2025-04-08 19:05:05 +03:00
## Built-in operators
The following operators can be used in expressions:
| Operator | Description | Example |
|----------|-------------------------------|-----------------|
| `+` | Addition or unary plus | `2 + 3` or `+3` |
| `-` | Subtraction or unary minus | `5 - 2` or `-3` |
| `*` | Multiplication | `4 * 2` |
| `/` | Division | `10 / 2` |
| `^` | Exponentiation | `2 ^ 3` |
| `%` | Modulo | `10 % 3` |
## Implicit multiplication
Expressions supports implicit multiplication, allowing you to omit the multiplication operator in certain cases. For example, the expression `2cos(yx)` is interpreted as `2*cos(y*x)` . Similarly, `3x` is interpreted as `3*x` , and `xy` as `x*y` . This feature makes writing expressions more concise and natural.
## Built-in constants
Available constants for calculations:
| Constant | Description | Value |
|-------------|-----------------------------|-------------------|
| `π` or `pi` | The mathematical constant π | 3.141592653589793 |
| `e` | Euler's number | 2.718281828459045 |
| `φ` | The golden ratio | 1.618033988749895 |
2025-04-08 17:15:52 +03:00
## Built-in mathematical functions
2025-04-08 19:05:05 +03:00
The following built-in mathematical functions can be used to perform various calculations:
2025-04-08 17:15:52 +03:00
| Function | Description | Example |
|---------------|---------------------------------------------------------------------|-------------------|
| `abs(x)` | Absolute value of `x` . | `abs(-7) = 7` |
| `acos(x)` | Arc cosine of `x` , result in radians. Requires `-1 ≤ x ≤ 1` . | `acos(1) = 0` |
| `asin(x)` | Arc sine of `x` , result in radians. Requires `-1 ≤ x ≤ 1` . | `asin(0) = 0` |
| `atan(x)` | Arc tangent of `x` , result in radians. | `atan(0) = 0` |
| `cbrt(x)` | Cube root of `x` . | `cbrt(8) = 2` |
| `ceil(x)` | Rounds `x` up to the nearest integer. | `ceil(3.1) = 4` |
| `cos(x)` | Cosine of `x` , where `x` is in radians. | `cos(0) = 1` |
| `cosh(x)` | Hyperbolic cosine of `x` . | `cosh(0) = 1` |
| `cot(x)` | Cotangent of `x` (1 / tan(`x` )), where `x` is in radians. | `cot(0.7854) ≈ 1` |
| `exp(x)` | Computes `e^x` . | `exp(0) = 1` |
| `expm1(x)` | Computes `e^x - 1` accurately for small `x` . | `expm1(0) = 0` |
| `floor(x)` | Rounds `x` down to the nearest integer. | `floor(3.9) = 3` |
| `ln(x)` | Natural logarithm (base *e* ) of `x` . Requires `x > 0` . | `ln(1) = 0` |
| `log(x)` | Natural logarithm (base *e* ) of `x` . Requires `x > 0` . | `log(1) = 0` |
| `lg(x)` | Natural logarithm (base 10) of `x` . Requires `x > 0` . | `lg(10) = 1` |
| `log10(x)` | Logarithm base 10 of `x` . Requires `x > 0` . | `log10(100) = 2` |
| `log2(x)` | Logarithm base 2 of `x` . Requires `x > 0` . | `log2(8) = 3` |
| `logab(a, b)` | Logarithm of `b` with base `a` . Requires `a > 0` , `b > 0` , `a ≠ 1` . | `logab(2, 8) = 3` |
| `log1p(x)` | Computes `ln(1 + x)` accurately for small `x` . Requires `x > -1` . | `log1p(0) = 0` |
| `pow(x, y)` | Raises `x` to the power of `y` (`x^y` ). | `pow(2, 3) = 8` |
| `signum(x)` | Returns the sign of `x` : -1 if `x < 0` , 0 if `x = 0` , 1 if `x > 0` . | `signum(-5) = -1` |
| `sin(x)` | Sine of `x` , where `x` is in radians. | `sin(0) = 0` |
| `sinh(x)` | Hyperbolic sine of `x` . | `sinh(0) = 0` |
| `sqrt(x)` | Square root of `x` . Requires `x ≥ 0` . | `sqrt(4) = 2` |
| `tan(x)` | Tangent of `x` , where `x` is in radians. | `tan(0) = 0` |
| `tanh(x)` | Hyperbolic tangent of `x` . | `tanh(0) = 0` |
