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Template:MAX

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The {{MAX}} mathematical function template gives the maximum of one to eighty-one numbers or mathematical expressions. (For up to three arguments, please use {{max}} instead.)

Usage

{{MAX|expression}} (trivial case)

or

{{MAX|expression 1|...|expression 81}}

Valid arguments

One to eighty-one numbers or mathematical expressions as arguments.

Examples

Examples with valid arguments

Code Result
{{MAX|7|2|15}} 15
{{MAX|2|-7|-15}} 2
{{MAX|-7|2|-15}} 2
{{MAX|2|-15|-7}} 2
{{MAX|-7|-15|2}} 2
{{MAX|-15|2|-7}} 2
{{MAX|-15|-7|2}} 2
{{MAX|34|-3}} 34
{{MAX|-34|-3}} -3
{{MAX|-34}} -34
{{MAX|7|2|15|40}} 40


{{MAX|7|2|15|56|90|34|-65}} yields

90

{{MAX|7|2|15|56|90|34|-65|-8|78|878|-74|867|564|75|-67|77836|53565|-2|837|873|-84|2874|287|4289|93|9927|-2731}} yields

77836

{{MAX|7|2|15|56|90|34|-65|{{formatnum:2,000|R}}|78}} yields (remove format from formatted numbers)

2000
{{MAX
|   7|   2|   15|   56|  90|  34| -65|  -8|  78| 878| -74| 867| 564|  75| -67|77836|53565|   -2|  837|  873|  -84| 2874|  287| 4289|   93| 9927|-2731
|   3|   0|   35|   56|  90|  34| -65|  -8|  67| 878| -74| 367| 564|  75| -62| -789|53565|   -2|  837|  873|-2884| 2874|  287| 4289|   93| 9927|-7771
}}

yields

77836
{{MAX
|   7|   2|   15|   56|  90|  34| -65|  -8|  78| 878| -74| 867| 564|  75| -67|77836|53565|   -2|  837|  873|  -84| 2874|  287| 4289|   93| 9927|-2731
|   3|   0|   35|   56|  90|  34| -65|  -8|  67| 878| -74| 367| 564|  75| -62| -789|53565|   -2|  837|  873|-2884| 2874|  287| 4289|   93| 9927|-7771
|3645|   0| 2335| -756|-890|  34| -65|  -8|  67| 878|-653| 367| 564|  75| -62| -789|99565|   -2|  837|  873|-2884| 2874|  287| 4289|   93| 9927|-9995
}}

yields

77836
{{MAX
|   7|   2|   15|   56|  90|  34| -65|  -8|  78| 878| -74| 867| 564|  75| -67|77836|53565|   -2|  837|  873|  -84| 2874|  287| 4289|   93| 9927|-2731
|   3|   0|   35|   56|  90|  34| -65|  -8|  67| 878| -74| 367| 564|  75| -62| -789|53565|   -2|  837|  873|-2884| 2874|  287| 4289|   93| 9927|-7771
|3645|   0| 2335| -756|-890|  34| -65|  -8|  67| 878|-653| 367| 564|  75| -62| -789|99565|   -2|  837|  873|-2884| 2874|  287| 4289|   93| 9927|-7771
}}

yields

77836

Examples with invalid arguments

Code Result
{{MAX}} MAX error: One to eighty-one unformatted numbers required as arguments
{{MAX|one}} MAX error: One to eighty-one unformatted numbers required as arguments
{{MAX|34|-3 blobs}} Expression error: Unexpected < operator.
{{MAX|34|blobs}} Expression error: Unexpected < operator.
{{MAX|7|blob|15}} Expression error: Unexpected < operator.
{{MAX|7|15|blob}} Expression error: Unexpected < operator.
{{MAX|34|-3,000}} Expression error: Unexpected < operator. 


{{MAX
|   7|   2|   15|   56|  90|  34| -65|  -8|  78| 878| -74| 867| 564|  75| -67|77836|53565|   -2|  837|  873|  -84| 2874|  287| 4289|   93| 9927|-2731
|   3|   0|   35|   56|  90|  34| -65|  -8|  67| 878| -74| 367| 564|  75| -62| -789|53565|   -2|  837|  873|-2884| 2874|  287| 4289|   93| 9927|-7771
|3645|   0| 2335| -756|-890|  34| -65|  -8|  67| 878|-653| 367| 564|  75| -62| -789|-9565|   -2|  837|  873|-2884| 2874|  287| 4289|   93| 9927|-7771
|99995
}}

yields

MAX error: Too many arguments (one to eighty-one unformatted numbers required as arguments)

{{MAX|7|2|15|56|90|34|-65|-8|78|878|-74|867|564|75|-67|oops|837|873|-84|2874|287|4289|93|9927|-2731|63}} yields

Expression error: Unexpected < operator.

{{MAX|7|2|15|56|90|34|-65|-8|78|878|-74|867|564|75|-67|2,000|837|873|-84|2874|287|4289|93|9927|-2731|63}} yields

Expression error: Unexpected < operator. (formatted numbers are not allowed!)

Code


<noinclude>{{Documentation}}</noinclude><includeonly><!--

This function uses the core functions 

* {{tlxb|~Max3}}, {{tlxb|~Max9}}, {{tlxb|~Max27}}, {{tlxb|~Max81}}

-->{{#if: {{{82|}}}
| {{error| MAX error: Too many arguments (one to eighty-one [[unformatted numbers]] required as arguments) }}
| {{ifnum| {{{1}}}
  | {{#if: {{{4|}}}
    | {{#if: {{{10|}}}
      | {{#if: {{{28|}}}
        | {{~Max81 
          |  {{{1|}}} |  {{{2|}}} |  {{{3|}}} |  {{{4|}}} |  {{{5|}}} |  {{{6|}}} |  {{{7|}}} |  {{{8|}}} |  {{{9|}}}
          | {{{10|}}} | {{{11|}}} | {{{12|}}} | {{{13|}}} | {{{14|}}} | {{{15|}}} | {{{16|}}} | {{{17|}}} | {{{18|}}}
          | {{{19|}}} | {{{20|}}} | {{{21|}}} | {{{22|}}} | {{{23|}}} | {{{24|}}} | {{{25|}}} | {{{26|}}} | {{{27|}}}
          | {{{28|}}} | {{{29|}}} | {{{30|}}} | {{{31|}}} | {{{32|}}} | {{{33|}}} | {{{34|}}} | {{{35|}}} | {{{36|}}}
          | {{{37|}}} | {{{38|}}} | {{{39|}}} | {{{40|}}} | {{{41|}}} | {{{42|}}} | {{{43|}}} | {{{44|}}} | {{{45|}}}
          | {{{46|}}} | {{{47|}}} | {{{48|}}} | {{{49|}}} | {{{50|}}} | {{{51|}}} | {{{52|}}} | {{{53|}}} | {{{54|}}}
          | {{{55|}}} | {{{56|}}} | {{{57|}}} | {{{58|}}} | {{{59|}}} | {{{60|}}} | {{{61|}}} | {{{62|}}} | {{{63|}}}
          | {{{64|}}} | {{{65|}}} | {{{66|}}} | {{{67|}}} | {{{68|}}} | {{{69|}}} | {{{70|}}} | {{{71|}}} | {{{72|}}}
          | {{{73|}}} | {{{74|}}} | {{{75|}}} | {{{76|}}} | {{{77|}}} | {{{78|}}} | {{{79|}}} | {{{80|}}} | {{{81|}}}
          }}
        | {{~Max27
          |  {{{1|}}} |  {{{2|}}} |  {{{3|}}} |  {{{4|}}} |  {{{5|}}} |  {{{6|}}} |  {{{7|}}} |  {{{8|}}} |  {{{9|}}}
          | {{{10|}}} | {{{11|}}} | {{{12|}}} | {{{13|}}} | {{{14|}}} | {{{15|}}} | {{{16|}}} | {{{17|}}} | {{{18|}}}
          | {{{19|}}} | {{{20|}}} | {{{21|}}} | {{{22|}}} | {{{23|}}} | {{{24|}}} | {{{25|}}} | {{{26|}}} | {{{27|}}}
          }}
        }}
      | {{~Max9
        |  {{{1|}}} |  {{{2|}}} |  {{{3|}}} |  {{{4|}}} |  {{{5|}}} |  {{{6|}}} |  {{{7|}}} |  {{{8|}}} |  {{{9|}}}
        }}
      }}
    | {{~Max3
      | {{{1|}}} | {{{2|}}} | {{{3|}}}
      }}  
    }} 
  | {{error| MAX error: One to eighty-one [[unformatted numbers]] required as arguments }}
  }}
}}</includeonly>

Alternate code using the arithmetic form of De Morgan's laws

The following code sample uses the arithmetic form of De Morgan's laws

 
MAX(a, b, c, ...) = ~ MIN(~a, ~b, ~c, ...)
 
MIN(a, b, c, ...) = ~ MAX(~a, ~b, ~c, ...)

Unfortunately, it doesn't work when we negate arguments which are empty string or white space only, unless we wrap each parameter {{{nn|}}} thusly

{{#if: {{{nn|}}} | -({{{nn|}}}) }}

which uses one more [parser function and/or template] nesting level (MediaWiki imposes a low limit for those), on top of another nesting level used by {{#expr: -( ) }} which is done before returning the result. 


<noinclude>{{Documentation}}</noinclude><includeonly><!--

The MAX function uses the core functions 

* {{tlxb|~Min3}}, {{tlxb|~Min9}}, {{tlxb|~Min27}}, {{tlxb|~Min81}}

-->{{#if: {{{82|}}}
| {{error| MAX error: Too many arguments (one to eighty-one [[unformatted numbers]] required as arguments) }}
| {{ifnum| {{{1}}} 
  | {{#expr: -( {{#if: {{{4|}}}
    | {{#if: {{{10|}}}
      | {{#if: {{{28|}}}
        | {{~Min81 
          | -( {{{1|}}}) | -( {{{2|}}}) | -( {{{3|}}}) | -( {{{4|}}}) | -( {{{5|}}}) | -( {{{6|}}}) | -( {{{7|}}}) | -( {{{8|}}}) | -( {{{9|}}})
          | -({{{10|}}}) | -({{{11|}}}) | -({{{12|}}}) | -({{{13|}}}) | -({{{14|}}}) | -({{{15|}}}) | -({{{16|}}}) | -({{{17|}}}) | -({{{18|}}})
          | -({{{19|}}}) | -({{{20|}}}) | -({{{21|}}}) | -({{{22|}}}) | -({{{23|}}}) | -({{{24|}}}) | -({{{25|}}}) | -({{{26|}}}) | -({{{27|}}})
          | -({{{28|}}}) | -({{{29|}}}) | -({{{30|}}}) | -({{{31|}}}) | -({{{32|}}}) | -({{{33|}}}) | -({{{34|}}}) | -({{{35|}}}) | -({{{36|}}})
          | -({{{37|}}}) | -({{{38|}}}) | -({{{39|}}}) | -({{{40|}}}) | -({{{41|}}}) | -({{{42|}}}) | -({{{43|}}}) | -({{{44|}}}) | -({{{45|}}})
          | -({{{46|}}}) | -({{{47|}}}) | -({{{48|}}}) | -({{{49|}}}) | -({{{50|}}}) | -({{{51|}}}) | -({{{52|}}}) | -({{{53|}}}) | -({{{54|}}})
          | -({{{55|}}}) | -({{{56|}}}) | -({{{57|}}}) | -({{{58|}}}) | -({{{59|}}}) | -({{{60|}}}) | -({{{61|}}}) | -({{{62|}}}) | -({{{63|}}})
          | -({{{64|}}}) | -({{{65|}}}) | -({{{66|}}}) | -({{{67|}}}) | -({{{68|}}}) | -({{{69|}}}) | -({{{70|}}}) | -({{{71|}}}) | -({{{72|}}})
          | -({{{73|}}}) | -({{{74|}}}) | -({{{75|}}}) | -({{{76|}}}) | -({{{77|}}}) | -({{{78|}}}) | -({{{79|}}}) | -({{{80|}}}) | -({{{81|}}})
          }}
        | {{~Min27
          | -( {{{1|}}}) | -( {{{2|}}}) | -( {{{3|}}}) | -( {{{4|}}}) | -( {{{5|}}}) | -( {{{6|}}}) | -( {{{7|}}}) | -( {{{8|}}}) | -( {{{9|}}})
          | -({{{10|}}}) | -({{{11|}}}) | -({{{12|}}}) | -({{{13|}}}) | -({{{14|}}}) | -({{{15|}}}) | -({{{16|}}}) | -({{{17|}}}) | -({{{18|}}})
          | -({{{19|}}}) | -({{{20|}}}) | -({{{21|}}}) | -({{{22|}}}) | -({{{23|}}}) | -({{{24|}}}) | -({{{25|}}}) | -({{{26|}}}) | -({{{27|}}})
          }}
        }}
      | {{~Min9
        | -({{{1|}}}) | -({{{2|}}}) | -({{{3|}}}) | -({{{4|}}}) | -({{{5|}}}) | -({{{6|}}}) | -({{{7|}}}) | -({{{8|}}}) | -({{{9|}}})
        }}
      }}
    | {{~Min3
      | -({{{1|}}}) | -({{{2|}}}) | -({{{3|}}})
      }}  
    }} ) }} 
  | {{error| MAX error: One to eighty-one [[unformatted numbers]] required as arguments }}
  }}
}}</includeonly>

See also

  • {{min}} minimum of one to three expressions yielding numbers
  • {{max}} maximum of one to three expressions yielding numbers


  • {{MIN}} minimum of one to eighty-one expressions yielding numbers
  • {{MAX}} maximum of one to eighty-one expressions yielding numbers


  • Core function templates (used ONLY by {{MIN}}; do NOT use directly!)
    • {{~Min3}} (should be used for up to three numbers or mathematical expressions)
    • {{~Min9}} (should be used for four to nine numbers or mathematical expressions)
    • {{~Min27}} (should be used for ten to twenty-seven numbers or mathematical expressions)
    • {{~Min81}} (should be used for twenty-eight to eighty-one numbers or mathematical expressions)


  • Core function templates (used ONLY by {{MAX}}; do NOT use directly!)
    • {{~Max3}} (should be used for up to three numbers or mathematical expressions)
    • {{~Max9}} (should be used for four to nine numbers or mathematical expressions)
    • {{~Max27}} (should be used for ten to twenty-seven numbers or mathematical expressions)
    • {{~Max81}} (should be used for twenty-eight to eighty-one numbers or mathematical expressions)
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