index: add document for partial index

[YangKeao]

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1. Add the document for partial index.

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• This PR is translated from: index: add document for partial index docs-cn#20999
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[gemini-code-assist]

Summary of Changes

Hello @YangKeao, I'm Gemini Code Assist¹! I'm currently reviewing this pull request and will post my feedback shortly. In the meantime, here's a summary to help you and other reviewers quickly get up to speed!

This pull request adds comprehensive documentation for the partial index feature. The changes provide users with a clear understanding of how to define, use, and optimize queries with partial indexes, along with their limitations and performance advantages. This update aims to improve user experience by making this database feature more accessible and understandable.

Highlights

• Documentation for Partial Indexes: Introduced comprehensive documentation for partial indexes, covering their definition, creation methods (CREATE INDEX, ALTER TABLE, CREATE TABLE), and usage examples within the sql-statement-create-index.md file.
• Usage and Performance Benefits: Detailed how partial indexes can be effectively used with SQL examples and EXPLAIN outputs, highlighting their benefits in reduced storage and faster DML operations.
• Limitations and Scenarios: Outlined the specific limitations of partial indexes, such as supported operators and column referencing, and identified key scenarios where they are most useful (selective filtering, conditional uniqueness).

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[gemini-code-assist]

Code Review

This pull request adds documentation for the new partial index feature. The documentation is well-structured and provides good examples. I've made a few suggestions to improve clarity and address potential user confusion, particularly around when the optimizer chooses to use a partial index. I've also suggested minor wording improvements for better readability and a more formal tone, in line with the style guide.

[gemini-code-assist]

The current phrasing "Then the following queries can use the partial index:" is slightly misleading, as the last example (SELECT * FROM users WHERE status = 'pending';) does not use the partial index. To improve clarity, I suggest explaining that for a partial index to be used, the query must benefit from the indexed columns.

Suggested change

	Then the following queries can use the partial index:
	The following examples show how the optimizer uses (or does not use) partial indexes based on the query structure. For a partial index to be used, the query must not only match the `WHERE` condition of the index but also benefit from the indexed columns for filtering or ordering.

[gemini-code-assist]

This example correctly shows that the optimizer might not choose the partial index. To help users understand why, I suggest adding a note explaining that since the query doesn't filter or order by created_at, a full table scan is more efficient.

Suggested change

	```
	> **Note:**
	> In this case, although the `WHERE status = 'pending'` condition matches the partial index `idx_pending_status (created_at) WHERE status = 'pending'`, the query does not filter or order by `created_at`. Therefore, the optimizer chooses a full table scan as it is more efficient.

[gemini-code-assist]

The phrase "don't meet the index definition" is a bit vague. For better clarity, I suggest rephrasing to explain that the query's WHERE clause must imply the condition of the partial index for it to be used.

Suggested change

	If the predicates in query don't meet the index definition, the index will not be chosen even with hint:
	If the query's `WHERE` clause does not imply the condition of the partial index, the index will not be used, even with a hint:

[gemini-code-assist]

The use of "It'll" is informal. I suggest rephrasing for a more professional tone and improved clarity, and adding backticks to DML operations as per the style guide.

Suggested change

	2. **Faster DML**: It'll be faster to maintain the index of a subset of data during INSERT, UPDATE, and DELETE operations
	2. **Faster DML**: Index maintenance during `INSERT`, `UPDATE`, and `DELETE` operations is faster, as only a subset of data is indexed.