Math. Js: An Advanced Mathematics Library For JavaScript

Description Math.js 
syntax 
JavaScript 
API 
A range from 1 to 5 
1:5 math.range(1, 
6) 
Transpose matrix A 
A' math.transpose(A) 
Get the second col-
umn of rows 1 
through 4 of matrix 
A 
A[1:4, 2] 
math.subset(A, 
math.index(math.range(0, 4), 1)) 
Add two physical 
quantities 
0.5 m + 5 cm 
math.add(math.unit(0.5, 'm'),
math.unit(5, 'cm')) 
Multiply a complex 
number 
2 * (2 + 3i) 
math.multiply(2, math.complex(2, 3)) 
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January/February 2018
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THE RISE OF JAVASCRIPT 
Create and use an 
object 
obj = {a: 2, b: 
3} 
c = obj.a + 
obj.b 
obj = {a: 2, b: 3} 
c = obj.a + obj.b 
The math.js syntax is much more concise than the native JavaScript API. Math.js also uses one-
based indices rather than zero-based, since the former is more common in mathematics software 
applications. Each math.js operator has an associated function in the native JavaScript API, 
which satisfies the needs of both audiences served by math.js: programmers and mathematicians. 
The math.js syntax is understood by the built-in expression parser. Parsing an expression returns 
an abstract syntax tree
27,28
representing the expression: 
var tree = math.parse('3x ^ 2 + 5'); // abstract syntax tree 
Math.js evaluates this expression by first compiling the tree into native JavaScript code. The 
compiled code can then be evaluated while providing values for any symbols used in the expres-
sion:
var compiled = tree.compile(); 
var result = compiled.eval( {x: 4} ); // 53 
Math.js can also perform algebraic operations by transforming abstract syntax trees: 
var tree = math.parse('x * x^2 '); 
math.simplify(tree); // x ^ 3 
math.derivative(tree); // 3 * x ^ 2 
The math.js syntax and expression parser are demonstrated further in the following case study. 
CASE STUDY: ROCKET TRAJECTORY 
OPTIMIZATION 
In this example, we show how math.js can be extended using a custom function to solve a sys-
tem of ordinary differential equations (ODEs). We will demonstrate this by simulating the ascent 
stage of the Apollo Lunar Module. In solving this problem, we will try to maintain generality so 
that the same methods can be used to solve many different systems of ODEs. For reference, the 
full code of this case study can be found in the examples section of the math.js library.
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The lunar ascent can be modeled using the following system of ODEs, representing the motion 
of an object in orbit around a planet or moon: 
 
( )
dr
v sin
dt
γ
= ⋅
 
 
( )
2
dv
T
sin
dt
r
m
μ
γ
−
=
⋅
+
 
 
0
sp
dm
T
dt
g I
−
=
 
 
( )
d
v
cos
dt
r
φ
γ
=
 
 
( )
1
d
v
cos
dt
r
r v
γ
μ
γ


=
−


⋅


 
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January/February 2018
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COMPUTING IN SCIENCE & ENGINEERING 
The quantities 
r
and 
φ
specify the object’s position in polar coordinates and represent, respec-
tively, the distance from the object to the center of the moon and the angular position of the ob-
ject relative to some reference point. The quantity