Elementary Symmetric Polynomials for the HP-41

Overview
 

 1°)  Program#1
 2°)  Program#2
 

-Given n real numbers  p₁ , ............... , p_n , these programs calculate the sums:

   s₁ = p₁ + .............. + p_n = SUM_1<=i<=n p_i
   s₂ = SUM_{1<=i1<i2 <=n} p_i1 p_i2
   s₃ = SUM_{1<=i1<i2<i3 <=n} p_i1 p_i2 p_i3
   .......................................................

   s_n = p₁ .............. p_n
 

1°)  Program#1
 
 

Data Registers:   R00 to R2n+8: temp
Flags: /
Subroutine:  "PRO"  product of 2 polynomials ( cf "Polynomials for the HP-41" ) & "LCO" ( cf "Short routines for the HP-41" )

-Line 13 is   append  ?
 
 

01  LBL "SYMP"  02  8.008  03  STO 04          04  1  05  STO 05  06  STO 06  07  STO 08  08  LBL 01

09  " P"  10  FIX 0  11  CF 29  12  ARCL 05       13  "~?"  14  FIX 4  15  SF 29  16  PROMPT

17  FC?C 22  18  GTO 00  19  STO 07          20  6.007  21  RCL 04  22  RCL 04  23  FRC  24   E3

25  *  26  1  27  +  28  XEQ "PRO"  29  8  30  XEQ "LCO"  31  STO 04          32  ISG 05

33  CLX  34  GTO 01  35  LBL 00  36  RCL 04  37  1  38  +  39  STO 04          40  END

 
   ( 79 bytes / SIZE 2n+9 )
 
 

STACK	INPUT	OUTPUT
X	/	bbb.eee

  where   bbb.eee  is the control number of the results  ( Rbb = s₁ , .............. , Ree = s_n )

Example:    We have 4 numbers p_i      3   5   7   12

    XEQ "SYMP"   >>>   " P1?"
               3            R/S    " P2?"
               5            R/S    " P3?"
               7            R/S    " P4?"
              12           R/S    " P5?"                           Press R/S without any digit entry when all the numbers are keyed in:
                             R/S     >>>>    9.012

-And we get:         R09 = s₁ = 27  ;   R10= s₂ = 251  ;   R11 = s₃ = 957  ;  R12 = s₄ = 1260
 

Notes:

-The delay between 2 successive PROMPTs increases with the number of data.
-If possible, replace  XEQ "LCO"  ( line 30 )  by the M-Code routine  LCO.
 

2°)  Program#2
 

-In this variant, you store n into R00 and p₁ into R01 , ............... , p_n into Rnn
-Moreover, the products of polynomials are performed directly,  without calling "PRO"
-Thus, the routine is both shorter and faster.
 

Data Registers:           •  R00 = n                 ( Registers R00 thru Rnn are to be initialized before executing "SYMP" )

                                      •  R01 = p₁     •  R02 = p₂   .......................   •  Rnn = p_n

              >>>>  When the program stops,   Rn+2 = s₁ ,  Rn+3 = s₂ , ................... , R2n+1 = s_n           ( and Rn+1 = 1 )

Flags: /
Subroutines: /

-Line 28 is a synthetic TEXT0
-It may be replaced by another NOP instruction like  STO X  ,   LBL 00  ...
 
 

01  LBL "SYMP"  02  RCL 00          03  STO M  04  1  05  ST+ Y  06  STO IND Y  07  CLX  08  .1  09  %

10  +  11  LBL 01  12  ENTER^  13  ENTER^  14  SIGN  15  +  16  STO N          17  RCL IND M  18  SIGN

19  CLX  20  STO IND Y  21  LBL 02          22  CLX  23  RCL IND Z  24  LASTX  25  *  26  ST+ IND Y  27  DSE Z

28  ""  29  DSE Y  30  GTO 02  31  X<> N  32  DSE M  33  GTO 01          34  INT  35   E3  36  /

37  2  38  +  39  RCL 00          40  +  41  CLA  42  END

 
     ( 67 bytes / SIZE 2n+2 )
 
 

STACK	INPUT	OUTPUT
X	/	bbb.eee

  where   bbb.eee  is the control number of the results  ( Rbb = s₁ , .............. , Ree = s_n )

Example:    With the same 4 numbers p_i =  3   5   7   12

    4  STO 00         3  STO 01   5  STO 02   7  STO 03   12  STO 04

    XEQ "SYMP"   >>>   6.009                     ---Execution time = 5s---

-And we get:

     R06 = s₁ = 27  ,   R07 = s₂ = 251  ,   R08 = s₃ = 957  ,  R09 = s₄ = 1260

Notes:

-With n = 10 ,  execution time =  21s
-With n = 50 ,  execution time = 7m41s