Template:Expr

The following documentation is located at Template:Expr/doc. [<Edit> Template:Expr/doc]
[Purge Template:Expr]

The {{expr}} mathematical function template evaluates an expression yielding a numeric result (although an undefined or empty string parameter/subparameter evaluates as an empty string), otherwise an error message is returned. The expression may be an anonymous function (similar to, though not quite a lambda expression) using up to eight subparameters, all of which must be yielding real numeric values.

Usage

{{expr|expression}}

or

{{expr|anonymous function (using <<<1>>> up to <<<8>>> to refer to up to eight numeric values)|up to eight numeric values separated by semicolons}}

where in either expression or anonymous function we are allowed to use:

• either log or ln (whereas in {{#expr: ... }} one may only use ln for the natural logarithm);
• − or - (whereas in {{#expr: ... }} one may only use -, i.e. an hyphen, for the minus sign).

Examples

Examples with valid input

Note: an undefined or empty string parameter/subparameter evaluates as an empty string.

Code	Result
{{expr}}
{{expr|}}
{{expr|-1}}	−1
{{expr|{{op|-}}1}}	−1
{{expr|-0}}	−0
{{expr|-(5 - 5)}}	−0
{{expr|{{op|-}}(5 {{op|-}} 5)}}	−0
{{expr|123/100}}	1.23
{{expr|1 + 9}}	10
{{expr|not 10}}	0
{{expr|(7 <= 8) * 9}}	9
{{expr|2 + 3}}	5
{{expr|0^(-1)}}	INF
{{expr|-0^(-1)}}	−INF
{{expr|(-0)^(-1)}}	−INF
{{expr|-(0^(-1))}}	−INF
{{expr|0^0}}	1
{{expr|0^1}}	0
{{expr|5^2 * 7 * 13 * 17}}	38675
{{expr|cos(pi/3)}}	0.5
{{expr|ln (e^2)}}	2
{{expr|log (e^2)}}	2
{{expr|log log (e^(e^2))}}	2

Examples using the {{math}} template

The code

{{math| 0.5 {{-)|u&u}} 3 {{=}} 0.5{{^|0.5{{^|0.5}}}} {{=}} <!-- -->{{expr| 0.5^( 0.5^( 0.5 ) ) }}{{...|ldots}} |&&}}

yields the HTML+CSS formatted

0.5 ⇈ 3 = 0.5 0.5 0.5 = 0.61254732653607…

The code

{{math| 0.5 {{-)|u&u|tex}} 3 {{=}} 0.5{{^|0.5{{^|0.5|tex}}|tex}} {{=}} <!-- -->{{expr| 0.5^( 0.5^( 0.5 ) ) }}{{...|ldots|tex}} |$$}}

yields the LaTeX formatted

$\begin{array}{l}0.5\upuparrows 3=0.5^{0.5^{0.5}}=0.61254732653607\dots \end{array}$

Examples with invalid input

Code	Result
{{expr|1/0}}
{{expr|0/0}}
{{expr|6,500}}
{{expr|- one}}
{{expr|3 blobs}}
{{expr|INF}}
{{expr|NAN}}

Formatted numbers

This template requires unformatted numbers, it will not recognize formatted numbers, e.g. comma separated, which is by design since formatted numbers will break expression parsers. To remove the formatting from a number, you can wrap the number first in {{formatnum:number|R}}.

Code	Result
{{expr|1,000.50}}
{{expr|{{formatnum:1,000.50|R}}}}	1000.5
{{formatnum:{{expr|{{formatnum:1,000.50|R}}}}}}	1,000.5

Examples with anonymous functions

Code	Result
{{expr| <<<1>>>^2 | 3 + 4 }}	49
{{expr| <<<1>>> + <<<2>>> | 3; 4 }}	7
{{expr| <<<1>>>^<<<2>>> | 3; 4 }}	81
{{expr| <<<1>>>^<<<2>>> | 5 - 2; 2 + 2 }}	81
{{expr| <<<2>>>^<<<1>>> | 3; 4 }}	64
{{expr| <<<1>>>^2 + <<<2>>>^2 | 3; 4 }}	25
{{expr| 5 * <<<1>>> + <<<2>>> | 3; 4 }}	19
{{expr| {{phi}}^<<<1>>> | 2 }}	2.6180339887499
{{expr| <<<1>>>^<<<2>>> | {{phi}}; 2 }}	2.6180339887499
{{expr| cos <<<1>>> | pi/3 }}	0.5
{{expr| sin <<<1>>> + cos <<<2>>> | pi/6 ; pi/3 }}	1
{{expr| ln <<<1>>> | e^2 }}	2
{{expr| log <<<1>>> | e^2 }}	2
{{expr| log log <<<1>>> | e^(e^2) }}	2
{{expr| log <<<1>>> + log log <<<2>>> | e^2 ; e^(e^2) }}	4
{{expr| <<<1>>>^<<<3>>> + <<<2>>>^<<<3>>> | sin(pi/6); cos(pi/6); 2 }}	1
{{expr| (sin <<<1>>>)^<<<2>>> + (cos <<<1>>>)^<<<2>>> | pi/6; 2 }}	1
{{expr| <<<1>>>+<<<2>>>+<<<3>>>+<<<4>>>+<<<5>>>+<<<6>>>+<<<7>>>+<<<8>>> | 1; 20; 300; 4000; 50000; 600000; 7000000; 80000000 }}	87654321

Examples with anonymous functions and anonymous subfunctions

The code

: {{expr| <<<1>>>^2 + <<<2>>>^2 | 
  sin <<<3>>> ; 
  cos <<<3>>> ; 
  pi/3 
}}

yields

1

The code

: {{expr| <<<1>>> * <<<2>>> + <<<1>>> * <<<3>>> + <<<2>>> * <<<3>>> | 
  <<<4>>> + 1 ; 
  <<<4>>>^2 + 1 ; 
  <<<4>>>^3 + 1 ;
  5 - 2   
}}

yields (<<<1>>> is 4, <<<2>>> is 10, <<<3>>> is 28, so we get 4 * 10 + 4 * 28 + 10 * 28 = 432)

432

Anonymous functions that don't work

Code	Result	Comment
{{expr| <<<1>>>(<<<2>>>) | cos; pi/3 }}		Since each subparameter is parenthesized, we get (cos)(pi/3).
{{expr| {{cos|<<<1>>>}} | pi/3 }}		The {{cos}} template is called before <<<1>>> is replaced by pi/3.

Test

The code

{{expr| {{#replace: {{#replace: <<<1>>> |<< | {{((}} }} | >>| {{))}} }} | << Fibonacci {{!}} <<<2>>> >> ; 10 }} 

yields

Maximum and minimum numbers allowed

Testing for maximum and minimum numbers allowed with {{expr}}

Code	Result		Code	Result
{{expr|{{formatnum:99,999,999,999,999|R}}}}	99999999999999		{{expr|{{formatnum:-99,999,999,999,999|R}}}}	−99999999999999
{{expr|{{formatnum:999,999,999,999,999|R}}}}	1.0E+15		{{expr|{{formatnum:-999,999,999,999,999|R}}}}	−1.0E+15
{{expr|2^1023}}	8.9884656743116E+307		{{expr|2^(-1023)}}	1.1125369292536E−308
{{expr|(2*0.999999999999999)*(2^1023)}}	1.7976931348623E+308		{{expr|1 / ((2*0.999999999999999)*(2^1023))}}	5.562684646268E−309
{{expr|2^1024 - 1}}	INF		{{expr|1 / (2^1024 -1)}}	0
{{expr|2^1024}}	INF		{{expr|2^(-1024)}}	5.562684646268E−309
{{expr|2^(-1025)}}	2.781342323134E−309		{{expr|2^(-1026)}}	1.390671161567E−309
{{expr|2^(-1027)}}	6.953355807835E−310		{{expr|2^(-1028)}}	3.4766779039175E−310
{{expr|2^(-1029)}}	1.7383389519588E−310		{{expr|2^(-1074)}}	4.9406564584125E−324
{{expr|2^(-1075)}}	0		{{expr|2^(-2048)}}	0
{{expr|2^1024}}	INF		{{expr|-(2^(2^1024))}}	−INF
{{expr|2^1024 - 2^1024}}	NAN		{{expr|(2^1024 - 1) / (2^1024 - 1)}}	NAN
{{expr|(2^1024)^0}}	1		{{expr|(2^1024)^-(2^1024)}}	0
{{expr|(2^1024 - 1) + ((2^1024 - 1) / (2^1024 - 1))}}	NAN

Code

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

  Inside {{#expr: ... }} we must:

  * remove "operator space" annotations (which are for the {{math}} template): @opsp@
  * convert log to ln  
  * convert {{sym|-}}, i.e. &minus;, into a hyphus -, i.e. either a hyphen or minus (depending on context)    

--></noinclude><includeonly>{{#replace: {{#expr: 
{{#replace: 
  {{#replace: 
    {{#replace:
      {{#replace:
        {{#replace:
          {{#replace:
           {{#replace:
              {{#replace:
                {{#replace:
                  {{#replace: 
                    {{#replace: {{{1|}}} |@opsp@|}}
                  |<<<1>>>|({{#explode:{{{2|}}}|;|0}})
                  }}
                |<<<2>>>|({{#explode:{{{2|}}}|;|1}})
                }}
              |<<<3>>>|({{#explode:{{{2|}}}|;|2}})
              }}
            |<<<4>>>|({{#explode:{{{2|}}}|;|3}})
            }}
          |<<<5>>>|({{#explode:{{{2|}}}|;|4}})
          }}
        |<<<6>>>|({{#explode:{{{2|}}}|;|5}})
        }}
      |<<<7>>>|({{#explode:{{{2|}}}|;|6}})
      }}
    |<<<8>>>|({{#explode:{{{2|}}}|;|7}})
    }}
  | log | ln }}
| {{sym|-}} |-}}  
}} |-| {{sym|-}} }}</includeonly>

See also

• {{0expr}}
• {{lambda}}

External links

• Anonymous function—Wikipedia.org. (function literal, lambda abstraction)