- From: Rushforth, Peter <prushfor@NRCan.gc.ca>
- Date: Thu, 18 Sep 2008 21:33:31 -0400
- To: "David Carlisle" <davidc@nag.co.uk>
- Cc: <www-math@w3.org>
Hi David, Thanks for your reply. I got rid of the <declare> element. It's not so much presentation (I seem to be able to get a good presentation markup from cut and paste from MathType). that I'm looking for, but good content markup. I include below (at the bottom) the equations as received from MathType via cut and paste, in presentation markup, where the equivalent (or approaching equivalent, I hope) content markup is at the top, with each equation documented by a comment. What I want to do is to enable re-usable functions on the one hand. I would think I need to assign a symbolic name to the result of the functions in order to reference that equation from elsewhere, but I'm not quite sure how to do that. <csymbol> and <declare> don't appear to be the way, and <fn> seems to be deprecated, so I'm at a bit of a loss. I'm not quite certain what you mean by marking up definitions as equations. I've got each separate one as a distinct 1st level <apply> element. Is there a specific element you would use to capture the result of an apply as a symbolic value? Pardon my complete newness at this subject! Thanks for any advice! Cheers, Peter .... here's the markup I've come up with to this point: (for clarity there's presentation markup at the bottom which if you have a viewer application should show you what I intend to encode in content markup, at least) <math xmlns="http://www.w3.org/1998/Math/MathML"> <!-- parameters that are supplied for an instance of a particular coordinate reference system: a => ellipsoid semi-major axis if => inverse flattening p1 => phi one, latitude of 1st std parallel p2 => phi two, latitude of 2nd std parallel pF => phi False, latitude of false origin lambdaF => lambda False, longitude of false origin EsubF => Easting at False origin NsubF => Northing at False origin phi, lambda phi => latitude of the coordinate to be transformed to Northing lambda => longitude of coordinate to be transformed to Easting --> <!-- solve for flattening (f), if you know inverse flattening (if), this is the formula for f --> <!-- this doesn't have an equivalent in the presentation markup below, it is just used to solve for eccentricity --> <apply> <divide/> <cn>1</cn> <ci>if</ci> </apply> <!-- e is derived from the flattening of the ellipsoid and is used in many of the equations below --> <!-- solve for eccentricity , or e --> <apply> <root/> <apply> <times/> <ci>f</ci> <apply> <minus/> <cn>2</cn> <ci>f</ci> </apply> </apply> </apply> <!-- solve for m, this should be a reuseable function because different values of m are used to derive Easting and Northing based on 2 standard parallels --> <apply> <divide/> <apply> <cos/> <!-- p, or phi is one of the standard parallels --> <ci>p</ci> </apply> <!-- denominator is an expression --> <apply> <power/> <apply> <minus/> <cn type="real">1</cn> <apply> <times/> <apply> <power/> <apply> <!-- eccentricity --> <ci>e</ci> </apply> <cn type="integer">2</cn> </apply> <apply> <power/> <apply> <sin/> <!-- p stands for phi --> <ci>p</ci> </apply> <cn>2</cn> </apply> </apply> </apply> <cn>0.5</cn> </apply> </apply> <!-- solve for t, this should also be a reusable function --> <apply> <divide/> <!-- numerator is expression based on tan --> <apply> <tan/> <apply> <minus/> <apply> <divide/> <pi/> <cn type="real">4</cn> </apply> <apply> <divide/> <ci>p</ci> <cn type="real">2</cn> </apply> </apply> </apply> <!-- denominator is expression based on power of e/2 expression --> <apply> <power/> <apply> <!-- the expression being raised --> <apply> <divide/> <apply> <!-- 1 minus e sin phi --> <minus/> <cn type="real">1</cn> <apply> <times/> <ci>e</ci> <apply> <sin/> <ci>p</ci> </apply> </apply> </apply> <apply> <!-- 1 plus e sin phi --> <plus/> <cn type="real">1</cn> <apply> <times/> <ci>e</ci> <apply> <sin/> <ci>p</ci> </apply> </apply> </apply> </apply> </apply> <apply><!-- the value of the exponent is e/2 --> <divide/> <ci>e</ci> <cn type="real">2</cn> </apply> </apply> </apply> <!-- solve for n, this should be a function --> <apply> <!-- quotient --> <divide/> <!-- numerator --> <apply> <minus/> <apply> <ln/> <cn>m1</cn> </apply> <apply> <ln/> <cn>m2</cn> </apply> </apply> <!-- denominator --> <apply> <minus/> <apply> <ln/> <cn>t1</cn> </apply> <apply> <ln/> <cn>t2</cn> </apply> </apply> </apply> <!-- solve for F (not sure what this F is, it's *not* False) --> <apply> <!-- quotient --> <divide/> <!-- numerator is m1 --> <ci>m1</ci> <apply> <!-- denominator --> <times/> <ci>n</ci> <apply> <power/> <ci>t1</ci> <ci>n</ci> </apply> </apply> </apply> <!-- solve for radius --> <apply> <times/> <ci>a</ci> <apply> <times/> <ci>F</ci> <apply> <power/> <ci>t</ci> <ci>n</ci> </apply> </apply> </apply> <!-- solve for theta --> <apply> <times/> <ci>n</ci> <apply> <minus/> <ci>lambda</ci> <ci>lambdaF</ci> </apply> </apply> <!-- E , or Easting --> <apply> <plus/> <ci> <msub> <mi>E</mi> <mi>F</mi> </msub> </ci> <apply> <times/> <ci>r</ci> <apply> <sin/> <!-- t is theta --> <ci>t</ci> </apply> </apply> </apply> <!-- N, or Northing --> <apply> <plus/> <ci> <!-- the F subscript means False --> <msub> <mi>N</mi> <mi>F</mi> </msub> </ci> <apply> <minus/> <ci> <msub> <mi>r</mi> <mi>F</mi> </msub> </ci> <apply> <times/> <ci>r</ci> <apply> <cos/> <!-- t is theta --> <ci>t</ci> </apply> </apply> </apply> </apply> <!-- end content markup --> <!-- begin presentation markup --> <!-- the following was cut and pasted from MathType and should graphically represent what I'm trying to encode as content markup, above --> <semantics> <mtable columnalign='left'> <mtr> <mtd> <mi>E</mi><mo>=</mo><msub> <mi>E</mi> <mi>F</mi> </msub> <mo>+</mo><mi>r</mi><mi>sin</mi><mo>⁡</mo><mi>θ</mi> </mtd> </mtr> <mtr> <mtd> <mi>N</mi><mo>=</mo><msub> <mi>N</mi> <mi>F</mi> </msub> <mo>+</mo><msub> <mi>r</mi> <mi>F</mi> </msub> <mo>−</mo><mi>r</mi><mi>cos</mi><mo>⁡</mo><mi>θ</mi> </mtd> </mtr> <mtr> <mtd> <mi>m</mi><mo>=</mo><mi>cos</mi><mo>⁡</mo><mi>φ</mi><mo>/</mo><msup> <mrow><mo>(</mo> <mrow> <mn>1</mn><mo>−</mo><msup> <mi>e</mi> <mn>2</mn> </msup> <msup> <mrow> <mi>sin</mi><mo>⁡</mo> </mrow> <mn>2</mn> </msup> <mi>φ</mi> </mrow> <mo>)</mo></mrow> <mrow> <mn>0.5</mn> </mrow> </msup> </mtd> </mtr> <mtr> <mtd> <mi>t</mi><mo>=</mo><mi>tan</mi><mo>⁡</mo><mrow><mo>(</mo> <mrow> <mi>π</mi><mo>/</mo><mn>4</mn><mo>−</mo><mi>φ</mi><mo>/</mo><mn>2</mn> </mrow> <mo>)</mo></mrow><msup> <mrow><mo>[</mo> <mrow> <mrow><mo>(</mo> <mrow> <mn>1</mn><mo>−</mo><mi>e</mi><mi>sin</mi><mo>⁡</mo><mi>φ</mi> </mrow> <mo>)</mo></mrow><mo>/</mo><mrow><mo>(</mo> <mrow> <mn>1</mn><mo>+</mo><mi>e</mi><mi>sin</mi><mo>⁡</mo><mi>φ</mi> </mrow> <mo>)</mo></mrow> </mrow> <mo>]</mo></mrow> <mrow> <mi>e</mi><mo>/</mo><mn>2</mn> </mrow> </msup> </mtd> </mtr> <mtr> <mtd> <mi>n</mi><mo>=</mo><mrow><mo>(</mo> <mrow> <mi>ln</mi><mo>⁡</mo><msub> <mi>m</mi> <mn>1</mn> </msub> <mo>−</mo><mi>ln</mi><mo>⁡</mo><msub> <mi>m</mi> <mn>2</mn> </msub> </mrow> <mo>)</mo></mrow><mo>/</mo><mrow><mo>(</mo> <mrow> <mi>ln</mi><mo>⁡</mo><msub> <mi>t</mi> <mn>1</mn> </msub> <mo>−</mo><mi>ln</mi><mo>⁡</mo><msub> <mi>t</mi> <mn>2</mn> </msub> </mrow> <mo>)</mo></mrow> </mtd> </mtr> <mtr> <mtd> <mi>F</mi><mo>=</mo><msub> <mi>m</mi> <mn>1</mn> </msub> <mo>/</mo><mrow><mo>(</mo> <mrow> <mi>n</mi><msub> <mi>t</mi> <mn>1</mn> </msub> </mrow> <mo>)</mo></mrow> </mtd> </mtr> <mtr> <mtd> <mi>r</mi><mo>=</mo><mi>a</mi><mi>F</mi><msup> <mi>t</mi> <mi>n</mi> </msup> </mtd> </mtr> <mtr> <mtd> <mi>θ</mi><mo>=</mo><mi>n</mi><mrow><mo>(</mo> <mrow> <mi>λ</mi><mo>−</mo><msub> <mi>λ</mi> <mi>F</mi> </msub> </mrow> <mo>)</mo></mrow> </mtd> </mtr> </mtable> <annotation encoding='MathType-MTEF'> </annotation> </semantics> <!-- end presentation markup --> </math>
Received on Friday, 19 September 2008 01:34:15 UTC