On Thu, 20 Feb 2020 16:27:27 -0800 William Michels <w...@caa.columbia.edu> wrote:
> On Thu, Feb 20, 2020 at 2:25 PM ToddAndMargo via perl6-users > <perl6-us...@perl.org> wrote: > > > > On 2020-02-19 23:21, Shlomi Fish wrote: > > > Hi Paul, > > > > > > > > Well, it is not unthinkable that a > > > https://en.wikipedia.org/wiki/Computer_algebra_system (CAS)-like system > > > will be able to tell that the abstract number sqrt(2) is irrational, as > > > well as some derivative numbers such as 3 + sqrt(2). E.g: > > > > Hi Shlomi, > > > > Those "academic exercises" where enterprising college > > students run pi out to a bazillion digits to see if they > > can find a repeating patterns came up with some > > way of handling an "unbounded" number. A "Real" (Cap R) > > perhaps? > > > > -T > > You can identify repeating patterns in decimal fractions using the > method "base-repeating": > > mbook:~ homedir$ perl6 -e 'say (1/7).base-repeating();' > (0. 142857) > mbook:~ homedir$ perl6 -e 'say (1/7).base-repeating(10);' > (0. 142857) > mbook:~ homedir$ perl6 -e 'say (1/7).base-repeating(10).perl;' > ("0.", "142857") > mbook:~ homedir$ perl6 -e 'say (5/2).base-repeating(10).perl;' > ("2.5", "") > mbook:~ homedir$ > > According to the Raku docs, "If no repetition occurs, the second > string is empty... ." > And the docs say: "The precision for determining the repeating group > is limited to 1000 characters, above that, the second string is ???." > https://docs.raku.org/type/Rational#method_base-repeating > > HTH, Bill. > > PS For those following along at home--unless it's been added since > Rakudo 2019.07--I don't see the "is_irrational()" function in the Raku > language referred to by Shlomi Fish. Or maybe I/we was/were to > understand that there isn't an "is_irrational()" function in the Raku > language as of yet. > Hi, just for the record - I was not talking about Raku, just about a hypothetical language with CAS-like capabilities (see https://en.wikipedia.org/wiki/Computer_algebra_system ) that would be able to do it. I was just using Raku-like syntax for familiarity. I am aware that the functionality is not built in in Raku. > https://stackoverflow.com/questions/42302488/identify-a-irrational-or-complex-number > https://mathoverflow.net/questions/91915/detecting-recognizing-irrational-number-by-computers > https://reference.wolfram.com/language/guide/ContinuedFractionsAndRationalApproximations.html > https://www.wolframalpha.com/examples/mathematics/numbers/irrational-numbers/ > https://www.wolframalpha.com/examples/mathematics/number-theory/continued-fractions/
