############################################## # Gosper surdburgers: http://gosper.org/surdburger.pdf Digits := 99; evalf( (1 + 3^(2/3))^2 - ((1 + 3^(1/3))*(1 + 2*3^(1/3))) ); if (1 + 3^(2/3))^2 = ((1 + 3^(1/3))*(1 + 2*3^(1/3))) then true else false fi; Digits := 10; ############################################## Digits := 99 -0.1e-97 false Digits := 10 ############################################## I could understand Maple surrendering and returning a failure message --- indeed, it might be argued that the arguments of the (complex) roots are indeterminate --- however _immediately_ returning a wrong answer appears to qualify for a monumental raspberry. And while I'm having my customary Maple moan, why the devil must logical expressions be buried inside if-expressions to persuade the beast to evaluate them at all, correctly or otherwise? Which expressions incidentally may appear nowhere else but at top level, or as the result of a function --- oh why, why, why?! These things are sent to try us ... Amen. WFL On 2/1/19, Bill Gosper <billgosper@gmail.com> wrote:
OOPS, no! 3 () () () = () () () () () () is the product of ((2 - Power[3, (3)^-1]) (1 + Power[3, (3)^-1]))/((Power[3, (3)^-1] - 1) (1 + 3^(2/3))) == 1 and ((1+Power[2, (3)^-1])^3 (1+2^(2/3)) (Sqrt[3]-2^(2/3)) (Sqrt[3]+2^(2/3)))/(1+3 Power[2, (3)^-1])==3 . More: <http://gosper.org/surdburger.pdf> My objective is to use PSLQ to replace giant Chowla-Selberg surdbergs with smaller surdburgers in DedekindEta valuations. Besides, surdburgers are neat. —rwg
On Tue, Jan 29, 2019 at 3:51 PM Bill Gosper <billgosper@gmail.com> wrote:
Another tasty morsel: (1 + 3^(2/3))^2 == ((1 + 3^(1/3)) (1 + 2 3^(1/3))) (!)—rwg
On Sun, Jan 27, 2019 at 9:13 AM Bill Gosper <billgosper@gmail.com> wrote:
(Empirical)
Bogus
claim: This identity is "primitive" or "irreducible" in the sense that it
holds for no other rational exponents of the 3 and the binomials if any exponent is 0, unless they all are. —rwg
On Sat, Jan 26, 2019 at 7:54 AM Bill Gosper <billgosper@gmail.com> wrote:
3 (1 + 3 2^(1/3)) (2 - 3^(1/3)) (1 + 3^(1/3)) = = (1 + 2^(1/3))^3 (1 + 2^(2/3)) (-1 + 3^(1/3)) (-2^(2/3) + Sqrt[3]) (2^(2/3) + Sqrt[3]) (1 + 3^(2/3)) —rwg
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