MathML 1.0 Changes

Changes from the 7 April 1998 Specification

Editorial changes

Title page and abstract

Errata and Translatation pages were added. The available formats section was moved and expanded. A link to MathML 1.0 Changes (this document) was added. The phrase "upon which MathML is based" has been added to the sentence "The fundamental eXtensible Markup Language (XML) 1.0 specification has been adopted as a W3C Recommendation" for clarification.

Section 4.2.3.4

Missing discussions of the max, min, forall and exists operators which belong in this section were added.

Section 4.2.5

The categorical assertion that a condition element must always be accompanied by one or more bvar elements was modified to take into account the exceptional usage with min and max. The first two examples were extended to show the surrounding apply elements so that they would be complete MathML expressions instead of fragments.

Section 4.4.10.6

A note was added explaining that even though select is classified as an n-ary operator, it can only take one, two or three arguments. The definition of the ordering of elements in a sequence of matrix elements was also clarified.

Chapter 6

A new section 6.2.6, "Additional Entity Set Grouping", and corresponding table of contents entry were added. This table collects together entities referred to in the MathML 1.0 specification, but which are not included in the ISO entity lists.

Section 6.2

In order to provide complete and technically valid entity declarations in the MathML 1.0 DTD, entities without current Unicode points have been assigned values in the Unicode Private Zone. The text and tables of values has been amended accordingly.

The entity lists in Section 6.2.4 have been updated to be more in line with the ISO character sets, in that if some part of a set is included then the entire set is included. Also, ISOCHEM has been dropped. These changes have also been reflected in the entity declarations in the DTD in Appendix A.

Section 6.2.6

This section was added for completeness, as described above.

Appendix A. The MathML DTD

A parseable, online version of the DTD has been added in addition to the preformatted HTML version. In addition, complete entity declarations have been added.

Appendix B. Glossary

The definition of "Attribute" was reworded to be more technically correct, and less misleading. A broken link to a fonts FAQ was removed.

Error Corrections

Section 2.2.2

A bogus over element was changed to divide, and a spurious occurrence attribute was removed, and a missing '/' character in an end apply element tag in the second example.

Section 4.2.1.4

A bad link to appendix F was fixed.

Section 4.2.1.6

Quotes were added around the vector attribute in the first example.

Section 4.2.1.7

A missing '/' character was added to a bvar end tag.

Section 4.2.1.8

A bad link to section 4.2.3.4 was fixed.

Section 4.2.2.3

Missing '/' characters were added to end tags for bvar, uplimit and lowlimit.

Section 4.2.3

<var> was changed to <variance>, and <select> was changed to <selector>.

Section 4.2.3.4

A missing '/' character was added to an apply element end tag in the first example. A missing '/' character was added to an degree element end tag in the diff example, and a missing ci element was added around the function identifier f. The sentence "Qualifier schemata are always optional." was removed, as the quantifiers forall and exists require a bound variable.

Section 4.2.6

The outdated AM_APP element was replaced with the more current OMA element.

Section 4.3.2.4

A misspelling of xml-annotation was corrected.

Section 4.4

The var and select elements were renamed to variance and selector throughout, to avoid a namespace collision with HTML. Missing trailing '/' characters denoting an empty element were added for ln, log, inverse, mean, sdev, variance, median, mode and moment. The same error was corrected in the corresponding section heading when necessary.

Section 4.4.1.1

Missing quotes around attribute values were added.

Section 4.4.2.8

A missing bvar element was added to the lambda construct in the fourth example. A missing '>' character was added to the function declaration in the first example.

Section 4.4.2.9

Misplaced '/' characters were corrected in lambda elements in the examples. Out of order qualifiers for the int element in the example were corrected by moving the apply element to the end.

Section 4.4.2.10

Missing '/' characters were added to the end tags of apply elements in the last two examples. An extra '<' character was removed from the fourth example.

Section 4.4.3.18

The textual equivalent of the second example was changed to use the words "such that" in place of "where" for clarity and for agreement with 4.2.5. A missing power element was added in the second example. A missing '/' was added to an apply end tag, a nesting problem in the reln element, and a missing apply construct in the second condition were corrected in the third example.

Section 4.4.3.21

A missing '/' was added to the conjugate tag in the first example.

Section 4.4.4.6

A garbled reln tag was corrected in the example.

Section 4.4.5.3

Missing '/' characters were added to the end tags of qualifier schemata in all three examples.

Section 4.4.5.4

A misleading omission of reference to the fact that the diff operator can take an optional degree element was corrected to be as in 4.4.5.5. The default rendering was improved.

Section 4.4.5.5

Missing '/' characters were added to degree, bvar and ci end tags in the first example. A missing exponent in the numerator of the first differential operator in the sample equation has been added. An incorrect exponent in the default rendering was corrected.

Section 4.4.5.6

Missing '/' characters were added to the end tags of qualifier schemata in the example.

Section 4.4.5.7

A missing '/' character was added to the end tag of the bvar in the example.

Section 4.4.5.8

An incorrect diff element was changed to an int element in the second example.

Section 4.4.5.9

An incorrect diff element was changed to a partialdiff element in the example.

Section 4.4.7.2

A missing '/' was added to a bvar tag in the second example.

Section 4.4.9.3

As noted above, var has been renamed to variance to avoid a namespace collision with HTML.

Section 4.4.9.6

An incorrectly place degree element was moved in the example.

Section 4.4.10.6

As noted above, select has been renamed to selector to avoid a namespace collision with HTML. A missing '/' was added to the end tag for the selector element.

Section 4.4.11.2

The outdated AM_APP element was replaced with the more current OMA element.

Section 5.1.2

A garbled msup element in the first example was corrected. A missing '/' character was added to the eq element in the fourth example. An outdated OMSymbol element was replaced with the more current OMS element. A missing '/' character was added to the times element in the fourth example.

Section 5.3

An outdated OMSymbol element was replaced with the more current OMS element. Missing '/' characters were added to the transpose and times elements.

Section 7.1.3

Missing '/' characters were added to the mi element in the mathml-rendererB example.

Section 7.1.5

Missing emboldening of the anchor tag name was added.

Appendix B. Glossary

Some inconsistent capitalization was corrected in the definitions of Pt, Ex and Em. An extra '(' was removed from the SGML definition. Several instances "schema" were replaced by the plural "schemata". The phrase "free variable" was changed to "variable" in the definition of lambda expression, since the variables referred to are not free. The second use of the word "construct" in the definition of Pre-defined function was changed to "build". The second use of the word "sizes" in the definition of Pt was changed to "objects". The word "of" was changed to "or" in the definition of Token element. Definitions for Box and Bounding Box were added.

Appendix D. Working Group Membership

The first paragraph has been modified to include a reference to the current working group co-chairs, and a pointer to the current working group membership. A new paragraph has been added crediting a number of people who helped identify the errors corrected in this revision. Finally, a broken link to the American Mathematical Society has been corrected.

Appendix F

The var and select elements were renamed to variance and selector throughout, to avoid a namespace collision with HTML. Missing '/' characters were added to selector elements where they were missing from the corresponding select elements.

Section F.2.1.1

A missing ';' was added to the "complex i" entity in the description. A missing '/' was added to the sep tag in the second example. A missing '/' was added to the root element in the third property, a missing '<' character was added to an apply in the fifth property, an erroneous apply end tag was removed from the sixth property and a partial duplication of that property was corrected, and a missing cn end tag was added in the seventh property. Also, missing quotes were added to the "boolean" type attribute throughout.

Section F.2.2.3

A missing end tag was for the lambda element in the last example.

Section F.2.2.5

Garbled shorthand was expanded into proper markup in the last property.

Section F.2.2.9

A missing apply end tag was added to the variant sine function example.

Section F.2.2.10

A missing '/' was added to the forall element in the first property.

Section F.2.2.11

A missing '/' was added to the forall element in the first property.

Section F.2.3.1

Reversed start and end tags for the reln element were switched. A missing '/' was added to the last apply end tag in the second property.

Section F.2.3.2

A missing end tags for the apply element was added, and a missing '/' was added to a ci end tag, in the property.

Section F.2.3.4

Missing ci tags were added withing the bvar in the property, and garbled nesting of the reln element was corrected.

Section F.2.3.7

A missing bvar end tag was added in the property.

Section F.2.3.18

A misplaced '/' character in the forall element was corrected, and a missing apply end tag was added in the property.

Section F.2.9.3

<var> was changed to <variance>.

Section F.2.10.6

<select> was changed to <selector>.

Section F.2.10.5

A missing name sub-element was added to the MMLdefinition for transpose.