However: __ q: 403291461126567024928620025 2 3 11 439 405098581807 36 1 1 1 1 __ q: 403291461126567024928620025x |nonce error | __ q:403291461126567024928620025 <.@%: 403291461126567024928620025x 20082117944245
Sometimes it pays to take the brute force route. Thanks, -- Raul On Sun, May 17, 2020 at 10:00 PM 'Pascal Jasmin' via Programming <[email protected]> wrote: > > q: 729 > 3 3 3 3 3 3 > > > > __ q: 729 > > 3 > 6 > > a perfect square will have __&q: return even numbers for the 2nd row. > > > > On Sunday, May 17, 2020, 09:32:04 p.m. EDT, Hauke Rehr > <[email protected]> wrote: > > > > > > First, Skip already mentioned that. His posts are about J’s behaviour. > Second, your reasoning is flawed. > */ 3 ^ i.4 includes non-square factors and is a perfect square. > Think about prime numbers and their distribution, > and you’ll get a valid answer. > > Am 18.05.20 um 03:22 schrieb 'Pascal Jasmin' via Programming: > > Searching for perfect squares is best done by squaring the next integer. > > The first 1000 perfect squares are *: >: i.1000 No factorial number is a > > perfect square because it includes a non-square factors. > > > > > > > > > > > > > > On Sunday, May 17, 2020, 09:08:15 p.m. EDT, Skip Cave > > <[email protected]> wrote: > > > > > > > > > > > > Roger, > > > > I don't understand your last post. I'm trying to find a way to search for > > perfect squares. > > > > For smaller integers the plan is easy. > > 1. Generate a list of integers (eg. 1 to 30): > > ]n=.>:i.30 > > > > 2. Take the square root of each one (%:) > > %:n > > > > 1 1.4142 1.7321 2 2.2361 2.4495 2.6458 2.8284 3 3.1623 3.3166 3.4641 3.6056 > > 3.7417 3.873 4 4.1231 4.2426 4.3589 4.4721 4.5826 4.6904 4.7958 4.899 5 > > 5.099 5.1962 5.2915 5.3852 5.4772 > > > > > > 3. Find and mark the square roots of n that are integers (=>.) > > > > (=>.)%:n > > > > 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 > > > > > > 4. Use the marks to select the integers in n that are perfect squares (n#~): > > > > n#~(=>.)%:n > > > > 1 4 9 16 25 > > > > > > So we are able to find the perfect squares in the range 1 to 30. > > > > > > Now I want to find the perfect squares in the range of factorial 1 to 30: > > > > Actually I know that factorials of integers *can't* have square roots > > (except !1), but I want to check. See https://bit.ly/3fXevkr > > > > > > So we generate the factorials of the integers 1 to 30 and store them in n: > > > > ]n=.!>:i.30x > > > > 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 > > 87178291200 1307674368000 20922789888000 355687428096000 6402373705728000 > > 121645100408832000 2432902008176640000 51090942171709440000 > > 1124000727777607680000 25852016738884976640000 620448401733239439360000 > > 15511210043330985984000000 403291461126605635584000000 > > 10888869450418352160768000000 304888344611713860501504000000 > > 8841761993739701954543616000000 265252859812191058636308480000000 > > > > > > Now take the square roots of those 30 factorials, then find & mark any of > > the square roots that are integers. We know that only the first square root > > (%:!1) should be an integer, since 1 is a perfect square. all the square > > roots of the other factorials should not be integers, as they are not > > perfect squares. > > > > > > (=>.)%:n > > > > 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 > > > > Uh oh! J is telling me that factorials of the last 5 integers (n=.26 27 28 > > 29 30) are perfect squares! This is clearly not true. Roger showed this in > > his response to me, but he didn't propose a solution. > > > > > > How can I take the square root of large integers such as !26 27 28 29 30 in > > J, and get an accurate floating point or rational number? > > > > > > Skip Cave > > > > > > > > On Sun, May 17, 2020 at 4:18 PM Roger Hui <[email protected]> wrote: > > > >> Use <.@%: > >> > >> s=: <.@%: !26x > >> s > >> 20082117944245 > >> s*s > >> 403291461126567024928620025 > >> !26x > >> 403291461126605635584000000 > >> > >> > >> On Sun, May 17, 2020 at 2:00 PM Skip Cave <[email protected]> wrote: > >> > >>> We can find perfect squares in a list by taking the square root (%:) of a > >>> number, and checking to see if it is an integer: > >>> > >>> * n#~(=>.)%:n=.>:i.30* > >>> > >>> *1 4 9 16 25* > >>> > >>> > >>> Now we can try larger integers by taking the square root of the factorial > >>> of some small integers: > >>> > >>> * n#~(=>.)%:!n=.>:i.30* > >>> > >>> *1 26 27 28 29 30* > >>> > >>> > >>> Hmm. This says that !26 and up, are perfect squares. > >>> > >>> * !26x* > >>> > >>> *403291461126605635584000000* > >>> > >>> * %:!26x* > >>> > >>> *20082117944246* > >>> > >>> > >>> Well it looks like %:!26x is an integer, making !26x a perfect square. > >>> Let's check: > >>> > >>> * 20082117944246x^2* > >>> > >>> *403291461126607189164508516* > >>> > >>> * !26x* > >>> > >>> *403291461126605635584000000* > >>> > >>> > >>> * (!26x)-:20082117944246x^2 * > >>> *0* > >>> Clearly, !26x is not a perfect square. > >>> > >>> Looks like J has precision issues with the square root of large extended > >>> integers. How can I fix this, to find accurate square roots of large > >>> integers? > >>> > >>> Skip Cave > >>> ---------------------------------------------------------------------- > >>> For information about J forums see http://www.jsoftware.com/forums.htm > > > >>> > >> ---------------------------------------------------------------------- > >> For information about J forums see http://www.jsoftware.com/forums.htm > >> > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > > -- > ---------------------- > mail written using NEO > neo-layout.org > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
