Descriptions
Each attribute and constraint object has a defined value. For attributes, this includes the unit, the type of value, and any associated equations. For constraints, the value is simply a boolean statement. These values can either be simple values, like strings or numbers, or complex mathematical relations involving values from other objects.
Special handling is applied when resolving values containing strings of TBD (To Be Determined). This can be useful during the early stages of model formation to not resolve errors when the value is still being defined.
Math Syntax
Equations are powered by Math.js, providing a comprehensive set of mathematical operations and functions. The syntax follows standard mathematical conventions:
Basic Operations
| Operation | Syntax |
|---|
| Addition | A + B |
| Subtraction | A - B |
| Multiplication | A * B |
| Division | A / B |
| Modulus | A % B |
| Exponentiation | A ^ B |
Comparison Operators
| Operator | Syntax |
|---|
| Equal | == |
| Not Equal | != |
| Less Than | < |
| Greater Than | > |
| Less or Equal | <= |
| Greater or Equal | >= |
Mathematical Functions
| Function | Syntax | Description |
|---|
| Absolute Value | abs(x) | Returns the absolute value |
| Square Root | sqrt(x) | Returns the square root |
| Cube Root | cbrt(x) | Returns the cube root |
| Power | pow(x, y) | Returns x raised to power y |
| Exponential | exp(x) | Returns e raised to power x |
| Natural Log | log(x) | Returns the natural logarithm |
| Base-10 Log | log10(x) | Returns the base-10 logarithm |
| Minimum | min(a, b, ...) | Returns the minimum value |
| Maximum | max(a, b, ...) | Returns the maximum value |
| Round | round(x) | Rounds to nearest integer |
| Floor | floor(x) | Rounds down to integer |
| Ceil | ceil(x) | Rounds up to integer |
| Sign | sign(x) | Returns -1, 0, or 1 |
Trigonometric Functions
| Function | Syntax | Description |
|---|
| Sine | sin(x) | Sine of x (in radians) |
| Cosine | cos(x) | Cosine of x (in radians) |
| Tangent | tan(x) | Tangent of x (in radians) |
| Arcsine | asin(x) | Inverse sine |
| Arccosine | acos(x) | Inverse cosine |
| Arctangent | atan(x) | Inverse tangent |
| Arctangent2 | atan2(y, x) | Angle from x-axis to point |
| Hyperbolic Sine | sinh(x) | Hyperbolic sine |
| Hyperbolic Cosine | cosh(x) | Hyperbolic cosine |
| Hyperbolic Tangent | tanh(x) | Hyperbolic tangent |
Statistical Functions
| Function | Syntax | Description |
|---|
| Mean | mean(a, b, ...) | Returns the average value |
| Median | median(a, b, ...) | Returns the median value |
| Mode | mode(a, b, ...) | Returns the most frequent value |
| Standard Deviation | std(a, b, ...) | Returns standard deviation |
| Variance | variance(a, b, ...) | Returns variance |
| Sum | sum(a, b, ...) | Returns the sum of all values |
| Product | prod(a, b, ...) | Returns the product of all values |
Logical Functions
| Function | Syntax | Description |
|---|
| AND | and(a, b) | Logical AND |
| OR | or(a, b) | Logical OR |
| NOT | not(x) | Logical NOT |
| XOR | xor(a, b) | Logical XOR |
Constants
| Constant | Syntax | Value |
|---|
| Pi | pi | 3.14159… |
| Euler’s Number | e | 2.71828… |
| Golden Ratio | phi | 1.61803… |
Value Types
Attributes can have the following kind assoicated to a value, which handles how it is displayed or computed:
| Type | Description |
|---|
Boolean | Represents true or false values. Does not use a unit and clears any existing unit. |
Date | Used for date values. Does not use a unit and clears any existing unit. |
Number | Represents standard numeric values. Optionally includes a unit. |
String | Represents string values. Does not use a unit and clears any existing unit. |
Unit Referencing
Values can reference units inline, such as 10 kg, where the number is associated with the unit.
Object Referencing
To reference other objects within an equation, use the @ symbol followed by the object’s name. This will automatically resolve the object’s value and unit.
