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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><a name="_MailEndCompose"><o:p> </o:p></a></p><span style='mso-bookmark:_MailEndCompose'></span><p class=MsoNormal><b>From:</b> eb2mmrt@gmail.com [mailto:eb2mmrt@gmail.com] <b>On Behalf Of </b>MURATA Makoto<br><b>Sent:</b> Sunday, November 5, 2017 1:09 AM<br><b>To:</b> Francis Cave <francis@franciscave.com><br><b>Cc:</b> Rex Jaeschke <rex@rexjaeschke.com>; MURATA Makoto (FAMILY Given) <eb2m-mrt@asahi-net.or.jp><br><b>Subject:</b> SPAM-LOW: Re: N-ary objects in Office Math Markup Language (OMML)<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><div><div><p class=MsoNormal>Francis,<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>In Geneva, let's first divide this DR into smaller DRs and try to solve easy <o:p></o:p></p></div><div><p class=MsoNormal>ones.<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>Here are my observations Rex, I think that you do not <o:p></o:p></p></div><div><p class=MsoNormal>have to merge them into the current DR, since we should <o:p></o:p></p></div><div><p class=MsoNormal>first divide the DR.<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>>The term “math argument” as used in §22.1.2.5 is not defined. In fact, there are four elements in <o:p></o:p></p></div><div><p class=MsoNormal>>this category: §22.1.2.26 deg, §22.1.2.32 e, §22.1.2.112 sub and §22.1.2.114 sup.<br> <o:p></o:p></p></div><div><p class=MsoNormal>There are four more elements.<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>22.1.2.28 den (Denominator) <o:p></o:p></p></div><div><p class=MsoNormal>22.1.2.37 fName (Function Name)<o:p></o:p></p></div><div><p class=MsoNormal>22.1.2.52 lim (Limit)<o:p></o:p></p></div><div><p class=MsoNormal>22.1.2.75 num (Numerator) <o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>>§15.1 defines ‘n-ary operator’ to be “An operator that involves n terms when expanded…’.<o:p></o:p></p></div><div><p class=MsoNormal>> But in OMML the term n-ary applies not only to true n-ary operators, such as finite series <o:p></o:p></p></div><div><p class=MsoNormal>>summation and series product, but also to the integral operator, which is not normally<o:p></o:p></p></div><div><p class=MsoNormal>> described as an n-ary operator.<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>Is an equation array (22.1.2.34 eqArr (Array Object) ) is <o:p></o:p></p></div><div><p class=MsoNormal>also an n-ary operator? At least, it has an e element (Argument) <br>for each line.<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>I think that the definition in 15.1 is misleading and unnecessary.<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>>The only prose specification of the element <span class=gmail-element>sub</span> is in §22.1.2.112, but this specifies a particular case, not the general case.<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>Should we add two more simple examples?<o:p></o:p></p></div><div><p class=MsoNormal> <o:p></o:p></p></div><div><div><p class=MsoNormal><m:sPre><o:p></o:p></p></div><div><p class=MsoNormal> <m:sub/><o:p></o:p></p></div><div><p class=MsoNormal> <m:sup><o:p></o:p></p></div><div><p class=MsoNormal> <m:r><o:p></o:p></p></div><div><p class=MsoNormal> <m:t>2</m:t><o:p></o:p></p></div><div><p class=MsoNormal> </m:r><o:p></o:p></p></div><div><p class=MsoNormal> </m:sup><o:p></o:p></p></div><div><p class=MsoNormal> <m:e><o:p></o:p></p></div><div><p class=MsoNormal> <m:r><o:p></o:p></p></div><div><p class=MsoNormal> <m:t>A</m:t><o:p></o:p></p></div><div><p class=MsoNormal> </m:r><o:p></o:p></p></div><div><p class=MsoNormal> </m:e><o:p></o:p></p></div><div><p class=MsoNormal></m:sPre> <o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal><m:sPre><o:p></o:p></p></div><div><p class=MsoNormal> <m:sub><o:p></o:p></p></div><div><p class=MsoNormal> <m:r><o:p></o:p></p></div><div><p class=MsoNormal> <m:t>1</m:t><o:p></o:p></p></div><div><p class=MsoNormal> </m:r><o:p></o:p></p></div><div><p class=MsoNormal> </m:sub><o:p></o:p></p></div><div><p class=MsoNormal> <m:sup/><o:p></o:p></p></div><div><p class=MsoNormal> <m:e><o:p></o:p></p></div><div><p class=MsoNormal> <m:r><o:p></o:p></p></div><div><p class=MsoNormal> <m:t>A</m:t><o:p></o:p></p></div><div><p class=MsoNormal> </m:r><o:p></o:p></p></div><div><p class=MsoNormal> </m:e><o:p></o:p></p></div><div><p class=MsoNormal></m:sPre> <o:p></o:p></p></div></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>Regards,<o:p></o:p></p></div><div><p class=MsoNormal>Makoto<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div></div><div><p class=MsoNormal><o:p> </o:p></p><div><p class=MsoNormal>2017-11-03 3:38 GMT+09:00 Francis Cave <<a href="mailto:francis@franciscave.com" target="_blank">francis@franciscave.com</a>>:<o:p></o:p></p><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-right:0in'><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB>Hi Rex<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB> <o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB>DR attached. I’ve revised the wording to fit the DR template more cleanly.<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB> <o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB>Kind regards,<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB> <o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB>Francis<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB> <o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB> <o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB> <o:p></o:p></span></p><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><b>From:</b> Rex Jaeschke [mailto:<a href="mailto:rex@RexJaeschke.com" target="_blank">rex@RexJaeschke.com</a>] <br><b>Sent:</b> 02 November 2017 16:08<br><b>To:</b> 'Francis Cave' <<a href="mailto:francis@franciscave.com" target="_blank">francis@franciscave.com</a>>; 'MURATA Makoto' <<a href="mailto:eb2m-mrt@asahi-net.or.jp" target="_blank">eb2m-mrt@asahi-net.or.jp</a>><br><b>Subject:</b> RE: N-ary objects in Office Math Markup Language (OMML)<span lang=EN-GB><o:p></o:p></span></p></div></div><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB> <o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Francis, I think you should make this a DR, so we have a formal track record of it. How about you make it one DR, and if when we work on it we think it makes sense to split one or more items off into separate DRs, we can do that then.<span lang=EN-GB><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <span lang=EN-GB><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Regards, Rex<span lang=EN-GB><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <span lang=EN-GB><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <span lang=EN-GB><o:p></o:p></span></p><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><b>From:</b> Francis Cave [<a href="mailto:francis@franciscave.com" target="_blank">mailto:francis@franciscave.com</a>] <br><b>Sent:</b> Wednesday, November 1, 2017 3:10 PM<br><b>To:</b> 'MURATA Makoto' <<a href="mailto:eb2m-mrt@asahi-net.or.jp" target="_blank">eb2m-mrt@asahi-net.or.jp</a>>; Rex Jaeschke <<a href="mailto:rex@RexJaeschke.com" target="_blank">rex@RexJaeschke.com</a>><br><b>Subject:</b> N-ary objects in Office Math Markup Language (OMML)<span lang=EN-GB><o:p></o:p></span></p></div></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <span lang=EN-GB><o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB>Murata-san, Rex<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB> <o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB>I’ve had occasion to take a close look at §22.1 Math in 29500:2016-1.<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB> <o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB>There are a number of minor editorial nits in this section, but one particular point has struck me, and I’m wondering if this is worthy of a separate DR submission, or can be treated as an editorial nit.<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB> <o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB>Clause §22.1.2.70 defines the element <m:nary> (n-ary Operator Object). Clause §15.1 defines ‘n-ary operator’ to be “An operator that involves n terms when expanded…’. But in OMML the term n-ary applies not only to operators such as finite series summation and series product but also to the integral operator, which is not normally described as an n-ary operator. I think therefore that the definition of ‘n-ary operator’ in Clause §15.1 should be changed to read something like “A mathematical operator comprising an operator character and, optionally, expressions of a lower limit, an upper limit, or both.”<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB> <o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB>Clause §22.1.2.70 itself contains a typo and also contradicts the schema. The first paragraph should begin:<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB> <o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;margin-left:.5in'><span lang=EN-GB>This element specifies an n-ary object, consisting of an n-ary <s><span style='color:red'>object</span></s><u><span style='color:#2E75B6'>operator</span></u>, a base (or operand), and <s><span style='color:red'>optional</span></s><span style='color:red'> </span>upper and lower limits.<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB> <o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB>In syntactic terms the word ‘optional’ contradicts the schema, in which all the child elements <m:sub>, <m:sup> and <m:e> are mandatory. It might be worth noting that any of these elements may be empty.<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB> <o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB>Editorial “nits” that I’ve spotted include:<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB> <o:p></o:p></span></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l0 level1 lfo1'><span lang=EN-GB>In §22.1.2.4, the example includes “Example (OFF)” and “Example (ON)”, which I think we clearer if these were ‘not aligned’ and ‘aligned’ respectively.<o:p></o:p></span></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l0 level1 lfo1'><span lang=EN-GB>The term “math argument” as used in §22.1.2.5 is not defined. In fact, there are four elements in this category: §22.1.2.26 deg, §22.1.2.32 e, §22.1.2.112 sub and §22.1.2.114 sup. They all share the same complex type ‘CT_OMathArg’. I suppose it could be argued that the term doesn’t need to be defined, because it has the generally-accepted meaning in a mathematical context.<o:p></o:p></span></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l0 level1 lfo1'><span lang=EN-GB>In §22.1.2.6, the use of the term “degree argument” in the last line of text in the example doesn’t make sense.<o:p></o:p></span></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l0 level1 lfo1'><span lang=EN-GB>In §22.1.2.26 the second sentence contradicts the schema, as the element <m:deg> is not optional in the schema.<o:p></o:p></span></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l0 level1 lfo1'><span lang=EN-GB>In §22.1.2.71, two occurrences of “built down form”, which should be “built-down form” with a hyphen.<o:p></o:p></span></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l0 level1 lfo1'><span lang=EN-GB>The only prose specification of the element <m:sub> is in §22.1.2.112, but this specifies a particular case, not the general case. Either this Clause needs to be generalized, or a new Clause defining <m:sub> in the general case needs to be added. This element occurs in many content models in addition to <m:sPre>.<o:p></o:p></span></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l0 level1 lfo1'><span lang=EN-GB>In §22.1.2.88 the first sentence contradicts the schema, as the element <m:deg> is not optional in the schema. The example in §22.1.2.89 correctly shows an empty <m:deg/> element, for the case where there is no degree object/argument in the math expression as rendered.<o:p></o:p></span></li></ul><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB> <o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB>I’m happy to submit one or more DRs, if you think that appropriate.<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB> <o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB>Kind regards,<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB> <o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-GB>Francis<o:p></o:p></span></p></div></div></div></div></blockquote></div><p class=MsoNormal><br><br clear=all><o:p></o:p></p><div><p class=MsoNormal><o:p> </o:p></p></div><p class=MsoNormal>-- <o:p></o:p></p><div><p class=MsoNormal><br>Praying for the victims of the Japan Tohoku earthquake<br><br>Makoto<o:p></o:p></p></div></div></div></body></html>