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**A Third Order Linear Equation Solver for the HP-35S**

*Posted by Palmer O. Hanson, Jr. on 20 May 2008, 11:24 p.m.*

Program Description

This program is similar to my "A Label Saving Simultaneous Equation Solution for the 33s" (Article No. 599) but with modifications for use with the HP-35S. It will solve with real or complex coefficients. I wanted to use the same definition of the linear system and input routine as in the "Solution of Simultaneous Equations" program in pages 15-12 through 15-20 of the *hp 33s user's guide.* I couldn't because the indirect addressing registers (I and J) for the HP 35S are in the middle of the alphabetic data registers (a bad feature of the 35S to my way of thinking). Thus, the linear system is defined as

Ax + Dy + Gz = K

Bx + Ey + Hz = L

Cx + Fy + Iz = M

Where the definition of the matrix is the same but the definition of the vector uses data registers K through M rather than J through L as in the hp 33s manual..

The solution is obtained using Cramer's rule. The determinant subroutine is a copy of the subroutine on pages 15-16 and 15-17 of the *hp 33s user's guide*. The subroutine call is made using direct addressing to avoid using additional labels. The input data is restored at the completion of the solution. If the determinant is zero the calculator will stop with the message DIVIDE BY 0 in the display.

User Instructions

1. Press XEQ A ENTER to start the program.

2. The display will stop with a prompt for the coefficient to be entered. Press R/S to accept the displayed data or enter a new coefficient and press R/S. For complex coefficients use the Re i Im format.

3. The display will stop with a prompt for the next coefficient to be entered. Note that the entry is column by column not row by row.

4. Continue to enter the remaining coefficients in response to the prompts.

5. When you press R/S after entering the M value of the vector the program will proceed with the solution. If the determinant of the input matrix is zero program execution will stop with the message DIVIDE BY 0 in the display.

6. If the determinant of the input matrix is not zero the program willl stop with value of X in the display. Press R/S to see the value of Y. Press R/S again to see the value of Z.

7. Press R/S to return to the start of the input routine.and see the first element of the input matrix.

8. The solution values can be recalled for further use from data registers X, Y and Z. The determinant can be recalled for further use from data register W.

Program Listing

A001 LBL A A002 -1.1 A003 STO J A004 INPUT (J) A005 1.1 A006 STO- J A007 -14.3 A008 RCL J A009 x ne y? x is not equal to y A010 GTO A004 A011 XEQ A070 A012 STO W A013 1/x A014 RCL K A015 x<> A A016 STO K A017 RCL L A018 x<> B A019 STO L A020 RCL M A021 x<> C A022 STO M A023 XEQ A070 A024 STO X A025 RCL K A026 x<> A A027 x<> D A028 STO K A029 RCL L A030 x<> B A031 x<> E A032 STO L A033 RCL M A034 x<> C A035 x<> F A036 STO M A037 XEQ A070 A038 STO Y A039 RCL K A040 x<> D A041 x<> G A042 STO K A043 RCL L A044 x<> E A045 x<> H A046 STO L A047 RCL M A048 x<> F A049 x<> I A050 STO M A051 XEQ A070 A052 STO Z A053 RCL K A054 x<> G A055 STO K A056 RCL L A057 x<> H A058 STO L A059 RCL M A060 x<> I A061 STO M A062 RCL W A063 STO/ X A064 STO/ Y A065 STO/ Z A066 VIEW X A067 VIEW Y A068 VIEW Z A069 GTO A001 A070 RCL A A071 RCLx E A072 RCLx I A073 RCL D A074 RCLx H A075 RCLx C A076 + A077 RCL G A078 RCLx F A079 RCLx B A080 + A081 RCL G A082 RCLx E A083 RCLx C A084 - A085 RCL A A086 RCLx F A087 RCLx H A088 - A089 RCL D A090 RCLx B A091 RCLx I A092 - A093 RTNLength = 291; Check Sum = 2C23

Test problem:

The first number in each coefficient is the real part. The second number in each part is the imaginary part..

+1,+3 -1,+2 +4, 0 +10,-8The determinant of the matrix which can be read from W is +155,-66 .-3,-2 -5,+1 +1,+1 +10,-4

+2, 0 0,+3 -3,+4 +25,+12

The solution vector is

+3,+1-2,-2

+1,-4