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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72"><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><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal><b>From:</b> Francis Cave [mailto:francis@franciscave.com] <br><b>Sent:</b> Thursday, November 2, 2017 2:39 PM<br><b>To:</b> 'Rex Jaeschke' <rex@RexJaeschke.com>; 'MURATA Makoto' <eb2m-mrt@asahi-net.or.jp><br><b>Subject:</b> RE: N-ary objects in Office Math Markup Language (OMML)<o:p></o:p></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><span lang=EN-GB>Hi Rex<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB><o:p> </o:p></span></p><p class=MsoNormal><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><span lang=EN-GB><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-GB>Kind regards,<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-GB>Francis<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-GB><o:p> </o:p></span></p><p class=MsoNormal><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><b>From:</b> Rex Jaeschke [<a href="mailto:rex@RexJaeschke.com">mailto: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">francis@franciscave.com</a>>; 'MURATA Makoto' <<a href="mailto:eb2m-mrt@asahi-net.or.jp">eb2m-mrt@asahi-net.or.jp</a>><br><b>Subject:</b> RE: N-ary objects in Office Math Markup Language (OMML)<o:p></o:p></p></div></div><p class=MsoNormal><span lang=EN-GB><o:p> </o:p></span></p><p class=MsoNormal>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.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Regards, Rex<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal><b>From:</b> Francis Cave [<a href="mailto:francis@franciscave.com">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">eb2m-mrt@asahi-net.or.jp</a>>; Rex Jaeschke <<a href="mailto:rex@RexJaeschke.com">rex@RexJaeschke.com</a>><br><b>Subject:</b> N-ary objects in Office Math Markup Language (OMML)<o:p></o:p></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><span lang=EN-GB>Murata-san, Rex<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB><o:p> </o:p></span></p><p class=MsoNormal><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><span lang=EN-GB><o:p> </o:p></span></p><p class=MsoNormal><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><span lang=EN-GB><o:p> </o:p></span></p><p class=MsoNormal><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><span lang=EN-GB><o:p> </o:p></span></p><p class=MsoNormal><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><span lang=EN-GB><o:p> </o:p></span></p><p class=MsoNormal style='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><span lang=EN-GB><o:p> </o:p></span></p><p class=MsoNormal><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><span lang=EN-GB><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-GB>Editorial “nits” that I’ve spotted include:<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB><o:p> </o:p></span></p><ul style='margin-top:0in' type=disc><li class=MsoNormal style='mso-list:l0 level1 lfo3'><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-list:l0 level1 lfo3'><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-list:l0 level1 lfo3'><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-list:l0 level1 lfo3'><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-list:l0 level1 lfo3'><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-list:l0 level1 lfo3'><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-list:l0 level1 lfo3'><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><span lang=EN-GB><o:p> </o:p></span></p><p class=MsoNormal><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><span lang=EN-GB><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-GB>Kind regards,<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-GB><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-GB>Francis<o:p></o:p></span></p></div></body></html>