<=

$$\text{Output}_i = \begin{cases} \text{true} & \text{if } A_i \leq B_i \\ \text{false} & \text{otherwise} \end{cases}$$

The Less Than or Equal module performs an inclusive comparison—output is true when the first value is less than or equal to the second.

A	B	A ≤ B
5	10	true
10	10	true
15	10	false
0	0	true

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Inclusive vs Strict Comparison

⚠️ Key difference from LST (<): Equal values return true with LSTE.

Comparison	10 vs 10 Result
LST (<)	false
LSTE (≤)	true

Use LSTE when touching a threshold should count as meeting the condition (e.g., "at or below stop-loss level").

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Missing Data

If either input is missing (null) at a position — a data gap or a closed-market day — the comparison at that position is null. The module never invents an answer for missing data: a gap in your inputs stays a gap in the output, not a fabricated false.

A	B	A ≤ B
5	null	null
null	10	null
null	null	null

There are no mathematically undefined cases for this comparison: any two present values — including infinities — always produce a real true or false. Null appears only where an input is missing.

Missing data is separate from input alignment (below): alignment reconciles two series of different lengths or frequencies, while a null is a missing datapoint inside an already-aligned series — it is never filled in and stays null in the output.

In live execution the module returns exactly one datapoint — the newest position — which is null when either input is missing there.

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Input Alignment

When inputs have different lengths or frequencies, Systemic automatically aligns them:

Scenario	Behavior
Different lengths	Shorter series is padded by repeating its last value
Different frequencies	Lower-frequency series is upsampled to match
Constant vs series	Constant is broadcast to all time points

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Practical Example

Risk limit check: Verify that portfolio drawdown stays within limits using Drawdown <= Max Drawdown. The inclusive comparison means exactly hitting the limit still passes the check.

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Related Modules

• LST (<) — Strict less-than (excludes equality)
• GTR (>) — Strict greater-than
• GTRE (≥) — Greater than or equal
• EQ (==) — Equality only