isInteger(…) false negatives

[xBZZZZ]

version: 92faec94811d5b2b1617bbbdac1ac6051fb6bfd8

> exact
> 0.1^log10(0.01)

  0.1^log10(0.01) = 100^(ln(10) / ln(10))

> 0.1^log10(0.01) = 100

  ((0.1^log10(0.01)) = 100) = true

> isInteger(100)

  isInteger(100) = 1

> isInteger(0.1^log10(0.01))

  isInteger(0.1^log10(0.01)) = 0

> x+1

  x + 1 = x + 1

> isInteger(x)

  isInteger(x) = 0

• isInteger(0.1^log10(0.01)) = 0 is wrong because 0.1^log10(0.01) = 100 and isInteger(100) = 1
• isInteger(x) = 0 is wrong because x is unknown

[hanna-kn]

isInteger() is an utility function primarily for use in other functions (e.g. in Fibonacci function: if(isInteger(\1),(golden^\1−(1−golden)^\1)/sqrt(5),(golden^\x-cos(\x*pi*rad)*golden^(-\x))/sqrt(5))) and tests if the argument is explicitly an integer (is of integer type). 0.1^log10(0.01) is approximated as an floating point interval and therefor returns false. isRational(), isReal(), and isNumber() exhibits the same behaviour.

This behaviour should either be properly documented or changed.

[xBZZZZ]

What is representsInteger (seems like isInteger with less false negatives)?

isInteger(100) = 1
representsInteger(100) = 1

isInteger(0.1^log10(0.01)) = 0
representsInteger(0.1^log10(0.01)) = 0

isInteger(x) = 0
representsInteger(x) = 0

isInteger(trunc(x)) = 0
representsInteger(trunc(x)) = 1

isInteger(floor(x)) = 0
representsInteger(floor(x)) = 1

isInteger(ceil(x)) = 0
representsInteger(ceil(x)) = 1

isInteger(round(x)) = 0
representsInteger(round(x)) = 0

[hanna-kn]

The behaviour can be summarized as: false negatives are allowed, false positives are not.

I've now added descriptions and examples to the functions, fixed some false negatives (representsInteger(round(x)), and implemented exact calculation of log10() for negative integer return values.