ecca

ecca is the symbolic math library for Equation Cloud, it handles the parsing of mathmatical expressions, the simplification and manipulation of expression trees and conversion of expression trees into TeX strings.

Table of Contents

• Install
• Parsing
• Elements
• Variables
• Tex Output

Install

npm install ecca

Parsing

let ecca = require('ecca')
console.log(new ecca.Expression('y=x^2').ElementTree)

Will output the correct expression tree:

EqualsElement {
  type: 'equals',
  operands: [
    IdentifierElement { type: 'identifier', identifier: 'y' },
    PowerElement { type: 'power', operands: [Object] }
  ]
}

Elements

The following elements are currently supported

Element Name	Type	Parameters	Notes
IntegerElement	Value	Value	Can only be positive
FractionElement	Value	Numerator, Denominator	Both values will only be positive
IdentifierElement		Identifier	Will represent either variables or constants
FunctionElement	Identifier	Identifier, Operands	Operands can be of any length
BracketsElement	Operator	Operands	Can only have one operand
NegateElement	Operator	Operands	Can only have one operands, used for negative numbers
FactorialElement	Operator	Operands	Can only have one operand
PowerElement	Operator	Operands	Can only have two operands
DivisionElement	Operator	Operands	Can only have two operands
ProductElement	Operator	Operands	Operands can be any length
SumElement	Operator	Operands	Operands can be any length
SubtractionElement	Operator	Operands	Can only have two operands
EqualsElement	Operator	Operands	Can only have two operands

Variables

Any identifer will be automatically assigned to be a variable, with details of each variable stored in a Variable class, and returned as an element of the ReadonlyArray<Variable> Expression.Variables. The Variable class contains the name of the variable and an array of elements which are this variable in the expression. The identified variables are also assigned string ids as part of the element.

TeX Output

To convert an expression into the TeX representation the following code could be used

let ecca = require('ecca')
let expression = new ecca.Expression('y=x^2/4')
let texString = generateRawTeX(expression)

will give the output

y=\frac{x^{2}}{4}

It is also possible to output a decorated TeX string, useful for libraries such as MathJax where the \cssId{id}{...} tag is used around any elements which have a associated id set. To convert the expression into such a decorated string the function generateDecoratedTeX(expression) should be used instead, the above example would then output the following

\cssId{y0}{y}=\frac{\cssId{x0}{x}^{2}}{4}