Arithmetic Functions

CalcTree supports a full range of arithmetic functions using MathJS syntax. These functions form the foundation of most calculations, supporting scalars, vectors, units, and element-wise operations.

You can use these with both raw values (e.g. 3) and unit-aware values (e.g. 3 kN, 200 mm).

Core Arithmetic

Function	Description	CalcTree Example
add(a, b)	Addition	add(2, 3) → 5
subtract(a, b)	Subtraction	subtract(10, 4) → 6
multiply(a, b)	Multiplication	multiply(3, 4) → 12
divide(a, b)	Division	divide(10, 2) → 5
mod(a, b)	Modulus (remainder)	mod(7, 3) → 1
pow(a, b)	Power (a^b)	pow(2, 3) → 8
unaryMinus(x)	Negate a value	unaryMinus(5) → -5
unaryPlus(x)	Returns value unchanged	unaryPlus(5) → 5

Element-wise (Array) Arithmetic

Function	Description	CalcTree Example
dotAdd(a, b)	(Not explicit in MathJS, but implied)	add([1,2], [3,4]) → [4,6]
dotSubtract(a,b)	(Same idea as above)	subtract([5,6], [1,2]) → [4,4]
dotMultiply(a,b)	Element-wise multiplication	dotMultiply([2,3], [4,5]) → [8,15]
dotDivide(a,b)	Element-wise division	dotDivide([6,8], [2,4]) → [3,2]
dotPow(a, b)	Element-wise power	dotPow([2, 3], 2) → [4, 9]

Roots, Logs & Exponents

Function	Description	CalcTree Example
sqrt(x)	Square root	sqrt(25) → 5
cbrt(x)	Cube root	cbrt(27) → 3
nthRoot(x, n)	n-th root	nthRoot(16, 4) → 2
nthRoots(x)	All n-th roots (returns array)	nthRoots(4) → [2, -2]
exp(x)	Euler’s number e to the power of x	exp(1) → 2.718...
expm1(x)	e^x - 1	expm1(1) → 1.718...
log(x)	Natural logarithm (base e)	log(10) → 2.302...
log10(x)	Base-10 log	log10(1000) → 3
log2(x)	Base-2 log	log2(8) → 3
log1p(x)	log(x + 1)	log1p(1) → 0.693...

Rounding & Sign

Function	Description	CalcTree Example
round(x [, n])	Round to nearest integer or decimal	round(2.345, 2) → 2.35
ceil(x)	Round up	ceil(2.1) → 3
floor(x)	Round down	floor(2.9) → 2
fix(x)	Round toward zero	fix(-2.7) → -2
sign(x)	Returns 1 if positive, -1 if negative	sign(-8) → -1

Other Utilities

Function	Description	CalcTree Example
abs(x)	Absolute value	abs(-5) → 5
cube(x)	x * x * x	cube(3) → 27
square(x)	x * x	square(4) → 16
hypot(...)	Euclidean length (Pythagorean)	hypot(3, 4) → 5
norm(x [, p])	Vector or matrix norm	norm([3, 4]) → 5

Discrete Math Functions

Function	Description	CalcTree Example
gcd(a, b)	Greatest common divisor	gcd(18, 24) → 6
xgcd(a, b)	Extended GCD — returns coefficients	xgcd(8, 12) → {gcd: 4, x: -1, y: 1}
lcm(a, b)	Least common multiple	lcm(6, 8) → 24
invmod(a, b)	Modular inverse: x such that a·x ≡ 1 (mod b)	invmod(3, 11) → 4

Notes for CalcTree

• All arithmetic functions support unit-aware values: e.g., sqrt(25 m²) → 5 m

• dot* functions are useful when applying operations across arrays from tables

• Use round(..., n) when formatting outputs for display (e.g. 2 decimal places)

• Avoid ^ for arrays — prefer pow() or dotPow() to be explicit

📘 Looking for more functions? CalcTree’s expression engine is powered by MathJS. For a full list of available functions, visit the MathJS Function Reference. Most functions listed there are supported in CalcTree unless otherwise noted.