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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
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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