Update script level proposals after yesterday's discussions.

Author: fred-wang

math-script-level-and-math-style-comments.md

@@ -2,27 +2,8 @@
 
 ## Script level increment in `munder`, `mover`, `munderover` scripts
 
-When these elements are really drawn as under/over scripts then the script
-level increment should not happen when `accentunder` or `accent` are specified:
-
-<pre>
-munder[accentunder="false"] > :nth-child(2),
-mover[accent="false"] > :nth-child(2),
-munderover[accentunder="false"] > :nth-child(2),
-munderover[accent="false"] > :nth-child(3) {
-  math-script-level: inherit;
-}
-</pre>
-
-Unfortunately whether the elements are drawn with under/over scripts as well
-as the default values of the `accentunder` and `accent` attributes have to be
-determined from the MathML DOM and even using an
-[operator dictionary](https://www.w3.org/Math/draft-spec/appendixc.html).
-This is not possible to do in the CSS side. Maybe this feature could be removed
-from MathML and the authors should explicitly indicate whether they want
-to prevent increment in scriptlevel in this case.
-Gecko implements it via pseudo-element set in the layout code 
-but that's [causing some issues](https://bugzilla.mozilla.org/show_bug.cgi?id=1361766).
+The current proposal does not handle the case when underover scripts are
+"accents". See [issue 76](https://github.com/mathml-refresh/mathml/issues/76).
 
 ## `scriptsizemultiplier` and `scriptminsize` attributes
 
@@ -32,14 +13,7 @@ approximately one over square root of 2) and ensure
 script level change cannot scale down `font-size` lower than a minimal value.
 This is implemented in Gecko but that [makes things very complex](https://dxr.mozilla.org/mozilla-central/source/servo/components/style/properties/gecko.mako.rs#2481).
 
-It's not clear whether the `scriptsizemultiplier` and `scriptminsize` attributes
-are used a lot in practice so this MathML attributes could probably be removed.
-Additionally, taking into account `scriptminsize` (even the default value of
-8pt) means that for very deeply nested mathematical formulas, the `font-size`
-will stop being scaled down in scripts etc. It's not clear whether that's
-an important use case and whether that's better than reaching too small
-̀font-size`. There are user features (e.g. zoom-in) to workaround that kind
-of not frequent issues.
+We should probably [remove these attributes](https://github.com/mathml-refresh/mathml/issues/1#issuecomment-474261094) from MathML Core.
 
 ## OpenType MATH values: `scriptPercentScaleDown` and `scriptScriptPercentScaleDown`
 
@@ -49,15 +23,6 @@ going from script level 0 to script level 1 (`scriptPercentScaleDown`) or 2
 `scriptsizemultiplier` is not really want, instead the one specified by the
 font designer should be used.
 
-This proposal chose a simple solution as it's not clear whether reading the
-MATH table is a good idea or possible during the style resolution. Also
-`scriptPercentScaleDown` and `scriptScriptPercentScaleDown` are not implemented
-by any web engine right now ([Gecko bug](https://bugzilla.mozilla.org/show_bug.cgi?id=1187682)). An algorithm could be:
-
-* Use S = `scriptPercentScaleDown` when `math-script-level` goes from 0 to 1.
-* Use S = `scriptScriptPercentScaleDown` divided by `scriptPercentScaleDown` when `math-script-level` goes from 1 to 2.
-* Use S = 0.71 in other situation when `math-script-level` is incremented by 1.
-* Generalize to values of Δ other than +1 by using product and inversion.
-
-with adjustments when specified scales are zero and deciding whether to ignore
-suggested values from the MATH table.
+Note that TeX or Microsoft Office ignore other script level changes, which would
+be equivalent to replacing 0.71 with 1 in the definition of S<sub>p,p+1</sub>.
+The current definition tries to preserve MathML's special behavior.

math-script-level-and-math-style-explainer.md

@@ -12,7 +12,7 @@ on this proposal see
 ## Examples
 
 * `<div class="my-underover"><div>Base</div><div>Overscript</div><div>Underscript</div></div>`
-  and `.my-underover > :not(:first-child) { math-script-level: add 1; }` would
+  and `.my-underover > :not(:first-child) { math-script-level: add(1); }` would
   scale down the font size in under and over scripts.
 
 * In the previous example, one could do
@@ -36,7 +36,7 @@ on this proposal see
 * Polyfills and native implementations can emulate MathML behavior such as
   `<mstyle displaystyle="true">...</mstyle>`,
   `<mstyle scriptlevel="2">...</mstyle>` or `<mstyle scriptlevel="+3">...</mstyle>` by mapping to `math-style: display`, `math-script-level: 2;` and
-  `math-script-level: add 3;` respectively.
+  `math-script-level: add(3);` respectively.
 
 ## Rationale
 
@@ -139,7 +139,7 @@ such constraints into consideration.
 <table>
   <tbody>
     <tr><th>Name:</th><td>math-script-level'</td></tr>
-    <tr><th>Value:</th><td>auto || add? &amp;&amp; &lt;integer&gt;</td></tr>
+    <tr><th>Value:</th><td>auto | add(&lt;integer&gt;) | &lt;integer&gt;</td></tr>
     <tr><th>Initial:</th><td>inline</td></tr>
     <tr><th>Applies to:</th><td>All elements</td></tr>
     <tr><th>Inherited:</th><td>yes</td></tr>
@@ -160,27 +160,43 @@ value of `math-style` is 'inline' then the computed value of
 `math-script-level` is the inherited value plus one.
 
 If the specified value of `math-script-level` is of the form
-'add &lt;integer&gt;' then
+'add(&lt;integer&gt;)' then
 the computed value of `math-script-level` is the inherited value
 plus the specified integer.
 
 If the specified value of `math-script-level` is of the form '&lt;integer&gt;'
-then
-the computed value of `math-script-level` is set to the specified integer.
-
-`math-script-level` affects the calculation of the computed value of
-`font-size`. If `font-size` is not specified, then it is obtained by
-multiplying the inherited value by S to the Δ power, where S is a scale factor
-set to 0.71 and Δ is the change of script level i.e.
-computed `math-script-level` minus inherited `math-script-level`.
+then the computed value of `math-script-level` is set to the specified integer.
+
+If ̀font-size` is specified then `math-script-level` does not affect the
+computed value of ̀font-size`.
+Otherwise, if A is the inherited `math-script-level` and B the computed
+`math-script-level` then the computed value of `font-size`
+is obtained by multiplying the inherited value of ̀font-size` by the nonzero
+scale factor S<sub>A,B</sub>, defined recursively as follows:
+* S<sub>p,p</sub> = 1 for every integer p.
+* S<sub>0,1</sub> = `scriptPercentScaleDown` if a nonzero value is provided by
+  the OpenType MATH table of the current font. Otherwise use the suggested
+  default S<sub>0,1</sub> = 0.8.
+* S<sub>0,2</sub> = `scriptScriptPercentScaleDown` if a nonzero value is
+  provided by the OpenType MATH table of the current font. Otherwise use the
+  suggested default S<sub>0,1</sub> = 0.6.
+* S<sub>1,2</sub> = S<sub>0,2</sub> / S<sub>0,1</sub>.
+* S<sub>p,p+1</sub> = 0.71 for every integer p ≠ 0, 1.
+* S<sub>p,q</sub> is the product of S<sub>i,i+1</sub> where i ranges from p to
+  q - 1 for every integers p, q such that q ≥ p + 2 and (p,q) ≠ (0,2).
+* S<sub>p,q</sub> = 1 / S<sub>p,q</sub> for every integers p, q such that
+  q < p.
+
+The clamping of `font-size` implied by ̀font-min-size` and `font-max-size` must
+apply after the change due to `math-script-level`.
 
 ### Native implementations of `display`, `displaystyle` and `scriptlevel`
 
 The proposal allows to partially implement the `display`, `displaystyle` and
 `scriptlevel` attributes as follows:
 
-* Map `scriptlevel="+U"` to 'math-script-level: add U' (where U is an [unsigned integer](https://www.w3.org/Math/draft-spec/chapter2.html#type.unsigned-integer)).
-* Map `scriptlevel="-U"` to 'math-script-level: add -U' (where U is an [unsigned integer](https://www.w3.org/Math/draft-spec/chapter2.html#type.unsigned-integer)). 
+* Map `scriptlevel="+U"` to 'math-script-level: add(U)' (where U is an [unsigned integer](https://www.w3.org/Math/draft-spec/chapter2.html#type.unsigned-integer)).
+* Map `scriptlevel="-U"` to 'math-script-level: add(-U)' (where U is an [unsigned integer](https://www.w3.org/Math/draft-spec/chapter2.html#type.unsigned-integer)).
 * Map `scriptlevel="U"` to 'math-script-level: U' (where U is an [unsigned integer](https://www.w3.org/Math/draft-spec/chapter2.html#type.unsigned-integer)).
 
 Then add rules equivalent to the following user agent stylesheet for MathML.
@@ -223,7 +239,7 @@ mfrac > * {
   math-style: inline;
 }
 mroot > :not(:first-child) {
-  math-script-level: add 2;
+  math-script-level: add(2);
   math-style: inline;
 }
 msub > :not(:first-child),
@@ -233,7 +249,7 @@ mmultiscripts > :not(:first-child),
 munder > :not(:first-child),
 mover > :not(:first-child),
 munderover > :not(:first-child) {
-  math-script-level: add 1;
+  math-script-level: add(1);
   math-style: inline;
 }
 </pre>