expressions are not allowed
console.log(mathParser.parse('f(x).someProperty.fn(y).result ^ 2  \n!', {
  functions: ['f'],
  extra: { memberExpressions: false }
}));

Operators Schema

Operator	Precedence	Associativity
!	6	N/A
^	5	left-to-right
*	4	left-to-right
/	4	left-to-right
+	3	left-to-right
-	3	left-to-right
!=	2	left-to-right
>=	2	left-to-right
<=	2	left-to-right
>	2	left-to-right
<	2	left-to-right
=	1	left-to-right

AST Node

The parse function returns a Node, which may have array of other Nodes in its args.

Node.prototype.type

The Node type, see the available types.

Node.prototype.isBuiltin

If the Node is either id or function it maybe a builtin.

See builtinFunctions, builtinIDs.

Node.prototype.check(props: Object)

This method can check all properties except args, it will be ignored.

let node = mathParser.parse("2!");
console.log(node.check({
  type: "operator",
  operatorType: "postfix",
  name: "!"
}));
// true

Node.prototype.checkType(type: string)

You can check for type directly here, but why not node.type === "the_type"? Because "the_type" is not a valid type, .checkType will throw if you passed invalid type.

let node = mathParser.parse("1");
console.log(node.checkType("member expression"));
// false

Node.prototype.hasChild(props: Object)

This method can check for any of args with properties props. It doesn't check forargs, it will be ignored.

let node = mathParser.parse("1+2");
// { type: "operator", args: [...], operatorType: "infix" }
console.log(node.hasChild({ type: "number", value: 1 }));
// true

Node.prototype.hasChildR(props: Object)

The same as hasChild, but recursively.

let node = mathParser.parse("sin(1+2)");
// { type: "function", name: "sin", args: [...], isBuiltin: true }
console.log(node.hasChildR({ type: "number", value: 1 }));
// true

Node.types

Available values for Node.prototype.type .

Array of literal strings: Node.types.values .

All Valid operators: Node.types.operators .

Options

When invalid options passed, mathParser.OptionsError is thrown.

.autoMult

Type = boolean, default: true.

To perform multiplication in these cases:

1. 2x
2. sinxcosx
3. sinx(5y)

Notice: sinxcosx when singleCharName is false will be a variable name

.singleCharName

Type = boolean, default: true.

Maths conventionally works with single char named variables and constants, but in programming languages you have freedom. The convention in programming is to use multi-char named identifier. See: options.builtinIDs.

When a member expression is found, properties and methods are allowed to be multi-char, despite of options.singleCharName, see: options.extra.memberExpressions.

You can use a1, a2, etc... as single-char names.

.extra

All extra features are enabled.

Example:

mathParser.parse(tex, {
  extra: {
    // ...
  }
});

• memberExpressions, for example:
  • p.x
  • point.x
  • f(x).someProperty.fn(y).result: valid syntax in both cases of singleCharName.
  • .......... etc, and so on.
• intervals: true or false, will return node with properties { startInlusive: boolean, endInclusive: boolean }.
  • [1,2]
  • (-.5, infinity)
  • (-pi, 1]
  • [2,5)
• sets: e.g., { 1, sqrt(pi), ..., sqrt(pi)^10 }
• tuples: e.g., (1, 2, x, ...)
• matrices: e.g., [ sinx, 1, 3; cosy, sqrt(3), 0 ]
• ellipsis: to allow the 3-dots "...", e.g., { 1, 3, 5, ... }

---

Notes

• You can use ellipsis as valid Factor, e.g., 1 + 2 + ... + 10

• This expression will throw syntax error, 1 + 2 + (...) + 10

• extra.ellipsis is more customizable:

  • extra.ellipsis.matrices: boolean

• extra.ellipsis.tuples: boolean

  • extra.ellipsis.sets: boolean
  • extra.ellipsis.funcArgs: boolean

• Intervals, should have 2 terms as math expression:

  • (..., a]: throw syntax error
  • (..., a): is a tuple, parsed if extra.ellipsis is true
  • [..., a]: is a matrix, parsed if extra.matrices is true

.functions

Type = Array<string>, default = [];

When autoMult is true, some expression like f(x) will be considered as multiplication f*(x), in order to parse it as a function with name = "f", you can pass options.functions = ['f'].

When singleCharName == true, you should pass single-char functions.

When parsing a.method(...), regardless of singleCharName, method names will be always multi-char name.

        member expression
              /\
            /    \
        __/        \________
        id          function
   name  |          | name = "method"
   = "a" |          | args = [ ... ]

.builtinIDs

Type = Array<string>, default = ["infinity", "pi", "phi"];

If you want to expand the defaults put "..." as the first item in the array, at index 0, for example:

mathParser.parse(math, { builtinIDs: [ "...", "mynewID" ] });

To use multi-char names when setting singleCharName to true, for example:

Math Expression	Equivalent To	singleCharName
1 + pix	1 + p*i*x	true
1 + xpi	1 + x*p*i	true
1 + x pi	1 + x*pi	true
1 + pi	1 + pi	true
1 + pi x	1 + pi*x	false
1 + pix	1 + pix	false

.builtinFunctions

Type = { primary: Array<string>, secondary: Array<string> }, default 👇.

• primary: can be used like sinx and logx.
• secondary: has to be used with parenthesis, exp(pi) and arcoth(1.2^2). The secondary builtin functions could be passed throw options.functions, but let them be here to avoid putting them redundantly in options.functions.

If you want to expand the defaults put "..." as the first item in the array, at index 0.

Notice, when singleCharName == true, all primary and secondary has to be used with parenthesis "(...)", sinx is considered as node with type "id" and name "sinx".

////////    primary   ///////
// can be used like "sinx, logx"
"sin", "cos", "tan", "sec",  "csc",  "cot", "asin", "acos", "atan",
"asec", "acsc", "acot", "sinh", "cosh", "tanh", "sech", "csch", "coth",
"ln", "log",

////////   secondary   ///////
"exp", "floor", "ceil", "round", "random", "sqrt",
// hyperbolic function
"arsinh", "arcosh", "artanh", "arsech", "arcsch", "arcoth",
"arcsin", "arccos", "arcotan", "arcsec", "arccsc", "arccot",

.keepParen

Type = boolean, default = false.

If you want to make grouping parenthesis nodes in the result AST, { type: 'parenthesis', ... }.

Ambiguous expressions

In these confusing cases, you can handle the parsed expression to transform to what you want.

• 5^2x! To be 5^(2x!) or (5^2)(x!) or (5^2x)!, ... The current result AST is equivalent to 5^(2(x!)).

• x!y I am not sure whether parse as (x!)(y) or to throw a SyntaxError. Now it is parsed with no errors.

License

MIT