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| 1 | +<?xml version='1.0' encoding='utf-8'?> |
| 2 | +<chapter xml:id="ch-M2"> |
| 3 | + <title>Macaulay 2</title> |
| 4 | + <introduction> |
| 5 | + <p> |
| 6 | +This chapter is co-authored by Francesca Gandini, Sumner Strom, |
| 7 | + </p> |
| 8 | + </introduction> |
| 9 | + <section xml:id="sec-template"> |
| 10 | + <title>Template </title> |
| 11 | + <p> |
| 12 | + This is the introduction to the template. |
| 13 | + </p> |
| 14 | + <subsection xml:id="subsec-template"> |
| 15 | + <title>Template Subsection</title> |
| 16 | + <p> |
| 17 | + This is the template subsection. |
| 18 | + </p> |
| 19 | + |
| 20 | + </subsection> |
| 21 | + <subsection xml:id="subsec-notes"> |
| 22 | + <title>Notes Subsection</title> |
| 23 | + <p> |
| 24 | + To build in pretext use the template subsection and pretext environment features. |
| 25 | + Make sure that you are building and compiling from main using preview code chat. |
| 26 | + Additionally, when running if the compilation fails run the command "pretext build web" in terminal. |
| 27 | + Make sure that all of the xml have unique ids so that you dont run into compilation errors. |
| 28 | + Follow the other chapters to find out how things are used. |
| 29 | + Make sure that the sections are properly linked within the main.ptx. Additionally, use the subsections and sections for organization. |
| 30 | + If something doesnt display there is a paragraph line missing. |
| 31 | + |
| 32 | + </p> |
| 33 | + |
| 34 | + </subsection> |
| 35 | + </section> |
| 36 | +<section xml:id="sec-m2-codespace"> |
| 37 | + <title>Creating a M2 Codespace</title> |
| 38 | + |
| 39 | + <p> |
| 40 | + A turn-key repository for creating a Codespace |
| 41 | + (<xref ref="sec-codespaces"/>) for Macaulay 2 is available at |
| 42 | + <url href="https://github.com/fragandi/M2-codespace"> |
| 43 | + fragandi/M2-codespace |
| 44 | + </url>. Below we provide detailed instructions. If you have some experience with codespaces, |
| 45 | +you might be able to follow directly the README in the repo. Otherwise, keep reading! |
| 46 | + |
| 47 | + </p> |
| 48 | + <p> |
| 49 | + (WRITE DOWN NOTES HOW TO START A CODESPACE AND USE THE M2 CODESPACE IN THE ABOVE PARAGRAPH.) |
| 50 | + </p> |
| 51 | + </section> |
| 52 | +<section xml:id="sec-m2-commands"> |
| 53 | + <title>Basic M2 commands </title> |
| 54 | + </section> |
| 55 | +<section xml:id="sec-invariantrings-package"> |
| 56 | + <title>InvariantRings package </title> |
| 57 | + </section> |
| 58 | +<section xml:id="sec-theory-invariant-rings"> |
| 59 | + <title>Theory for invariant rings </title> |
| 60 | + <p> |
| 61 | + hello <m>4 \in \mathbb{Z}</m> this is true. |
| 62 | + <theorem> <p>Nöether: |
| 63 | + <me> |
| 64 | + R^G = \mathbb{K} [ R_G(\bar x^{\bar \beta}) | \; |\bar \beta| \leq |G|] |
| 65 | + </me> |
| 66 | + NDB: The ring of invariants is generated in degrees <m>\leq |G|</m> </p> |
| 67 | + </theorem> |
| 68 | + </p> |
| 69 | + </section> |
| 70 | +</chapter> |
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