{"id":3076,"date":"2013-02-19T20:13:37","date_gmt":"2013-02-19T20:13:37","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=3076"},"modified":"2013-02-19T20:15:04","modified_gmt":"2013-02-19T20:15:04","slug":"standard-macros","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3076","title":{"rendered":"Standard macros?"},"content":{"rendered":"

In this comment<\/a> Yuhao Huang suggests we could start having some standard macros in algebraic geometry. I have two comments:<\/p>\n

    \n
  1. It makes sense to reserve some commands<\/strong> such as \\Spec<\/code> and \\colim<\/code><\/li>\n
  2. It doesn’t make sense, I think, to fix the actual macros for these commands.<\/li>\n<\/ol>\n

    I think I can convince most of you to agree with 2. For example, I like to define<\/p>\n

    \\def\\Spec{\\mathop{\\rm Spec}}<\/code><\/p><\/blockquote>\n

    but (and I am happy to get feedback) I am sure this is completely utterly totally wrong! And let’s not even talk about<\/p>\n

    \\def\\SheafHom{\\mathop{\\mathcal{H}\\!{\\it om}}\\nolimits}<\/p><\/blockquote>\n

    <\/code>which I am sure you like to define with an underline or a squiggly underline. It is clear that we are never ever going to agree on the “correct” macro even for something as simple as \\Spec<\/code>. Right?<\/p>\n

    I think I can make some argument for 1, but I agree it isn’t so clear. Namely, wouldn’t it be nice if you could download another algebraic geometer’s latex code and run it locally on you machine with your own preamble? After all, my preamble is better than yours (as we’ve already discussed above).<\/p>\n

    Finally, many people define macros for things that take just one letter, typically with something like<\/p>\n

    \\newcommand{\\CC}{\\mathbb{C}}<\/code><\/p><\/blockquote>\n

    I may have done this myself in the past. But now I think just typing \\mathbb{C}<\/code> is just as fast and it makes it clear what you get. The argument that it is faster to change the macro doesn’t really hold water as you can do a search and replace (or run a sed command) quite easily. Moreover, the letter C is going to occur as blackboard bold, gothic, greek, german, calligraphic, italic, roman, etc, etc so don’t try to tell me that it is better to use a short macro because who knows which of \\CC, \\bC, \\cC, \\iC<\/code> is the one you want? No, the only reason for having a macro for blackboard bold C is if you wanted to have a macro for the complex numbers. Then you would probably name<\/strong> it \\ComplexNumbers<\/code> or something long like that so you never get confused.<\/p>\n

    I guess then the question becomes: Is \\ComplexNumbers<\/code> a good choice for one of the standard command names? I’m not convinced.<\/p>\n

    Another aspect of the situation is that, if we are inclined to introduce the command \\ComplexNumbers<\/code>, then also some things that never get macros should get macros. For example there should probably be a macro (untested)<\/p>\n

    \\def\\DerivedCategory#1{\\mathop{\\rm D}(#1)}<\/code><\/p><\/blockquote>\n

    because part of the value of having macros may be that it makes it easier for our LaTeX files to be parsed by machines in the future. Madness!<\/p>\n

    I hope there is a lot here you can disagree with. My stance on most of this stuff is that it is much easier<\/em> to fix this kind of thing (if it turns out we made a bad choice of coding a symbol or whatever), than it is to add new mathematics. So essentially, it doesn’t matter, but I am still interested to hear if you more or less agree with what I said above. Leave a comment!<\/p>\n

    PS: Here is a complete list of the currently defined macros in the Stacks project: \\lim, \\colim, \\Spec, \\Hom, \\SheafHom, \\Sch, \\Mor, \\Ob, \\Sh<\/code>. You can find these in preamble.tex<\/a>.<\/p>\n

    PPS: Of course there is the whole other issue of choice of macro names. As you can see above I have been tempted by the Capitalization Curse. Why didn’t we name the macros \\lim, \\colim, \\spec, \\hom, \\sheafhom, \\sch, \\mor, \\ob, \\sh<\/code>? I guess an easy way out is to simply have both?<\/p>\n","protected":false},"excerpt":{"rendered":"

    In this comment Yuhao Huang suggests we could start having some standard macros in algebraic geometry. I have two comments: It makes sense to reserve some commands such as \\Spec and \\colim It doesn’t make sense, I think, to fix … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-3076","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3076","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3076"}],"version-history":[{"count":20,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3076\/revisions"}],"predecessor-version":[{"id":3095,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3076\/revisions\/3095"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3076"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3076"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3076"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}