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Text File | 1987-06-16 | 97KB | 4,591 lines

!!? 8+Y #LG !#S "N# "N# 002 #LG .Y6 000 001 #O1 002 Help Index !"L Top Level Commands !%+ 001 #[E 001 Help on Help !!S 001 0HZ 004 Help on Help !!S Configuration !$\ Load File "16 Top Level Commands !%+ 001 16N 000 001 0\W 000 001 1S- 003 Function Keys !&= Slash Commands ""= Navigation Commands !'% 001 1Y- 001 Top Level Commands !%+ 001 2%E 001 Top Level Commands !%+ 001 24< 001 Model Structure !(2 001 $(; 001 Problem Solving with TK !'M 001 $R8 002 Expression !+) Logical Expression !.# 001 $XV 001 Name Syntax !*9 001 $^) 000 001 &IJ 001 Name Syntax !*9 001 &PA 005 Arithmetic Expression !02 Relational Expression !/7 Logical Expression !.# Symbolic Expression !-C Indeterminate Expressions "E9 001 &V7 001 Expression !+) 001 &ZI 003 Relational Expression !/7 Boolean Functions !8+ Expression !+) 001 &^6 002 Expression !+) Arithmetic Operators !1- 001 '%= 002 Expression !+) Arithmetic Operators !1- 001 5F. 002 Arithmetic Expression !02 Relational Expression !/7 012 %,+ %2+ %4@ %<7 %<@ %?Y %B= %GD %QQ %YB &&F &2] 000 001 %2+ 001 Built-in Functions !24 001 %4@ 001 Built-in Functions !24 001 %<@ 001 Built-in Functions !24 001 %?Y 001 Built-in Functions !24 001 %B= 001 Built-in Functions !24 001 %GD 001 Built-in Functions !24 001 %QQ 002 Built-in Functions !24 Complex Arithmetic !:< 001 %YB 002 Logical Expression !.# Built-in Functions !24 001 &&F 001 Built-in Functions !24 001 &2] 001 Built-in Functions !24 001 '*T 001 Complex Functions !7* 001 *U- 000 001 *\3 002 Expression !+) Rule Syntax !(_ 001 +!# 002 Expression !+) Rule Syntax !(_ 001 +)" 001 Expression !+) 001 +,Y 001 Built-in Functions !24 001 +3D 001 Name Syntax !*9 001 +6H 001 Built-in Functions !24 001 +;2 001 Built-in Functions !24 001 +?R 001 Values !*H 001 +D$ 001 Built-in Functions !24 001 +I' 001 Expression !+) 001 +OB 001 Complex Arithmetic !:< 001 +S= 001 Expression !+) 001 +W* 002 Rule Syntax !(_ Complex Arithmetic !:< 001 +]I 001 Expression !+) 001 ,"+ 001 Values !*H 001 ,%M 000 001 ,)S 001 Editing Commands "$H 001 ,.* 001 Blank Command "&$ 001 ,1F 001 Editing Commands "$H 001 ,9@ 001 Save Command "4- 001 ,F( 001 Load Command "16 001 ,R[ 001 Disk Index "0A 001 ,]G 001 Load Command "16 001 -## 000 001 -(\ 000 001 -,@ 000 001 -1> 001 Blank Command "&$ 001 -:$ 000 001 ->) 001 Expression !+) 001 -BG 001 Disk Index "0A 001 -H# 001 Disk Index "0A 001 -L; 000 001 -P2 001 Status Field "7' 001 -V+ 000 001 -Z6 001 Configuration !$\ 001 -]Q 001 Disk Index "0A 001 .#% 001 Disk Index "0A 001 .(* 001 Disk Index "0A 001 .*# 001 Disk Index "0A 001 ..S 000 001 .2S 001 Disk Index "0A 002 .7X .Y6 000 001 .8: 000 001 .>1 000 001 .CB 000 001 .GP 000 001 .KA 000 001 .Q! 001 Disk Index "0A 001 .TB 000 002 .X0 .Y6 000 002 .\O .Y6 000 002 /%8 ._0 000 001 /)) 000 002 /-< ._0 000 002 //7 ._0 000 002 /0T ._0 000 002 /26 ._0 000 002 /6@ ._0 000 002 /8` ._0 000 002 /;B ._0 000 002 />6 ._0 000 002 /A+ ._0 000 001 /CC 000 002 /FL ._0 000 001 /H1 000 002 /K' ._0 000 001 /LH 000 002 /OP /P, 000 002 /S\ ._0 000 002 /V" ._0 000 002 /Y) /P, 000 002 /YE /P, 000 001 /Z! 000 001 /\E 001 Symbolic Value !*H 001 /^J 001 Iterative Solver "+B 001 0)O 000 001 0*[ 000 001 0/T 001 Iterative Solver "+B 001 09. 002 Overdefined !\% Comparison Tolerance "F$ 001 0A1 001 Inconsistent ![) 001 *:N 001 Storage Command "// 001 *AJ 002 Slash Commands ""= Sheet Select Command !_L 001 '00 004 Variable Sheet !`= Rule Sheet !`L Unit Sheet "!@ Select Sheet Command !_L 001 '7+ 002 Sheets !^+ Window Command !], 001 2:R 000 001 2D# 002 Status Field "?& Rule Syntax !(_ 001 2H[ 002 Unit Sheet Fields "@' Unit Conversion "@G 001 '=J 008 Editing Commands "$H Window !], Storage "// Print ".' Examine "6X Reset "6I Quit ".K Top Level Commands !%+ 001 'LF 006 Edit Field "'0 Blank "&$ Delete "'V Insert "(< Copy "&J Move ")" 001 'W? 001 Editing Commands "$H 001 '\U 001 Editing Commands "$H 001 (*+ 001 Editing Commands "$H 001 ($W 001 Editing Commands "$H 001 (3< 001 Editing Commands "$H 001 (:G 001 Editing Commands "$H 001 *L1 002 Direct Solver "*Q Iterative Solver "+B 001 -49 000 001 $1V 002 Solvers "K( Solve Command ")H 001 $<X 007 Solvers "K( Solve Command ")H Direct Solver "*Q Comparison Tolerance "F$ Iteration Count "H" Convergence Factor "I! Troubleshooting "J" 001 (F\ 001 Slash Commands ""= 001 (RN 001 Slash Commands ""= 001 )$J 004 Load File "16 Save File "4- Delete File "5S Disk Index "0A 001 )-' 002 Storage Command "// Wildcards "ME 001 )D@ 003 Storage Command "// Disk Index "0A FREETK Limits !$M 001 )V/ 005 Save Model "4- Save Variables "4O Save Units "51 Disk Index "0A Storage Command "// 001 )]= 001 Save Options "2@ 001 *%] 001 Save Options "2@ 001 *-/ 001 Save Options "2@ 001 *4! 002 Storage Command "// Disk Index "0A 001 (Z+ 000 001 3.B 000 001 3=( 001 Variable Sheet !`= 001 3FX 003 Variable Sheet !`= Values !*H Expressions !+) 001 3MZ 002 Name Syntax !*9 Variable Sheet !`= 001 3PF 001 Variable Sheet !`= 001 3Y+ 004 Variable Sheet !`= Unit Conversion "@G Display Unit ";L Calculation Unit "=) 001 46G 004 Unit Field ":( Calculation Unit "=) Unit Name !*9 Unit Conversion "@G 001 40U 003 Display Unit ";L Unit Name !*9 Unit Conversion "@G 001 4%: 000 001 4(_ 001 Iterative Solver "+B 001 4<K 001 Rule Sheet !`L 001 4G% 001 Rule Syntax !(_ 001 2N( 001 Unit Sheet "!@ 001 2[/ 002 Unit Sheet "!@ Unit Field ":( 001 5^2 005 Status Line "C: Prompt/Error Line "D" Window Command !], Configuration File !$\ Select Sheet Command !_L 001 5%W 001 Screen Composition "A8 001 52_ 003 Screen Composition "A8 Iteration Count "H" Convergence Factor "I! 001 5UJ 001 Zero-by-Zero Division "L" 001 4KH 003 Typical Value "G8 Iterative Solver "+B Overdefined Problem !\% 001 4YC 001 Comparison Tolerance "F$ 001 6%R 002 Iterative Solver "+B Convergence Factor "I! 001 63( 002 Iterative Solver "+B Comparison Tolerance "F$ 001 7BZ 003 Solvers "K( Examine Command "6X Help on Help !!S 001 6C) 002 Direct Solver "*Q Iterative Solver "+B 001 73Z 001 Indeterminate Expressions "E9 001 7:D 001 Troubleshooting "J" 001 6:S 000 001 58` 000 001 #M< 000 145 ┌────── Getting Started ──────┐ !#. │ Problem Solving with TK │ !'M │ Model Structure │ !(2 │ Rule Syntax │ !(_ │ S o l v e r s │ "K( │ Unit Conversion │ "@G │ Screen Composition │ "A8 │ S h e e t s │ !^+ │ Top Level Commands │ !%+ │ Saving and Loading │ "// │ Troubleshooting │ "J" │ How to Use Help │ !!S └──────── Help Index ─────────┘ !"L ═════════════ A ═════════════ !!S Arithmetic Expression !02 Arithmetic Operators !1- ═════════════ B ═════════════ !!S Beep Signal "LQ Blank Command, /B "&$ Boolean Functions !8+ Built-in Functions !24 ═════════════ C ═════════════ !!S Calculation Unit "=) Comment Field ">1 Comparison Tolerance "F$ Complex Arithmetic !:< Complex Functions !7* Conditional Rule !(_ Configuration !$\ Convergence Factor "I! Copy Command, /C "&J ═════════════ D ═════════════ !!S Delete Command, /D "'V Delete File, /SD "5S Direct Solver "*Q Disk Index "0A Display Unit ";L ═════════════ E ═════════════ !!S Edit Field Command, F5 "'0 Editing Commands "$H Examine Command, /E "6X Exponential and Logarithmic Functions !4J Expression !+) Expression, Arithmetic !02 Expression, Logical !.# Expression, Relational !/7 Expression, Symbolic !-C ═════════════ F ═════════════ !!S First Guess ">@ FREETK !$M Function Keys !&= Function Reference !)X ═════════════ G ═════════════ !!S Getting Started !#. Global Filename Characters "ME ═════════════ H ═════════════ !!S Help !!S Help Index !"L Hyperbolic Functions !52 ═════════════ I ═════════════ !!S IF Rules !(_ Inconsistent Rule ![) Indeterminate Expressions "E9 Input Field, Variable Sheet "7K Insert Command, /I "(< Iteration Count "H" Iterative Solver "+B ═════════════ L ═════════════ !!S Limits of FREETK !$M Load File, /SL "16 Logical Expression !.# ═════════════ M ═════════════ !!S Mathematical Constants !3: Memory Indicator "C: Model Structure !(2 Move Command, /M ")" Multi-Argument Functions !9, ═════════════ N ═════════════ !!S Name Field, Variable Sheet "8N Name Syntax !*9 Navigation Commands !'% Non-Invertible Mathematical Functions !6B Numeric Value !*H ═════════════ O ═════════════ !!S Other Invertible Mathematical Functions !5Z Output Field, Variable sheet "9D Overdefined Problem !\% Overwrite Filename !\G ═════════════ P ═════════════ !!S Precedence of Operators !1- Print Command, /P ".' Problem Solving !'M Prompt/Error Line "D" ═════════════ Q ═════════════ !!S Question Mark, ? "M6 Quit Command, /Q ".K ═════════════ R ═════════════ !!S Relational Expression !/7 Reset Command, /R "6I Rule Field "?F Rule Sheet !`L Rule Syntax !(_ Rule, Conditional !(_ Rule, Unconditional !(_ ═════════════ S ═════════════ !!S Save Model, /SS "4- Save Options of Storage Command "2@ Save Units, /SU "51 Save Variables, /SV "4O Screen Composition "A8 Select Sheet Command, = !_L Sheets !^+ Slash Commands, / ""= Solution Indicator "C: Solve Command, F9 ")H Solvers "K( Status Field, Rule Sheet "?& Status Field, Variable Sheet "7' Status Functions !9T Status Line "C: Storage Command, /S "// Symbolic Expression !-C Symbolic Value !*H ═════════════ T ═════════════ !!S TK-Specific Functions !9T Top Level Commands !%+ Trigonometric Functions !4" Troubleshooting "J" Typical Value "G8 ═════════════ U ═════════════ !!S Unconditional Rule !(_ Unit Conversion "@G Unit Field, Variable Sheet ":( Unit Name !*9 Unit Sheet "!@ ═════════════ V ═════════════ !!S Values !*H Variable Name !*9 Variable Sheet !`= Variable Subsheet !`= ═════════════ W ═════════════ !!S Wildcards "ME Window Command, /W !], ═════════════ Z ═════════════ !!S Zero-by-Zero Division "L" 003 UNKNOWN No Help was found for this context. 003 This help file was composed by Magnus St. Norddahl in 1986. Copyright 1986 Universal Technical Systems, Inc. 019 HOW TO USE HELP: - From anywhere in FREETK press F1 to get help on the feature, error, or place that the cursor is covering (e.g. to get help on Rule Sheet, press = R F1). - If (More) is shown in the lower right corner, PgDn will show more information. - The arrow keys will move you among the Related Topics, if any, or among the entries in the Index. Press ─┘ to select a topic. - Help commands: ┌─────────┬──────────────────────────┐ │ PgDn │ displays next screen │ │ PgUp │ displays previous screen │ │ L │ displays last topic │ │ I │ displays the Help Index │ │ F1 │ displays this screen │ │ Q or F2 │ quits Help │ └─────────┴──────────────────────────┘ 019 HOW TO USE THE HELP INDEX: - From any Help screen press I to invoke the Help Index. If you are anywhere else in FREETK, press F1 I or ? I . - The arrow keys or will move you along the index. Pressing ─┘ will select the topic covered by the cursor. - The next time the Help Index is displayed, the cursor will be in the same place you left it the last time. - You may read through the major topics listed in the box on the first page of Help Index to familiarize yourself quickly with FREETK. - The Help commands apply to the Help Index with the following additions or modifications: - PgDn or PgUp displays the next or the the previous index page, - Home or End moves the cursor to the beginning or end of the Index. 017 TK MODELS serve as a base for problem solving in TK. The models used with FREETK consist of: - Rules declared in the RULE SHEET - Variables declared in the VARIABLE SHEET with attributes defined in Variable Subsheets - Unit conversions defined in the UNIT SHEET NOTES: - TK models used with TK Solver Plus may take advantage of six other sheets in addition to the three sheets mentioned above: List Sheet Global Sheet Plot Sheet Function Sheet Table Sheet Numeric Format Sheet - Models developed in FREETK can be used with TK Solver Plus 019 The DIRECT SOLVER is activated by pressing F9. The Output fields on the Variable Sheet are then cleared and the new solution displayed. SOLUTION OF A SINGLE EQUATION: The Direct Solver solves an equation (rule) for an unknown variable, provided the values of all the other variables in that equation are known. The unknown must not appear more than once and must not be an argument of a non-invertible function. SOLUTION OF A SYSTEM OF EQUATIONS: The Direct Solver scans through the rules of a model and resolves them one after another until no further evaluation is possible. After each variable is evaluated it is substituted into the other rules. 040 The ITERATIVE SOLVER solves equations or sets of equations that cannot be solved by the Direct Solver alone. DESCRIPTION: The Iterative Solver has to be used for solving equations or sets of equations which cannot be solved by the simple substitution, inversion and evaluation performed by the Direct Solver. In order to invoke the Iterative Solver, one or more unknown variables must be assigned guess values which temporarily play the role of inputs. The additional inputs make some equations overdefined (i.e., they cause errors inter- nally). The Iterative Solver manipulates the guess values, and calls the Direct Solver repeatedly until each of the error terms is reduced below the Comparison Tolerance. USAGE: - Make sure that your problem is well-defined, i.e. there are no fewer independent equations than unknowns. - Determine which variables remain unsolved after applying the Direct Solver, and which of them, if known, would trigger solving the rest of the equations (even at the expense of causing inconsistencies); select as few of them as needed. - Type G in the Status field and a guess value in the Input field of the selected variables. - Press F9 . NOTE: The Iteration Count and Convergence Factor are displayed on the Prompt/Error line during iteration. 019 RULE SYNTAX An UNCONDITIONAL RULE has the form: <expression> = <expression> EXAMPLES: 1. a + b = c * d 2. remainder = mod(a,b) 3. theta = pi()^2 + r/2 4. y * (cos(x) - sin(y)) = ln(x) 5. x = 5 A CONDITIONAL RULE has the form: IF <logical expr> THEN <unconditional rule> EXAMPLES: 1. IF x >= 0 THEN y = sqrt(x) 2. IF and(w>0, given('z)) THEN q=ln(w)*z 3. IF evltd('a) THEN b=a*c+d 015 A FUNCTION REFERENCE has the form: function name(arguments) EXAMPLES: 1. pi() 2. ln(x) 3. cos(x*y) 4. max(a,b,c,d) 5. given('a,b*c,0) NOTE: In TK Solver Plus you can refer to both built-in and user-defined functions. Also, you can call user-defined List Functions, Rule Functions and Procedure Functions. 026 TK NAME SYNTAX: - TK Names can be up to 200 characters long and can consist of letters (including interna- tional letters, ASCII values 128-154 and 160- 165; and Greek letters, ASCII values 224-238), digits and the special characters @ # $ % _ - TK Names CANNOT begin with a digit or contain blanks. - TK Names are used as variable names. - TK Names preceded by an apostrophe are used as symbolic values. - TK Names are case-sensitive, i.e. the names RESULT, Result, and result are all different names (names of built-in functions are not case-sensitive). UNIT NAMES Unit names can contain any typeable characters, except for leading and trailing blanks (embedded blanks are allowed). DUPLICATE NAMES - The same name CANNOT appear twice in the Name Field column of a sheet; however, the same name can be used for a variable and a unit. 014 BUILT-IN FUNCTIONS in FREETK can be classified into the following groups: - Mathematical Constants - Trigonometric Functions - Exponential and Logarithmic Functions - Hyperbolic Functions - Other Invertible Mathematical Functions - Non-Invertible Mathematical Functions - Complex Functions - Boolean Functions - Multi-Argument Functions - TK-Specific Functions 006 MATHEMATICAL CONSTANTS: PI() constant π, 3.141592653589793 E() constant e, 2.718281828459045 EXAMPLE: perimeter = 2*PI()*radius 018 TRIGONOMETRIC FUNCTIONS: SIN(x) ASIN(x) R a d i a n s COS(x) ACOS(x) ~~~~~~~~~~~~~ TAN(x) ATAN(x) ATAN2(y,x) (4-Quadrant arc tangent of y/x) SIND(x) ASIND(x) D e g r e e s COSD(x) ACOSD(x) ~~~~~~~~~~~~~ TAND(x) ATAND(x) ATAN2D(y,x) (4-Quadrant arc tangent of y/x) EXAMPLES: 1. y - y0 = sin(x)/x 2. a/sind(α)=b/sind(ß) NOTE: The inverse trigonometric functions return principal values. 002 009 EXPONENTIAL AND LOGARITHMIC FUNCTIONS: EXP(x) number e raised to the xth power LN(x) natural (base e) logarithm of x LOG(x) common (base 10) logarithm of x EXAMPLE: exp(-t^2)=phi 011 HYPERBOLIC FUNCTIONS: SINH(x) ASINH(x) COSH(x) ACOSH(x) TANH(x) ATANH(x) EXAMPLE: (y1-y0)*k + 1 = COSH(k*(x1-x0)) 020 OTHER INVERTIBLE MATHEMATICAL FUNCTIONS: SQRT(x) positive square root of x ROOT(x,n) nth root of x ERF(x) error function GAMMA(x) gamma function, x-1 factorial for integer x>0 EXAMPLES: 1. ROOT(-512,3) returns -8 2. GAMMA(6) returns 120 020 NON-INVERTIBLE MATHEMATICAL FUNCTIONS: SGN(x) -1 if x < 0 0 if x = 0 1 if x > 0 ABS(x) absolute value of x INT(x) integer part of x ROUND(x) x rounded to nearest integer ROUND(x,y) x rounded to the nearest multiple of y CEILING(x) smallest integer ≥ x FLOOR(x) largest integer ≤ x MOD(x1,x2) remainder of x1/x2 DIVIDE(x1,x2) returns two values: int(x1/x2) and mod(x1,x2) STEP(x1,x2) 1 if x1 ≥ x2, 0 if x1 < x2 EXAMPLES: 1. CEILING(-9.7) returns -9 2. FLOOR(-9.7) returns -10 020 COMPLEX FUNCTIONS: POWER((x1,x2),n) calculates a complex number equivalent to the complex number (x1,x2) raised to the nth power RCIS(x1,x2) calculates a complex number in rectangular form equivalent to the complex number in polar form where x1 is the radius and x2 is the angle in radians RCISD(x1,x2) same as rcis, except x2 is in degrees EXAMPLES: 1. POWER((5,2),3) returns (65,142) 2. RCISD(2,60) returns (1,sqrt(3)) 034 BOOLEAN FUNCTIONS: NOT(x) EQV(x,y) AND(series) IMPLY(x,y) OR(series) where: x,y ... logical expressions series .. any number of logical expressions EXAMPLES: 1. if or(k<3,k>5) then a=4*k 2. if and(not(w+y>15),w+y>0) then z=ln(w+y) 3. Answer = eqv(eqv(Tiger,Liar),not(Liar)) DEFINITIONS (1 = true, 0 = false): ┌────────────┬─────┬─────┬─────┬─────┐ │ x │ 1 │ 1 │ 0 │ 0 │ │ y │ 1 │ 0 │ 1 │ 0 │ ╞════════════╪═════╪═════╪═════╪═════╡ │ NOT(x) │ 0 │ 0 │ 1 │ 1 │ │ AND(x,y) │ 1 │ 0 │ 0 │ 0 │ │ OR(x,y) │ 1 │ 1 │ 1 │ 0 │ │ EQV(x,y) │ 1 │ 0 │ 0 │ 1 │ │ IMPLY(x,y) │ 1 │ 0 │ 1 │ 1 │ └────────────┴─────┴─────┴─────┴─────┘ 026 MULTI-ARGUMENT FUNCTIONS: MAX(series) returns largest value from the series MIN(series) returns smallest value from the series SUM(series) returns sum of values in the series MEMBER(x,series) returns 1 or 0 if the value of x is or is not among the values in the series POLY(x,series) returns value of a polynomial function of x with coefficients specified by the series of values (highest-degree coefficient first, coefficients of 0 for missing terms) NPV(x,series) returns net present value of the series of payments, assuming interest rate x EXAMPLES: 1. max(a,34,b,c,40) returns 43 if a=12, b=35, and c=43 2. poly(x,1,0,0,1) returns 9 if x=2 3. poly(x,1,4,3) returns 143 if x=10 041 TK-SPECIFIC FUNCTIONS VALUE(var) returns the value of variable var Status functions, short form: GIVEN(var) returns 1 or 0 if the variable var is or is not assigned an input value EVLTD(var) returns 1 if the variable var was evaluated KNOWN(var) returns 1 if the variable var is known (i.e. given or evaluated) where var is an expression that evaluates into a symbolic value representing a variable name; in the simplest case it may be just a variable name preceded by an apostrophe. EXAMPLES: 1. VALUE(a) (returns 12 if a='R and R=12) 2. if KNOWN('phi) then L=phi*rho (the L=phi*rho rule applies if phi is known) Status functions, long form: GIVEN(vars,expr1,expr2) KNOWN(vars,expr1,expr2) EVLTD(vars,expr1,expr2) where vars means one or more expressions that evaluate into variable names. If all the vars variables are given, known or evaluated, the functions return expr1; else, they return expr2. EXAMPLES: 1. Rate = GIVEN('Rate,Rate,10) (if Rate is assigned an input value, the rule represents trivial identity Rate=Rate; else, the rule assigns a default value Rate=10) 2. L = KNOWN('phi,phi*rho,0/0) (if phi is known the rule becomes L=phi*rho; if phi is not known the rule is ignored) 3. if GIVEN('Θ,'α,'ß,1,0) then L=Θ*R (rule applies only if all Θ,α,ß are given) 016 VALUES are either NUMERIC or SYMBOLIC NUMERIC values are any real number in standard or exponential format with up to 16 significant digits and non-zero absolute value between 1E-307 and 1E308, or zero. EXAMPLES: 1. 1.09092 3. 18437560000000000000000 2. 6.672E-11 4. 0 Symbolic values are any TK names preceded by an apostrophe. EXAMPLES: 1. 'x 2. 'Bank 3. 'a_row_1 018 An EXPRESSION can be: - a CONSTANT VALUE - a VARIABLE name - a FUNCTION REFERENCE - an ARITHMETIC expression - a RELATIONAL expression - a LOGICAL expression - a SYMBOLIC expression EXAMPLES (in respective order): 1. 3409 or 'size 2. size 3. SQRT(speed) 4. (y2-y1)/(x2-x1) 5. a >= 34 6. AND(a <= 34,b > a) 7. GIVEN('Gas,Gas,'Oxygen) 011 A SYMBOLIC EXPRESSION can be: - a symbolic value - an expression that evaluates into a symbolic value EXAMPLES: 1. given('soup,'entree,'dessert,'OK,'Incomplete) 2. pet (if pet equals, say, 'baboon) 3. 'wood 4. '$100_note 5. 'DOG_and_PONY_show 011 A LOGICAL EXPRESSION can be: - a relational expression - a Boolean function - any other expression that evaluates into 1 (true) or 0 (false) EXAMPLES: 1. x <= y 2. or(x <= y,x >= w) 3. given('x) 4. abs(sgn(x)) 018 A RELATIONAL EXPRESSION has the form of two expressions linked by a relational operator. Relational operators are: = equal < less than > greater than <= =< less than or equal to >= => greater than or equal to <> >< not equal Relational expressions evaluate into numerical values 1 (true) or 0 (false). EXAMPLE: 1. x*y <= u*v 2. animal <> 'dog 013 An ARITHMETIC EXPRESSION can be: - two expressions linked by an arithmetic operator (+ - * / ^). The constituent expressions (operands) must evaluate into numeric values. - any expression preceded by unary + or - . EXAMPLES: 1. a + b / (c * d) 2. (b > 3) + a 3. (a+b)^ln(x) 4. exp(cos(x)+sin(y)) 5. -SIN(X) 012 COMPLEX ARITHMETIC: A complex number, a+bi, is represented as a pair of two real numbers (a,b). When doing complex arithmetic, all operands in the rule must be paired expressions. If a function is used as an operand it must be two-valued. EXAMPLES: 1. (y,yi)=(a,0)*power((x,xi),3)+(b,0) 2. (a,b) = (c,d) * (e,f) 018 SHEETS Communication between the user and TK is conducted through the sheets. Each sheet contains a different kind of information. In FREETK there are three sheets: - Variable Sheet - Rule Sheet - Unit Sheet NOTE: TK Solver Plus has six other sheets in addition to the three sheets mentioned above: - Function Sheet - List Sheet - Plot Sheet - Table Sheet - Numeric Format Sheet - Global Sheet 014 The SELECT command (=) displays any TK sheet in the current window. USAGE: - Type the Select command (=) - Type the first letter of the sheet you want to select, or move the cursor to the desired sheet name in the Option Box and press ─┘. NOTES: - You can use the Select command from any sheet or subsheet - To display a new sheet in the opposite window, use the Window command (/W) 024 SLASH COMMANDS (/): Press / to bring up the Option Box, then press the first letter, or move the cursor over the desired command and press ─┘. ┌──────────────────┐ ┌────────────┐ │ Editing Commands │ │ I/O │ ├──────────────────┤ ├────────────┤ │ B Blank fields │ │ S Storage │ │ C Copy fields │ │ P Print │ │ D Delete rows │ └────────────┘ │ I Insert rows │ ┌────────────┐ │ M Move rows │ │ Other │ ╞══════════════════╡ ├────────────┤ │ Changing Display │ │ E Examine │ ├──────────────────┤ │ R Reset │ │ W Window │ │ Q Quit │ └──────────────────┘ └────────────┘ NOTES: - Use the Help facility to find more information on specific commands; e.g. /S F1 gives you help on the Storage command; or press /, move the cursor over "Storage" and press F1. - The Function Keys duplicate some of the slash commands with one keystroke. 016 EDITING COMMANDS ╔══════╤═════════════════════════════════════╗ ║ F5 │ Edit Field: make changes in a field ║ ╟──────┼─────────────────────────────────────╢ ║ /B │ Blank a specified block of fields ║ ╟──────┼─────────────────────────────────────╢ ║ /D │ Delete a specified block of rows ║ ╟──────┼─────────────────────────────────────╢ ║ /I │ Insert blank lines in a specified ║ ║ │ block of rows; Ins inserts one line ║ ╟──────┼─────────────────────────────────────╢ ║ /C │ Copy a specified block of fields ║ ╟──────┼─────────────────────────────────────╢ ║ /M │ Move a specified block of rows ║ ╚══════╧═════════════════════════════════════╝ 014 The BLANK command (/B) blanks out a block of fields in a single column. USAGE: - Move the cursor to the first item you want blanked and type /B - Move the cursor to highlight the block of fields you want blanked - Press ─┘ NOTE: - Use the Arrow keys or , and Home, End, PgUp or PgDn keys to move the cursor 019 The COPY command (/C) copies a block of fields in a single column to another location. USAGE: - Move the cursor to the first field to copy - Type /C - Move the cursor to highlight the block of fields to be copied - Press ─┘ - Move the cursor to the desired location to begin copying the defined block - Press ─┘ NOTES: - Use the Arrow keys, and Home, End, PgUp or PgDn keys to move the cursor - COPYING INFORMATION INTO A FIELD OVERWRITES THE PREVIOUS CONTENTS OF THE FIELD 014 The DELETE command (/D) deletes a block of rows you specify. USAGE: - Move the cursor to any location in the first row you want deleted - Type /D - Move the cursor to highlight the block of rows you want deleted - Press ─┘ NOTE: - Use the Arrow keys or , and Home, End, PgUp or PgDn keys to move the cursor 018 The EDIT FIELD command (F5) The in-field editor is invoked in the field marked by the cursor when: - you type F5 or Ctrl-E. - FREETK detects an error in attempted entry. WHEN IN THE EDITOR: - Move the cue with the Arrow or Tab keys - Add characters by typing them at the location marked by the cue - Delete characters to the right of the cue with the Delete key (Del) - Delete characters to the left of the cue with the Backspace key (──) - Enter the changed contents by pressing ─┘ - Exit the Editor without making any changes by pressing F2 or Ctrl-Break 016 The INSERT command (/I) inserts blank row(s) in the current sheet. USAGE: - Move the cursor to the row where you want to start inserting. - Type /I. - Move the cursor to highlight the number of rows you want to be displaced by blank rows. - Press ─┘. NOTES: - The row marked by the cursor and all the rows below it are displaced downward, but the cursor remains in the same place. - Press the Ins key to insert a single row. 025 The MOVE command (/M) moves a specified block of rows. USAGE: - Move the cursor to the first row to be moved - Type /M - Move the cursor to highlight the block of rows you want to move - Press ─┘ - Move the cursor to the destination row where you want to place the highlighted block - Press ─┘ NOTES: - Use the Arrow keys or , and Home, End, PgUp or PgDn keys to move the cursor - The Move command places the first row of the specified block in the destination row and the rest of the block in the following rows. - Existing row(s) at and below the destination row are displaced to make room; they move upward if the block is moved down, and downward if the block is moved up. - Blank rows move the same way as if they were filled. 025 The PRINT command (/P) prints a block of rows from a TK sheet to a printer. USAGE: - Move the cursor to the sheet and row where you want printing to begin - Move the cursor to highlight the rows you want to print - Press ─┘ NOTES: - Use the Arrow keys or , and Home, End, PgUp or PgDn keys to move the cursor - The block is momentarily displayed on the screen while it is being printed - Ctrl-Break can be used to stop printing. - This command is more useful in the full TK Solver Plus where it is possible to define printer settings on the Global Sheet and/or to save the specified rows under a chosen filename. Missing these options in FREETK, you may prefer to dump the screen using PrtSc. 016 The QUIT command (/Q) USAGE: - Type /Q - Type Y to confirm the Quit command, or - Type N or press F2 to cancel the Quit command NOTES: - If you want to clear information from the sheets without leaving FREETK, use the Reset command (/R). - WHEN YOU QUIT TK, THE INFORMATION IN THE CURRENT SHEETS IS LOST. If you want to save what you have done before you leave FREETK, use the Save option of the Storage command (F4 or /SS) before quitting. 021 The RESET command (/R) has three options: V (Variables) clears all input and output values from the Variable Sheet and Variable Subsheets (the First Guess values are not affected). S (Sheet) clears the current sheet or subsheet. A (All) clears all sheets and subsheets. USAGE: - Type /R - Type V, S or A to select the option you want - Type Y to confirm or N to cancel the Reset NOTES: - NOTHING WILL STOP A CONFIRMED RESET - Instead of pressing V, S or A and Y or N, you may move the cursor in the Option Box to the appropriate position and press ─┘. - Use the Quit command (/QY) rather than Reset if you want to leave FREETK 018 The STORAGE command (/S) loads, saves and deletes files from the disk. ┌───┬─────────────────────┐ │ L │ Load TK File │ │ S │ Save Model │ │ V │ Variables Save │ │ U │ Units Save │ │ D │ Delete Any File │ └───┴─────────────────────┘ USAGE: - Type /S and the first letter of the option - Respond to any additional prompts (Press F2 or Ctrl-Break to cancel the Storage command without taking any action) NOTES: - F3 is equivalent to /SL. - F4 is equivalent to /SS. 053 DISK INDEX lists disk files available to the current Storage command option. USAGE: - Type /S followed by any option character (You can press F3 instead of typing /SL or press F4 instead of typing /SS). - Type a drive designator and pathname if needed. - Type a partial filename with wildcards if you want to limit the display to related filenames. - Press ─┘ to display the Disk Index. - Move the cursor to the row of the desired file. - Press ─┘. NOTES: - If the desired file is not listed you will have to press F2 to exit the Disk Index and start over. - The Disk Index displays only files with .TK extension for all Storage options, except the Delete option (/SD) which displays files with any extension. - The Disk Index displays also the names of subdirectories. You can dive into a subdirectory by pressing > and return to the parent directory by pressing < . To load multiple files: - Access the Disk Index with F3 ─┘. - Type numbers in the Selection column to specify the order of loading (you can change the order by typing new numbers, or 0 to blank a selection). - Press ─┘. To delete multiple files: - Access the Disk Index with /SD ─┘. - Type numbers in the Selection column to specify the order of deletion (you can change the order by typing new numbers, or blank the selection by typing 0). - Press ─┘. - FREETK will ask for confirmation on each deletion. 035 The LOAD option (F3 or /SL) USAGE: - Press F3 or type /SL. - Type a drive designator and pathname if needed. - Type a filename, or access the Disk Index and move the cursor to the row of the filename. - Press ─┘. NOTES: - If FREETK is not reset first, contents of new model are appended to end of current model. - Values from new model replace current values of duplicate variables. - Duplicate rules and unit conversions are repeated. - A model can be loaded right after TK is started by supplying the model name as an argument from DOS. For example: FREETK LOAN ─┘ will start FREETK and then load the model LOAN. - If you load a TK model that has more variables, units, or rules than FREETK can accommodate, FREETK will only load as many lines from each sheet as are allowed by FREETK and give the message "Incomplete load" (See "Limits of FREETK"). TK Solver Plus does not have these limitations. - If you load a TK model that contains rules that cannot be understood by FREETK, those rules will be marked with the unparsed-sign % and ignored. 018 SAVE OPTIONS: - Save MODEL: Saves the entire model to a file. - Save VARIABLES: Saves only the Variable Sheet to a file. - Save UNITS: Save only the Unit Sheet with selected unit conversions to a file. NOTE: TK Solver Plus has eight other save options, in addition to the three mentioned above: - Function Save - Numeric Format Save - Plot Save - Table Save - DIF Save - WKS Save - ASCII Save - Configuration save 018 The SAVE option (F4 or /SS) USAGE: - Press F4 or type /SS - Type a drive designator and pathname if needed - Type a filename or, if you want to overwrite a file, access the Disk Index - Press ─┘ NOTES: - FREETK adds the .TK extension to filenames saved under this option if no other extension is specified - If you use the Disk Index but find no file to overwrite, you must start over (F2) - See the Help screen on the Storage command for information on saving parts of a model rather than the whole model 016 The SAVE VARIABLES option (/SV) saves the current Variable Sheet and Variable Subsheets in a TK file. USAGE: - Type /SV - Type a drive designator and pathname if needed - Type a filename or, if you want to overwrite a file, access the Disk Index - Press ─┘ NOTES: - FREETK adds the .TK extension to the filenames if no other extension is specified - If you use the Disk Index but find no file to overwrite, you must start over (F2) 015 The SAVE UNITS options (/SU) saves the current Unit Sheet in a TK file. USAGE: - Type /SU - Type a drive designator and pathname if needed - Type a filename or, if you want to overwrite a file, access the Disk Index - Press ─┘ NOTES: - FREETK adds the .TK extension to the filenames if no other extension is specified - If you use the Disk Index but find no file to overwrite, you must start over (F2). 016 The DELETE option (/SD) deletes files from disk. USAGE: - Type /SD - Type a drive designator and pathname if needed - Type the filename, or access the Disk Index to mark the file(s) to be deleted - Press ─┘ - Confirm the deletion(s) by typing Y NOTES: - The Delete option can delete any kind of file, not just TK files - See the Help screen on the Disk Index for information on multiple deletions 014 OVERWRITING A FILE means saving new information in the file in place of old information. OVERWRITING DESTROYS THE OLD CONTENTS OF A FILE: - If you want to replace the old information with the new information, confirm the command by typing Y. This destroys the old contents of the file. - If you want to preserve the old file, type N to cancel the Storage command. Save the new file under another filename. 022 The WINDOW command (/W) controls the number of windows on the screen (one or two) and determines which sheet is displayed in the other window. To change the display from two windows to a SINGLE window: - Place the cursor on the sheet you want to retain - Press F6, or type /W1 To split the screen into TWO windows and/or to display any sheet in the OTHER window: - Type /W - Type the first letter of the sheet you want displayed in the other window (or move the cursor in the Option Box to desired sheet and press ─┘) NOTE: - To display a different sheet in the current window, use the Select command (=) instead of the /W command 018 The SOLVE command (F9) solves a model with the Direct or Iterative Solvers and displays the results in the Output fields of the Variable Sheet. USAGE: - Assign the known values of input and/or guess values for variables in the Variable Sheet. - Press F9 NOTES: - TK applies the Iterative Solver only if you have provided guess values for one or more variables (by typing G in the Status field on the Variable Sheet or entering a First Guess value in the Variable Subsheet) - The Solve command may be used from anywhere in FREETK 014 PARSER ERROR This error should not have occurred. REMEDIAL ACTION: - Write down everything that might relate to this problem; copy the offending rule or expression and/or dump the screen to the printer by pressing [PrtSc]. - If a rule entry was attempted, put a " in front of it and press [Enter]. Else, exit the editor pressing F2. In any case save the current model to a disk. - Notify UTS (call 1-800-HELP-UTS). 011 MISSING OPERAND CAUSE: Attempting to enter a rule or expression which contains a dangling operator, equal sign, or other symbol. SOLUTION: The cue points to the problem spot. Edit the entry so that each operator has a name, value, or valid expression on either side of it. 010 MISSING OPERATOR CAUSE: Attempting to enter a rule or expression which contains two parenthetical expressions with no operator between them. SOLUTION: Edit the entry so that adjacent parenthetical expressions are related by an operator. 010 INVALID SYMBOLIC VALUE CAUSE: You attempted to enter an apostrophe followed by a character string which is not a valid TK name. SOLUTION: Edit the entry to replace the invalid symbolic value with a valid symbolic value. 009 EXPECTED OPERATOR NOT FOUND CAUSE: You attempted to enter a rule that contains an invalid TK expression, i.e. the expression is missing an operator between two operands. SOLUTION: Change the expression so that it is valid. 017 UNDEFINED FUNCTION CAUSES: - You entered an undefined function name immediately preceding a left parenthesis. - You entered a variable name immediately preceding a left parenthesis. SOLUTIONS: - Edit the expression to add an operator between the variable name and the left parenthesis. NOTE: - In TK Solver Plus, you would have the option to define your own function in the Function Sheet. 009 INVALID FUNCTION NAME CAUSE: You entered an invalid TK name immediately preceding a left parenthesis. SOLUTION: Specify a valid function name when referring to a function. 011 TOO MANY FUNCTION ARGUMENTS CAUSE: Attempt to enter a rule or expression that contains a function reference with more arguments than the definition of the function specifies. SOLUTION: Edit the entry so that the function reference has the correct number of arguments. 011 TOO FEW FUNCTION ARGUMENTS CAUSE: Attempt to enter a rule or expression that contains a function reference with less arguments than the definition of the function specifies. SOLUTION: Edit the entry so that each function has the correct number of arguments. 010 NUMBER OUTSIDE NUMERIC RANGE OF PROGRAM CAUSE: You attempted to enter an input value or a rule with a value whose absolute value is greater than 1E308. SOLUTION: Edit the input value or the rule so that all values fit the numeric range of FREETK. 012 COMPLEX ARGUMENT FOUND WHERE REAL ARGUMENT EXPECTED CAUSE: Using a pair of numbers (complex number) or an expression which returns a complex result as an argument of a function requiring real number argument(s). SOLUTION: Supply the real number argument to the function where it is required. 015 EXPRESSION TOO COMPLICATED CAUSE: You attempted to enter an expression with too many pending operations or operands, or a rule that contains such an expression. SOLUTION: Edit the expression to reduce the number of pending operations or operands and enter the new rule or expression. NOTE: The cue indicates the point at which FREETK could no longer handle the expression 010 INVALID COMPLEX COMPUTATION CAUSE: Attempting to enter in a value field an expression which includes complex numbers. SOLUTION: Enter only numeric value or symbolic value or an expression that evaluates into a single value. 010 IF CLAUSE IN EXPRESSION CAUSE: Attempting to enter a conditional clause or rule into a field which accepts only evaluable expressions. SOLUTION: Enter only an expression which evaluates to an acceptable value. 016 MIXED REAL AND COMPLEX OPERANDS CAUSE: An expression must not have both single and paired expressions as operands to the same operator. SOLUTION: Edit the expression or rule so that it contains only single operands or only paired (complex) operands. NOTE: As an exception, POWER requires the first argument to be a complex number, and the second to be a single expression. 010 MISPLACED COMMA CAUSE: Attempting to enter a rule or expression which contains a comma between values or names that are neither function arguments nor the real and imaginary components of a complex number. SOLUTION: Edit the entry to remove any extraneous comma. 009 MISSING SYMBOLIC VALUE CAUSE: Specifying an empty symbolic value, i.e. having an apostrophe not followed by name. SOLUTION: Edit the rule or expression so that each apostrophe precedes a valid TK name. 011 OUT OF MEMORY CAUSE: FREETK ran out of memory while loading a file or parsing an entry. SOLUTION: Save information with the Storage command and then clear some or all of the model with the Reset command (/R) or Delete command (/D). 011 INVALID RANGE SPECIFIED CAUSE: Attempting to specify a block for blanking, moving, inserting or copying which includes the top area of the sheet. SOLUTION: When specifying the range (block), do not include the fields in the fixed area of the sheet. 009 BLOCK INCLUDES FIELD THAT CANNOT BE BLANKED CAUSE: You attempted to blank a block of fields that included one or more fields that cannot be blanked or left blank. SOLUTION: Leave the field as is. 018 NOT ENOUGH ROWS AVAILABLE ON SHEET CAUSES: - Attempting to insert row(s) in a sheet so that it would have more than 32 lines in it (16 lines in Rule Sheet). - Attempting to use the Move command in a sheet that is full. SOLUTIONS: - Delete unnecessary lines, if any, before inserting new line(s) or moving line(s). - If possible, combine lines to make room for new lines. NOTE: - The limitation of a specific number of rows in a sheet does not apply to full TK Solver. 024 INCOMPLETE SAVE CAUSES: - When you used the /SS (F4) command it caused a disk error. (Disk errors may be caused by saving to a faulty disk drive, a damaged diskette, a write-protected diskette, or a diskette that is full.) - You pressed Ctrl-Break during the save procedure. SOLUTIONS: - If the error has occurred because the Ctrl-Break key was pressed, begin the Storage command again and allow the save procedure to be completed. - If the problem is elsewhere, check the disk to determine whether it is full or write- protected. Try saving the file to a different disk drive or diskette. - The incomplete save may have created a partial file on the first diskette. Delete this file using the /SD command or an appropriate command at DOS level. 026 INCOMPLETE LOAD CAUSES: - Attempting to load a damaged file with the /SL (F3) command. - Attempting to load a TK file which is not compatible with the running version of FREETK. - You pressed the Ctrl-Break key during the loading procedure. - Attempting to load a model that contains more lines for the Variable, Rule, or Unit Sheet than allowed in FREETK. (Excess ignored.) SOLUTIONS: - If the file has been damaged, the load is completed up to the damaged section. Information that has been damaged must be recreated. - If the error occurred because Ctrl-Break was pressed, reset FREETK (/RAY) and load the file again; allow the load procedure to be completed. NOTE: The limitation of a specific number of rows in a sheet does not apply to full TK Solver. 021 NO FILES FOUND WITH MATCHING FILENAMES CAUSES: You attempted to view the files on the disk with the Disk Index when there were either: - No files available for the current Storage command option - No filenames matching the wildcard you specified - No diskette found in the specified drive SOLUTION: Start the Storage command again and: - Use a different wildcard specification to look for files on the disk - Type a complete filename instead of looking at the Disk Index - Type a path to a subdirectory containing files relevant to the Storage command option before looking at the Disk Index - Insert a diskette into the specified drive. 012 NOT A VALID STORAGE FILE CAUSES: - Attempting to load a file that is not a valid TK model file. - Attempting to load a TK model file that has been incorrectly changed with a text editor. SOLUTIONS: - Specify a filename for a valid TK model file. - Modify the file again with a text editor to make it a valid TK model file. 012 OBJECT DELETED; SUBSHEET NO LONGER ACCESSIBLE CAUSE: You attempted an action in a subsheet which does not exist anymore. (When a variable is deleted, the associated subsheet is also deleted, even if the subsheet still appears on the screen in the other window.) SOLUTION: Create a new variable. Dive to the new subsheet to enter information. 010 FIELD RESERVED FOR OUTPUT CAUSE: Attempting to enter a value in the Output field on the Variable Sheet or on a Variable Subsheet. SOLUTIONS: - Leave the field as is. - Enter a new value in an Input field. 012 OUT OF MEMORY CAUSE: Any action which uses up the remaining memory available for running FREETK results in an error and cancellation of the action in progress. SOLUTION: Save information with the Storage command (/SS) and then clear some or all of the model with the /D or /R command. 009 FIELD CANNOT BE BLANKED CAUSE: You attempted to enter blanks in a FREETK field that cannot be left blank. SOLUTIONS: - Leave the field as is - Enter a non-blank value 015 ACTION COMMAND (!) HAS NO EFFECT ON THIS SHEET CAUSE: You attempted to use the Action command (!) from the Unit Sheet. SOLUTIONS: - Press F9 to invoke the solvers. - Go to the Variable Sheet or Rule Sheet and press ! . NOTE: In TK Solver Plus, the Action command has additional uses in sheets which are not available in FREETK. 011 UNDEFINED VARIABLE CAUSE: You attempted to enter the name of a variable that does not exist or does not have a value. SOLUTIONS: - Edit the variable name so that it refers to a defined variable name. - Press F2 to cancel and try again. 011 EXPRESSION CANNOT BE EVALUATED CAUSES: - Attempting to enter an unevaluable expression on the Prompt Line during /EE or /EC. - Attempting to enter an unevaluable expression in a value field (e.g. 0/0). SOLUTION: Enter only valid TK expressions for evaluation. 012 DISK INDEX: NOT ENOUGH MEMORY TO CONTINUE CAUSE: Using the Disk Index to view the contents of the disk exhausted the memory available to FREETK. SOLUTION: Save all or part of the model with F4 without using the Disk Index so you can delete all or part of the model to free up memory to allow use of the Disk Index. 011 NO FILES SELECTED CAUSE: Pressing ─┘ while pointing to a subdirectory in the Disk Index. SOLUTION: Start the Storage command again and, when the cursor points to a subdirectory, use the Dive command > to see the files stored in that subdirectory. 010 VARIABLE DOES NOT EXIST CAUSE: You attempted to enter a nonexistent variable for evaluation when using the Variable option of the Examine command. SOLUTION: Repeat the command and enter the name of an existing variable. 014 NO VARIABLE NAME CAUSE: Attempting to enter a "G" in the Status field of a variable when there was no name in the Name field. SOLUTIONS: - Enter a rule containing the variable in the Rule field on the Rule Sheet before using the Status field. - Enter the variable name into the Name field on the Variable Sheet before using the Status field. 008 WARNING: PARSER ERRORS DETECTED DURING LOADING CAUSE: Loading a model with invalid rules. Those rules that are left unparsed are marked with a % sign in the Status field. These rules should be edited and modified before the model is used. 009 INVALID CONFIGURATION FILE CAUSE: The FREETK.CFG file is not set up correctly. SOLUTION: Refer to the related topic "Configuration" for the correct format and contents of the configuration file. 013 INVALID FILE SPECIFICATION CAUSE: A string of up to 200 characters may be entered as a filename, but the length and validity of a file specification is usually determined by the operating system of the computer. SOLUTIONS: - Check your operating system manual for a valid filename. - Enter a valid filename. 012 FILE DOES NOT EXIST CAUSE: Attempting to load a file that does not exist in the specified directory. SOLUTIONS: - Specify an existing filename (and a pathname if applicable) for the file to be loaded - Access the Disk Index to view the files available in the current directory and subdirectories 007 FILE ALREADY EXISTS CAUSE: Same filename has been used before. SOLUTION: Try entering another filename 011 FILE IS PROTECTED CAUSES: - You attempted a storage action to a filename that is protected by the operating system. - You attempted a storage action specifying a directory rather than a file name. SOLUTIONS: - Specify another filename or drive specifier. - Insert another diskette. 011 DISK IS PROTECTED CAUSE: Attempting to save a model to a write-protected diskette. SOLUTIONS: - Take the write-protection tab off the diskette, so it can be written to. - Save to a different diskette which is not write protected. 012 DISK SPACE OR DISK DIRECTORY FULL CAUSES: - Attempting to save to a disk that has too little space left to store the file. - The disk already contains the maximum number of files allowed on the disk by your operating system. SOLUTIONS: - Delete some files first. - Save the file to a different disk. 001 DISK RELATED SOFTWARE ERROR 014 NO SUCH DEVICE OR DEVICE NOT READY CAUSE: Most likely you tried to save a file to a drive that was not ready (no diskette, or drive door not closed). SOLUTIONS: - Check the disk and the drive. - Check the drive specifier in the file specification. - See your operations manual for further information about device names and drive specifiers. 013 DISK DATA OR I/O ERROR CAUSES: - You attempted an action that caused a hardware read/write error. - You attempted to use a worn or damaged diskette. SOLUTION: Try another diskette; refer to your hardware operations manual for hardware diagnostic tests; note this message and contact your computer dealer. 010 DISK HARDWARE ERROR You attempted an action that caused a hardware read/write error. SOLUTION: Try another diskette; refer to your hardware operations manual for hardware diagnostic tests; note this message and contact your computer dealer. 010 END OF FILE CAUSE: You attempted to load an incomplete or improperly formed file with the Load file (/SL) option of the Storage command. SOLUTION: Try creating a new copy of the file and repeating the load action. 014 LINE TOO LONG CAUSES: - You attempted to load a file that contains a line that is too long. - You attempted to load an improperly formatted file. - A line end character was removed with a text editor. SOLUTIONS: - Press Ctrl-Break to cancel the load action. - Try to recreate the file and reload it using the same machine. 010 FILENAME CONTAINS WILDCARD CAUSE: Wildcards can not be used in filenames in FREETK. SOLUTION: If you want a directory listing when saving or loading a file, press ─┘ when prompted for a filename. 010 DEVICE IS NOT MOUNTED CAUSE: You attempted a print or storage action to a device name that is not connected. SOLUTION: See your operations manual for further information about device names and drive specifiers. 004 UNKNOWN ERROR CAUSE: This error should not have occurred. 007 SOLUTION: - Dump the screen to a printer and/or write down everything that might relate to this problem. - Save the current model to a disk right away if possible. - Notify UTS (call 1-800-HELP-UTS). 006 SYSTEM ERROR CAUSE: This error message appears as the result of an unknown program error that interfered with the evaluation of an expression. 011 SOLUTIONS: - Review the offending rule and other rules and input values to see what caused the error. - If the error occurred during iteration: change the guess value(s) and/or review the strategy of using the Iterative Solver. - If the error occurred when entering or exami- ning an expression: edit the expression or examine the ingredients or make a new entry. 008 DIVISION BY ZERO CAUSES: - Attempting to enter an expression the evaluation of which would involve division of a non-zero number by zero. - Attempting to divide a non-zero number by zero in the process of solving a rule. 011 EXPONENT OVERFLOW CAUSE: Arithmetic operation or function evaluation produced a value that is outside the numeric range of FREETK, i.e. its absolute value is greater than 1E308. NOTE: Exponent underflow is ignored (the result is taken as zero). 005 ARGUMENT ERROR CAUSE: The function argument supplied to the function is outside the domain of the function. 005 SQRT: ARGUMENT ERROR CAUSE: Attempt to take square root of negative argument. 005 LOG: ARGUMENT ERROR CAUSE: Attempt to take logarithm of zero or negative argument. 008 EXPONENTIATION: ARGUMENT ERROR CAUSE: Attempt to perform the direct or inverse exponentiation operation (^) with negative argument and fractional exponent combined (e.g. evaluating (-32)^.2 or solving y=x^2 for x when y is negative or zero). 006 ASIN: ARGUMENT ERROR CAUSE: Attempt to evaluate arc sine of an argument with absolute value greater than 1. (SIN inverse may be responsible.) 006 ACOS: ARGUMENT ERROR CAUSE: Attempt to evaluate arc cosine of an argument with absolute value greater than 1. (COS inverse may be responsible.) 007 ASINH: ARGUMENT ERROR CAUSE: Attempt to evaluate hyperbolic arc sine of an argument with absolute value greater than 1E154. (SINH inverse may be responsible.) 007 ATANH: ARGUMENT ERROR CAUSE: Attempt to evaluate hyperbolic arc tangent with an argument with absolute value greater than 1. (TANH inverse may be responsible.) 006 ATAN2: ARGUMENT ERROR CAUSE: Known argument and function values are not consistent with each other, e.g. z=0 and y=1 in z=atan2(y,x). 007 VALUE: ARGUMENT ERROR CAUSE: Attempt to use built-in function VALUE with an argument which is not a symbolic value, or which does not evaluate into a name of an existing variable. 005 MOD: ARGUMENT ERROR CAUSE: The second argument of the MOD function evaluates to zero. 007 ACOSH: ARGUMENT ERROR CAUSE: Attempt to evaluate hyperbolic arc cosine of an argument with absolute value greater than 1E154. (COSH inverse may be responsible.) 005 LN: ARGUMENT ERROR CAUSE: Attempt to take logarithm of zero or negative argument. 009 POWER: ARGUMENT ERROR CAUSE: The second argument supplied to the function was not an integer. SOLUTION: Modify the model so that the second argument evaluates into an integer. 001 GIVEN: ARGUMENT ERROR 010 CAUSES: - An argument specifying a variable to be examined does not evaluate into a symbolic value. - Attempt to use two arguments. SOLUTIONS: - Check and modify the arguments. - Use 1, 3 or more arguments. 006 ERF: ARGUMENT ERROR CAUSE: Attempt to evaluate an inverse erf of an argument with an absolute value greater than 1. 007 GAMMA: ARGUMENT ERROR CAUSES: - Attempt to evaluate gamma function of zero or negative argument. - Attempt to evaluate the inverse gamma function of a value less than .886 . 001 KNOWN: ARGUMENT ERROR 001 EVLTD: ARGUMENT ERROR 006 INVALID BOOLEAN ARGUMENT CAUSE: Attempt to evaluate a Boolean function or inverse Boolean function of an argument or arguments other than 0 or 1. 005 INVALID SYMBOLIC COMPUTATION CAUSE: Attempt to perform a numeric operation on a symbolic value, e.g. 3*'p or sin('q). 022 > ITERATION: DEPENDENCY ERROR CAUSES: - The number of independent equations in the model is less than the number of unknowns. - The error terms generated by guesses become too small or too insensitive to small changes in guess values. SOLUTIONS: - Check the choice of guess variables and/or guess values. - Check the number of independent equations vs. the number of unknowns; modify the model and/ or reformulate the problem. - Scale the problem up or down; review the strategy of using the Iterative Solver. NOTE: TK Solver Plus with the Comparison Tolerance and Typical Value settable on the Global Sheet offers additional means to control the Iterative Solver. 004 SOLUTION ABORTED CAUSE: Ctrl-Break was pressed during solution. 012 OUT OF MEMORY (during iteration) CAUSE: There is no room accommodate additional information generated and used by the Iterative Solver. SOLUTION: Save information with the Storage command and then clear some or all of the model with the Reset command (/R) or Delete command (/D). 023 > ITERATION: TOO MANY GUESSES CAUSES: - The number of error terms generated by guesses is less than the number of guess variables. - Some of the error terms are too small (i.e. they are within the Comparison Tolerance). SOLUTIONS: - Solve the problem with a reduced number of guess variables. - Change the guess values. - Scale the problem up or down; review the strategy of using the Iterative Solver. NOTE: TK Solver Plus with the Comparison Tolerance and Typical Value settable on the Global Sheet offers additional means to control the Iterative Solver. 016 > INCONSISTENT CAUSE: The marked rule was checked by the Direct Solver and found in error. This happens most often when all variables in an equation have have input values or were evaluated from other equations, and the difference between the left- and right-hand side is greater than the Comparison Tolerance. SOLUTION: - Blank the input value of a variable marked 'Overdefined' or some other variable that may be responsible. - Delete, cancel or edit the offending rule. 016 > OVERDEFINED CAUSE: The marked variable appears in an equation that was found inconsistent. The variable may be directly or indirectly responsible for this condition, which usually means that the problem was overdefined. SOLUTION: - Blank the input value of the offending variable (if assigned) or of any other variable marked 'Overdefined' or some other variable that may be responsible. - Delete, cancel or edit the rule marked 'Inconsistent'. 035 GETTING STARTED If you have never used TK before, print out the file TUTORIAL.TXT and follow the directions given in that file. If, on the other hand, you have used TK before, you may want to look at some of the models that are supplied with the FREETK package; for instance, LOAN.TK. You can load the model using the Load command (F3). It is also possible to load a model at the same time you start up FREETK. For example, from DOS you can type: FREETK LOAN ─┘ which will start FREETK and then load the model LOAN. NOTES: - Remember that the Help file has to be in the current directory to be accessible. - FREETK is compatible with TK!Solver and TK Solver Plus, but if you load a model that contains objects that cannot be understood by FREETK (e.g. plots, lists, tables, user- defined functions, etc.), FREETK will ignore them. Also if you load a model containing rules that cannot be interpreted by FREETK, those rules will be marked with a % sign (see "Load File"). - FREETK can be configured to your computer system with a FREETK.CFG file (see "Configuration"). - You may find it helpful to read through the rest of the major topics in the Help Index box. 044 CONFIGURATION OF FREETK FREETK can be configured by modifying the EXAMPLE.CFG text file that is provided with the package. This ASCII file contains the default settings and can be modified with a text editor. The default settings are: " TK Solver configuration file Use Color: Yes Slow Redisplay: Yes Solid Line Headings: Yes Bottom Prompt Line: Yes USAGE: - To change the configuration, edit EXAMPLE.CFG and change the "Yes" to "No" for each setting that you want to change. Then save the file under the name FREETK.CFG. - If the FREETK.CFG file is not found in the current directory, FREETK will default to the values above. - If you have a color card, but use a monochrome monitor, you should change the "Use Color" setting to "No." - "Slow Redisplay" set to "Yes" prevents snow from appearing when using color cards with memory which is not dual-ported. If your color card can handle fast redisplay, then change this setting to "No." - If you use the screen-dump feature (shift PrtSc) or the Print command to print parts of the model to the printer, and your printer cannot print graphics characters, "Solid Line Headings" should be set to "No." - If you are familiar with the command structure of TK and you do not need the assistance of the bottom prompt line, you may want to set "Bottom Prompt Line" to "No." - In TK Solver Plus the above configuration can be done by modifying the values on the Global Sheet and saving the values directly from the program with a "Save configuration" command. 053 LIMITS OF FREETK FREETK represents the central components of TK Solver Plus, the equation solvers, complete with an automatic unit conversion feature. The purpose of FREETK is to offer the PC user community at large the taste of rule-based programming applied to numeric computation. Available in FREETK are three out of nine information sheets: Rule Sheet - Variable Sheet - Unit Sheet Present in TK Solver Plus but omitted here are (User-defined) Function Sheet - List Sheet Plot Sheet - Table Sheet - Global Sheet Numeric Format Sheet The names of missing sheets indicate the limits of FREETK: TK Solver Plus works not only with single values but also with lists of values, it plots the results, it provides spreadsheet- like tabular interface, it accepts global settings, and it offers numeric formatting. Most importantly, TK Solver Plus supports so- called user-defined functions that are used for handling empirical relationships, blen- ding numeric and non-numeric information, complementing TK with sequential programs and, generally, turning it into an integrated and open-ended problem-solving environment. FREETK even without all these additional features is a powerful equation processor ready to handle countless real-life problems. FREETK also has limits on the number of lines that can be accessed on its three sheets: 1. Maximum of 32 lines on Variable Sheet. 2. Maximum of 16 lines on Rule Sheet. 3. Maximum of 32 lines on Unit Sheet. 4. Maximum of 32 entries in Disk Index. (Use subdirectories if you have more than 32 files on your disk.) In TK Solver Plus these limits are 32000. Refer to the README.TXT, FTKINTRO.TXT and REFCARD.TXT files for information on TK Solver Plus and FREETK. 015 TOP LEVEL COMMANDS └──┬─────────────┘ ├──────── Function Keys ├──────── Slash Commands └──────── Navigation Commands Move the cursor over one of the Related Topics below and press ─┘. NOTES: - If you need help on Help, press F1. - If you ever need to get back to this screen: Press F1 ─┘ (from within Help). Press F1 F1 ─┘ (from FREETK). 019 FUNCTION KEYS ╔═════════════════════╦═══════════════════════╗ ║ F1: On-Line Help (?)║ F2: Cancel Entry ║ ╠═════════════════════╬═══════════════════════╣ ║ F3: Load File (/SL) ║ F4: Save File (/SS) ║ ╠═════════════════════╬═══════════════════════╣ ║ F5: Edit (Ctrl-E) ║ F6: One-Window (/W1) ║ ╠═════════════════════╬═══════════════════════╣ ║ ║ ║ ╠═════════════════════╬═══════════════════════╣ ║ F9: Solve ║ ║ ╚═════════════════════╩═══════════════════════╝ USAGE: From any sheet, press the desired key and the command (command sequence) will be executed. NOTE: F7, F8, and F10 are for displaying plots, displaying tables, and List Solving, respectively, in TK Solver Plus. 028 NAVIGATION COMMANDS: ─ Moves the cursor to the right ─ Moves the cursor to the left Moves the cursor up one line Moves the cursor down one line ──▌ Moves the cursor to the rightmost field ▐── Moves the cursor to the leftmost field Home Moves the cursor to the top of the sheet End Moves the cursor to the end of the sheet PgDn Moves the cursor N-2 lines down PgUp Moves the cursor N-2 lines up (where N is the number of lines displayed in the current window) = Select Sheet command. It selects the sheet to be displayed in the current window. ; Switch command. If two windows are displayed on the screen, the Switch command moves the cursor between them, otherwise it has no affect. > Dive command. Brings up a relevant subsheet in the current window. < Return command. Brings back original sheet or subsheet. 013 PROBLEM SOLVING WITH FREETK involves three stages: 1. Bringing up the model either by loading an appropriate TK file or by developing the model (i.e. typing in the rules into the Rule Sheet). 2. Formulating the problem (i.e. assigning appropriate input or guess values to selected variables in the Variable Sheet). 3. Solving the model by pressing F9. 017 The VARIABLE SHEET contains information about the variables used in the model. Each row can contain data related to one variable. There are VARIABLE SUBSHEETS containing more information about each variable; items entered into fields in the Variable Sheet are updated simultaneously in corresponding fields in Variable Subsheet. ACCESS: - Type =V to display it in the current window. - Type /WV from one-window display to display it in the second window. - Use the Dive command (>) to see the Variable Subsheet associated with a specific variable. 010 The RULE SHEET contains the equations for a model. Each row can contain one equation and its status (and, optionally, a comment following a double quote, " ). ACCESS: - Type =R to display it in the current window. - Type /WR from one-window display to display it in the second window. 010 The UNIT SHEET contains definitions for conversions between units of measurement used in a model. Each row in the Unit Sheet defines a conversion between two units of measurement. ACCESS: - Type =U to display it in the current window. - Type /WU from one-window display to display it in the second window. 030 UNIT SHEET FIELDS FROM Field: Contains the first unit. TO Field: Contains the second unit. MULTIPLY BY Field: Contains the unit conversion factor, i.e. number of second units equivalent to a single first unit. If left blank, a factor of 1 is assumed. ADD OFFSET Field: Contains the value in the second unit equivalent to a value of zero in the first unit. If left blank, an offset of 0 is assumed. NOTE: MULTIPLY BY and ADD OFFSET fields accept any valid numeric value or expression. EXAMPLES: 1. Conversion from degrees Celsius to degrees Fahrenheit is defined by a conversion factor of 1.8 (may be entered as 9/5) and an offset value of 32. 2. Conversion from radians to degrees may be defined by a conversion factor of 180/pi() which evaluates into 57.2957795131 . 033 UNIT CONVERSION The Unit Conversion feature in FREETK works as follows: - Each variable may be optionally assigned a Calculation Unit and a Display Unit. - All calculations are performed in Calculation Units and the input and output values are displayed in Display Units. - The Display Units are defined in the Unit Fields in the Variable Sheet. - A Display Unit entered into a blank Unit Field also becomes a Calculation Unit. - Both Calculation and Display Units may be changed in the appropriate fields in the Variable Subsheets. - When the Display Unit is changed the input or output value is converted instantaneously. - The conversion is performed according to the unit conversion definitions in the Unit Sheet. NOTES: - The assigned Calculation Units must be consistent with the usage of the variables in the rules. - The unit conversion may be defined indirectly. For instance, if the conversions in/cm, ft/in and m/cm are defined, the conversion between ft and m is automatically defined. - If the conversion between the Calculation Unit and the desired Display Unit is not defined in the Unit Sheet, a question mark (?) appears in front of the value. 036 The EXAMINE command (/E) has three options: Variable, Expression, and Copy. The VARIABLE option allows you to EXAMINE the value of a variable when debugging the model or analyzing error conditions. USAGE: - Type /EV. - Enter variable name and press ─┘. The EXPRESSION option allows you to EXAMINE the value of an expression when debugging the model or analyzing error conditions. USAGE: - Type /EE. - Type in the expression and press ─┘. The COPY option allows you to copy the field highlighted by the cursor onto the Prompt/Error line. Depending on contents, this text may be evaluated as an expression immediately or after editing. USAGE: - Type /EC. - Type F5 for editing, if necessary - Press ─┘ for evaluation NOTE: - The Expression option or Copy option can also be used as a calculator: just type /EE or /EC and the expression you want to evaluate. 020 STATUS Field PURPOSE: Shows the status of the variable and may be used for changing the status. The default is blank. A > symbol indicates that the vari- able is involved in an error condition. SELECTING OPTIONS: Type into the Status field the first letter of the option you want to apply: I - current value will be assigned as input (equivalent to entering that value in the Input field) O - current value will appear in the Output field B - blanks the Input or Output field G - current value will be assigned as a guess (this is a toggle switch) 016 INPUT Field DESCRIPTION: Contains the input value for a variable. VALID ENTRIES: - A numeric or a symbolic value. - A syntactically correct expression that evaluates to a numeric or a symbolic value. NOTE: If a variable is assigned units, its value appears in the Display Unit. (If the con- version between Display Unit and Calculation Unit is not defined in the Unit Sheet, a ? precedes the displayed value.) 008 NAME Field DESCRIPTION: Contains the name of a variable. VALID INPUTS: - TK name (NO DUPLICATES ALLOWED WITHIN A NAME FIELD COLUMN ON A SHEET). 017 OUTPUT Field DESCRIPTION: Contains the output value of the variable if the variable has one. USAGE: - FREETK uses the Output field for displaying the solution results. - An input value or a blanked (but internally held) value may be moved to the Output field by typing letter O in the Status field. - If a variable is assigned units, its value appears in the Display Unit. (If the con- version between Display Unit and Calculation Unit is not defined in the Unit Sheet, a ? precedes the displayed value.) 023 UNIT FIELD, Variable Sheet defines the Display unit used to display the value of the variable. USAGE: - Typing a unit name into a blank Unit field ALSO defines the Calculation unit. - Typing another unit name changes ONLY the Display unit. - The Calculation unit may be changed in the Variable Subsheet. - When you change the Display unit, the variable value changes instantaneously provided that the conversion between the Display and Calculation units is defined directly or indirectly in the Unit Sheet. If a conversion is not defined, a ? will appear in front of the value. - Blanking out the Unit field in the Variable Sheet will blank out both the Display and Calculation unit fields in the associated Variable Subsheet. 010 The COMMENT Field USAGE: - Use for commenting your model. - Accepts any typeable characters. NOTE: If you want to include or append a comment in the Rule Sheet, precede the comment with a double quote ("). 018 FIRST GUESS Field DESCRIPTION: Contains a blank or the default guess value you specify for the variable. USAGE: Serves for automatic assignment of the spe- cified value as a guess and initiation of the Iterative Solver. It works when the variable is not assigned an input value, cannot be evaluated by the Direct solver, and is not assigned another guess value manually. VALID INPUTS: - A numeric value. - An expression that evaluates into a numeric value. 012 CALCULATION UNIT The Calculation Unit may be assigned to a variable by: - entering its name in the Calculation Unit Field of the associated Variable Subsheet, or - entering its name into a blank Unit Field in the Variable Sheet (in that case it becomes a Display Unit as well). See "Unit Conversion" for the role of calculation units in FREETK. 013 DISPLAY UNIT The Display Unit may be assigned to a variable by: - entering its name into the Unit Field in the Variable Sheet (if the field is blank, then the Display Unit becomes a Calculation Unit as well), or - entering its name into the Display Unit Field of the associated Variable Subsheet. See "Unit Conversion" for the role of display units in FREETK. 019 The STATUS Field shows the status of the rule: - A blank indicates a successful solution of that rule. - An asterisk (*) indicates an unsolved rule. - A C indicates that the rule is switched off. - An error symbol (>) indicates an error during the evaluation of the rule. - A % indicates an unparsed rule. The rule probably refers to a user-defined function that was defined in TK!Solver or TK Solver Plus. USAGE: - Place the cursor in the field to display an explanatory message on the Status line. If there is an error symbol > press F1 for a help screen explaining the error. - Press C to switch the rule off or on. 011 RULE Field DESCRIPTION: Accepts equations according to the conventions for valid TK rules. NOTE: A Rule field can also contain a comment. FREETK regards all text after a quotation mark (") in a Rule field as a comment, not subject to evaluation by the solvers. 030 COMPARISON TOLERANCE DESCRIPTION: The Comparison Tolerance (CT) and the Typical value (TV) serve for checking the consistency of rules. A rule is considered satisfied and an equation is presumed to hold if either RELERR ≤ CT or MABVAL ≤ CT * TV , where relative error RELERR = ABSERR / MABVAL absolute error ABSERR = abs(LHE-RHE) maximum absolute value MABVAL = max(abs(LHE),abs(RHE)) LHE,RHE are values of left-hand side and right-hand side expressions. The CT and TV parameters play important role in controlling the Iterative Solver and terminating the iteration upon successful completion. NOTE: In FREETK CT = .000001 and TV = 1 . In TK Solver Plus these parameters may be changed on the Global Sheet, in order to fine-tune the solvers to specific needs. 028 TYPICAL VALUE DESCRIPTION: The Typical Value (TV) in conjunction with the Comparison Tolerance (CT) serves for checking the consistency of rules, and, in particular, for deciding on successful completion of iteration. A rule is considered satisfied and an equation is presumed to hold if max(abs(LHE),abs(RHE)) ≤ CT * TV where LHE,RHE are values of left-hand and right-hand side expressions If this condition is not satisfied, the 'relative error ≤ CT' criterion is used for checking the rule consistency. In FREETK there is a fixed TV=1. In TK Solver Plus this parameter may be changed on the Global Sheet and thus the checking criterion adjusted to the order of magnitude of computed values. 027 STATUS LINE The Status Line is the top line on TK screen. It contains the following information (from left to right): - Information related to the current cursor position: - row number and field label, - field name, - field contents (e.g. full internal representation of a numeric value with up to 16 significant digits). - Memory Indicator, approximate amount of unused memory, in kbytes. - Solution Indicator, shows the status of the Variable Sheet: OK -- indicates no change in the Variable or Rule Sheet since the last solution, i.e. the displayed output values may be trusted, F9 -- there has been a change, and the Solve command F9 should be invoked to restore the integrity of the sheets' contents. 012 PROMPT/ERROR LINE The Prompt/Error Line is the second line on TK screen. It serves for - displaying error messages and prompts, - indicating which solver is being used, - entering names of files to be loaded, saved or deleted, - specifying variables or expressions to be evaluated with the /E commands, and - typing in other command-related information. 030 WILDCARDS or GLOBAL FILENAME CHARACTERS are special characters you can use within a filename and extension to specify a group of files to be displayed in the Disk Index. ? indicates that any character can occupy the given position (question mark in TK must be typed by pressing Ctrl-Q because ? invokes Help), * indicates that any character can occupy the given position and all the remaining positions in the filename or extension. EXAMPLES: 1. F3 rlc??a ─┘ will bring up RLC01A.TK, RLC05A.TK and RLC23A.TK in the Disk Index, and will ignore RLC01B.TK, RLC23B.TK and RLC01AB.TK . 2. F3 rlc0* ─┘ applied to the same directory will bring up RLC01A.TK, RLC05.TK, RLC01B.TK and RLC01AB, and it will ignore RLC23A.TK and RLC23B.TK . 030 ARITHMETIC OPERATIONS are (in order of precedence): ^ exponentiation + - unary plus and minus * / multiplication and division + - addition and subtraction NOTES: - Operations at the same precedence level are performed from left to right, except for exponentiation operations, which are performed from right to left. - When arithmetic and relational operators are combined, the relational operators have the lowest precedence level. - The order of operations may be controlled by parentheses. EXAMPLES: 1. 2 + 3 * 4 evaluates into 14 2. (2+3) * 4 evaluates into 20 3. 4e150 / 2e180 * 3e200 evaluates into 6e170 4. 4e150 * 3e200 / 2e180 causes exponent overflow 5. 4 ^ 2 ^ 3 evaluates into 65536 6. (4^2) ^ 3 evaluates into 4096 7. 3 > 2 > 4 evaluates into 0 8. 3 > (2>4) evaluates into 1 9. 2 < 3 * 4 evaluates into 1 10. (2<3) * 4 evaluates into 4 018 INDETERMINATE EXPRESSIONS When evaluating expressions, the values of operands or function arguments may be available, but the information they carry may be insuffi- cient to determine the result. There are seven such situations in TK: x = 0/0 0 = 0^x 1 = 1^x x = 0^0 1 = x^0 x = atan2(0,0) x = atan2d(0,0) (the unknown x cannot be evaluated from any of these equations) TK ignores an indeterminate expression when encountered, and leaves the rule 'unsatisfied'. 016 SCREEN COMPOSITION The FREETK screen consists of - Message Area: Top two lines called Status Line and Prompt/Error Line. - Information Area: Lines 3 through 24, may contain one or two windows with TK sheets. The windows may be split or unsplit using the Window command, /W, and the sheets may changed using the Select Sheet command, = . - Bottom Prompt Line (optional, may be turned off by an appropriate setting in the configuration file). 022 ITERATION COUNT The steps performed by the Iteration Solver are counted and the current step numbers are displayed during the iteration on the Prompt/ Error Line. In FREETK the Maximum Iteration Count is set to 10. If the Iterative Solver does not find a solution within 10 steps, it stops, FREETK beeps, and the latest guess values and the flag G remain in the Input and Status fields respectively. You may press F9 again. If the Iterative Solver just needed more steps, there is a chance that it will eventually converge to the solution. (It is more likely, however, that the iteration diverged, and you should try again with different guess values and/or variables.) NOTE: In TK Solver Plus the Maximum Iteration Count may be set on the Global Sheet according to the needs of a particular problem. 018 CONVERGENCE FACTOR is displayed during iteration on the Prompt/ Error Line. It shows the progress of the Iterative Solver toward the solution. The Convergence Factor is defined as ln ( ABSERR / (CT*TV) ) (see explanation of terms in "Comparison Tolerance") If there are more guesses and error terms than one, the maximum ABSERR (i.e. the bottleneck) is used. The iteration is usually considered successful when the convergence factor falls below zero. 015 QUESTION MARK, ? The Question Mark's main role in FREETK is invocation of Help (though, pressing the function key F1 serves the same purpose). The most frightening event for the uninitiated is the appearance of ? in front of an input or output value in the Variable Sheet. It indi- cates an error in the unit specification or a missing unit conversion (check the Unit Sheet!). If you wish to use the character ? (e.g. in a comment), you have to type it by pressing Ctrl-Q, because typing ? invokes Help. 083 S O L V E R S FREETK and other versions of TK Solver program employ two major mechanisms for solving mathe- matical problems numerically: - the Direct Solver using a consecutive sub- stitution procedure, and - the Iterative Solver using a modified Newton- Raphson procedure on top of the Direct Solver. The main strength of TK is detecting and per- forming automatically any inverse operations required in the process of solving equations or satisfying rules and constraints. This technique covers what is commonly known as 'backsolving' or 'goal seeking'. EXAMPLES: 1. If y = sin(x) is stated and y is known, TK takes arc sine of y to evaluate x . 2. If ln(a) = b + c*d is stated (spelling out addition and multiplication), and a,b,c are known, TK uses subtraction and division to evaluate d=(ln(a)-b)/c . 3. If or(sick,tired)=and(home,rest) is stated, and "tired" is known to be 1 (true), then the Direct Solver infers that one should stay home=1 and have rest=1 ; it doesn't matter "sick" is known to be 1 or 0 , or if it is unknown. TK action in most applications comes down to solving one or more equations, linear or non- linear, algebraic or transcendental (hence the epithet 'equation processor'). Typically there are m independent equations with n unknowns (m<n). Possible outcomes of applying the solvers are as follows: - Values of n-m variables are given, the Direct solver solves for m unknowns. - The same, the Iterative Solver solves for m unknowns. - The same, solution not completed because of indeterminacy condition. - The same, solution not completed because of domain error. - The values of less than n-m variables given, solution is incomplete. - The values of more than n-m variables given, one of the equations becomes inconsistent, and the solution process is terminated. EXAMPLES (in order of the above cases): Assume two equations with four variables: a * (.5+x)^2 = sin(y/2) b * (y-pi()) = ln(x) 1. x=1.5 and y=2 assigned as inputs; Direct Solver returns a=.21036775 and b=-.3551749. 2. a=.2 and b=-.5 assigned as inputs and x is made guess = 1.5; Iterative Solver returns x=1.6085001 and y=2.1909884. 3. a=4/9 and y=pi() assigned as inputs; Direct Solver evaluates x=1 from the 1st equation, and the 2nd is ignored because of b=0/0. 4. a=pi() and y=4/9 assigned as inputs; Direct Solver returns x=-.2351325 from the 1st eq-n, and solution stops on attempt to take ln(x). 5. only a=pi() assigned as input; nothing is evaluated. 6. b=-.5, x=1.5 and y=2 assigned as inputs; Direct Solver evaluates a=.21036775 from the 1st equation and stops on inconsistency error in the 2nd. The solvers form the basis of TK's declarative nature. They are complemented in TK Solver Plus by user-definable procedures, i.e. sequential programs for specific tasks that are hard or impossible to accomplish in the purely declarative FREETK (e.g. solving differential equations). 014 ZERO-BY-ZERO DIVISION is one of seven indeterminate expressions that are ignored when encountered by the solvers. The 0/0 constructs may be used as an alternative to conditional rules. EXAMPLE: a + b = GIVEN('x,'y,c*d,0/z) (if x and y are assigned input values then the rule is a+b=c*d; else, if z<>0 then the rule is a+b=0, and if z=0 then the rule is ignored and bypassed by the solvers) 017 B E E P indicates that FREETK was unable to follow a command and/or complete an action because some error conditions developed, or because the command or action was terminated by pressing F2 or Ctrl-Break. In most error situations FREETK displays an error message, and provides additional explana- tion when F1 or ? is pressed for Help. In some cases (such as trying to move the cursor beyond the sheet boundary or FREETK limits) it just beeps. When in Help, your illegal actions produce a deeper 'thud'. 066 TROUBLESHOOTING Most of the problems encountered when using FREETK are not caused by the program doing something wrong, or even by lack of TK skills on your part (that, anyway, should be remedied by resorting to the Help frequently). More often than not trouble comes from half- baked or unfit mathematical models and/or infeasible input data or constraints. In fact, TK may be useful in sorting out mathematical and other fallacies. EXAMPLE: How long would it take to repay a $100,000 loan at 10% interest with a monthly payment of $500? You can protect TK and your- self from such absurd questions by letting your model check for an infinite payment term. Here are a few troubleshooting hints: - Check the balance of number of equations, total number of variables, number of inputs and number of unknowns. There is no way (TK or other) to solve for more unknowns than the number of independent equations. - Mimic the Direct or Iterative Solver path to find out what unknown is evaluated by what equation. - Use toggle switch C (in the rule's Status field) to 'turn off' the selected equations and isolate trouble spots. - Add error terms to equations showing incon- sistency, and test them. - Use the Examine (/E) command to check on variables and expressions. - Beware of the hard-to-predict effects of conditional rules. - Pay serious attention to the selection of guess variables and choice of guess values. - Consider two or more roots or solutions to your problem when applicable. - Remember that the sqrt function returns a positive root although the negative one may be appropriate; likewise inverse trigonometric functions return principal values. - Try to avoid the iteration process straying into the regions of argument errors (easier to say than to do; it may take some luck and some sleuthing assisted by TK itself, i.e. turning the knowns and unknowns around, checking the error terms at the trouble spots, trying alternative ways, etc.). - Beware of divergence when using the Iterative Solver. Refer to the FREETK follow-up package (see FTKINTRO.TXT) or numerical analysis lite- rature for information about inner workings of the Newton-Raphson procedure. The full TK Solver Plus with list solving, graphics, procedure functions, interactive tables, etc. is much better equipped for thorough diagnostics and efficient trouble- shooting than FREETK. 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