HP50g simplifing a root
10-04-2020, 06:05 PM (This post was last modified: 10-04-2020 06:06 PM by peacecalc.)
Post: #9
 peacecalc Member Posts: 205 Joined: Dec 2013
RE: HP50g simplifing a root
Hello Albert,

I tried two way, the first was to probe every small a from 1 until third root of A. From your example a has to tested from 1 to 670, what a luck, that a = 99. My second approach is to calculate every divisor of A (with DIVI) as a possible candidate for small a. Then I'm calculate the difference A - third power of a. Negative results can be sorted out. The rest is divided by 3*k*a and be square rooted. If the result is a integer and not a algebraic expression would be a solution for smal b. and we get:

$\left( A\pm B\cdot\sqrt{k} \right)^{1/3} = a \pm b\cdot\sqrt{k}$.

For me the second approach makes mor sense, because the numbers of possibilities can be reduce very fast.

Code:
 « \-> E   « E 3 ^ DUP 'E' STO OBJ-> ->STR     IF "+" ==     THEN 1     ELSE -1     END SWAP DROP SWAP OBJ-> DROP2 DUP 2 ^ EVAL \-> A SG B RT K     « A DIVIS SORT \-> L       « A L 3 ^ -         «  \-> B           «             IF B 0 >             THEN B             END           »         » DOLIST          \-> L3         « L 1.0000 L3 SIZE SUB 'L' STO L3 L / 3 K * / \SQRT 'L3' STO            L3           «  \-> B             « B TYPE               IF 28.0000 ==               THEN B               ELSE 0               END             »           » DOLIST            'L3' STO { }                       1.0000 L3 SIZE           FOR I L3 I GET DUP             IF 0 ‹             THEN + I +             ELSE DROP             END           NEXT 'L3' STO                      IF L3 { } <>           THEN              1.0000 L3 SIZE             FOR I L3 I GET SG * L L3 I 1.0000 + GET GET SWAP RT * +             EVAL              2.0000 STEP           ELSE A B SG RT * * + 3 INV ^ EVAL           END         »       »     »   » »
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 Messages In This Thread HP50g simplifing a root - peacecalc - 09-29-2020, 09:22 PM RE: HP50g simplifing a root - Albert Chan - 09-29-2020, 11:47 PM RE: HP50g simplifing a root - Albert Chan - 09-30-2020, 02:22 AM RE: HP50g simplifing a root - Albert Chan - 09-30-2020, 10:50 PM RE: HP50g simplifing a root - Albert Chan - 10-01-2020, 07:31 AM RE: HP50g simplifing a root - peacecalc - 09-30-2020, 05:33 AM RE: HP50g simplifing a root - peacecalc - 10-01-2020, 02:20 PM RE: HP50g simplifing a root - Albert Chan - 10-01-2020, 05:22 PM RE: HP50g simplifing a root - peacecalc - 10-04-2020 06:05 PM RE: HP50g simplifing a root - Albert Chan - 10-04-2020, 11:48 PM RE: HP50g simplifing a root - peacecalc - 10-04-2020, 07:36 PM RE: HP50g simplifing a root - peacecalc - 10-05-2020, 11:36 AM RE: HP50g simplifing a root - Albert Chan - 10-05-2020, 05:01 PM RE: HP50g simplifing a root - peacecalc - 10-06-2020, 05:25 AM RE: HP50g simplifing a root - Albert Chan - 10-06-2020, 09:40 AM RE: HP50g simplifing a root - Albert Chan - 10-06-2020, 12:06 PM RE: HP50g simplifing a root - Albert Chan - 10-06-2020, 04:13 PM RE: HP50g simplifing a root - Albert Chan - 10-07-2020, 06:12 PM RE: HP50g simplifing a root - Albert Chan - 10-09-2020, 12:20 AM RE: HP50g simplifing a root - Albert Chan - 10-09-2020, 02:31 PM RE: HP50g simplifing a root - Albert Chan - 10-11-2020, 06:28 PM RE: HP50g simplifing a root - Albert Chan - 10-12-2020, 03:17 AM RE: HP50g simplifing a root - Albert Chan - 10-24-2020, 02:19 PM RE: HP50g simplifing a root - Albert Chan - 10-12-2020, 10:54 PM RE: HP50g simplifing a root - CMarangon - 10-12-2020, 11:45 PM RE: HP50g simplifing a root - grsbanks - 10-13-2020, 06:46 AM RE: HP50g simplifing a root - Albert Chan - 10-09-2020, 05:21 PM RE: HP50g simplifing a root - Albert Chan - 10-10-2020, 03:58 PM RE: HP50g simplifing a root - Albert Chan - 10-10-2020, 04:49 PM RE: HP50g simplifing a root - peacecalc - 10-12-2020, 08:49 PM RE: HP50g simplifing a root - peacecalc - 10-13-2020, 06:30 AM RE: HP50g simplifing a root - peacecalc - 10-13-2020, 06:36 AM

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