Math

Classes

complex

A class representing a complex number, composed of a real part r and an imaginary part i.

complex();
complex(const complex&in other);
complex(float r, float i = 0.0);

Arguments (3):

float r: The real part of the complex number.
float i = 0.0: The imaginary part of the complex number. Defaults to 0 if not specified.

Remarks:

The complex class supports basic arithmetic operations (add, subtract, multiply, divide) and can be compared for equality. It also provides access to magnitude (abs()), and utilities for working with real/imaginary order via ri and ir properties.

Example:

void main() {
	complex a(2, 3); // 2 + 3i
	complex b(1, -1); // 1 - i
	complex c = a + b; // (2+1, 3-1) = (3, 2)
	alert("result", "real: " + c.r + ", imag: " + c.i);
}

Functions

abs

Returns the absolute value (magnitude) of the complex number.

float complex::abs() const;

Example:

void main() {
	complex c(3, 4);
	alert("Magnitude =", c.abs());
}

Operators

opAdd

Adds two complex numbers and returns the result.

complex complex::opAdd(const complex&in other) const;

Arguments:

const complex&in other: the complex number to add.

Returns:

complex: a new complex object containing the value of the addition.

Example:

// Helper function to print a complex number.
string to_string(const complex&in c) {
	return "(" + c.r + ", " + c.i + ")";
}
void main() {
	complex a(1, 2);
	complex b(3, 4);
	complex c = a + b;
	alert("a + b =", to_string(c));
}

opAddAssign

Adds another complex number to this one.

complex& complex::opAddAssign(const complex&in other);

Arguments:

const complex&in other: the complex number to add.

Returns:

complex&: a reference to the complex number being operated on.

Example:

// Helper function to print a complex number.
string to_string(const complex&in c) {
	return "(" + c.r + ", " + c.i + ")";
}
void main() {
	complex a(1, 2);
	complex b(3, 4);
	a += b;
	alert("a + b =", to_string(a));
}

opDiv

Divides this complex number by another and returns the result.

complex complex::opDiv(const complex&in other) const;

Arguments:

const complex&in other: the complex number to divide by.

Returns:

complex: a new complex object containing the value of the division.

Example:

// Helper function to print a complex number.
string to_string(const complex&in c) {
	return "(" + c.r + ", " + c.i + ")";
}
void main() {
	complex a(1, 2);
	complex b(3, 4);
	complex c = a / b;
	alert("a / b =", to_string(c));
}

opDivAssign

Divides this complex number by another.

complex& complex::opDivAssign(const complex&in other);

Arguments:

const complex&in other: the complex number to divide by.

Returns:

complex&: a reference to the complex number being operated on.

Example:

// Helper function to print a complex number.
string to_string(const complex&in c) {
	return "(" + c.r + ", " + c.i + ")";
}
void main() {
	complex a(1, 2);
	complex b(3, 4);
	a /= b;
	alert("a / b =", to_string(a));
}

opEquals

Checks if two complex numbers are equal.

bool complex::opEquals(const complex&in other) const;

Arguments:

const complex&in other: the complex number to compare to.

Returns:

bool: true if the two complex numbers are equal, false otherwise.

Example:

void main() {
	complex a(1, 2);
	complex b(1, 2);
	alert("a equals b?", a == b);
}

opMul

Multiplies two complex numbers and returns the result.

complex complex::opMul(const complex&in other) const;

Arguments:

const complex&in other: the complex number to multiply with.

Returns:

complex: a new complex object containing the value of the multiplication.

Example:

// Helper function to print a complex number.
string to_string(const complex&in c) {
	return "(" + c.r + ", " + c.i + ")";
}
void main() {
	complex a(1, 2);
	complex b(3, 4);
	complex c = a * b;
	alert("a * b =", to_string(c));
}

opMulAssign

Multiplies this complex number by another.

complex& complex::opMulAssign(const complex&in other);

Arguments:

const complex&in other: the complex number to multiply with.

Returns:

complex&: a reference to the complex number being operated on.

Example:

// Helper function to print a complex number.
string to_string(const complex&in c) {
	return "(" + c.r + ", " + c.i + ")";
}
void main() {
	complex a(1, 2);
	complex b(3, 4);
	a *= b;
	alert("a * b =", to_string(a));
}

opSub

Subtracts a complex number from this one and returns the result.

complex complex::opSub(const complex&in other) const;

Arguments:

const complex&in other: the complex number to subtract.

Returns:

complex: a new complex object containing the value of the subtraction.

Example:

// Helper function to print a complex number.
string to_string(const complex&in c) {
	return "(" + c.r + ", " + c.i + ")";
}
void main() {
	complex a(5, 6);
	complex b(2, 3);
	complex c = a - b;
	alert("a - b =", to_string(c));
}

opSubAssign

Subtracts another complex number from this one.

complex& complex::opSubAssign(const complex&in other);

Arguments:

const complex&in other: the complex number to subtract.

Returns:

complex&: a reference to the complex number being operated on.

Example:

// Helper function to print a complex number.
string to_string(const complex&in c) {
	return "(" + c.r + ", " + c.i + ")";
}
void main() {
	complex a(5, 6);
	complex b(2, 3);
	a -= b;
	alert("a - b =", to_string(a));
}

Properties

i

Represents the imaginary component of the complex number.

float complex::i;

Example:

void main() {
	complex c(0, 1);
	alert("The imaginary part is", c.i);
}

ir

Accesses the complex number in imaginary-real order.

complex complex::ir [property];

Example:

// Helper function to print a complex number.
string to_string(const complex&in c) {
	return "(" + c.r + ", " + c.i + ")";
}
void main() {
	complex c(1, 2);
	alert("Imaginary-Real =", to_string(c.ir));
}

ri

Accesses the complex number in real-imaginary order.

complex complex::ri;

Example:

// Helper function to print a complex number.
string to_string(const complex&in c) {
	return "(" + c.r + ", " + c.i + ")";
}
void main() {
	complex c(1, 2);
	alert("Real-Imaginary =", to_string(c.ri));
}

vector

A class containing x, y and z coordinates, usually used to represent a 3d point in space.

vector();
vector(const vector& in vec);
vector(float x, float y = 0.0, float z = 0.0);

Arguments (3):

float x: The initial x point or coordinate this vector represents.
float y = 0.0: The initial y point or coordinate this vector represents.
float z = 0.0: The initial z point or coordinate this vector represents, defaulted to 0 because it may not be needed in some 2d applications.

Remarks:

An advantage with vectors is that they contain basic addition and scaling operators.

Example:

void main() {
	vector v1(5, 5, 5);
	vector v2(10, 10, 0);
	vector v3 = v1 + v2;
	alert("example", "the new vector is "+v3.x + ", " + v3.y + ", " + v3.z); // will show that the vector is 15, 15, 5.
}

Operators

opAssign

Overloads the = operator, allowing you to assign a vector to another, already existing one.

vector& opAssign(const vector &in other);

Arguments:

const vector&in other: the vector to assign to.

Example:

void main() {
	vector v1;
	vector v2(1.2, 2.3, 9.3);
	v1 = v2;
	alert("The first vector =", "(" + round(v1.x, 2) + ", " + round(v1.y, 2) + ", " + round(v1.z, 2) + ")");
}

Properties

x

Represents the x coordinate of the vector.

float vector::x const;

Example:

void main() {
	vector v(2.9);
	alert("The x value of the vector is", round(v.x, 2));
}

y

Represents the y coordinate of the vector.

float vector::y const;

Example:

void main() {
	vector v(2.9, 19.2);
	alert("The y value of the vector is", round(v.y, 2));
}

z

Represents the z coordinate of the vector.

float vector::z const;

Example:

void main() {
	vector v(2.9, 19.2, 4.1);
	alert("The z value of the vector is", round(v.z, 2));
}

Functions

abs

Returns the absolute value of a value.

double abs(double x);

Arguments:

double x: The value whose absolute value is to be calculated.

Returns:

double: the absolute value of the given value.

Example:

void main() {
	alert("Example", "The absolute value of -5 is " + abs(-5));
}

acos

Returns the arc cosine of a value in radians.

double acos(double x);

Arguments:

double x: The value whose arc cosine is to be calculated.

Returns:

double: the arc cosine of the given value.

Example:

void main() {
    alert("Example", "The arc cosine of 0.5 is " + acos(0.5) + " radians");
}

asin

Returns the arc sine of a value in radians.

double asin(double x);

Arguments:

double x: The value whose arc sine is to be calculated.

Returns:

double: the arc sine of the given value.

Example:

void main() {
    alert("Example", "The arc sine of 0.5 is " + asin(0.5) + " radians");
}

atan

Returns the arc tangent of a value in radians.

double atan(double x);

Arguments:

double x: The value whose arc tangent is to be calculated.

Returns:

double: the arc tangent of the given value.

Example:

void main() {
    alert("Example", "The arc tangent of 1 is " + atan(1) + " radians");
}

atan2

Returns the arc tangent of y/x, where y and x are the coordinates of a point.

double atan2(double y, double x);

Arguments:

double y: The ordinate coordinate.
double x: The abscissa coordinate.

Returns:

double: the arc tangent of y/x.

Example:

void main() {
    alert("Example", "The arc tangent of (1, 2) is " + atan2(1, 2) + " radians");
}

ceil

Returns the smallest integer greater than or equal to a value.

double ceil(double x);

Arguments:

double x: The value whose ceiling is to be calculated.

Returns:

double: the smallest integer greater than or equal to x.

Example:

void main() {
	alert("Example", "The ceiling of 3.14 is " + ceil(3.14));
}

cos

Returns the cosine of an angle given in radians.

double cos(double x);

Arguments:

double x: The angle (in radians) to get the cosine of.

Returns:

double: the cosine of the angle.

Example:

void main() {
	alert("Example", "The cosine of 45 is " + cos(45 * 3.14159 / 180) + " radians");
}

cosh

Returns the hyperbolic cosine of a value.

double cosh(double x);

Arguments:

double x: The value whose hyperbolic cosine is to be calculated.

Returns:

double: the hyperbolic cosine of the given value.

Example:

void main() {
    alert("Example", "The hyperbolic cosine of 2 is " + cosh(2));
}

floor

Returns the largest integer less than or equal to a value.

double floor(double x);

Arguments:

double x: The value whose floor is to be calculated.

Returns:

double: the largest integer less than or equal to x.

Example:

void main() {
	alert("Example", "The floor of 3.14 is " + floor(3.14));
}

fraction

Returns the fractional part of a value.

double fraction(double x);

Arguments:

double x: The value whose fractional part is to be extracted.

Returns:

double: the fractional part of the given value.

Example:

void main() {
	alert("Example", "The fractional part of 3.75 is " + fraction(3.75));
}

log

Returns the natural logarithm (base e) of a value.

double log(double x);

Arguments:

double x: The value whose natural logarithm is to be calculated.

Returns:

double: the natural logarithm of the given value.

Example:

void main() {
    alert("Example", "The natural logarithm of 10 is " + log(10));
}

log10

Returns the base 10 logarithm of a value.

double log10(double x);

Arguments:

double x: The value whose base 10 logarithm is to be calculated.

Returns:

double: the base 10 logarithm of the given value.

Example:

void main() {
    alert("Example", "The base 10 logarithm of 100 is " + log10(100));
}

pow

Returns x raised to the power of y.

double pow(double x, double y);

Arguments:

double x: The base.
double y: The exponent.

Returns:

double: x raised to the power of y.

Example:

void main() {
    alert("Example", "2 raised to the power of 3 is " + pow(2, 3));
}

round

Returns the value of a number rounded to the nearest integer.

double round(double n, int p);

Arguments:

double n: The number to be rounded.
int p: The number of decimal places to round to.

Returns:

double: The value of the number rounded to the nearest integer.

Example:

void main() {
	alert("Example", "Rounding 3.14159 to 2 decimal places gives " + round(3.14159, 2));
}

sin

Returns the sine of an angle given in radians.

double sin(double x);

Arguments:

double x: The angle (in radians) to get the sine of.

Returns:

double: the sine of the angle.

Example:

void main() {
	alert("Example", "The sine of 45 is " + sin(45 * 3.14159 / 180) + " radians");
}

sinh

Returns the hyperbolic sine of a value.

double sinh(double x);

Arguments:

double x: The value whose hyperbolic sine is to be calculated.

Returns:

double: the hyperbolic sine of the given value.

Example:

void main() {
    alert("Example", "The hyperbolic sine of 2 is " + sinh(2));
}

sqrt

Returns the square root of a value.

double sqrt(double x);

Arguments:

double x: The value whose square root is to be calculated.

Returns:

double: the square root of the given value.

Example:

void main() {
	alert("Example", "The square root of 16 is " + sqrt(16));
}

tan

Returns the tangent of an angle given in radians.

double tan(double x);

Arguments:

double x: The angle (in radians) to get the tangent of.

Returns:

double: the tangent of the angle.

Example:

void main() {
	alert("Example", "The tangent of 45 is " + tan(45 * 3.14159 / 180) + " radians");
}

tanh

Returns the hyperbolic tangent of a value.

double tanh(double x);

Arguments:

double x: The value whose hyperbolic tangent is to be calculated.

Returns:

double: the hyperbolic tangent of the given value.

Example:

void main() {
    alert("Example", "The hyperbolic tangent of 2 is " + tanh(2));
}

tinyexpr

Evaluate a mathematical expression using the tinyexpr library.

double tinyexpr(const string&in expression);

Arguments:

const string&in expression: the expression to evaluate.

Returns:

double: the result of the expression.

Example:

void main() {
	string expression = input_box("Expression", "Enter expression to evaluate");
	if (expression.is_empty()) exit();
	alert("Result", expression + "= " + tinyexpr(expression));
}