challenge HP50G RPL

[compsystems]

PROOT It is a very primitive command (HP48 series) only accepts real an complex coefficients, does not allow symbolic coefficients, the code « →V3 PROOT » fails with symbolic and complex coefficients

Code:

« →V3 PROOT » 'QUADRATIC1' STO

1. -3. 2. QUADRATIC1 returns [1, 2] // ok
1. 2. 3. QUADRATIC1 returns [(-1.,1.41421356238) (-1., -1.41421356238)] // ok
'A' 'B' 'C' QUADRATIC1 returns "→V3 ERROR Bad Argument Type" =(
(1,0) (-1,-1) (0,1) QUADRATIC1 returns "→V3 ERROR Bad Argument Type" =(

Now are 4 instructions or objects with PROOT

Code:


« 
   3 →LIST
   AXL PROOT
»
 'QUADRATIC4' STO

1. -3. 2. QUADRATIC4 returns [1, 2] // ok
1. 2. 3. QUADRATIC4 returns [(-1.,1.41421356238) (-1., -1.41421356238)] // ok
(1,0) (-1,-1) (0,1) QUADRATIC4 returns [(1, 0) (0, 1)] // OK

Using a more powerful predefined function SOLVE CAS, real/complex and/or symbolic entry

12 instructions or objects

Code:

«
  3 →LIST                     @ crea una lista de 3 elementos con los coeficientes ingresados
  'X^(N-1)' 'N' 3 1 -1 SEQ    @ crea una lista de monomios de un polinomio de grado 2 en X
  *                           @ multiplica paralelamente o elemento a elemento las dos listas anteriores 
  ∑LIST                       @ crea el polinomio, como la suma de monomios
  'X' SOLVE                   @ halla las raíces      
»
 'QUADRATIC5' STO

or

only 6 instructions or objects, perhaps the minimal instructions for full function (HP50) to get the roots of a quadratic equation, from the coefficients in stack

Code:

«
  3 →LIST { 'X^2' 'X' 1 } * ∑LIST SOLVEVX
»
'QUADRATIC6' STO

1. -3. 2. QUADRATIC6 returns { 'X=1' 'X=2' }// ok
1. 2. 3. QUADRATIC6 returns { 'X=(-1, -1.41421356237)' 'X=(-1, 1.41421356237)' } // ok
'A' 'B' 'C' QUADRATIC6 returns { 'X=-(b+√-(4*c*a-b^2.))/(2*a)' 'X=-(b-√-(4*c*a-b^2.))/(2*a)' } // ok
(1,0) (-1,-1) (0,1) QUADRATIC6 { 'X=(7.5E-15,1.)' 'X=(1.,-1.E-14)' } ~ 'X=(0,1)' 'X=(1,0)'

// ok