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Template:Expr/doc

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This documentation subpage contains instructions, categories, or other information for Template:Expr. [<Edit> Template:Expr]

[⧼Purge⧽ Template:Expr/doc]

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);
  • &minus; 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

Examples with invalid input

Code Result
{{expr|1/0}} Division by zero.
{{expr|0/0}} Division by zero.
{{expr|6,500}} Expression error: Unrecognized punctuation character ",".
{{expr|- one}} Expression error: Unrecognized word "one".
{{expr|3 blobs}} Expression error: Unrecognized word "blobs".
{{expr|INF}} Expression error: Unrecognized word "inf".
{{expr|NAN}} Expression error: Unrecognized word "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}}.[1]

Code Result
{{expr|1,000.50}} Expression error: Unrecognized punctuation character ",".
{{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 }}      Expression error: Missing operand for cos.      Since each subparameter is parenthesized, we get (cos)(pi/3).
{{expr| {{cos|<<<1>>>}} | pi/3 }} Expression error: Unexpected < operator. The {{cos}} template is called before <<<1>>> is replaced by pi/3.

Test

The code

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

yields

Expression error: Unrecognized punctuation character "{".


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

Notes

External links