{"id":5429,"date":"2026-02-16T11:00:22","date_gmt":"2026-02-16T17:00:22","guid":{"rendered":"https:\/\/ykim.synology.me\/wordpress\/?p=5429"},"modified":"2026-02-16T22:17:51","modified_gmt":"2026-02-17T04:17:51","slug":"rm-ai-prompt-question-on-a-math-problem","status":"publish","type":"post","link":"https:\/\/ykim.synology.me\/wordpress\/rm-ai-prompt-question-on-a-math-problem-5429\/","title":{"rendered":"RM AI Prompt: Question on a Math Problem"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">This prompt provides mathematical definitions, derivations, step-by-step solutions, and detailed walkthroughs of mathematical processes.<br>This is optimized for posting in a WordPress bbPress topic.<br>Version 6, 2026.2.16<\/p>\n\n\n\n<div class=\"wp-block-kevinbatdorf-code-block-pro cbp-has-line-numbers\" data-code-block-pro-font-family=\"Code-Pro-JetBrains-Mono\" style=\"font-size:.875rem;font-family:Code-Pro-JetBrains-Mono,ui-monospace,SFMono-Regular,Menlo,Monaco,Consolas,monospace;--cbp-line-number-color:#24292e;--cbp-line-number-width:calc(2 * 0.6 * .875rem);line-height:1.25rem;--cbp-tab-width:2;tab-size:var(--cbp-tab-width, 2)\"><span role=\"button\" tabindex=\"0\" style=\"color:#24292e;display:none\" aria-label=\"Copy\" class=\"code-block-pro-copy-button\"><pre class=\"code-block-pro-copy-button-pre\" aria-hidden=\"true\"><textarea class=\"code-block-pro-copy-button-textarea\" tabindex=\"-1\" aria-hidden=\"true\" readonly>### User\nHow to calculate Lower Triangular Matrix in Cholesky Decomposition?\n* Note that the reader is AI learner.\n\n### System\n* Your entire response must be contained within a **single markdown code block** (```).\n* **Line Breaks**: Strictly use \\cr for line breaks instead of \\\\ for matrcies to avoid WordPress rendering issues,\n  while providing LaTex formulas especially matrices.\n  (example) $$A = \\begin{pmatrix} 1 &amp; 2 \\cr 3 &amp; 4 \\end{pmatrix}$$\n* **Encapsulation**: Always wrap math expressions in `$$...$$` for line-break math or `$...$` for inline math.\n   This signals the MathJax\/KaTeX renderer to process the content before the WordPress Markdown parser can alter the characters.\n* **Subscripts &amp; Underscores**: To prevent WordPress from converting math into italics, escape underscores \n   by using `\\_` instead of `_` (e.g., `a\\_{ij}`), or omit the underscore entirely (e.g., `aij`)\n   if the multi-underscore conflict persists.\"\n* **Subscripts with Asterisks**: To prevent italicization and ensure correct rendering,\n   always escape the underscore before an asterisk within curly braces\n   (e.g., use `$f\\_{\\ast}$` or `$x\\_{\\ast}$` instead of $f_{\\ast}$ or $f_*$).\n* **Subscripts with Accents**: When a subscript asterisk follows an accent (e.g., \\bar or \\hat),\n   strictly use an escaped underscore within curly braces (e.g., `$\\bar{f}\\_{\\ast}$`) to prevent rendering failure.\n* **Vertical Bar in a Table**: When representing the vertical bar character `|` inside a markdown table,\n  strictly use the escaped character `\\|` to ensure correct table rendering.\n* **Code Snippets**: Always wrap code snippets and identifiers in a single pair of single backticks (\\`code\\`), \n and strictly avoid using triple backticks for any reason.\n* &#091;CRITICAL&#093; Never inject Markdown tags like &lt;em> or &lt;strong> inside math blocks.\n    \n### Assistant\n\n\n### Absolute Prohibitions\n- Any text outside the code block (greetings, \"Understood,\" \"Here is the result,\" etc.).\n- Creating multiple code blocks (all content must be in one single block).<\/textarea><\/pre><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:24px;height:24px\" fill=\"none\" viewBox=\"0 0 24 24\" stroke=\"currentColor\" stroke-width=\"2\"><path class=\"with-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2m-6 9l2 2 4-4\"><\/path><path class=\"without-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2\"><\/path><\/svg><\/span><pre class=\"shiki github-light\" style=\"background-color: #fff\" tabindex=\"0\"><code><span class=\"line\"><span style=\"color: #005CC5; font-weight: bold\">### User<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">How to calculate Lower Triangular Matrix in Cholesky Decomposition?<\/span><\/span>\n<span class=\"line\"><span style=\"color: #E36209\">*<\/span><span style=\"color: #24292E\"> Note that the reader is AI learner.<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #005CC5; font-weight: bold\">### System<\/span><\/span>\n<span class=\"line\"><span style=\"color: #E36209\">*<\/span><span style=\"color: #24292E\"> Your entire response must be contained within a <\/span><span style=\"color: #24292E; font-weight: bold\">**single markdown code block**<\/span><span style=\"color: #24292E\"> (```).<\/span><\/span>\n<span class=\"line\"><span style=\"color: #E36209\">*<\/span><span style=\"color: #24292E\"> <\/span><span style=\"color: #24292E; font-weight: bold\">**Line Breaks**<\/span><span style=\"color: #24292E\">: Strictly use \\cr for line breaks instead of <\/span><span style=\"color: #005CC5\">\\\\<\/span><span style=\"color: #24292E\"> for matrcies to avoid WordPress rendering issues,<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">  while providing LaTex formulas especially matrices.<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">  (example) $$A = \\begin{pmatrix} 1 &amp; 2 \\cr 3 &amp; 4 \\end{pmatrix}$$<\/span><\/span>\n<span class=\"line\"><span style=\"color: #E36209\">*<\/span><span style=\"color: #24292E\"> <\/span><span style=\"color: #24292E; font-weight: bold\">**Encapsulation**<\/span><span style=\"color: #24292E\">: Always wrap math expressions in <\/span><span style=\"color: #005CC5\">`$$...$$`<\/span><span style=\"color: #24292E\"> for line-break math or <\/span><span style=\"color: #005CC5\">`$...$`<\/span><span style=\"color: #24292E\"> for inline math.<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">   This signals the MathJax\/KaTeX renderer to process the content before the WordPress Markdown parser can alter the characters.<\/span><\/span>\n<span class=\"line\"><span style=\"color: #E36209\">*<\/span><span style=\"color: #24292E\"> <\/span><span style=\"color: #24292E; font-weight: bold\">**Subscripts &amp; Underscores**<\/span><span style=\"color: #24292E\">: To prevent WordPress from converting math into italics, escape underscores <\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">   by using <\/span><span style=\"color: #005CC5\">`\\_`<\/span><span style=\"color: #24292E\"> instead of <\/span><span style=\"color: #005CC5\">`_`<\/span><span style=\"color: #24292E\"> (e.g., <\/span><span style=\"color: #005CC5\">`a\\_{ij}`<\/span><span style=\"color: #24292E\">), or omit the underscore entirely (e.g., <\/span><span style=\"color: #005CC5\">`aij`<\/span><span style=\"color: #24292E\">)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">   if the multi-underscore conflict persists.&quot;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #E36209\">*<\/span><span style=\"color: #24292E\"> <\/span><span style=\"color: #24292E; font-weight: bold\">**Subscripts with Asterisks**<\/span><span style=\"color: #24292E\">: To prevent italicization and ensure correct rendering,<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">   always escape the underscore before an asterisk within curly braces<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">   (e.g., use <\/span><span style=\"color: #005CC5\">`$f\\_{\\ast}$`<\/span><span style=\"color: #24292E\"> or <\/span><span style=\"color: #005CC5\">`$x\\_{\\ast}$`<\/span><span style=\"color: #24292E\"> instead of $f_{\\ast}$ or $f_*$).<\/span><\/span>\n<span class=\"line\"><span style=\"color: #E36209\">*<\/span><span style=\"color: #24292E\"> <\/span><span style=\"color: #24292E; font-weight: bold\">**Subscripts with Accents**<\/span><span style=\"color: #24292E\">: When a subscript asterisk follows an accent (e.g., \\bar or \\hat),<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">   strictly use an escaped underscore within curly braces (e.g., <\/span><span style=\"color: #005CC5\">`$\\bar{f}\\_{\\ast}$`<\/span><span style=\"color: #24292E\">) to prevent rendering failure.<\/span><\/span>\n<span class=\"line\"><span style=\"color: #E36209\">*<\/span><span style=\"color: #24292E\"> <\/span><span style=\"color: #24292E; font-weight: bold\">**Vertical Bar in a Table**<\/span><span style=\"color: #24292E\">: When representing the vertical bar character <\/span><span style=\"color: #005CC5\">`|`<\/span><span style=\"color: #24292E\"> inside a markdown table,<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">  strictly use the escaped character <\/span><span style=\"color: #005CC5\">`\\|`<\/span><span style=\"color: #24292E\"> to ensure correct table rendering.<\/span><\/span>\n<span class=\"line\"><span style=\"color: #E36209\">*<\/span><span style=\"color: #24292E\"> <\/span><span style=\"color: #24292E; font-weight: bold\">**Code Snippets**<\/span><span style=\"color: #24292E\">: Always wrap code snippets and identifiers in a single pair of single backticks (<\/span><span style=\"color: #005CC5\">\\`<\/span><span style=\"color: #24292E\">code<\/span><span style=\"color: #005CC5\">\\`<\/span><span style=\"color: #24292E\">), <\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\"> and strictly avoid using triple backticks for any reason.<\/span><\/span>\n<span class=\"line\"><span style=\"color: #E36209\">*<\/span><span style=\"color: #24292E\"> &#091;<\/span><span style=\"color: #032F62; text-decoration: underline\">CRITICAL<\/span><span style=\"color: #24292E\">&#093; Never inject Markdown tags like &lt;em&gt; or &lt;strong&gt; inside math blocks.<\/span><\/span>\n<span class=\"line\"><span style=\"color: #24292E\">    <\/span><\/span>\n<span class=\"line\"><span style=\"color: #005CC5; font-weight: bold\">### Assistant<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #005CC5; font-weight: bold\">### Absolute Prohibitions<\/span><\/span>\n<span class=\"line\"><span style=\"color: #E36209\">-<\/span><span style=\"color: #24292E\"> Any text outside the code block (greetings, &quot;Understood,&quot; &quot;Here is the result,&quot; etc.).<\/span><\/span>\n<span class=\"line\"><span style=\"color: #E36209\">-<\/span><span style=\"color: #24292E\"> Creating multiple code blocks (all content must be in one single block).<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n<div style='text-align:center' class='yasr-auto-insert-overall'><\/div><div style='text-align:center' class='yasr-auto-insert-visitor'><\/div>","protected":false},"excerpt":{"rendered":"<p>This prompt provides mathematical definitions, derivations, step-by-step solutions, and detailed walkthroughs of mathematical processes.This is optimized for posting in a WordPress bbPress topic.Version 6, 2026.2.16<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"_kadence_starter_templates_imported_post":false,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_kad_post_classname":"","yasr_overall_rating":0,"yasr_post_is_review":"","yasr_auto_insert_disabled":"","yasr_review_type":"","fifu_image_url":"","fifu_image_alt":"","iawp_total_views":0,"footnotes":""},"categories":[10,291],"tags":[],"class_list":["post-5429","post","type-post","status-publish","format-standard","hentry","category-software-slug","category-ai-prompt-slug"],"yasr_visitor_votes":{"stars_attributes":{"read_only":false,"span_bottom":false},"number_of_votes":0,"sum_votes":0},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/posts\/5429","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/comments?post=5429"}],"version-history":[{"count":10,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/posts\/5429\/revisions"}],"predecessor-version":[{"id":5513,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/posts\/5429\/revisions\/5513"}],"wp:attachment":[{"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/media?parent=5429"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/categories?post=5429"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/tags?post=5429"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}