The following is in the Hewlett Packard ASCII format used by hp link and other hp datainterchange programs. There are four issues that you should be aware of if you areattempting to type this program into your calculator 'by hand':
) is denoted by '\->', the 'store as a list' command, 
, is denoted by '\->LIST', and the double angle brackets that enclose a program are denoted by '\<<' and '\>>'. \GSLIST denotes the 'sum list term by term' function, 
, found in MTH/LIST. The 'to tag' function, 
, is denoted by \->TAG. Finally, the '|' (often found on the shifted '\' key on computer keyboards) is the 'evaluate at' function.THIS PROGRAM HAS NOT BEEN PLACED IN THE PUBLIC DOMAIN. IN UNALTERED FORM, IT CAN BE USED FOR ANY NON-COMMERCIAL EDUCATIONAL PURPOSE. THECODE GIVEN BELOW SHOULD NOT BE MODIFIED IN ANY WAY WITHOUT THEWRITTEN PERMISSION OF THE AUTHOR. IF YOU USE ANY PART OF THE CODE OR ANY OF THEIDEAS WORKED OUT WITHIN IT, THE COPYRIGHT NOTICE INCLUDED IN THIS PROGRAM MUSTBE DISPLAYED AT YOUR PROGRAM'S STARTUP.
%%HP: T(3)A(D)F(.);\<< CLLCD @ "HP 48G(X) RIEMANN SUMS" 2 DISP @ " Copyright (c) 1996" 4 DISP " by Jack Courtney" 5 DISP " All Rights Reserved" 6 DISP @ @ Calculate a Riemann sum for an arbitrary function, over an arbitrary real interval, @ by using an arbitrary number of subintervals. @ @ Varieties of sums available: left hand @ right hand @ trapezoidal 1 @ 1/0: plotting is on/off { "Left Hand" "Right Hand" "Trapezoidal" @ "Maximal" @ "Minimal" } \-> plot choices \<< 0 WHILE 0 == REPEAT 440 0.01 BEEP "CHOOSE SUM TYPE" choices 1 CHOOSE END choices OVER POS \-> choice \<< " Sum" + @ Push the INFORM title onto the stack VARS 'EQ' POS @ Push the list of INFORM rset values onto the stack IF 0 == THEN {NOVAL} ELSE RCEQ END VARS 'PPAR' POS IF 0 == THEN {NOVAL 10 NOVAL NOVAL} ELSE PPAR 3 GET 10 PPAR 1 GET RE PPAR 2 GET RE 4 \->LIST END + \-> title rset \<< 0 WHILE 0 == REPEAT title @ Title { { "EQ:" "ENTER INTEGRAND" 6 8 9 } { } @ Large entry field { "Indep:" "ENTER INTEGRATION VARIABLE NAME" 6 9 } @ Small entry field { "Subs:" "ENTER INTEG. VAR. SAMPLE COUNT" 0 } @ Small entry field { "H-Min:" "ENTER MIN. VALUE FOR INTEG. VAR." 0 } @ Small entry field { "H-Max:" "ENTER MAX. VALUE FOR INTEG. VAR." 0 } @ Small entry field } { 2 0 } @ {cols,tabs} rset @ rset values VARS 'RPAR' POS @ init values IF 0 == THEN rset ELSE RPAR END 440 0.01 BEEP IFERR INFORM THEN "Illegal values in EQ, PPAR or RPAR. Please purge these vars." MSGBOX 5 DROPN KILL END SWAP @ SAVE rc DUP 'RPAR' STO @ Output is RPAR LIST\-> DROP DUP2 @ Test Hmin and Hmax IF \>= THEN CLEAR 0 @ Change rc to 0 "ERROR: H-max >= H-min" MSGBOX ELSE DUP2 IF > THEN SWAP END XRNG @ Set XRNG in PPAR DROP INDEP @ Set Indep in PPAR 'EQ' STO @ Set EQ END END \>> IF plot THEN ERASE FUNCTION AUTO @ Make certain that the horizontal axis @ is within the viewing window. 'PPAR' 1 GETI IM 3 ROLLD GETI IM 3 ROLLD DROP2 \-> y0 y1 \<< y0 y1 * IF 0 > THEN IF y0 0 > THEN 0 y1 YRNG ELSE y0 0 YRNG END END \>> DRAX DRAW END RPAR TAIL LIST\-> DROP @ x n a b IF 'choice==2' THEN SWAP END @ (RH sum?) Work from right to left \-> x n a b \<< 1 n 1 - @ 1 n-1 b a - n / \->NUM @ 1 n-1 h 0 0 @ 1 n-1 h xL yL IFERR @ Flag illegal values a RCEQ x 3 PICK 2 \->LIST | \->NUM @ 1 n-1 h xL yL xR yR DUP TYPE IF 1 == THEN DOERR END @ A complex value is an error THEN 7 DROPN 7 FREEZE "Integrand is complex or undefined at " x \->STR + " = " + a \->STR + MSGBOX KILL END CASE @ Push the initial sum onto the stack 'choice==1 OR choice==2' THEN DUP END @ xR yR sum 'choice==3' THEN DUP IFERR RCEQ x b 2 \->LIST | \->NUM DUP TYPE IF 1 == THEN DOERR END THEN 8 DROPN 7 FREEZE "Integrand is complex or undefined at " x \->STR + " = " + b \->STR + MSGBOX KILL END + 2 / END @ 'choice==4' THEN END @ 'choice==5' THEN END "ERROR!: Unknown sum type!" MSGBOX 7 DROPN KILL @ Flag an illegal choice END \-> h xL yL xR yR sum \<< START IF plot THEN xR 'xL' STO yR 'yL' STO END h 'xR' STO+ @ Update xR IFERR RCEQ x xR 2 \->LIST | \->NUM DUP 'yR' STO @ Update yR DUP TYPE IF 1 == THEN DOERR END @ A complex value is an error THEN DROP 7 FREEZE "Integrand is complex or undefined at " x \->STR + " = " + xR \->STR + MSGBOX KILL END 'sum' STO+ @ Update sum IF plot THEN CASE '(choice==1) OR (choice==2)' THEN xL 0 R\->C xR yL R\->C BOX END 'choice==3' THEN xL yL R\->C xL 0 R\->C OVER LINE xR yR R\->C xR 0 R\->C OVER LINE LINE END @ 'choice==4' THEN END @ 'choice==5' THEN END @ Error trap is unnecessary here, since earlier trap is sufficient. END END NEXT sum h ABS * DUP choices choice GET " Sum" + \->TAG @ Push tagged result onto stack SWAP IF plot @ Draw the last strip THEN xR 'xL' STO yR 'yL' STO b 'xR' STO IFERR RCEQ x xR 2 \->LIST | \->NUM DUP TYPE IF 1 == THEN DOERR END THEN 3 DROPN 7 FREEZE "Integrand is complex or undefined at " x \->STR + " = " + xR \->STR + MSGBOX KILL END 'yR' STO CASE '(choice==1) OR (choice==2)' THEN xL 0 R\->C xR yL R\->C BOX END 'choice==3' THEN xL yL R\->C xL 0 R\->C OVER LINE xR yR R\->C xR 0 R\->C OVER LINE LINE END @ 'choice==4' THEN END @ 'choice==5' THEN END @ Error trap is unnecessary here, since earlier trap is sufficient. END 2 FIX LABEL STD 7 FREEZE 2 WAIT "sum" \->TAG \->STR MSGBOX ELSE DROP END \>> \>> \>> \>>\>>Click here to download an electronic copy. (To load this directly into your calculator, you will need hplink hardware and hplink or hpcomm software or an equivalent.)