🌐 [translation-sync] [rational_expectations] Update content and styling

[mmcky]

Automated Translation Sync

This PR contains automated translations from QuantEcon/lecture-python.myst.

Source PR

#764 - [rational_expectations] Update content and styling

Files Updated

• ✏️ lectures/rational_expectations.md
• ✏️ .translate/state/rational_expectations.md.yml

Details

• Source Language: en
• Target Language: zh-cn
• Model: claude-sonnet-5

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This PR was created automatically by the translation action.

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✅ Translation Quality Review

Verdict: PASS | Model: claude-sonnet-5 | Date: 2026-08-06
Routing: editor — 3 minor finding(s) in gating categories (accuracy/terminology/syntax/diff-check/other); accuracy 8 below floor 9; terminology 8 below floor 9; formatting 7 below floor 8
Shadow gate: would NOT auto-merge (recorded only; no action taken)

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📝 Translation Quality

Criterion	Score
Accuracy	8/10
Fluency	8/10
Terminology	8/10
Formatting	7/10
Overall	7.9/10

Summary: The translation of the changed sections is accurate, technically sound, and terminologically consistent with the glossary. Mathematical content, MyST directives, and code blocks are well preserved. A few minor fluency issues exist in transitional sentences (e.g., the opening of the Rational Expectations Equilibrium section reads slightly awkwardly), and there are small non-substantive additions in a couple of sentences, but none affect comprehension or introduce factual errors. No syntax errors were found in the MyST/Markdown structure of the modified sections. Highly consistent and accurate rendering of technical/economic terminology (e.g., 理性预期均衡, 贝尔曼方程, 欧拉方程, 横截条件) matching the glossary. Mathematical notation, LaTeX equations, and MyST directive labels are preserved correctly throughout all changed sections. Full-width Chinese punctuation is used consistently in prose, and spacing around inline directives/math is properly applied. Code blocks and comments are faithfully translated (e.g., '# 模型参数', '# 信念') while preserving code structure and variable names.

Suggestions:

• [minor · accuracy] lectures/rational_expectations.md — ### The big Y, little y trick: The English says 'There is a uniform unit measure of identical firms named ω ∈ Ω = [0,1]' which simply states a unit measure of firms. The translation adds interpretive phrasing '假设存在一个由同质企业组成的连续体，其测度为 1' which is an acceptable paraphrase but slightly expands on the source; this is minor and doesn't distort meaning.
• [minor · fluency] lectures/rational_expectations.md — ## Rational expectations equilibrium (intro paragraph): The sentence '我们首次对理性预期均衡的说明，考虑一个由连续体同质企业组成的市场。' is grammatically awkward in Chinese; '我们首次对...的说明' does not flow naturally as a standalone clause before '考虑'. → 我们首次说明理性预期均衡时，考虑一个由连续体同质企业组成的市场，每个企业都在存在调整成本的情况下最大化自身利润的贴现现值。
• [minor · accuracy] lectures/rational_expectations.md — ### Competitive equilibrium with adjustment costs: English: 'consider a collection of n firms producing a homogeneous good' — translated as '考虑一个包含 $n$ 个企业的市场，这些企业生产并销售一种同质产品'. The added '并销售' (and sell) is a minor addition not in the source, though harmless given context.
• [minor · terminology] lectures/rational_expectations.md — #### Optimal behavior given beliefs: Minor phrasing: '现在，让我们先固定{eq}ree_hlom中的特定信念 $H$' — missing space before the inline math/eq reference is fine, but the '先' is slightly redundant with '现在' and reads a bit awkwardly; consider simplifying. → 现在，让我们固定 {eq}ree_hlom 中的特定信念 $H$，并研究企业对它的反应。
• [minor · formatting] lectures/rational_expectations.md — Imports code cell after 'The big Y, little y trick' intro: The translated code cell inserts extra font-configuration lines (FONTPATH, mpl.font_manager, plt.rcParams) not present in the English source. While this is a common practice in this translation pipeline for CJK font rendering and not a translation-quality issue per se, it does deviate from a literal 1:1 code match; flagging as minor since it's likely intentional/standard for this doc series and n…

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🔍 Diff Quality

Check	Status
Scope Correct	✅
Position Correct	✅
Structure Preserved	✅
Heading-map Correct	✅
Overall	10/10

Summary: The translation sync correctly applied all source changes (heading case normalization, new explanatory sentences, equation corrections, definition block wrapping, and updated heading map) to the target document in matching positions.

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This review was generated automatically by action-translation review mode.

[Copilot]

Pull request overview

This automated translation-sync PR updates the zh-cn rational_expectations lecture content/styling to match the upstream English source PR (#764), and refreshes the translation state metadata.

Changes:

• Updated translated headings and multiple lecture paragraphs/equations for clarity and consistency with upstream.
• Added/adjusted several explanatory sentences and a formal {prf:definition} block for the REE definition.
• Updated translation-sync state metadata (source SHA, sync date, mode, tool version).

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 1 comment.

File	Description
lectures/rational_expectations.md	Synced lecture text, headings, math, and MyST styling to upstream updates.
.translate/state/rational_expectations.md.yml	Updated translation state to reflect the new upstream source commit and tooling.

Suppressed comments (1)

lectures/rational_expectations.md:401

• Minor LaTeX formatting: there is an extra space before the closing parenthesis and no space in =0; this should be = 0 for readability and consistency with other displayed equations in the file.

-\gamma (y_{t+1} - y_t) + \beta [a_0 - a_1 H(Y_t) + \gamma (y_{t+2} - y_{t+1} )] =0

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