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add fep: Formatting Mathematics
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Calvin Lee
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---
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slug: "dc88"
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authors: Calvin Lee <pounce@integraldoma.in>
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status: DRAFT
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dateReceived: 1970-01-01
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---
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# FEP-dc88: Formatting Mathematics
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## Summary
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This FEP recommends a method for formatting mathematics in ActivityPub
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post content in [MathML Core]. Furthermore, this FEP describes how to
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sanitize and convert such mathematics to plain text, if an
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implementation does not wish to support mathematical formatting.
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## Requirements
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The key words “MUST”, “MUST NOT”, “REQUIRED”, “SHALL”, “SHALL NOT”,
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“SHOULD”, “SHOULD NOT”, “RECOMMENDED”, “MAY”, and “OPTIONAL” in this
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specification are to be interpreted as described in [RFC-2119]. “The
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implementation” is to be interpreted as an ActivityPub conformant
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Client, ActivityPub conformant Server or ActivityPub conformant
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Federated Server as described in [ActivityPub] which wishes to produce
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or consume mathematically formatted content.
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## History
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Written mathematics depends very heavily on a system of notation which
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has been continuously evolving over thousands of years. Despite its
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ubiquity, mathematical notation is anything but constant. Mathematicians
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rely heavily on complicated typesetting systems such as [LaTeX] to
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layout text in their desired fashion.
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Several fediverse instances, such as [Mathstodon] have emerged to host
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discussion related to mathematics. This is to no small part due to the
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difficulty of conveying and formatting mathematical text, and many
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provide their own typesetting implementation based on [LaTeX]. However,
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rendering TeX-like formats is expensive and fraught with issues due to
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security and implementation-specific quirks. This has resulted in
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multiple instances with incompatible TeX-like implementations.
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In recent years, [MathML Core] has become standardized by all major web
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browsers, and offers an alternative method to communicate mathematics
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between differing fediverse implementations that is compatible with the
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ActivityPub standard.
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## Formatting Mathematics
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The implementation MAY produce mathematical formatting in the
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`summary` or `content` properties of [ActivityStreams] objects, as
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defined in [Activity Vocabulary] if the `mediaType` is `text/HTML` (the
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default). This formatting MUST be placed within one or more top-level
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`<math>` elements, hereon referred to as 'a math element'.
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A math element MUST contain one `<semantics>` child element, and no
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other children. The `<semantics>` element MUST contain a [MathML Core]
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expression as its first child, and at least one `<annotation>` element.
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The `encoding` property of this `<annotation>` element SHOULD be
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`"application/x-tex"`, but MAY be `"text/plain"`, and MUST contain
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a plain-text description of the mathematics—preferably in the authored
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format. The implementation MAY include additional `<annotation>` or
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`<annotation-xml>` elements with other semantic information.
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All elements contained within a math element MUST be **MathML Core
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Elements** as defined in [MathML Core], excluding those contained within
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`<annotation>` elements.
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## Sanitizing Mathematically Formatted Text
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The implementation SHOULD sanitize incoming mathematical formatting
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before displaying it to a user. There are two methods by which an
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implementation may sanitize incoming mathematical formatting.
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### Sanitizing a math element
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The implementation MAY sanitize a math element before displaying it to
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a user. The implementation SHOULD remove all non **MathML Core
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Elements** as defined in [MathML Core]. The implementation MAY remove
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any attribute which does not contain semantic information (see [Semantic
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Attributes]). The implementation SHALL NOT remove any [Semantic
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Attributes] or **MathML core Elements** and instead should replace
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a math element with text.
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### Replacing a math element with text
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The implementation MAY remove a math element completely, and replace it
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with text within the `<annotation>` element with encoding
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`"application/x-tex"` as described in [Formatting Mathematics] and
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SHOULD fall back to a `"text/plain"` annotation. If a math element is
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not formatted as described in [Formatting Mathematics], then the
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implementation MUST remove it completely.
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The implementation MAY surround the text from the `<annotation>` element
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with a pair of delimiters. For example, if a math element has the
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attribute `display="block"`, it may choose the delimiters `$$` and `$$`,
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and if `displaystyle="inline"` it may choose `$` and `$` to match the
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TeX typesetting system.
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## Examples
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```json
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{"@context": ["https://www.w3.org/ns/activitystreams", {"@language": "en"}],
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"type": "Note",
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"id": "http://postparty.example/p/2415",
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"content": "I have a truly marvelous proof that
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<math>
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<semantics>
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<mrow>
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<msup><mi>x</mi><mi>n</mi></msup>
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<mo>+</mo>
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<msup><mi>y</mi><mi>n</mi></msup>
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<mo>≠</mo>
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<msup><mi>z</mi><mi>n</mi></msup>
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</mrow>
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<annotation encoding=\"application/x-tex\">x^n+y^n\\ne z^n</annotation>
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</semantics>
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</math>
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which this note is too small to contain!",
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"source": {
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"content": "I have a truly marvelous proof that \\(x^n+y^n\\ne z^n\\) which this note is too small to contain!",
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"mediaType": "text/markdown+math"}}
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```
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This object's source content represents a valid sanitization of its
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`content` field.
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## Semantic Attributes
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| Element | Attributes | Values |
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| ------- | ------------ | ---------------- |
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| all | `mathvariant` | `normal` |
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| all | `displaystyle`, `scriptlevel` | all |
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| `<math>` | `display` | all |
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| `<mfrac>` | `linethickness` | `0`, `1` |
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| `<mspace>`| `width`, `height`, `depth` | all |
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| `<mo>` | `form` `stretchy`, `symmetric`, `largeop`, `movablelimits`, `lspace`, `rspace`, `minsize`, | all |
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## References
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- [ActivityPub] Christine Lemmer Webber, Jessica Tallon, [ActivityPub](https://www.w3.org/TR/activitypub/), 2018
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- [ActivityStreams] James M Snell, Evan Prodromou, [ActivityStreams 2.0](https://www.w3.org/TR/activitystreams-core), 2017
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- [Activity Vocabulary] James M Snell, Evan Prodromou, [Activity Vocabulary](https://www.w3.org/TR/activitystreams-vocabulary/), 2017
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- [LaTeX] LaTeX authors, [The LaTeX Project](www.latex-project.org)
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- [MathML Core] David Carlisle, Frédéric Wang, [MathML Core W3C Candidate Reccomendation Snapshot](https://w3c.github.io/mathml-core/), 2023
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- [Mathstodon] Mathstodon Admins, [About Mathstodon](https://mathstodon.xyz/about), retrieved 2023
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- [RFC-2119] S. Bradner, [Key words for use in RFCs to Indicate Requirement Levels](https://datatracker.ietf.org/doc/html/rfc2119), 1997
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## Copyright
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CC0 1.0 Universal (CC0 1.0) Public Domain Dedication
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To the extent possible under law, the authors of this Fediverse Enhancement Proposal have waived all copyright and related or neighboring rights to this work.
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