TESTS OF MACROS FOR CATEGORY THEORY

December 17, 2002

Each case shows a call of a macro (or occasionally a combination of macros) followed by one or more displays of the result. When four displays are given, they are for display style, text style, script style, and scriptscript style, respectively.

1 Miscellaneous Special Symbols and Other Macros

\displayaxis : 3.0pt

\textaxis : 3.0pt

\scriptaxis : 2.0pt

\scriptscriptaxis : 1.5pt

\eqper : .
\eqcom : ,
\reflect{p_{1}} : p_{1}^{†} p_{1}^{†} p_{1}^{†} p_{1}^{†}
\inverse{p_{1}} : p_{1}^{−1} p_{1}^{−1} p_{1}^{−1} p_{1}^{−1}
\dual{p_{1}} : p_{1}^{op} p_{1}^{op} p_{1}^{op} p_{1}^{op}
\identgen\{p_{1}\}\{p_{2}\} : I_{p_{2}}^{p_{1}} I_{p_{2}}^{p_{1}} I_{p_{2}}^{p_{1}} I{p_{1} \atop p_{2}}

\ident{p_{1}} : I_{p_{1}} I_{p_{1}} I_{p_{1}} Ip_{1}

\startproof This is an example … \endproof : Proof : This is an example of a short proof. (End of Proof ) Proof : This is a longer proof that forces “End of Proof” to the next line. (End of Proof )

2 Unary Operators

\domainop : dom dom dom dom

\rangeop : ran ran ran ran

\sizeop : # # # # \objectsop : Ob Ob Ob Ob

\morphsop : Mor Mor Mor Mor \apop : ap ap ap ap \abop : ab ab ab ab

3 Binary Operators

\restrictop : ⌉ ⌉ ⌉ ⌉ \corestrictop : ⌈ ⌈ ⌈ ⌈ \sccompop : ; ; ; ; \godmult : ; ; ; ;

4 Relations

\eqdef : =^{def} =^{def} =^{def} {def \atop =} \noteq : ≠ ≠ ≠ ≠

\finsubset : ⊆^{fin} ⊆^{fin} ⊆^{fin} {fin \atop ⊆} \oldin : ∈ ∈ ∈ ∈ \oldnotin : ∉ ∉ ∉ ∉

\in : ^{∈} ^{∈} ^{∈} ∈ \notin : ∉ ∉ ∉ ∉

\uniquein : ^{∈}! ^{∈}! ^{∈}! ∈! \arrow : → → → →

\arrowsub\{p_{1}\} : ⟶_{p_{1}} ⟶_{p_{1}} _{⟶_{p_{1}}} _{\overrightarrow{p_{1}}}

\arrowsub\{long_{1}\} : ⟶_{long_{1}} ⟶_{long_{1}} _{⟶_{long_{1}}} _{\overrightarrow{long_{1}}}

\arrowsuper\{p_{1}\} : ⟶^{p_{1}} ⟶^{p_{1}} ⟶^{p_{1}} \underrightarrow{p_{1}}

\arrowsuper\{long_{1}\} : ⟶^{long_{1}} ⟶^{long_{1}} ⟶^{long_{1}} \underrightarrow{long_{1}}

\arrowsubsuper{p_{1}}{p_{2}} : ⟶_{p_{1}}^{p_{2}} ⟶_{p_{1}}^{p_{2}} ⟶_{p_{1}}^{p_{2}} p_{2} ; ⟶ ; p_{1}

\arrowsubsuper{long_{1}}{long_{2}} : ⟶_{long_{1}}^{long_{2}} ⟶_{long_{1}}^{long_{2}} ⟶_{long_{1}}^{long_{2}} long_{2} ; ⟶ ; long_{1}

\Arrow : ⇒ ⇒ ⇒ ⇒

\Arrowsub\{p_{1}\} : ⟹_{p_{1}} ⟹_{p_{1}} _{⟹_{p_{1}}} _{\overrightarrow{p_{1}}}

\Arrowsub\{long_{1}\} : ⟹_{long_{1}} ⟹_{long_{1}} _{⟹_{long_{1}}} _{\overrightarrow{long_{1}}}

\Arrowsuper\{p_{1}\} : ⟹^{p_{1}} ⟹^{p_{1}} ⟹^{p_{1}} \underrightarrow{p_{1}}

\Arrowsuper\{long_{1}\} : ⟹^{long_{1}} ⟹^{long_{1}} ⟹^{long_{1}} \underrightarrow{long_{1}}

\Arrowsubsuper{p_{1}}{p_{2}} : ⟹_{p_{1}}^{p_{2}} ⟹_{p_{1}}^{p_{2}} ⟹_{p_{1}}^{p_{2}} p_{2} ; ⟹ ; p_{1}

\Arrowsubsuper{long_{1}}{long_{2}} : ⟹_{long_{1}}^{long_{2}} ⟹_{long_{1}}^{long_{2}} ⟹_{long_{1}}^{long_{2}} long_{2} ; ⟹ ; long_{1}

5 Delimiters

In each of the following examples, the indicated expression is printed in: 1. textstyle, without enlargement (e.g. as a parameter to \normsize)

2. textstyle, big size (e.g. as a parameter to \bigsize)

3. textstyle, Big size (e.g. as a parameter to \Bigsize)

4. textstyle, bigg size (e.g. as a parameter to \biggsize)

5. textstyle, Bigg size (e.g. as a parameter to \Biggsize)

6. scriptstyle, without enlargement (e.g. as a parameter to \normsize)

7. scriptstyle, scriptbig size (e.g. as a parameter to \scriptbigsize)

8. scriptscriptstyle, without enlargement (e.g. as a parameter to \normsize)

9. scriptscriptstyle, scriptscriptbig size (e.g. as a parameter to \scriptscriptbigsize)

\varlpar : ( ( ( ( ( ( ( ( _{(}
\varrpar : ) ) ) ) ) ) ) ) _{)}
\varlbrack : [ [ [ [ [ [ [ [ _{[}
\varrbrack : ] ] ] ] ] ] ] ] _{]}
\varlbrace : { { { { { { { { _{{}
\varrbrace : } } } } } } } } _{}}
\varlangle : ⟨ ⟨ ⟨ ⟨ ⟨ ⟨ ⟨ ⟨ _{⟨}
\varrangle : ⟩ ⟩ ⟩ ⟩ ⟩ ⟩ ⟩ ⟩ _{⟩}
\varlvert : | | | | | | | | _{|}
\varrvert : | | | | | | | | _{|}
\varmid : | | | | | | | | _{|}

\varlsembr : [[ [ [ [ ^{[ ; [} [[ [[ [[ [[

\varrsembr : ]] ] ] ] ^{] ; ]} ]] ]] ]] ]]

\varbdlangle : ⟨⟨⟨⟨ ^{⟨ ⟨ ⟨ ⟨} ^{⟨ ⟨ ⟨ ⟨} ^{⟨ ⟨ ⟨ ⟨} ^{⟨ ⟨ ⟨ ⟨} ⟨^{⟨}_{⟨}⟨ ⟨⟨⟨⟨ ⟨^{⟨}_{⟨}⟨ _{⟨}_{⟨}_{⟨}_{⟨}

\varbdrangle : ⟩⟩⟩⟩ ^{⟩ ⟩ ⟩ ⟩} ^{⟩ ⟩ ⟩ ⟩} ^{⟩ ⟩ ⟩ ⟩} ^{⟩ ⟩ ⟩ ⟩} ⟩^{⟩}_{⟩}⟩ ⟩⟩⟩⟩ ⟩^{⟩}_{⟩}⟩ _{⟩}_{⟩}_{⟩}_{⟩}

\paren{p_{1}} : (p_{1}) (p_{1}) (p_{1}) (p_{1}) (p_{1}) (p_{1}) (p_{1}) (p_{1}) (p_{1})

\paren{\paren{p_{1}}} :
((p_{1})) ((p_{1})) ((p_{1})) ((p_{1})) ((p_{1})) ((p_{1})) ((p_{1})) ((p_{1})) ((p_{1}))

\carrier{p_{1}} : |p_{1}| |p_{1}| |p_{1}| |p_{1}| |p_{1}| |p_{1}| |p_{1}| |p_{1}| |p_{1}|

\carrier{\carrier{p_{1}}} : ||p_{1}|| ||p_{1}|| ||p_{1}|| ||p_{1}|| ||p_{1}|| ||p_{1}|| ||p_{1}|| ||p_{1}|| ||p_{1}||

\sembr{p_{1}} : [[p_{1}]] [p_{1}] [p_{1}] [p_{1}] [ ; [p_{1}] ; ] [[p_{1}]] [[p_{1}]] [[p_{1}]] [[p_{1}]]

\sembr{\sembr{p_{1}}} :
[[[[p_{1}]]]] [[[p_{1}]]] [[[p_{1}]]] [[[p_{1}]]] [ ; [[[p_{1}]]] ; ] [[[[p_{1}]]]] [[[[p_{1}]]]] [[[[p_{1}]]]] [[[[p_{1}]]]]
\setdef{p_{1}}{p_{2}} :
{ p_{1} | p_{2} } { p_{1} | p_{2} } { p_{1} | p_{2} } { p_{1} | p_{2} } { p_{1} | p_{2} }
{p_{1}|p_{2}} {p_{1}|p_{2}} {p1|p2} {p1|p2}

\setdef{\paren{p_{1}}}{\paren{p_{1}}} :

{ (p_{1}) | (p_{2}) } { (p_{1}) | (p_{2}) } { (p_{1}) | (p_{2}) } { (p_{1}) | (p_{2}) } { (p_{1}) | (p_{2}) }
{(p_{1})|(p_{2})} {(p_{1})|(p_{2})} {(p1)|(p2)} {(p1)|(p2)}

6 Macros with a Variable Number of Parameters

\simplist0{p_{1}}{p_{2}}{p_{3}}{p_{4}} : p_{4} \simplist1{p_{1}}{p_{2}}{p_{3}}{p_{4}}{p_{5}} : p_{1}p_{5}p_{2}

\simplist2{p_{1}}{p_{2}}{p_{3}}{p_{4}}{p_{5}}{p_{6}} : p_{1}p_{5}p_{3}p_{6}p_{2} \simplist3{p_{1}}{p_{2}}{p_{3}}{p_{4}}{p_{5}}{p_{6}}{p_{7}} : p_{1}p_{5}p_{3}p_{6}p_{3}p_{7}p_{2}

… etc.

\emptyset : {} {} {} {}

\setlist0 : {} \setlist1{p_{1}} : {p_{1}}

\setlist2{p_{1}}{p_{2}} : {p_{1}, p_{2}} \setlist3{p_{1}}{p_{2}}{p_{3}} : {p_{1}, p_{2}, p_{3}}

… etc.

\emptysqlist : [ ] [ ] [ ] [ ]

\sqlist0 : [ ] \sqlist1{p_{1}} : [p_{1}]

\sqlist2{p_{1}}{p_{2}} : [p_{1}, p_{2}] \sqlist3{p_{1}}{p_{2}}{p_{3}} : [p_{1}, p_{2}, p_{3}]

… etc.

\emptyanglelist : ⟨⟩ ⟨⟩ ⟨⟩ ⟨⟩

\anglelist0 : ⟨⟩ \anglelist1{p_{1}} : ⟨p_{1}⟩

\anglelist2{p_{1}}{p_{2}} : ⟨p_{1}, p_{2}⟩

\anglelist3{p_{1}}{p_{2}}{p_{3}} : ⟨p_{1}, p_{2}, p_{3}⟩

… etc.

\emptybdanglelist : ⟨⟨⟨⟨⟩⟩⟩⟩ ⟨⟨⟨⟨⟩⟩⟩⟩ ⟨^{⟨}_{⟨}⟨⟩^{⟩}_{⟩}⟩ ⟨^{⟨}_{⟨}⟨⟩^{⟩}_{⟩}⟩

\bdanglelist0 : ⟨⟨⟨⟨⟩⟩⟩⟩

\bdanglelist1{p_{1}} : ⟨⟨⟨⟨p_{1}⟩⟩⟩⟩

\bdanglelist2{p_{1}}{p_{2}} : ⟨⟨⟨⟨p_{1}, p_{2}⟩⟩⟩⟩

\bdanglelist3{p_{1}}{p_{2}}{p_{3}} : ⟨⟨⟨⟨p_{1}, p_{2}, p_{3}⟩⟩⟩⟩

… etc.

\pairlist0{p_{1}}{p_{2}}{p_{3}}{p_{4}}{p_{5}} : p_{5}

\pairlist1{p_{1}}{p_{2}}{p_{3}}{p_{4}}{p_{5}}{p_{6}}{p_{7}} : p_{1}p_{6}p_{4}p_{7}p_{2}

\pairlist2{p_{1}}{p_{2}}{p_{3}}{p_{4}}{p_{5}}{p_{6}}{p_{7}}{p_{8}}{p_{9}} : p_{1}p_{6}p_{4}p_{7}p_{3}p_{8}p_{4}p_{9}p_{2}

… etc.

\pairlistdots{p_{1}}{p_{2}}{p_{3}}{p_{4}}{p_{5}}{p_{6}}{p_{7}}{p_{8}} : p_{1}p_{5}p_{4}p_{6}p_{3} … p_{3}p_{7}p_{4}p_{8}p_{2}

\sqpairlist0 : [ ]

\sqpairlist1{p_{1}}{p_{2}} : [ p_{1}: p_{2} ]

\sqpairlist2{p_{1}}{p_{2}}{p_{3}}{p_{4}} : [ p_{1}: p_{2} | p_{3}: p_{4} ]

\sqpairlist3{p_{1}}{p_{2}}{p_{3}}{p_{4}}{p_{5}}{p_{6}} : [ p_{1}: p_{2} | p_{3}: p_{4} | p_{5}: p_{6} ]

… etc.

\sqpairlistdots{p_{1}}{p_{2}}{p_{3}}{p_{4}} : [ p_{1}: p_{2} | … | p_{3}: p_{4} ]

\anglepairlist0 : ⟨⟩

\anglepairlist1{p_{1}}{p_{2}} : ⟨ p_{1}: p_{2} ⟩

\anglepairlist2{p_{1}}{p_{2}}{p_{3}}{p_{4}} : ⟨ p_{1}: p_{2} | p_{3}: p_{4} ⟩

\anglepairlist3{p_{1}}{p_{2}}{p_{3}}{p_{4}}{p_{5}}{p_{6}} : ⟨ p_{1}: p_{2} | p_{3}: p_{4} | p_{5}: p_{6} ⟩

… etc.

\anglepairlistdots{p_{1}}{p_{2}}{p_{3}}{p_{4}} : ⟨ p_{1}: p_{2} | … | p_{3}: p_{4} ⟩

\bdanglepairlist0 : ⟨⟨⟨⟨⟩⟩⟩⟩

\bdanglepairlist1{p_{1}}{p_{2}} : ⟨⟨⟨⟨ p_{1}: p_{2} ⟩⟩⟩⟩

\bdanglepairlist2{p_{1}}{p_{2}}{p_{3}}{p_{4}} : ⟨⟨⟨⟨ p_{1}: p_{2} | p_{3}: p_{4} ⟩⟩⟩⟩

\bdanglepairlist3{p_{1}}{p_{2}}{p_{3}}{p_{4}}{p_{5}}{p_{6}} : ⟨⟨⟨⟨ p_{1}: p_{2} | p_{3}: p_{4} | p_{5}: p_{6} ⟩⟩⟩⟩

… etc.

\bdanglepairlistdots{p_{1}}{p_{2}}{p_{3}}{p_{4}} : ⟨⟨⟨⟨ p_{1}: p_{2} | … | p_{3}: p_{4} ⟩⟩⟩⟩

\pairext0{p_{1}}{p_{2}}{p_{3}}{p_{4}}{p_{5}} : p_{1}p_{5}p_{2}

\pairext1{p_{1}}{p_{2}}{p_{3}}{p_{4}}{p_{5}}{p_{6}}{p_{7}} : p_{1}p_{5}p_{3}p_{6}p_{4}p_{7}p_{2}

\pairext2{p_{1}}{p_{2}}{p_{3}}{p_{4}}{p_{5}}{p_{6}}{p_{7}}{p_{8}}{p_{9}} : p_{1}p_{5}p_{3}p_{6}p_{4}p_{7}p_{3}p_{8}p_{4}p_{9}p_{2}

… etc.

\pairextdots{p_{1}}{p_{2}}{p_{3}}{p_{4}}{p_{5}}{p_{6}}{p_{7}}{p_{8}}{p_{9}} : p_{1}p_{5}p_{3}p_{6}p_{4}p_{7}p_{3} … p_{3}p_{8}p_{4}p_{9}p_{2}

\sqpairext0{p_{1}} : [ p_{1} ]

\sqpairext1{p_{1}}{p_{2}}{p_{3}} : [ p_{1} | p_{2}: p_{3} ]

\sqpairext2{p_{1}}{p_{2}}{p_{3}}{p_{4}}{p_{5}} : [ p_{1} | p_{2}: p_{3} | p_{4}: p_{5} ]

\sqpairext3{p_{1}}{p_{2}}{p_{3}}{p_{4}}{p_{5}}{p_{6}}{p_{7}} : [ p_{1} | p_{2}: p_{3} | p_{4}: p_{5} | p_{6}: p_{7} ]

… etc.

\sqpairextdots{p_{1}}{p_{2}}{p_{3}}{p_{4}}{p_{5}} : [ p_{1} | p_{2}: p_{3} | … | p_{4}: p_{5} ]

\anglepairext0{p_{1}} : ⟨ p_{1} ⟩

\anglepairext1{p_{1}}{p_{2}}{p_{3}} : ⟨ p_{1} | p_{2}: p_{3} ⟩

\anglepairext2{p_{1}}{p_{2}}{p_{3}}{p_{4}}{p_{5}} : ⟨ p_{1} | p_{2}: p_{3} | p_{4}: p_{5} ⟩

\anglepairext3{p_{1}}{p_{2}}{p_{3}}{p_{4}}{p_{5}}{p_{6}}{p_{7}} : ⟨ p_{1} | p_{2}: p_{3} | p_{4}: p_{5} | p_{6}: p_{7} ⟩

… etc.

\anglepairextdots{p_{1}}{p_{2}}{p_{3}}{p_{4}}{p_{5}} : ⟨ p_{1} | p_{2}: p_{3} | … | p_{4}: p_{5} ⟩

\bdanglepairext0{p_{1}} : ⟨⟨⟨⟨ p_{1} ⟩⟩⟩⟩

\bdanglepairext1{p_{1}}{p_{2}}{p_{3}} : ⟨⟨⟨⟨ p_{1} | p_{2}: p_{3} ⟩⟩⟩⟩ \bdanglepairext2{p_{1}}{p_{2}}{p_{3}}{p_{4}}{p_{5}} : ⟨⟨⟨⟨ p_{1} | p_{2}: p_{3} | p_{4}: p_{5} ⟩⟩⟩⟩

\bdanglepairext3{p_{1}}{p_{2}}{p_{3}}{p_{4}}{p_{5}}{p_{6}}{p_{7}} : ⟨⟨⟨⟨ p_{1} | p_{2}: p_{3} | p_{4}: p_{5} | p_{6}: p_{7} ⟩⟩⟩⟩

… etc.

\bdanglepairextdots{p_{1}}{p_{2}}{p_{3}}{p_{4}}{p_{5}} : ⟨⟨⟨⟨ p_{1} | p_{2}: p_{3} | … | p_{4}: p_{5} ⟩⟩⟩⟩

\infix1{p_{1}}{p_{2}} : p_{2} \infix2{p_{1}}{p_{2}}{p_{3}} : p_{2}p_{1}p_{3}

\infix3{p_{1}}{p_{2}}{p_{3}}{p_{4}} : p_{2}p_{1}p_{3}p_{1}p_{4}

… etc.

\compo1{p_{1}} : p_{1} \compo2{p_{1}}{p_{2}} : p_{1} ; p_{2}

\compo3{p_{1}}{p_{2}}{p_{3}} : p_{1} ; p_{2} ; p_{3}

… etc.

\compogen1{p_{1}}{p_{2}} : p_{2} \compogen2{p_{1}}{p_{2}}{p_{3}} : p_{2} ;_{p_{1}} p_{3}

\compogen3{p_{1}}{p_{2}}{p_{3}}{p_{4}} : p_{2} ;_{p_{1}} p_{3} ;_{p_{1}} p_{4}

… etc.

\fcompo1{p_{1}} : p_{1} \fcompo2{p_{1}}{p_{2}} : p_{1} · p_{2}

\fcompo3{p_{1}}{p_{2}}{p_{3}} : p_{1} · p_{2} · p_{3}

… etc.

\fcompogen1{p_{1}}{p_{2}} : p_{2} \fcompogen2{p_{1}}{p_{2}}{p_{3}} : p_{2} ·_{p_{1}} p_{3}

\fcompogen3{p_{1}}{p_{2}}{p_{3}}{p_{4}} : p_{2} ·_{p_{1}} p_{3} ·_{p_{1}} p_{4}

… etc.

\godcompo1{p_{1}} : p_{1} \godcompo2{p_{1}}{p_{2}} : p_{1} ; p_{2}

\godcompo3{p_{1}}{p_{2}}{p_{3}} : p_{1} ; p_{2} ; p_{3}

… etc.

7 Lambda Notation

\lambin{p_{1}}{p_{2}} : λp_{1} ^{∈} p_{2}. λp_{1} ^{∈} p_{2}. λp_{1}^{∈}p_{2}. λp_{1}∈p_{2}.

\emptylambin : λ⟨⟩. λ⟨⟩. λ⟨⟩. λ⟨⟩. \multlambin0 : λ⟨⟩. \multlambin1{p_{1}}{p_{2}} : λ⟨ p_{1} ^{∈} p_{2} ⟩.

\multlambin2{p_{1}}{p_{2}}{p_{3}}{p_{4}} : λ⟨ p_{1} ^{∈} p_{2}, p_{3} ^{∈} p_{4} ⟩. \multlambin3{p_{1}}{p_{2}}{p_{3}}{p_{4}}{p_{5}}{p_{6}} : λ⟨ p_{1} ^{∈} p_{2}, p_{3} ^{∈} p_{4}, p_{5} ^{∈} p_{6} ⟩.

… etc.

\multlambindots{p_{1}}{p_{2}}{p_{3}}{p_{4}} : λ⟨ p_{1} ^{∈} p_{2}, …, p_{3} ^{∈} p_{4} ⟩.

\lambsub{p_{1}}{p_{2}} : λp_{1}_{p_{2}}. λp_{1}_{p_{2}}. λp_{1}_{p_{2}}. λp_{1}_{p_{2}} . \Lambop{p_{1}} : Λp_{1}. Λp_{1}. Λp_{1}. Λp_{1}.

\Deltop{p_{1}} : Δp_{1}. Δp_{1}. Δp_{1}. Δp_{1}.

8 Large Operators

Under the influence of \expandlargeops (the default): \Union : ⋃ ⋃ ∪ _{∪}

\Intersect : ⋂ ⋂ ∩ _{∩} \prod : ∏ ∏ Π Π \sum : ∑ ∑ Σ Σ \Lm : Lm Lm Lm Lm \Col : Col Col Col Col \Lub : ⨆ ⨆ ⊔ _{⊔} \Glb : ⊓ _{⊓}

Under the influence of \compresslargeops: \Union : ⋃ ⋃ ∪ _{∪} \Intersect : ⋂ ⋂ ∩ _{∩} \prod : ∏ ∏ Π Π \sum : ∑ ∑ Σ Σ \Lm : Lm Lm Lm Lm \Col : Col Col Col Col \Lub : ⨆ ⨆ ⊔ _{⊔} \Glb : ⊓ _{⊓}

\multscript{\displaystyle O}{l_{1}}{l_{2}}{S_{1}}{S_{2}}

{0pt}{0pt}{\displaystyle}{\scriptstyle} : O_{l_{1}}^{l_{2}}_{S_{1}}^{S_{2}} \multscript{\textstyle O}{l_{1}}{l_{2}}{S_{1}}{S_{2}}

{0pt}{0pt}{\textstyle}{\scriptstyle} : O_{l_{1}}^{l_{2}}_{S_{1}}^{S_{2}} \multscript{\scriptstyle O}{l_{1}}{l_{2}}{S_{1}}{S_{2}}

{0pt}{0pt}{\scriptstyle}{\scriptscriptstyle} : O_{l_{1}}^{l_{2}}_{S_{1}}^{S_{2}} \multscript{\scriptscriptstyle O}{l_{1}}{l_{2}}{S_{1}}{S_{2}}

\{0pt\}\{0pt\}\{\scriptscriptstyle\}\{\scriptscriptstyle\} : \begin{matrix}l_{2} \\ O & {S_{2} \atop S_{1}} \\ l_{1} \end{matrix}

\multscript{\displaystyle O}{long_{1}}{long_{2}}{S_{1}}{S_{2}}

{0pt}{0pt}{\displaystyle}{\scriptstyle} : O_{S_{1}}^{S_{2}}_{long_{1}}^{long_{2}}

\multscript{\textstyle O}{long_{1}}{long_{2}}{S_{1}}{S_{2}}

{0pt}{0pt}{\textstyle}{\scriptstyle} : O_{S_{1}}^{S_{2}}_{long_{1}}^{long_{2}}

\multscript{\scriptstyle O}{long_{1}}{long_{2}}{S_{1}}{S_{2}}

{0pt}{0pt}{\scriptstyle}{\scriptscriptstyle} : O_{S_{1}}^{S_{2}}_{long_{1}}^{long_{2}}

\multscript{\scriptscriptstyle O}{long_{1}}{long_{2}}{S_{1}}{S_{2}}

\{0pt\}\{0pt\}\{\scriptscriptstyle\}\{\scriptscriptstyle\} : \begin{matrix}long_{2} \\ O & {S_{2} \atop S_{1}} \\ long_{1} \end{matrix}

\compscript{\displaystyle O}{l_{1}}{l_{2}}{S_{1}}{S_{2}}

{0pt}{0pt}{\displaystyle}{\scriptstyle} : O_{S_{1}}^{S_{2}} _{l_{1}}^{l_{2}}

\compscript{\textstyle O}{l_{1}}{l_{2}}{S_{1}}{S_{2}}

{0pt}{0pt}{\textstyle}{\scriptstyle} : O_{S_{1}}^{S_{2}} _{l_{1}}^{l_{2}}

\compscript{\scriptstyle O}{l_{1}}{l_{2}}{S_{1}}{S_{2}}

{0pt}{0pt}{\scriptstyle}{\scriptscriptstyle} : O_{S_{1}}^{S_{2}} _{l_{1}}^{l_{2}}

\compscript{\scriptscriptstyle O}{l_{1}}{l_{2}}{S_{1}}{S_{2}}

{0pt}{0pt}{\scriptscriptstyle}{\scriptscriptstyle} : O_{S_{1}}^{S_{2}} _{l_{1}}^{l_{2}}

\compscript{\displaystyle O}{l_{1}}{}{}{S_{2}}

{0pt}{0pt}{\displaystyle}{\scriptstyle} : O^{S_{2}}_{l_{1}}

\compscript{\textstyle O}{l_{1}}{}{}{S_{2}}

{0pt}{0pt}{\textstyle}{\scriptstyle} : O^{S_{2}}_{l_{1}}

\compscript{\scriptstyle O}{l_{1}}{}{}{S_{2}}

{0pt}{0pt}{\scriptstyle}{\scriptscriptstyle} : O^{S_{2}}_{l_{1}}

\compscript{\scriptscriptstyle O}{l_{1}}{}{}{S_{2}}

\{0pt\}\{0pt\}\{\scriptscriptstyle\}\{\scriptscriptstyle\} : \begin{aligned}O & ^{S_{2}} \\ & l_{1} \end{aligned}

Under the influence of \expandlargeops:

\prodms{p_{1}}{p_{2}}{p_{3}}{p_{4}} : ∏_{p_{1}}^{p_{2}}_{p_{3}}^{p_{4}} ∏_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}} Π_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}} Π_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}

\summs{p_{1}}{p_{2}}{p_{3}}{p_{4}} : ∑_{p_{1}}^{p_{2}}_{p_{3}}^{p_{4}} ∑_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}} Σ_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}} Σ_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}

\Lmms{p_{1}}{p_{2}}{p_{3}}{p_{4}} : Lm_{p_{1}}^{p_{2}}_{p_{3}}^{p_{4}} Lm_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}} Lm_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}} Lm_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}

\Colms{p_{1}}{p_{2}}{p_{3}}{p_{4}} : Col_{p_{1}}^{p_{2}}_{p_{3}}^{p_{4}} Col_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}} Col_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}} Col_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}

\Lubms{p_{1}}{p_{2}}{p_{3}}{p_{4}} : ⨆_{p_{1}}^{p_{2}}_{p_{3}}^{p_{4}} ⨆_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}} ⊔_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}} _{⊔}_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}

\Glbms\{p_{1}\}\{p_{2}\}\{p_{3}\}\{p_{4}\} : {p_{2} \atop p_{1}} _{p_{3}}^{p_{4}}  {p_{4} \atop p_{3}} _{p_{1}}^{p_{2}} ⊓_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{⊓}_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}

Under the influence of \compresslargeops:

\prodms{p_{1}}{p_{2}}{p_{3}}{p_{4}} : ∏_{p_{1}}^{p_{2}}_{p_{3}}^{p_{4}} ∏_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}} Π_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}} Π_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}

\summs{p_{1}}{p_{2}}{p_{3}}{p_{4}} : ∑_{p_{1}}^{p_{2}}_{p_{3}}^{p_{4}} ∑_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}} Σ_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}} Σ_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}

\Lmms{p_{1}}{p_{2}}{p_{3}}{p_{4}} : Lm_{p_{1}}^{p_{2}}_{p_{3}}^{p_{4}} Lm_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}} Lm_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}} Lm_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}

\Colms{p_{1}}{p_{2}}{p_{3}}{p_{4}} : Col_{p_{1}}^{p_{2}}_{p_{3}}^{p_{4}} Col_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}} Col_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}} Col_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}

\Lubms\{p_{1}\}\{p_{2}\}\{p_{3}\}\{p_{4}\} : \begin{matrix}p_{2} \\ ⨆ & {p_{4} \atop p_{3}} \\ p_{1} \end{matrix} ⨆_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}} ⊔_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}} _{⊔}_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}

\Glbms\{p_{1}\}\{p_{2}\}\{p_{3}\}\{p_{4}\} : p_{2} ; {p_{4} \atop p_{3}} ; p_{1}  {p_{4} \atop p_{3}} _{p_{1}}^{p_{2}} ⊓_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{⊓}_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}

9 Circled Operators

Under the influence of \expandlargeops and\largecircleops (the defaults):

\cirprodms{p_{1}}{p_{2}}{p_{3}}{p_{4}} : [figure: ∏]_{p_{1}}^{p_{2}} _{p_{3}}^{p_{4}}  ^{∏} _{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Π}_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Π}_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}

\cirsumms{p_{1}}{p_{2}}{p_{3}}{p_{4}} : [figure: ∑]_{p_{1}}^{p_{2}} _{p_{3}}^{p_{4}}  ^{∑} _{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Σ}_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Σ}_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}

\cirLmms{p_{1}}{p_{2}}{p_{3}}{p_{4}} : [figure: Lm]_{p_{1}}^{p_{2}} _{p_{3}}^{p_{4}} [figure: Lm] _{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Lm} _{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Lm} _{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}

\cirColms{p_{1}}{p_{2}}{p_{3}}{p_{4}} : [figure: Col]_{p_{1}}^{p_{2}} _{p_{3}}^{p_{4}} [figure: Col] _{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Col} _{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Col} _{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}

Under the influence of \compresslargeops and\largecircleops:

\cirprodms{p_{1}}{p_{2}}{p_{3}}{p_{4}} : ∏_{p_{1}}^{p_{2}} _{p_{3}}^{p_{4}}  ^{∏} _{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Π}_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Π}_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}

\cirsumms{p_{1}}{p_{2}}{p_{3}}{p_{4}} : ∑_{p_{1}}^{p_{2}} _{p_{3}}^{p_{4}}  ^{∑} _{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Σ}_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Σ}_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}

\cirLmms{p_{1}}{p_{2}}{p_{3}}{p_{4}} : [figure: Lm]_{p_{1}}^{p_{2}} _{p_{3}}^{p_{4}} [figure: Lm] _{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Lm} _{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Lm} _{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}

\cirColms{p_{1}}{p_{2}}{p_{3}}{p_{4}} : [figure: Col]_{p_{1}}^{p_{2}} _{p_{3}}^{p_{4}} [figure: Col] _{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Col} _{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Col} _{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}

Under the influence of \expandlargeops and\smallcircleops:

\cirprodms{p_{1}}{p_{2}}{p_{3}}{p_{4}} : ∏_{p_{1}}^{p_{2}} _{p_{3}}^{p_{4}}  Π^{}_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Π}_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Π}_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}

\cirsumms{p_{1}}{p_{2}}{p_{3}}{p_{4}} : ∑_{p_{1}}^{p_{2}} _{p_{3}}^{p_{4}}  Σ^{}_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Σ}_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Σ}_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}

\cirLmms{p_{1}}{p_{2}}{p_{3}}{p_{4}} : _{Lm}_{p_{1}}^{p_{2}} _{p_{3}}^{p_{4}}  _{Lm} _{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Lm} _{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Lm} _{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}

\cirColms{p_{1}}{p_{2}}{p_{3}}{p_{4}} : _{Col}_{p_{1}}^{p_{2}} _{p_{3}}^{p_{4}}  _{Col} _{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Col} _{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Col} _{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}

Under the influence of \compresslargeops and\smallcircleops:

\cirprodms{p_{1}}{p_{2}}{p_{3}}{p_{4}} : Π^{}_{p_{1}}^{p_{2}} _{p_{3}}^{p_{4}}  Π^{}_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Π}_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Π}_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}

\cirsumms{p_{1}}{p_{2}}{p_{3}}{p_{4}} : Σ^{}_{p_{1}}^{p_{2}} _{p_{3}}^{p_{4}}  Σ^{}_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Σ}_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Σ}_{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}

\cirLmms{p_{1}}{p_{2}}{p_{3}}{p_{4}} : _{Lm}_{p_{1}}^{p_{2}} _{p_{3}}^{p_{4}}  _{Lm} _{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Lm} _{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Lm} _{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}

\cirColms{p_{1}}{p_{2}}{p_{3}}{p_{4}} : _{Col}_{p_{1}}^{p_{2}} _{p_{3}}^{p_{4}}  _{Col} _{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Col} _{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}  _{Col} _{p_{3}}^{p_{4}} _{p_{1}}^{p_{2}}