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*********************************************** *********** RSC 3.10 ************ **************** Resident Scientific Calculator **************** **************** **************** **************** Copyright 1990,1993 **************** **************** Sergey Shmakov & Igor Evsikov **************** **************** **************** *********** March 1993 ************ *********************************************** CONTENTS -------- 0. News 0.1 New possibility 0.2 Bug fix list 1. Introduction 2. RSC Features 3. Installation 4. Getting started RSC. Parameters (loading option) 5. Expressions 6. Mouse support 7. Numerical Bases and Notations 8. Arithmetic operations 9. Boolean operations 10.Functions 10.1 Trigonometric Functions 10.2 Exponential, Logarithmic and Square root Functions 10.3 Special functions 10.4 Hyperbolic and Inverse Hyperbolic Functions 10.5 Numerical Integration 10.6 Statistical functions 10.7 Solving Equations 10.8 Absolute extrema searching 11.Constants 12.Other keys 13.Edit keys 14.Error messages 15.Disclaimer 16.Registration 17.Acknowledgments 0. News ---- 0.1 New possibility --------------- Version 3.1 1) Mouse support has been added. 2) The unary minus sign is now treated correctly. 3) Functions' precision have been added to DOC. 4) Gaussian quadrature uses now weights and nodes with the accuracy of 25 decimal digits. 5) Precision of the Erf- and Gamma- functions has been improved. 6) Constants' precision has been raised. 7) Constants "pi" and "e" now displayed by their name. 8) The termination condition of solve() function has been improved. 9) Absolute extrema searching has added 10) Known bugs have been fixed. 0.2 Bug fix list ------------ .________________________________________________________________. |Expression |Version |Comment | |------------------------+---------------------+-----------------| |arctan(X) |3.00 |operated properly| | | |in radian mode | | | |only | |------------------------+---------------------+-----------------| |for J to K step m (?) |3.00 |did not operate | `----------------------------------------------------------------' 1. Introduction ------------ Resident Scientific Calculator (RSC) is intended for scientific calculations and can be used on any IBM-compatible PC equipped with EGA/VGA/CGA or Hercules card and hard disc, running under DOS 3.3+. The program uses about 160 Kb of disc space or EMS/XMS (if present) for swapping. The resident part of the program is about 6-7Kb. RSC can handle expressions up to 255 symbols in length.Expressions are written in a form similar to the customary mathematical one. Expressions such as the following can be computed: cos(Z)+(?+tg(ln(Y)))/exp(sin(pi/10))-integral(1+cos(X)) 2. RSC Features ------------ - Mouse support - Line editor with expressions recall (last 10 expression) - Hot key Function prompt - Debug: Error position fixed - Online help with F1 - Decimal, Hexadecimal and Binary bases - Fixed point, Scientific, Engineering and Sexagesimal *) - Radian and Degree modes for trigonometric functions - Precision: 7-12 significant digits. - Range: √(3.4E-4392 to 1.1E+4392) - Trigonometric functions - Hyperbolic functions - Numerical Integration - Solving of equations - Absolute extrema searching - Arithmetic operations - Logical operations - Special functions (Gamma, Bessels, Si, Ci, erf) - Statistic functions (Average, Standard deviation) - Common functions such as exp, ln, sqrt, etc. - FOR-NEXT-type loop - 10 user defined variables - 10 user defined constants - Hard Copy - Stack for expressions - Stack for results (last 100) - Variables, Expressions and Results map ------------------------------------- *) (i.e., result in the form hours:minutes:seconds or degrees:minutes:seconds) notations ------------------------------------- The basic control keys are shown on the RSC panel, its layout is presented below(Upper-ASCII characters are replaced by as similar as possible Low-ASCII ones for printing) .--------------------------- ver 3.10 -. |.- BASE -------notation------angmode-.| || Result Error messages || || <-------Expression region--------->|| |`-[■]-[■]-[■]------------------------'| | help-(F1) map-(F2) clr-(F3) clm-(F4) | |----- function --- mode --- Display --| | sn-S as-^S Sf- $|dec?F5|not-F10 ()lr | | cn-O ac-^O Γ - !|hex?F6|*/^+-&|\%.?.:| | tg-T at-^T sq- Q|bin?F7|0123456789=b | | lg-G 10-^G 1/-^X|rad?F8|ESC, Unload | | ln-L ex-^L cn-^C|deg?F9|paste(R)esult| |----- move ---------------------------| |<ctrl->,<>,v,^ TAB-lastr, pusH/Pop str| `--------------------------------------' Hold down the <Shift> key to see a second screen of information .--------------------------- ver 3.10 -. |.- BASE -------notation------angmode-.| || Result Error messages || || <-------Expression region--------->|| |`-[■]-[■]-[■]------------------------'| | help-(F1) map-(F2) clr-(F3) clm-(F4) | |----- function --- mode --- Display --| | sh-S hs-^S ef- $|dec F5|not-F10 ()lr | | ch-O hc-^O Si- !|hex F6|*/^+-&|\%.?.:| | th-T ht-^T Ci- Q|bin F7|XYZVWKIJKLM=d| | Jn-G Yn-^G n!-^X|rad F8|ESC, Unload | | In-L Kn-^L cl-^C|deg F9|paste(R)esult| |----- move ---------------------------| |<ctrl->,<>,v,^ TAB-lastr, pusH/Pop str| `--------------------------------------' Hold down the <Alt> key to see a third screen of information .--------------------------- ver 3.10 -. |.- BASE -------notation------angmode-.| || Result Error messages || || <-------Expression region--------->|| |`-[■]-[■]-[■]------------------------'| | help-(F1) map-(F2) clr-(F3) clm-(F4) | |----------- misc Function ------------| | Average -(Alt-A) For cycle-(ALt-F) | | St.Dev. -(Alt-D) sEtup -(Alt-E) | | + digit -(Alt-+) Popresult-(Alt-P) | | - digit -(Alt--) savesTack-(Alt-T) | | History -(Alt-H) viewstaCk-(Alt-C) | | set var -(Alt- X,Y,Z,V,W,I,J,K,M,N) | | (c) CopyRight by I.Evsikov&S.Shmakov | `--------------------------------------' The position of the calculator display can be adjusted by the <up> and <down> arrow keys or by the <Ctrl><left> and<Ctrl><right> chords. Screen modes 132x25, 132x43, 80x43(50) (as, for example, with Ultravision installed) are also supported. 3. Installation ------------ The archive RSC310.ZIP contains: RSC.EXE - Version of the calculator RSC.DOC - This file. RSC.CFG - default config file (autocreate) RSC.REG - Registration File. Copy the files RSC.EXE to a directory defined in the PATH statement of your AUTOEXEC.BAT file (like your DOS or TOOLS directory). For changing colors and/or hot-key of the RSC use <Alt><E> keys. 4. Getting started RSC ------------------- To begin RSC, type the following command at the MS-DOS command prompt: >RSC You will see a label: ┌──────────────────────────────┐ │Resident Scientific Calculator│ │ by S.Shmakov & I.Evsikov. │ │ UNREGISTERED COPY │ │To PopUp press < Ctrl-Alt-C >.│ └──────────────────────────────┘ To recall RSC in any programs, editors etc. press the keys <Ctrl>, <Alt> and <C> simultaneously. The full syntax of command line to load RSC is: >RSC [/Spath] [/Fpath] [/Efile] [/Cfile] [/Dfile] [/W] [/N] [-X] [-E] /Spath ... the swap-file directory. By default, expanded (EMS) or extended (XMS) memory, or RAM disk are used (if presented). Otherwise, current directory is used. /Fpath ... path to RSC.CFG, if the configuration file is not in the same directory in which the executable file is situated. /Efile ... filename containing expressions with which to initialize the RSC stack. /Cfile ... filename of a user defined constant file. This file can contain up to 10 of constants, of the form: <constant_name>=<value>. For example: Pi=3.1415926535919 e=2.7182811828459 /Dfile ... the full path and file name of the HARDCOPY file. To print the output rather than store it to a file, use PRN or LPT1. /W ... DOS window application under WINDOWS 3.1 /N ... not resident version -M ... do not use mouse, even if it present -X ... prevents the use extended memory for swapping, even if extended memory is available. -E ... prevents the use expanded memory for swapping, even if expanded memory is available /? ... mini-help. 5. Expressions ----------- Expressions appear on the bottom line of the RSC display and can be edited/corrected during calculation. You can insert the result of the previous calculation in the current expression (using "?" key), as well as the values of up to 10 user defined constants. Result occurs in the top line of the RSC display. Expressions can make use of the symbols I,J,K; M,N; V,W,X,Y,Z. (must be upper case) as variables. To assign a value to a variable, use key chord <Alt>-<key> where "<key>" is one of the 10 valid symbols for variables. If you used an undefined variable in an expression, you will be prompted during calculation of the expression to define the variable. The variable, in their turn, can be defined by another expression. The last 10 typed expression can be reused by pressing the key chord <Alt>-<H> (or <Alt>-<F8>) keys. This brings up a menu of (up to) the last 10 expressions used (simple arithmetic expressions are not saved); move the light bar to the desired expression and press <Enter>; the expression will be copied to the expression line of the RSC display. Besides, up to 10 expressions can be saved/restored to/from the cyclic expression stack. When RSC is first loaded, the expression stack can be initialized from the external file. As well, the stack can be whenever saved to a file. A session can be HARDCOPied (see below option /D in command line) to printer or an external file. After some editing, these files can be used as input for another session. Examples: 3-5+4.61 (5-arcsin(0.4561))^2.1+sqrt(lg(25))+sin(Y/7) Ln(2)-solve(3*x^2+2*x-32) (?+tg(ln(Y)))/exp(sin(1.5/10))-integral(1+cos(X)) 6. Mouse support. -------------- RSC supports Microsoft-compatible mouses. In the case of another drivers usage cursor position can be set improperly. Use option -M to ignore mouse even if it is present. To switch RSC panels with the aid of the mouse click on -[■]- buttons. Mind the mouse switch of the RSC panels simulates pressing Shift/Alt keys. Be careful when using the mouse and keyboard simultaneously. 7. Numerical Bases and Notations ----------------------------- The range of numbers is approximately 3.4E-4932 to 1.1E+4932 with 19-20 significant digits. For changing of the base, angular measure and notation use follow hot keys: Key Switches F5 ... switch to decimal format F6 ... switch to hexadecimal format F7 ... switch to binary format F8 ... switch to radians F9 ... switch to degrees F10 ... switch notation (fixed point, scientific, engineering, sexagesimal) In the binary and hexadecimal format only integer part of the numbers is displayed. Calculator supports four notations: fixed point - fix, scientific - sci, engineering - eng and sexagesimal - sxg (i.e., result in the form hours:minutes:seconds or degrees: minutes:seconds). The current notation mode is displayed in the center of the RSC display. Any notation can be used for input independently of the current result mode. If the input and result notation differ one from another the conversion to the current result notation will be made. For example: .- dec ---------- fix --------- rad -. | 0.66666666667 | | 2/3 | `------------------------------------' Keystrokes: <2></><3><Enter> .- dec ---------- sci --------- rad -. | 6.6666666667E-01 | | 2/3 | `------------------------------------' Keystrokes: <F10> .- dec ---------- eng --------- rad -. | 666.66666667E-03 | | 2/3 | `------------------------------------' Keystrokes: <F10> .- dec ---------- sxg --------- rad -. | 0:40:0 | | 2/3 | `------------------------------------' Keystrokes: <F10> The number of displayed digits is controlled by <Alt><->, <Alt><+> keys. PS : The maxvalue in sxg notation 2^19. Binary numbers larger than 2^15-1 not correctly pasted because of the 15 positions pasted result. 8. Arithmetic operations --------------------- Key Description + ... Addition or unary plus - ... Subtraction or unary minus * ... Multiplication / ... Division ^ ... Power % ... Percentage () .. Prioritize an expression Example: (16+20*4)%6.5 .- dec ---------- fix --------- rad -. | 6.24 | | (16+20*4)%6.5 | `------------------------------------' Keystrokes: (16+20*4)%6.5<Enter> 9. Boolean operations ------------------ For Boolean operations, the fractional part of the numbers is ignored. Key Description & ... and | ... or \ ... xor Example: 3+(10 and 7) .- dec ---------- fix --------- rad -. | 5.0 | | 3+10&7 | `------------------------------------' Keystrokes: 3+10&7<Enter> 10. Functions --------- Expressions can contain trig functions, 10^X, exp, A^X, gamma, integral, statistic functions, hyperbolic functions, integral, Bessel functions and FOR-NEXT-type loop. To save typing, they are entered by the corresponding shortcut keys. Trigonometric functions can accept arguments expressed in radians and degrees; the angular mode is set by function keys F8 and F9. The current angular mode is displayed in the right corner of the RSC display. 10.1 Trigonometric Functions ----------------------- Keys Prompt Function Name S ... sin() ..... Sine of expression (..) O ... cos() ..... Cosine of (..) T ... tn() ...... Tangent of (..) Ctrl-S ... arcsin() .. Arc sine of (..) Ctrl-O ... arccos() .. Arc cosine of (..) Ctrl-T ... arctn() ... Arc tangent of (..) The trigonometric functions sin, cos ... have precision 12 digits. Example: sin(pi/2) in Radians .- dec ---------- sci --------- rad -. | 1.0E+0 | | sin(pi/2) | `------------------------------------' Keystrokes: <S><Ctrl-P>/2<Ehter> o Example: sin(45 30'15") in Degrees .- dec ---------- sci --------- deg--. | 7.1330141882E-1 | | sin(45:30:15) | `------------------------------------' Keystrokes: <F9><S><Ctrl-P>/2<Ehter> 10.2 Exponential, Logarithmic and Square root Functions -------------------------------------------------- Keys Prompt Function Name Q ... sqrt() .... Positive square root of (..) G ... lg() ...... Natural (base e) logarithm (..) L ... ln() ...... Common (base 10) logarithm (..) Ctrl-G ... 10^() ..... Number 10 raised to the (..)th power Ctrl-L ... exp() ..... Number e raised to the (..)th power The functions sqrt, lg ... have precision 12 digits. Example: exp(1.4)+ln(2) .- dec ---------- eng --------- rad -. | 4.748347147E+00 | | exp(1.4)+ln(2) | `------------------------------------' Keystrokes: <Ctrl-L>1.4<Right>+<L>2<Ehter> 10.3 Special functions ----------------- Keys Prompt Function Name ! ... Γ() ....... Gamma function of (..) Shift-G ... Jn(,) ..... Bessel function J (..th, ..) Shift-L ... In(,) ..... Bessel function I (..th, ..) Shift-Ctrl-G ... Yn(,) ..... Modify Bessel function Y (..th, of ..) Shift-Ctrl-L ... Kn(,) ..... Modify Bessel function K (..th, of ..) Shift-F ... erf() ..... Error func associated w/normal distribution Shift-D ... Si() ...... Integral Sine of (..) Shift-Q ... Ci() ...... Integral Cosine of (..) The function Γ has precision 15 digits (│delta│<1.0E-16). The functions Bessel have precision 7 digits (│delta│<3.0E-7). The function erf has absolute error value (│epsilon│<1.0E-9). The functions Si,Ci have absolute error value (│epsilon│<3.0E-7). Example: 1+J (5.4) 4 .- dec ---------- sci --------- rad -. | 1.3990575914E+0 | | 1+Jn(4,5.5) | `------------------------------------' Keystrokes: 1+<Shift-G>4<Right>5.4<Ehter> For calculating The Bessel's function integral representations were used. The calculation algorithms were tested for all available Bessel functions in the region 0 <= nu <= 100, 0 <= z <= 100 using "Handbook of mathematical functions with formulas, graphs and mathematical tables" Edited by Milton Abramowitz and Irene A. Stegun, National bureau of standards applied mathematics series 55, Issued June 1964. The testing results are shown in the diagram below. ▒ - stands for correct (within 7 significant digits) result, x - no data, - - calculation failed. J (z) Y (z) I (z) K (z) nu nu nu nu nu nu nu nu 100x▒▒xx▒xxxx▒▒- 100x▒▒xx▒xxxx▒▒▒ 100x▒▒xx▒xxxx▒▒▒ 100x--xx-xxxx--- 50x▒▒xx▒xxxx▒▒- 50x▒▒xx▒xxxx▒▒▒ 50x▒▒xx▒xxxx▒▒▒ 50x--xx-xxxx--- 40x▒▒xx▒xxxx▒▒- 40x▒▒xx▒xxxx▒▒▒ 40x▒▒xx▒xxxx▒▒▒ 40x--xx-xxxx▒-- 30x▒▒xx▒xxxx▒▒- 30x▒▒xx▒xxxx▒▒▒ 30x▒▒xx▒xxxx▒▒▒ 30x-▒xx▒xxxx▒-- 20x▒▒xx▒xxxx▒▒- 20x▒▒xx▒xxxx▒▒▒ 20x▒▒xx▒xxxx▒▒▒ 20x▒▒xx▒xxxx▒▒- 15▒▒▒▒▒▒▒▒▒▒▒▒- 15▒▒▒▒▒▒▒▒▒▒▒▒▒ 15▒▒▒▒▒▒▒▒▒▒▒▒▒ 15▒▒▒▒▒▒▒▒▒▒▒▒- 10▒▒▒▒▒▒▒▒▒▒▒▒▒ 10▒▒▒▒▒▒▒▒▒▒▒▒▒ 10▒▒▒▒▒▒▒▒▒▒▒▒▒ 10▒▒▒▒▒▒▒▒▒▒▒▒- 8▒▒▒▒▒▒▒▒▒▒▒▒▒ 8▒▒▒▒▒▒▒▒▒▒▒▒▒ 8▒▒▒▒▒▒▒▒▒▒▒▒▒ 8▒▒▒▒▒▒▒▒▒▒▒▒- 6▒▒▒▒▒▒▒▒▒▒▒▒▒ 6▒▒▒▒▒▒▒▒▒▒▒▒▒ 6▒▒▒▒▒▒▒▒▒▒▒▒▒ 6▒▒▒▒▒▒▒▒▒▒▒▒- 4▒▒▒▒▒▒▒▒▒▒▒▒▒ 4▒▒▒▒▒▒▒▒▒▒▒▒▒ 4▒▒▒▒▒▒▒▒▒▒▒▒▒ 4▒▒▒▒▒▒▒▒▒▒▒▒- 2▒▒▒▒▒▒▒▒▒▒▒▒▒ 2▒▒▒▒▒▒▒▒▒▒▒▒▒ 2▒▒▒▒▒▒▒▒▒▒▒▒▒ 2▒▒▒▒▒▒▒▒▒▒▒▒- 1▒▒▒▒▒▒▒▒▒▒▒▒▒ 1▒▒▒▒▒▒▒▒▒▒▒▒▒ 1▒▒▒▒▒▒▒▒▒▒▒▒▒ 1▒▒▒▒▒▒▒▒▒▒▒▒- 0▒▒▒▒▒▒▒▒▒▒▒▒▒ 0-▒▒▒▒▒▒▒▒▒▒▒▒ 0▒▒▒▒▒▒▒▒▒▒▒▒▒ 0-▒▒▒▒▒▒▒▒▒▒▒- 1 1 1 1 150 150 150 150 Z 0123456789000 Z 0123456789000 Z 0123456789000 Z 0123456789000 10.4 Hyperbolic and Inverse Hyperbolic Functions ------------------------------------------- Keys Prompt Function Name Shift-S ... sinh() ..... Hyperbolic sine of (..) Shift-O ... cosh() ..... Hyperbolic cosine of (..) Shift-T ... tanh() ..... Hyperbolic tangent of (..) Shift-Ctrl-S ... asinh() .... Hyperbolic arc sine of (..) Shift-Ctrl-O ... acosh() .... Hyperbolic arc cosine of (..) Shift-Ctrl-T ... atanh() .... Hyperbolic arc tangent of (..) The functions sinh, cosh ... have precision 12 digits. Example: sinh(4.6+X) where X=5 .- dec ---------- sci --------- rad -. | 7.3823907489E+3 | | sinh(4.6+X) | `------------------------------------' Keystrokes: <Shift-S>4.6+x<Alt-X>5<Ehter> Example: sinh(4.6+X) where X=3 .- dec ---------- sci --------- rad -. | 9.9909769732E+2 | | sinh(4.6+X) | `------------------------------------' Keystrokes: <Alt-X>3<Ehter> 10.5 Numerical Integration --------------------- Keys Prompt Function Name $ ... integral() . Numerical Integration of f(X) This approximates the value for the definite integral of f(X), using 10-point Gaussian formula: 10 integral = sum(W * f(X )) i=1 i i where W and X are the weights and nodes of the Gauss formula. i i This procedure gives accurate results for the polynomial functions up to the 19-th order. Upper and lower limits of the integral are defined throw the <Alt><U> and <Alt><L> keys, respectively. If the limits are not defined you will be prompted to define them. The variable X is used as integration variable but its value in previous expression is retained. To improve the accuracy of the integral, press <Enter> again without changing the integrand and limits. This will halve the integration interval and apply of the algorithm to each interval; the result is calculated by summation over all subintervals. Each time your press <Enter> the number of the subintervals is doubled. Changing of the integrand or/and limits of integration will restore the evaluation interval to one. For example, to integrate sin(x)^2 in the limits (0,10): .- dec ---------- sci --------- rad -. | Previous result | | integral(sin(X)^2) | `------------------------------------' Keystrokes: $sx<Right>^2 After pressing <Enter> you will be prompted to enter low integral limit: .- dec ---------- sci --------- rad -. | Previous result | | low=0 | `------------------------------------' Keystrokes: 0 After input <Enter> you will be prompted to enter up integral limit: .- dec ---------- sci --------- rad -. | Previous result | | up=10 | `------------------------------------' Keystrokes: 10<Enter> .- dec ---------- sci --------- rad -. | 4.771684898E+0 | | integral(sin(X)^2) | `------------------------------------' To improve result simply press <Enter>: .- dec ---------- sci --------- rad -. | 4.771763687E+0 | | integral(sin(X)^2) | `------------------------------------' 10.6 Statistical functions --------------------- Keys Prompt Function Name Alt-A ... x .......... Mean value Alt-D ... d .......... Standard deviation Ctrl-X ... random() ... Random number in [0..N] Random returns r/65536*n, where r is uniform random number in the interval 0..65535 Example: calculation of the mean value and standard deviation of 1.11, 2.22, 3.33, 4.44: .- dec ---------- sci --------- rad -. | Previous result | | x | `------------------------------------' Keystrokes: <Alt><A> .- dec ---------- sci --------- rad -. | Previous result | | x= | `------------------------------------' Keystrokes: <Enter> .- dec ---------- sci --------- rad -. | 1.11 | | x= | `------------------------------------' Keystrokes: 1.11<Enter> .- dec ---------- sci --------- rad -. | 1.665 | | x= | `------------------------------------' Keystrokes: 2.22<Enter> .- dec ---------- sci --------- rad -. | 2.22 | | x= | `------------------------------------' Keystrokes: 3.33<Enter> .- dec ---------- sci --------- rad -. | 2.775 | | x= | `------------------------------------' Keystrokes: 4.44<Enter><Esc> <Esc> - end of input data .- dec ---------- sci --------- rad -. | 1.433003838E+0 | | s | `------------------------------------' Keystrokes: <Alt><D><Enter> _ Both x and s can be used in a similar way as variables. x _ It should be noted, however, using of x in an expression forces new procedure of the average value calculation, while <Alt><D> simply inserts the corresponding standard deviation in the expression. 10.7 Solving Equations ----------------- Keys Prompt Function Name Shift-Ctrl-C ... solve() .... solves an equation of f(X) = 0 This returns a solution of the equation. The algorithm used in this program for solving equations is the bisection method. A solution can be found for continuous functions in the range low <= x <= up, only if f(low) <= 0 <= f(up). If the equation happens to have several solutions the method give only one of them. You can get the rest ones by step-by-step narrowing of the search interval. The solving process is terminated when abs(f(X)/(f(up)-f(low)) will be less then 1.E-11. If necessary, one can improve the result by narrowing of the search interval. Examples: Keystrokes: 1-<Shift-Ctrl-C><S>x<Right>-0.5 .- dec ---------- sci --------- rad -. | Previous result | | 1-solve(sin(X)-0.5) | `------------------------------------' Keystrokes: <Enter>0 .- dec ---------- sci --------- rad -. | Previous result | | low=0 | `------------------------------------' Keystrokes: <Enter><Ctrl-P>/2 .- dec ---------- sci --------- rad -. | Previous result | | up=pi/2 | `------------------------------------' Keystrokes: <Enter> .- dec ---------- sci --------- rad -. | 4.7640122342E-1 | | 1-solve(sin(X)-0.5) | `------------------------------------' As it is implemented one gets frequently the message "Interval Error". This is because of the fact, that requirements are not met. The user has to make some effort to meet these requirements. The adjusting of the interval is a problem, that can be circumvented. Also the restriction that f(low)*f(up) < 0. Solving x^x-27=0 is easier done by entering 100 as a wild guess and then several times .5*(?+27^(1/?)) or this with Alt-F. Ad hoc, but ? works nice for such simple iterative schemes. One gets easily the correct solution 3 exactly. Disregarding for a moment the stopping criterium, the method or accuracy, paying only attention to the definition. One could define uniquely the solution of f(x) = 0, where x in (a,b) to be the smallest x in (a,b), such that f(x) = 0. If there isn't any then we have an "Interval Error". Then it is much easier to obtain all solutions of f(x)=0 in some interval. Also easier to work with, because one needs not to have an up and low, that has the property f(low)*f(up) < 0. To do this requires some extra programming. The additional effort to do it, is something, that is implicit in my proposal below about max(). 10.8 Absolute extrema searching. -------------------------- Keys Prompt Function Name Shift-Ctrl-X ... ???() ...... Absolute extremum searching of (..) ??? is "min" or "max" depending on chosen extremum type. To switch between "min" or "max" searching press <Alt-1> or <Alt-2>. An algorithm by F. Gremmen (University of Nijmegen, Netherlands) is used. A global extremum can be found for continuous functions in the range low <= x <= up. If function has too many (approximately >40) extrema in the interval, the risk of overlooking an extremum is present. In this case you may press <Enter> again without changing the function and limits. This will halve the interval and apply of the algorithm to each interval; the result is selected between absolute extrema of all subintervals. Each time your press <Enter> the number of the subintervals is doubled. Changing of the expression or/and interval boundaries will restore the search interval to one. For example max(-X^2+2*X+3) will return 4 if low = 0 and up = 2 and X will be set to 1. It should return 0 if low = 3 and up = 4 and X should be set to 3. 11. Constants --------- Key Description Ctrl-C ... activate constant menu Ctrl-P ... constant "pi" Ctrl-E ... constant "e" By default You can use 10 constant from constant menu. Constant is inserted in expression at cursor position. ┌─────── Constants ──────┐ │ 0 me ....... 9.109558E-28 │ - electron mass [g] │ 1 mp ....... 1.672614E-24 │ - proton mass [g] │ 2 Euler .... 5.7721566E-01 │ - Euler const │ 3 GeV*Fm ... 5.0676531698 │ - │ 4 h/2pi .... 1.0545919E-27 │ │ 5 Compton e. 3.861592E-11 │ │ 6 Compton p. 1.3214409E-13 │ │ 7 Ridberg .. 1.0973731E+05 │ │ 8 Bohr R ... 5.2917715E-09 │ │ 9 Electron R 2.817939E-13 │ │ Your choice :_ │ └─ Exit-Esc ───── CGS ───────┘ To redefine constants You must create a file containing up to 10 of constant's definitions in the form : <constant_name>=<value> For example: Pi=3.14159265359... e=2.718281182845... - load RSC with next param: >RSC /CFileName - where FileName is Name of File defined constants. 12. Other keys ---------- Key Description F1 ... summary Help F2 ... show the variable definitions and result stack (the last 100 results are kept on the stack and can be pasted to the calculator window) F3 ... clear the RSC display F4 ... clear the RSC variables ESC ... hide RSC (i.e. return to DOS, Editor, Viewer, ...) U ... Unload RSC (No other resident programs must have been installed AFTER RSC) R ... paste result to cursor position (15 digits max) TAB ... restore the last expression H ... pusH expression to the RSC expression stack P ... Pop expression from the RSC expression stack <Alt><H> or <Alt><F8> ... activate the history menu <Alt><C> or <Alt><F7> ... activate the stack menu <Alt><T> ... save stack of expressions 13. Edit keys --------- All expression editions my be executed with next hot-keys: Key Description <left> ... move cursor one symbol left <right> ... move cursor one symbol right <Del> ... delete symbol under the cursor <Ins> ... insert/override mode <Bksp> ... delete symbol before cursor <Ctrl-F> ... move cursor one word right <Ctrl-D> ... move cursor one word left <Shift-Del> ... delete the word after cursor 14. Error Messages -------------- The error messages appear in the right side of top screen line. The cursor positions to the causing error symbol(s), which are blinking. Press any key to remove error message. Syntax error ............ Invalid function name or an operation sign omitted Overflow ................ Calculation result > 1.1E+4392 Stack overflow .......... Too many nested functions Scale Overflow .......... Expression length is more then 255 chars No possibility .......... No possibility to unload calculator due to another (TSR) program loaded after RSC Argument Error .......... Function is not defined for this argument value Argument Negative ....... Function is not defined for the negative argument value Average undefined ....... Attempt to use the standard deviation without the mean value calculation Division by zero ........ Division by zero Empty ................... Expression stack is empty Too many ")" ............ Too many closing parenthesis Missing "(" ............. Too many opening parenthesis Missing ")" ............. Missing closing parenthesis String stack saved ...... Informative message: expression stack is written to file "," expected ............ Function requires 2 arguments Interval Error .......... sign( f(Low_boundary)) = sign( f(Up_boundary)) User break .............. User break during calculations The error and warning messages appear to start RSC: File <FileName> not found ... Warning! Start. File <ConfigFileName> not correct ... Warning! Start. Unable to install RSC! ... Break. RSC is already loaded! ... Break. 15. Disclaimer. ----------- The Resident Scientific Calculator (RSC) is provided on an "as is" basis without warranty of any kind, expressed or implied. The person using the software bears all risk as to the quality and performance of the software. The author will not be held liable for any special, incidental, consequential, direct or indirect damages due to incorrect calculations or other malfunctions. 16. Registration. ------------- If you like this program and continue to use is, a registration fee is US$10 for noncommercial use. When registered, you will receive via e-mail conversion code to remove "UNREGISTERED COPY" message, full support and are entitled to a free upgrade. Registered users will get 1 free upgrade. Please mail Your registration form (see RSC.REG) and enclose CASH (I am not sure that I would be able to release check or money order in Russia) to: Igor Evsikov LCTA, JINR, (Dubna) PO Box 79, Head Post Office Moscow 101000 Russia Please send E-mail message when you mail your registration form !! We will try to extend support to unregistered users during their evaluation period. However, we reserve the right to limit support for unregistered users if their requests become taxing. ********************* Technical Support ************************* **** Questions and comments can be sent to us via e-mail **** **** evsikov@lcta5.jinr.dubna.su **** ***************************************************************** 17. Acknowledgments. ---------------- We would like to thank the following people: Prof. Stephen Smith University of Waterloo (Canada) Frans Gremmen University of Nijmegen (Netherlands) Dr. Eugen Cherepanov Join Institute of Nuclear Research (Russia) Prof. D. W. O. Heddle University of London (UK) Peter J. McKinney (USA) for valuable notes on previous RSC versions.