HP50g simplifing a root

[peacecalc]

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
        »
      »
    »
  »
»