# Logical & Comparison functions

CalcTree supports standard logical and comparison functions using [MathJS syntax](https://mathjs.org/docs/reference/functions.html#logical) and [comparison operators](https://mathjs.org/docs/reference/functions.html#relational).

These functions return `true` or `false`, and are often used in conditional expressions and ternary operations (e.g. `a > b ? "yes" : "no"`).

### If Statements

MathJS does not use a traditional `if(...) {}` structure. Instead, native CalcTree parameters support **conditional logic** using the **ternary operator**:

```
condition ? value_if_true : value_if_false
```

#### Example: Basic if logic

```
result = load > limit ? "Fail" : "Pass"
```

#### Nested conditions (like else if)

```
check = ratio < 1 ? "OK" : ratio < 1.5 ? "Warning" : "Fail"
```

### Comparison Functions

<table><thead><tr><th>Function</th><th width="219">Description</th><th>CalcTree Example</th></tr></thead><tbody><tr><td><code>IF(condition, a, b)</code></td><td>Returns <code>a</code> if true, <code>b</code> if false</td><td><code>IF(load > 100, "Fail", "Pass")</code> → <code>"Pass"</code></td></tr><tr><td><code>equal(a, b)</code></td><td>Checks strict equality</td><td><code>equal(2, 2)</code> → <code>true</code></td></tr><tr><td><code>unequal(a, b)</code></td><td>Checks inequality</td><td><code>unequal(2, 3)</code> → <code>true</code></td></tr><tr><td><code>smaller(a, b)</code></td><td>Less than</td><td><code>smaller(1, 2)</code> → <code>true</code></td></tr><tr><td><code>smallerEq(a, b)</code></td><td>Less than or equal</td><td><code>smallerEq(2, 2)</code> → <code>true</code></td></tr><tr><td><code>larger(a, b)</code></td><td>Greater than</td><td><code>larger(3, 1)</code> → <code>true</code></td></tr><tr><td><code>largerEq(a, b)</code></td><td>Greater than or equal</td><td><code>largerEq(3, 3)</code> → <code>true</code></td></tr></tbody></table>

### Natural and String Comparison

| Function               | Description                              | CalcTree Example                   |
| ---------------------- | ---------------------------------------- | ---------------------------------- |
| `compare(a, b)`        | General numerical comparison             | `compare(2, 3)` → `-1`             |
| `compareText(a, b)`    | Lexical string comparison                | `compareText("a", "b")` → `-1`     |
| `compareNatural(a, b)` | Natural-order comparison (e.g., v1 < v2) | `compareNatural("2", "10")` → `-1` |

### Deep & Elementwise Equality

| Function          | Description                               | CalcTree Example                     |
| ----------------- | ----------------------------------------- | ------------------------------------ |
| `deepEqual(a, b)` | Element-wise equality for arrays/matrices | `deepEqual([1, 2], [1, 2])` → `true` |
| `equalText(a, b)` | Text string equality                      | `equalText("abc", "abc")` → `true`   |

### Logical Functions

| Function    | Description  | CalcTree Example            |
| ----------- | ------------ | --------------------------- |
| `and(a, b)` | Logical AND  | `and(true, true)` → `true`  |
| `or(a, b)`  | Logical OR   | `or(false, true)` → `true`  |
| `not(a)`    | Logical NOT  | `not(true)` → `false`       |
| `xor(a, b)` | Exclusive OR | `xor(true, false)` → `true` |

### Notes for CalcTree

* Logical outputs (`true`, `false`) can be used in conditional formulas like:

  ```lua
  result = load > limit ? "Fail" : "Pass"
  ```
* For multi-value comparisons (e.g. arrays), use `deepEqual()` instead of `equal()`.
* Comparisons between unit-bearing quantities must be dimensionally consistent (e.g. `2 m > 1 m` is valid, `2 m > 1 kg` is not).

{% hint style="info" %}
📘 **Looking for more functions?**\
CalcTree’s expression engine is powered by [MathJS](https://mathjs.org/docs/reference/functions.html).\
For a full list of available functions, visit the [MathJS Function Reference](https://mathjs.org/docs/reference/functions.html).\
Most functions listed there are supported in CalcTree unless otherwise noted.
{% endhint %}


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