diff --git a/_data/core.yml b/_data/core.yml index d11caf2..7407655 100644 --- a/_data/core.yml +++ b/_data/core.yml @@ -210,6 +210,37 @@ defaultfixity: characters: [⁢U+2062] +largeop: + - concept: sum + characters: [∑,⅀] + - concept: product + characters: [∏,⨉] + - concept: union + characters: [⋃] + - concept: intersection + characters: [⋂] + - concept: logical-and + characters: [⋀] + - concept: logical-or + characters: [⋁] + - concept: integral + characters: [∫] + - concept: double-integral + characters: [∬] + - concept: triple-integral + characters: [∭] + - concept: contour-integral + characters: [∮] + - concept: surface-integral + characters: [∯] + - concept: clockwise-integral + characters: [∱] + - concept: clockwise-contour-integral + characters: [∲] + - concept: anticlockwise-contour-integral + characters: [∳] + + concepts: ## From chapter 4 of MathML3 @@ -293,9 +324,9 @@ concepts: en: $1 evaluated-at $2 comments: - "Two common notations are - x2|3 + x2|3 and - + x2 @@ -397,7 +428,7 @@ concepts: en: "polar coordinate $1 comma $2" comment: - "The first argument is the radius, the second argument is the polar angle, the third arguments is the azimuthal angle." - - "Example: (r, θ)" + - "Example: (r, θ)" - concept: spherical-coordinate arity: 3 @@ -405,14 +436,14 @@ concepts: en: "spherical coordinate $1 comma $2, comma $3" comment: - "The first argument is the radius, the second argument is the angle." - - "Example: (r,Φ,θ)" + - "Example: (r,Φ,θ)" - concept: cartesian-coordinate arity: ">=2" property: function en: "cartesian coordinate $1 comma $2 ..." comment: - - "Example: (1,2)" + - "Example: (1,2)" - concept: coordinate arity: ">=2" @@ -420,7 +451,7 @@ concepts: en: "coordinate $1 comma $2 ..." comment: - "This a generic coordinate that doesn't specify the coordinate system. It takes 2 or more arguments." - - "Example: (1,2)" + - "Example: (1,2)" - concept: floor arity: 1 @@ -438,9 +469,9 @@ concepts: en: rounded-value of $1 comments: - "This sometimes uses the notation - ⌊x⌉ + ⌊x⌉ or - [x]" + [x]" - concept: fractional-part arity: 1 @@ -451,16 +482,16 @@ concepts: - title: calculus intents: - concept: definite-integral - arity: 1 - property: ??? - en: "integral over $1" + arity: 2 + property: largeop + en: "integral over $1 of $2" comments: - "integral sign is not an argument" - concept: definite-integral - arity: 2 - property: ??? - en: "integral from $1 to $2" + arity: 3 + property: largeop + en: "integral from $1 to $2 of $3" comments: - "integral sign is not an argument" @@ -473,11 +504,11 @@ concepts: - "(terse) d <$3 if $3 != 1> $1 by d $2 <$3 if $3 != 1>" comments: - "the terse reading only makes sense for Leibniz notation such as - d2ydx2 + d2ydx2 or - d2dx2f(x). + d2dx2f(x). It does not make sense for other notations such as - f''(x) + f''(x) " - "The first of these examples might be marked up as" - | @@ -522,7 +553,7 @@ concepts: comments: - "limit is not an argument, but intent should be on `msub` or `munder`" - "There are several arrows used for limits. " - - "Example: + - "Example: lim x↗0 @@ -541,7 +572,7 @@ concepts: ``` - "Another notation that might be spoken similarly is - limx→0- + limx→0- " - concept: tends-to @@ -577,7 +608,7 @@ concepts: the argument to `set` is typically an `mrow`. For example: ``` - + { @@ -601,7 +632,7 @@ concepts: comments: - "This can be spoken in many ways. See other entry for infix speech." - "There are several notations that are used and their order of appearance differs: - A-B, A\\B" + A-B, A\\B" - concept: set-difference arity: 2 @@ -618,7 +649,7 @@ concepts: comments: - "This can be spoken in many ways. See other entry for functional speech." - "Two notations used for complement are: - AC, A'" + AC, A'" - concept: empty-set arity: 0 @@ -646,42 +677,48 @@ concepts: intents: - concept: sum arity: 1 - property: function + property: largeop en: "sum of $1" + mathml: + - "∑f(i)" comments: - usually on `` - concept: sum arity: 2 - property: function + property: largeop en: "sum over $1 of $2" + mathml: + - "∑i∈Xf(i)" comments: - usually on `` or `` - concept: sum arity: 3 - property: function + property: largeop en: "sum from $1 to $2 of $3" + mathml: + - "∑i=abf(i)" comments: - usually on `` or `` - concept: product arity: 1 - property: function + property: largeop en: "product of $1" comments: - usually on `` - concept: product arity: 2 - property: function + property: largeop en: "product over $1 of $2" comments: - usually on `` or `` - concept: product arity: 3 - property: function + property: largeop en: "product from $1 to $2 of $3" comments: - usually on `` or `` @@ -750,7 +787,7 @@ concepts: - "(verbose) arcsine $1" comments: - "used as 'arcsin', 'arc sin'" - - "this is distinct from sin inverse (sin-1)" + - "this is distinct from sin inverse (sin-1)" - concept: arccosine arity: 1 @@ -956,7 +993,7 @@ concepts: property: function en: "mean of $1" comments: - - "This might be display as x¯" + - "This might be display as x¯" - concept: standard-deviation arity: 1 @@ -989,7 +1026,7 @@ concepts: The intent should be on the `mrow` that includes the "P" ``` - + P ( @@ -1050,7 +1087,7 @@ concepts: arity: 1 property: prefix comments: - - "Example: x^" + - "Example: x^" en: "unit vector x" - concept: identity-matrix @@ -1079,7 +1116,7 @@ concepts: en: "$1 by $2 ..." comments: - "This is typically used with the `×` operator and can be placed on that character as a 0-arity concept name. - A common use would be describe the size of a matrix. For example m×n." + A common use would be describe the size of a matrix. For example m×n." ## ====================== 4.4.10 Constants and Sets ====================== @@ -1156,7 +1193,7 @@ concepts: en: - "line segment $1 $2" comments: - - "Example: (`mover`): AB_" + - "Example: (`mover`): AB_" - concept: directed-line-segment arity: 2 @@ -1164,7 +1201,7 @@ concepts: en: - "directed line segment $1 $2" comments: - - "Example: (`mover`): AB→" + - "Example: (`mover`): AB→" - concept: line arity: 2 @@ -1172,7 +1209,7 @@ concepts: en: - "line $1 $2" comments: - - "Example: (`mover`): AB↔" + - "Example: (`mover`): AB↔" - concept: ray arity: 2 @@ -1180,7 +1217,7 @@ concepts: en: - "ray $1 $2" comments: - - "Example: (`mover`): AB→" + - "Example: (`mover`): AB→" - concept: arc arity: 2 @@ -1188,7 +1225,7 @@ concepts: en: - "arc $1 $2" comments: - - "Example: (`mover`): AB⌒" + - "Example: (`mover`): AB⌒" - concept: length arity: 1 @@ -1197,7 +1234,7 @@ concepts: - "length of $1" comments: - "It may be necessary to 'nest' the intent as shown here for the example: - + A B " @@ -1217,7 +1254,7 @@ concepts: - "area of $1" comments: - "There are many notations. Here's one: - [ABCD]" + [ABCD]" - "The markup for this is:" - | ``` @@ -1239,7 +1276,7 @@ concepts: en: - "point $1 [comma $2 ...]" comment: - - "Example: (1,2,3)" + - "Example: (1,2,3)" - concept: volume arity: 1 @@ -1321,14 +1358,14 @@ concepts: property: function en: "translation by $1 comma $2" comments: - - "Example: T(1,3)" + - "Example: T(1,3)" - concept: constraint arity: 2 property: infix en: "fraction 2 over x minus 1 with constraint x not equal to 1" comments: - - "Example: 2x-1, x≠1" + - "Example: 2x-1, x≠1" - concept: binomial-coefficient arity: 2 @@ -1336,7 +1373,7 @@ concepts: en: "$1 choose $2" comments: - "There are many notations used for the binomial coefficient. Here are some of them: - + ( n @@ -1344,14 +1381,14 @@ concepts: ) , - + C k n , - + C k @@ -1366,7 +1403,7 @@ concepts: en: "$2 permutation of $1" comments: - "There are many notations for this: some of them are - + Pkn ,  Pkn @@ -1394,7 +1431,7 @@ concepts: property: function en: "permutation cycle of $1 $2 ..." comments: - - "A common notation for a permutation cycle is ( + - "A common notation for a permutation cycle is ( 132 )" - "This would be marked up as:" @@ -1433,7 +1470,7 @@ concepts: en: "$1 which is $2" comments: - "used with `mover` or `munder`" - - "Example: H2O⏟water" + - "Example: H2O⏟water" - concept: braced-group arity: 1 @@ -1441,7 +1478,7 @@ concepts: en: "grouped $1 end-grouped" comments: - "used with `mover` or `munder`" - - "Example: 13-16⏟" + - "Example: 13-16⏟" - concept: repeating-decimal arity: 1 @@ -1449,7 +1486,7 @@ concepts: en: "repeating decimal $1" comments: - "typically used in when there is a bar over the repeating part of a decimal or dots over the first and last digits." - - "Example: 122=0.045_" + - "Example: 122=0.045_" - "This right hand side of this might be might be marked up as:" - | ``` diff --git a/intent-core-concepts/index.md b/intent-core-concepts/index.md index f2e2adc..5ff444f 100644 --- a/intent-core-concepts/index.md +++ b/intent-core-concepts/index.md @@ -32,14 +32,31 @@ title: Core Concept List p.langs {margin:1em; padding:1em;background-color: #EEE} tr:target >td:first-child {border-left:solid thick black} span.cb {margin-right: 2em; white-space:nowrap} +.markdown-body table {font-size:85%} .markdown-body table tr.row0, .markdown-body table th.row0 {background-color:#F6F8FA} .markdown-body table tr.row1 {background-color:#FEFFFE} a.link {font-weight:500} a.self {color: black; font-weight:500} + [arg] { background-color: #ddfafa;} + [arg]:hover {display:inline;background-color: #add8e6;} + [arg]:hover::after {display:inline;vertical-align: sub; font-size: 0.7em; } + [arg="a1"]:hover::after { content: " $1" ; } + [arg="a2"]:hover::after { content: " $2" ; } + [arg="a3"]:hover::after { content: " $3" ; } + [arg="a4"]:hover::after { content: " $4" ; } + [arg="a5"]:hover::after { content: " $5" ; } + [arg="a6"]:hover::after { content: " $6" ; } + [arg="a7"]:hover::after { content: " $7" ; } + [arg="a8"]:hover::after { content: " $8" ; } + [arg="a9"]:hover::after { content: " $9" ; } +math:not(:has(*[intent])) { + color: red; + } +div.mmlshow {display:inline-block;padding:1em;margin:.5em;border-radius:1em;font-family:monospace;background-color:#EEE;white-space:pre;}

+ + +

+ + ---- @@ -101,7 +126,7 @@ but do have default fixity properties other than `function`. {%- for fix in site.data.core.defaultfixity -%} -
{{fix.fixity}} +
{{fix.fixity}} {%- for c in fix.concepts -%} {%- endfor %} @@ -132,14 +157,97 @@ if c.link ---- -## Core Concept Templates +## 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. + + + + + + +{%- for language in site.data.languages -%} + +{%- endfor -%} + + + + +{%- for c in site.data.core.concepts[3].intents -%} +{%- if c.concept == "sum" -%} +{%- assign arityr = c.arity | replace: ">=", "⩾" -%} +{%- assign arityu = c.arity | replace: ">=", "GEQ" -%} +{%- assign propertyu = c.property | replace: "?", "Q" -%} + + + + +{%- for language in site.data.languages -%} + +{%- endfor -%} + + +{%- endif -%} +{%- endfor -%} + +
ConceptArityPropertySpeech Template ({{language.language-code}})Comments
{{c.concept}}{{arityr}}{{c.property}}{%- unless c.default == false or c.arity == 0-%}*{%- endunless -%} +{%- if c[language.language-code] -%} +{%- for l in c[language.language-code] -%} +{{l}} {%- unless forloop.last -%}
{% endunless -%} +{% endfor %} +{%- else -%} +{%- for l in c.en -%} +{{l}} ({{language.language-code}}){%- unless forloop.last -%}
{% endunless -%} +{% endfor %} +{% endif %} +		 +{%- for com in c.comments -%} +{{com | markdownify | replace: "

", "" | replace: "

", "" }} +{%- unless forloop.last -%}
{% endunless -%} +{% endfor %} +{%- if c.comments and c.mathml -%}
{%- endif -%} +{%- for mml in c.mathml -%} +{{mml}} +{%- unless forloop.last -%}
{% endunless -%} +{% endfor %} +
-

- - -

+ + + +
+
largeop
+
+{%- for c in site.data.core.largeop -%} +{{c.concept}} +( +{%- for ch in c.characters -%} +{{ch}} +{%- unless forloop.last -%}, {% endunless -%} +{%- endfor -%} +) +{% unless forloop.last -%}, {% endunless -%} +{%- endfor %} +
+
+ + + +---- + +## Core Concept Templates @@ -155,7 +263,7 @@ if c.link