[Python] Python-polars: from coefficients, values and (nested) lists to weighted values

Let's say I've got a Polars DataFrame similar to this one:

import polars as pl
from decimal import Decimal

df = pl.from_dicts(
[
{"id": 1, "value": Decimal("100.0"), "items": ["A"]},
{"id": 2, "value": Decimal("150.000"), "items": ["A", "B"]},
{"id": 3, "value": Decimal("70.0000"), "items": ["A", "B", "C"]},
]
)

id → pl.Int64 value → pl.Decimal items → pl.List(str)
1 100 ["A"]
2 150 ["A", "B"]
3 70 ["A", "B", "C"]

And the following Python dictionary:

coef = {"A": Decimal("0.2"), "B": Decimal("0.35"), "C": Decimal("0.45") }


From here, how to get the following DataFrame in an efficient manner using Polars?

┌─────┬────────────────┬──────┐
│ id ┆ value ┆ item │
│ --- ┆ --- ┆ --- │
│ i64 ┆ decimal[*,10] ┆ str │
╞═════╪════════════════╪══════╡
│ 1 ┆ 100.0000000000 ┆ A │
│ 2 ┆ 54.5454000000 ┆ A │
│ 2 ┆ 95.4544500000 ┆ B │
│ 3 ┆ 14.0000000000 ┆ A │
│ 3 ┆ 24.5000000000 ┆ B │
│ 3 ┆ 31.5000000000 ┆ C │
└─────┴────────────────┴──────┘


In this example, 54.5454... for instance corresponds to 0.2 / (0.2 + 0.35) * 150.

Note that the length of the coef dictionary isn't always the same. It basically looks like {key1: coef1, key2: coef2, ... } with n keys and n values (whose sum is equal to Decimal(1)).

Also, I'm working with Decimal (not float64 values).

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