MathML Document Repository

Core Concept List

Matching the List

1. A intent processor should match a system-specifed list of known concept names. The list should include all the entries from the core list below.

2. Optionally intents may be defaulted based on the available content, so <mo>=</mo> may default to <mo intent="equals">=</mo> or <msup><mi>x</mi><mn>2</mn></msup> may default to <msup intent="power($x,$n)"><mi arg="x">x</mi><mn arg="n">2</mn></msup> Defaulting rules and options to control them to be specifed elsewhere, and are likely to be system specific.

3. An intent term matches a row in the table if the concept name, arity and property all match. Any intent literal that does not match is not an error but is handled by the general rules for unknown concept names (so treated as a literal). Note that unless the intent is explicitly or implicitly (by expanding $argref) used as a function head it will have arity 0.

4. The conditionals in the speech template should be constructed such that at least one row matches. If more than one speech template matches a system specific choice should be taken. The exact words in the speech templates are not normative so a system may have multiple possible wordings controlled by the context, or by system option settings such as “Verbosity”.

Sources

Additional language contributions are welcome.

Languages can be listed by extending the YAML file: languages.yml

Any concept that does not have a speech template in the specifed language will show the English text.

Localised texts can be added to the YAML file: core.yml

Show MathML Source Display typeset math

Core List

Core Concept Default Fixity properties

The following concepts do not require special speech templates but do have default fixity properties other than function.

function

curl (∇) , divergence (∇) , gradient (∇) , laplacian (∆)

prefix

angle (∠) , angle-measure (∡) , change (Δ) , for-all (∀) , measured-angle (∡) , minus (-, −) , not (¬) , number-of (#) , partial-derivative (∂) , right-angle (∟) , square-root-of (√) , there-does-not-exist (∄) , there-exists (∃)

infix

and (⁤∧) , applied-to (⁡U+2061) , approximately (≈) , congruent (≅) , cartesian-product (×) , composed-with (∘) , cross-product (×) , defined-as (≝, =, ≔) , dimensional-product (×) , divided-by (/, ÷, :) , divides (|, ∣) , does-not-belong-to (∉) , does-not-divide (∤) , dot-product (·) , downwards-diagonal-ellipsis (⋱) , direct-product (×) , element-of (∈, ∊) , ellipsis (…, ⋯) , equals (=) , equivalent-to (≡) , evaluates-to (→) , given (|) , greater-than (>) , greater-than-or-equal-to (≥, ≧) , identically-equals (≡) , if-and-only-if (⟺) , implies (⇒) , inner-product (⋅) , intersection (∩) , less-than (<) , less-than-or-equal-to (≤, ≦) , list-separator (,, ;) , maps-to (→) , member-of (∈, ∊) , minus (-, −) , minus-or-plus (∓) , not-subset (⊄) , not-superset (⊅) , not-equal-to (≠) , not-member-of (∉) , not-parallel-to (∦) , obtained-from (←) , or (∨) , outer-product (⊗) , parallel-to (∥) , perpendicular (⟂) , plus (+, U+2064) , plus-or-minus (±) , precedes (≺) , proportional (∝, ∷, ∼, ) , range-separator (-, ‐, ‑, –, —) , ratio (:, ∶) , set-difference (∼, ~, -, −, \) , similar (≅) , subset (⊂) , subset-or-equal (⊆) , succeeds (≻) , such-that (:, |) , superset (⊃) , superset-or-equal (⊇) , tilde () , times (*, ·, ×, ∗) , union (∪) , upwards-diagonal-ellipsis (⋰) , vertical-ellipsis (⋮) , xor (⊕)

postfix

factorial (!) , percent (%)

nofix

diameter (d) , distance (d, D) , probability (P) , radius (r) , volume (V)

silent

invisible-separator (⁣U+2063) , invisible-times (⁢U+2062)

Default Large Operator Concepts

Speech templates for “large” operators follow a similar pattern and are often strongly associated with particular characters. They are collected here to give a more convenient and compact presentation.

largeop

sum (∑, ⅀) , product (∏, ⨉) , union (⋃) , intersection (⋂) , logical-and (⋀) , logical-or (⋁) , integral (∫) , double-integral (∬) , triple-integral (∭) , contour-integral (∮) , surface-integral (∯) , clockwise-integral (∱) , clockwise-contour-integral (∲) , anticlockwise-contour-integral (∳)

Core Concept Templates

functions and inverses

calculus

<mfrac intent='derivative(y, x, 2)'>
  <mrow>
    <msup><mi>d</mi><mn arg>2</mn></msup>
    <mi>y</mi>
  </mrow>
  <mrow>
    <mi>d</mi>
    <msup><mi>x</mi><mn>2</mn></msup>
  </mrow>
</mfrac>

<mfrac intent='partial-derivative($f, x, 2, y, 1)'>
  <mrow>
      <msup><mo>&#x2202;</mo><mn>3</mn></msup>
      <mrow arg='f'><mi>sin</mi><mo>(</mo><mi>x</mi><mo>)</mo><mi>y</mi></mrow>
  </mrow>
  <mrow>
      <msup><mo>&#x2202;</mo><mn>2</mn></msup>
      <mi>x</mi><mo>&#x2202;</mo><mi>y</mi>
  </mrow>
</mfrac>

<munder intent='limit($lim)'>
    <mi>lim</mi>
    <mrow arg='lim' intent='tends-to-from-below($x, $val)''>
      <mi arg='x'>x</mi>
      <mo>↗</mo>
      <mn arg='val'>0</mn>
    </mrow>
</munder>

Sets

<math display='block'>
 <mrow intent='set($members)'>
  <mo>{</mo>
  <mrow arg='members'>
   <mn>2</mn>
   <mo>,</mo>
   <mn>4</mn>
   <mo>,</mo>
   <mn>6</mn>
   <mo>,</mo>
   <mn>8</mn>
  </mrow>
  <mo>}</mo>
 </mrow>
</math>

sequence and series

elementary classical functions

Statistics and Probability

 <math display='block'>
  <mrow intent='conditional-probability($arg1, $arg2)'>
   <mi>P</mi>
   <mo>(</mo>
   <mrow>
    <mi arg='arg1'>A</mi>
     <mo>|</mo>
     <mi arg='arg2'>B</mi>
   </mrow>
   <mo>)</mo>
  </mrow>
 </math>

Linear Algebra

Constants and Sets

Geometry

<mrow intent='length(line-segment($start, $end))'>
       <mi arg='start' mathvariant='normal'>A</mi>
       <mi arg='end' mathvariant='normal'>B</mi>
</mrow>

<mrow intent='area($shape)'>
    <mo>[</mo>
    <mrow arg='shape'>
        <mi mathvariant='normal'>A</mi>
        <mi mathvariant='normal'>B</mi>
        <mi mathvariant='normal'>C</mi>
        <mi mathvariant='normal'>D</mi>
        <mo>]</mo>
    </mrow>
</mrow>

Fill in the blank

Separators

General Concepts

<msubsup intent='pochhammer($n, $k)'>
    <mi>P</mi>
    <mi arg='k'>k</mi>
    <mi arg='n'>n</mi>
</msubsup>

<mrow intent='permutation-cycle($arg1, $arg2, $arg3)'
<mo>(</mo>
  <mtable><mtr>
     <mtd><mn arg='arg1'>1</mn></mtd>
     <mtd><mn arg='arg2'>3</mn></mtd>
     <mtd><mn arg='arg3'>2</mn></mtd>
  </mtr></mtable>
<mo>)</mo>

Grouping

<mn>0.0</mn>
<mover intent='repeating-decimal($repeat)'>
    <mn arg='repeat'>45</mn>
    <mo>_</mo>
</mover>

<mstack intent='_(0.0, repeating-decimal(45)'>
  <msline length="2"/>
  <mn>0.045</mn>
</mstack>

Key