Divide

$\text{Quotient}_i = \frac{A_i}{B_i}$

Computes element-wise division of two numeric series. Essential for ratios, normalization, and cross-asset analysis.

First (A)	Second (B)	Quotient
100	50	2.0
75	100	0.75
-10	5	-2.0

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Division by Zero

Division by zero is mathematically undefined, so the quotient at that position is a null (missing) datapoint — never a fabricated number, and never an error that fails the rest of your series.

First	Second	Result
100	0	null
0	0	null
-50	0	null

Only that position is affected; every other datapoint is computed normally. If you need a value at every point, filter or replace zeros in the divisor before connecting it to this module.

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Missing Data

A missing (null) datapoint in either input — a data gap or a closed-market slot — produces a null at the same position in the quotient. The math is never faked with substitute values.

First	Second	Result
null	50	null
100	null	null
100	50	2.0

A null from a missing input means "no data exists here"; a null from a zero divisor means "the math is undefined for this data". Both appear as gaps in your charts.

In live execution the module returns exactly one datapoint — the newest — which is null when either input is missing or the divisor is zero at that moment.

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Input Alignment

Systemic automatically aligns inputs before division:

Scenario	What Happens
Different lengths	Shorter series padded by repeating last value
Different frequencies	Lower-frequency upsampled to match higher
One constant	Constant expanded to match series length

Example: ETH (1h) ÷ BTC (15m) → ETH upsampled to 15m intervals first.

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Practical Example: Relative Strength

Dividing an asset's price by a benchmark creates a relative strength indicator:

$\text{Relative Strength} = \frac{\text{Asset Price}}{\text{Benchmark Price}}$

Interpretation	Meaning
Ratio rising	Asset outperforming benchmark
Ratio falling	Asset underperforming benchmark
Ratio = 1.0	Asset tracking benchmark exactly

This is the foundation of pair trading, sector rotation, and performance attribution.

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Related Modules

• MUL — Inverse operation
• SUB — Absolute difference (vs. ratio)
• POW — Exponentiation (e.g., for geometric returns)