From: Neil Soiffer <soiffer@wri.com>

Date: Fri, 26 Apr 1996 09:37:19 -0700

Message-Id: <199604261637.AA00584@drizzle.wri.com>

To: w3c-math-erb@w3.org

Date: Fri, 26 Apr 1996 09:37:19 -0700

Message-Id: <199604261637.AA00584@drizzle.wri.com>

To: w3c-math-erb@w3.org

I've finally got a little free time and am in the process of catching up on mail to the group in the last month. One of the topics discussed earlier was a notation for integrals: y = 1 + integral of sin(x) wrt x * cos(x) I think some others asked this, but let me ask it more directly: why are we trying to come up with another way of writing integrals when a short, almost universal notation already exists? Ie (using the SGML character for integral): ∫ sin(x) d x The only problem with this is the 'd' -- it is not really the letter 'd', but some funny operator on 'x' (delta x). We we make up a new character, ⅆ ('differential d' or 'delta d'), then with '∫' and 'ⅆ' being prefix operators, there is no problem with parsing. The "wordy" form has problems for multiple integrals (as someone pointed out) and for integrals such as: ∫ {ⅆ x} \over {sin(x)} Note that, unlike TeX, the current proposals are parser-based, and with sensible precedence levels, expressions like the above don't need to be grouped (although it never hurts to add {}s). So we could write the above as: ∫ ⅆ x \over sin(x) I claim that it is possible, for a vast majority of the notations, to have a simple notational schema that closely reflects the characters that people use to display an expression and still be able to semantic sense out of the notation. There are some ambiguities dealing with characters such as 'i', 'e', and 'd', but through the use of *simple* tricks such as the 'ⅆ' trick above, these are easily resolved. I plan to elaborate on this more in the next few days. At the workshop, I will be presenting what we did in Mathematica to deal with understanding 2d notation, and hope to be able to have a demo of how this might look in HTML. Along with the demo Dave is giving, I think that we will ample food for thought to move the discussion forward to the more challanging parts such as grouping macros so that different macros can be applied for rendering, copying to a CAS, speech, etc. NeilReceived on Friday, 26 April 1996 12:37:51 UTC

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