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.r:e MathPad, Version 1.0 August 20, 1987 MathPad (copyright 1987) is a scientific calculator for the IBM computers and compatibles. Features include: * addition, subtraction, multiplication, division, reciprocals, factorials. * raising to a power, extraction of roots, integer of a number, fraction of a number, squares and cubes, square roots. * exponential and logarithmic calculations (including natural logs, base 10, base 2). * full trigonometric capability including inverse and hyperbolic trig functions (selectable in degrees or radians). * summation of a series of numbers, automatic calculation and storage of mean, standard deviation, and variance. * coordinate conversion (polar to rectangular, rectangular to polar). * angle measure conversion (degrees to radians, radians to degrees). * calculation of permutations and combinations. * user-defined functions which are (a) solvable, via a half-interval search method, and (b) numerically integrable via user-selectable 20 point Gaussian quadrature or Trapezoidal Rule. * solution of up to eight simultaneous linear equations, with calculation of the determinant of the coefficient matrix as well as its inverse matrix. * (two) vector analysis, with dot and cross products, vector addition and subtraction. In addition, MathPad makes available twenty-six storage locations, (called REGISTERS), which are fully manipulable in terms of storage, recall, viewing, and erasure. Also, calculations are stack oriented. This means numbers are entered onto an existing stack of numbers four numbers deep. Some functions (addition, subtraction, etc., coordinate conversion, raising a number to a power) use the first two numbers on this (always completely visible) stack. Other functions, such as reciprocal, degree to radian conversion (and vice versa) use only the top stack element. Instructions and examples are given upon entry into more involved parts of MathPad, such as function definition. Please study this manual and have it handy as you begin learning to use MathPad. The goal has been to retain power in MathPad while making it understandable and easy to use for people with a basic high school math background. MathPad requires 204K of memory to run. It is not memory resident. I welcome comments, suggestions, and criticisms of any kind about MathPad. I will be delighted to credit in the manual anyone suggesting a refinement included in the next version of MathPad. Many thanks to my wife Kathie. I would not have finished this project without her steadfast, interested, and enthusiastic involvement. Tim Pera 605 Portland Ave. #1 St. Paul, MN 55102 MathPad Version 1.0, page 2 MAIN MENU To start, type the program name, MathPad, at the DOS prompt and press the carriage return (enter) key. This screen appears (here slightly modified): ╔════════════════════════════════════════════╗ ╔══════════════════════════════╗ ║ Top Input Area ║ ║ Stack Registers: ║ ║ ║ ╟──────────────────────────────╢ ╠════════════════════════════════════════════╣ ║ x: 0 ║ ║ Main Menu. ║ ║ y: 0 ║ ╠══════════════════════╤═════════════════════╣ ║ z: 0 ║ ║ F1 Utilities │ F2 Operations ║ ║ t: 0 ║ ╟──────────────────────┼─────────────────────╢ ╠══════════════════════════════╣ ║ F3 Arithmetic │ F4 Trig functions ║ ║ Storage Registers: ║ ╟──────────────────────┼─────────────────────╢ ╟──────────────────────────────╢ ║ F5 Int, Frac, Roots │ F6 Log functions ║ ║ 1: 0 ║ ╟──────────────────────┼─────────────────────╢ ║ 2: 0 ║ ║ F7 Store │ F8 Recall ║ ║ 3: 0 ║ ╟──────────────────────┼─────────────────────╢ ║ 4: 0 ║ ║ F9 Interchange x,y │ F10 Roll the stack ║ ║ 5: 0 ║ ╠══════════════════════╧═════════════════════╣ ║ 6: 0 ║ ║ ║ ║ 7: 0 ║ ║ ║ ║ 8: 0 ║ ║ ║ ║ 9: 0 ║ ║ Small Window ║ ║ 10: 0 ║ ║ ║ ║ 11: 0 ║ ║ ║ ║ 12: 0 ║ ║ ║ ║ 13: 0 ║ ╚════════════════════════════════════════════╝ ╚══════════════════════════════╝ Figure 1. Figure 1 shows a view of the Main Menu, as you can see by the title between the two sets of double lines near the upper left corner. All Menus accessible from this Main Menu will be similarly identified by a name located between this same set of double lines. This is a modified view of MathPad, i.e. the phrases "Small Window" and "Top Input Area" are shown only here to orient you to different areas of the MathPad screen. Several interactions with MathPad occur in the Small Window and Top Input Area. To the right are the Stack Registers and Storage Registers. While some MathPad functions will completely overwrite the left side of the screen, the Registers remain always visible. Figure 1 reveals the basic strategy behind using MathPad: identify the operation you wish to perform and press a Function Key to perform it. At the Main Menu are six submenus from which to choose, via the function keys F1 through F6, as shown. Since function keys F7 through F10 invoke the same procedures on all Menus except the Operations Menu and the Utilities Menu, these four procedures will be described first. TO EXIT MathPad: type an "x" or an "X" at the Main Menu (only) and press the carriage return. You are asked for confirmation to quit. MathPad Version 1.0, page 3 STORE The last four function keys, F7 through F10 access the four functions shown (Store, Recall, Interchange x,y, Roll the Stack) on each Menu except the Operations Menu and Utilities Menu. Notice that when F7 is pressed the Small Window at the bottom left opens up to initiate storage procedures. The Small Window during Store looks like this: ┌────────────────────────────────────────────┐ │ These registers contain zero: │ │ │ │ 1 2 3 4 5 6 7 8 9 │ │ 10 11 12 13 14 15 16 17 18 │ │ 19 20 21 22 23 24 25 26 │ │ │ │ Enter storage register number: _ │ └────────────────────────────────────────────┘ Figure 2. What number are you storing? In all cases, invoking storage procedures by pressing F7 means storing a COPY of the value in Stack Register x (top right screen in Figure 1) in the Storage Register (bottom right screen) you specify. Notice that only Storage Registers one through thirteen are initially visible. At all times, storing a value in one of the thirteen Storage Registers not visible toggles the Storage Registers so it DOES become visible. If any registers contain the value zero, that message is given (as shown) and the register(s) listed (see Figure 2). In this way you are informed that choosing to store a value in a register not listed means overwriting a value you may wish to preserve. The cursor blinks on the bottom line waiting for you to enter a Storage Register number. A carriage return here will cancel this procedure and return you to the Menu from which storage procedures were invoked, be it the Main Menu, Arithmetic Menu, etc. There are twenty-six Storage Registers so you must enter an integer between 1 and 26 inclusive. Out of range and illegal input (described below) is erased and MathPad awaits a valid number, or a carriage return to cancel storage procedures. A two-digit number entered here should not be followed by a carriage return; a one-digit number must be followed by a carriage return. ──────────────────────────────────────────────────────────────────────────────── RECALL Pressing F8 (from nearly all Menus) begins Recall activity. The message in Top Input Area reveals that a number from a Storage Register is about to be recalled and put into Stack Register x. Whenever Recall is executed, a value from a Storage Register you specify is put into the x-register. The same rules apply: (a) enter a number from 1 to 26 inclusive, (b) illegal input is erased and MathPad awaits legal input, and (c) a carriage return cancels the activity and returns you to the preceding Menu. MathPad Version 1.0, page 4 INTERCHANGE x,y F9 is very simple: in all cases it interchanges the values in the x- and y- Stack Registers. Thus what was in the y-register is placed into the x-register and vice versa. The z- and t-registers are unaffected. The options to Interchange x,y and to Roll the Stack (described below) are provided because some two-number calculations in MathPad require values of certain variables to be in specific Stack Registers. For example, polar to rectangular coordinate conversion assumes the x-register value is the radius and the y- register value is the angle measure. The procedures Interchange x,y and Roll the Stack provide for adjusting incorrect order without re-entering numbers. ──────────────────────────────────────────────────────────────────────────────── ROLL THE STACK F10 interchanges all values in the Stack Registers. It works this way: After pressing F10, what was in t-register is now in the z-register, what was in z-register is now in the y-register, y...x, x...t. Think of it as pushing up on the stack with everything moving up one register. The "lid" (the x- register value) pops off and assumes the z-register position. Pressing F10 four times in succession restores the original order. Enter four different numbers and experiment with F10. You will quickly see how it works. ──────────────────────────────────────────────────────────────────────────────── ENTERING NUMBERS Entering numbers is very easy in MathPad. If you do not have MathPad running, please start it now. A diamond shaped symbol and a blinking cursor, along with this message: Enter a number or press a Function Key. occupy the Top Input Area. This signals that you have the option of pressing a function key or entering a number. There are several things to keep in mind about entering numbers: (a) When you attempt to enter a number, only legal numeric symbols are accepted. The symbols are: i. the 10 digits (0 through 9), ii. the decimal point (period key), iii. the negative (minus) sign, iv. "e" and "E". All other (illegal) symbols are not displayed and MathPad waits for a legal symbol. (See examples below of legal and illegal number entry.) (b) Input is not allowed to spill past the first vertical double line to the right of the diamond input prompt. Attempting to enter numbers past this physical screen location forces an automatic carriage return and the number thus entered is displayed in Stack Register x. That number at the input prompt disappears. At this point the blank line beyond the diamond prompt, and blinking cursor, mean you may enter another number or press a function key to perform a calculation. In other parts of MathPad you will enter numbers at a prompt not located in the Top Input Area. But when you DO enter a number at the diamond prompt, it always ends up in Stack Register x. And it is there (at Stack Register x) that calculations are performed with it. MathPad Version 1.0, page 5 (c) To edit numeric input, press the backspace key (the left-pointing-arrow key). One press of this key erases the character to the cursor's immediate left. You may erase as many characters with this key as you wish. (d) You may enter numbers either with or without a modified scientific notation. In the former case, the symbols "e" and "E" are equivalent and always interchangeable. An integer following "e" or "E" represents the power to which the number 10 is raised. The result then multiplies the number appearing before the "e" or "E". A negative integer appearing after "e" or "E" is legal. Example: 2.34e11 and 2.34E11 both represent the number 2.34 times 10 raised to the eleventh power. Not using scientific notation, this number can be represented as 234000000000. Example: 0.18e-3 and 0.18E-3 both represent the number 0.18 times 10 raised to -3 power. Not using scientific notation, this number can be represented as 0.00018. Here are some examples of legal and illegal number entry: Legal: Illegal: 1 e4 ("e" and "E" must be preceded 1.23 E6 by a number.) -2.2E3 (= -2200) 2.3e.6 ("e" and "E" must be followed -.032 by an integer, not a decimal.) 1e6 (= 1000000) 1E2 (= 100) 23E45 (= 23 times 10 to the 45th power) 4.e4 (the decimal point is ignored, = 40000) 5.67E-2 (= .0567) Experiment with entering numbers. ──────────────────────────────────────────────────────────────────────────────── UTILITIES ┌───────────────────────────────────────────┐ │ 1. Toggle register contents. │ │ 2. Erase stack. │ │ 3. Erase registers. │ │ 4. Fix decimal point. │ │ 5. DOS shell. │ │ 6. Redraw screen. │ └───────────────────────────────────────────┘ F1 invokes the Utilities Menu. Utilities is available on nearly all Menus, and always (and only) by pressing F1. The options are displayed in the Small Window. They are: 1. TOGGLE REGISTER CONTENTS. Typing a 1 here (no carriage return is required when choosing options in Utilities) will cause the unseen half of the twenty-six Storage Registers to become visible in the lower right-hand corner of the screen. MathPad Version 1.0, page 6 2. ERASE STACK. The numbers in the x-, y-, z-, and t-registers are irretrievably (unless stored) lost and replaced with 0. 3. ERASE REGISTERS. The values in all Storage Registers are irretrievably lost (unless recalled to Stack Registers) and replaced with 0. After exercising any of the above three options you are left at the Utilities Menu. Press the carriage return to return to the Menu from which Utilities was invoked. 4. FIX DECIMAL POINT. MathPad always performs calculations using numbers with fifteen decimal places, called DOUBLE PRECISION numbers. MathPad shows numbers using all fifteen decimal places unless you specify a different number of decimal places to show. In all your calculations you have to be the judge of how many displayed digits are meaningful. You may choose how many of those decimal places to view. After typing 4 at the Utilities Menu, this message appears in the Top Input Area: Fix decimal point in stack and registers. How many decimal places (max = 15) ? _ Enter an integer between 1 and 15 inclusive. It is not necessary to press the carriage return after two-digit entry. Illegal characters are not displayed. From this point on all register values are displayed to the number of decimal points just specified. Only calculations done on the stack (such as add and multiply) are affected by "Fix decimal point" operations. For example, the inverse matrix in "Linear System" and the determinant and solutions calculated there are always displayed to fifteen decimal places although, as implied, often not all decimal places are significant. If you specified the number of decimal places TO SHOW as 4 however, the determinant that is automatically put in the x-register is shown to four decimal places. Likewise, if you choose to store the solutions, they are displayed to four decimal places in the Storage Registers. It is important to know however that in all cases calculations are performed in "double precision". This means that when you recall and calculate with a stored value that is displayed in a Storage Register to say six decimal places, the calculation is done with the double precision "twin" of that number, which MathPad always retains separately. If you choose to show less than fifteen decimal places, MathPad rounds displayed numbers up or down depending on the digit to the right of the right-most digit you wish to view. If the digit to the right of the right- most digit you wish to view is less than 5, then the digits you do not want displayed appear simply to have been chopped off. If the digit to the right of the right-most digit you wish to view is greater than or equal to five, then the right-most digit seen is one greater. For example, suppose you want numbers shown to six decimal places. Then .094657230123613 is shown as .094657 since 2 to the right of 7 is less than 5. .794250527128819 is shown as .794251 since 5 to the right of 0 is greater than or equal to 5. MathPad Version 1.0, page 7 5. DOS SHELL. Typing 5 here causes MathPad to turn control over to the Disk Operating System (DOS), where another program may be run or DOS housekeeping chores may be performed. When you wish to return to MathPad, type the DOS command EXIT at the DOS prompt (upper or lower case) and press the carriage return. You will return to MathPad at the point of exit (actually, at the Menu from which Utilities was called, from which then the DOS shell was invoked), with everything as it was when you left MathPad. All functions previously defined are preserved, as well as the most recent Integration and Solve results and all thirty Register values. ┌───────────────────────────────────────────────────────────┐ │ *** The DOS shell requires DOS VERSION 3.0 or higher. *** │ └───────────────────────────────────────────────────────────┘ 6. REDRAW SCREEN. In case unforeseen events occur that make the screen difficult to read, type 6 to redraw the screen while preserving every- thing stored in memory. This is nothing more or less than a screen redraw. ──────────────────────────────────────────────────────────────────────────────── OPERATIONS MENU ┌───────────────────────────────────────────┐ │ F1 Utilities F2 Statistics │ │ F3 (x,y) to (r,Θ) F4 Deg to rad │ │ F5 P(y,x), C(y,x) F6 Define function │ │ F7 Integrate F8 Solve │ │ F9 Linear system F10 Vector math │ └───────────────────────────────────────────┘ Focusing again on the Main Menu (Figure 1.), pressing F2 summons the Operations Menu. F1: UTILITIES. Whenever you press F1 to invoke Utilities, on this and on all Menus, the same options are available as described in Utilities above. F2: STATISTICS. Invokes a procedure which sums a series of numbers. As each number is entered the following information on the screen is updated: the most recently entered value, the sum of all values so far entered, and how many numbers have been entered so far. A carriage return signals end of input, after which the mean, standard deviation, variance, the number of numbers summed, and the sum itself are displayed. These statistics are automatically stored in Storage Registers 21 through 26. Options exist to (a) store a second copy of these statistics in Storage Registers 17 through 21 (in case you wish to sum a second series and not overwrite the previous results) and (b) to review the numbers you entered. F3: Rectangular to polar, polar to rectangular coordinate conversion. You may select which conversion to perform. For rectangular to polar conversion, x- and y- (Cartesian) coordinates are assumed to be in the x- and y-registers. For polar to rectangular conversion, r (radius) and Θ (angle measure in degrees or radians) values are are assumed to be in the x- and y-registers. The Small Window opens with several options offered: MathPad Version 1.0, page 8 ┌──────────────────────────────────┬─────────┐ │ Coordinate conversion: │ Mode: R │ │ └─────────┤ │ 1. (x,y) to (r,Θ) │ │ 2. (r,Θ) to (x,y) │ │ 3. Toggle degrees or radians. │ │ │ │ Enter number or <CR> to cancel _ │ └────────────────────────────────────────────┘ Conversion can occur in either degree (D) or radian (R) mode. The current mode is indicated in the upper right-hand corner of the Small Window. Op- tion 3 toggles the mode. Toggling here is global, i.e., the mode in all three trig Menus (explained below) is toggled also. Option 1 performs rectangular to polar conversion, option 2 performs polar to rectangular conversion. Enter the option number only, without a carriage return. The results are shown in the Small Window and are also pushed onto the Stack, with y (or Θ) in the y-register and x (or r) in the x-register. NOTE: A number "pushed onto the Stack" replaces the number previously in the x-register. This also means that: (a) what was in the x-register is now in the y-register, (b) what was in the y-register is now in the z-register, (c) what was in the z-register is now in the t-register and (d) what was in the t-register is irretrievably lost unless previously stored in a Storage Register. F4: CONVERT. This converts degrees to radians or radians to degrees. The Small Window opens up this way: ┌────────────────────────────────────────────┐ │ Convert: │ │ │ │ 1. Degrees to radians. │ │ 2. Radians to degrees. │ │ │ │ Enter number or <CR> to cancel _ │ │ │ └────────────────────────────────────────────┘ Enter the option number only, without a carriage return. The value in the x-register is converted accordingly and is placed in the x-register. F5: PERMUTATIONS AND COMBINATIONS. The Small Window opens and describes what is to be done: The total number of objects (N) should be in the y-register. The number (S) of these objects to be considered at a time should be in the x-register. Permutations and combinations are calculated, shown in the Small Window and pushed on the stack. MathPad Version 1.0, page 9 F6: DEFINE A FUNCTION. Selecting F6 presents these options: (a) define a new function, (b) view a previously defined function and (c) erase all existing functions. Option 1: defining a new function. You may define a function with regular polynomial terms such as 3x² and with trigonometric functions sin, cos, tan, cot, sec, csc. If the function you want to define has terms similar in form to 3x², you are asked to enter the coefficient (3 in this example) and exponent (2 above) for each term separately. There are no default values (i.e., MathPad does not assume a value for you). For example, if your function has the term x you must enter 1 for the coefficient and 1 for the exponent. Similarly, for constant terms (like -3), enter -3 for the coefficient and zero (0) for the exponent. Coefficients and exponents may be any real number. For trig terms, again there are no default values. Four numbers must be entered for each trig term. For example, consider this term: 6∙tan²(-5x²) where the dot means multiplication. For this as for all trig terms, you must enter all four numbers in order from left to right. You will be asked to enter values for A,B,C and D where (in this example) A = 6, B = 2, C = -5 and D = 2. If there are no explicit exponents, enter 1 for B and 1 for D. Also, note that if the example was 6∙tan²(x²) instead of 6∙tan²(-5x²) you would enter A = 6, B = 2, C = 1 and D = 2. Thus you must enter a 1 for implicit coefficients and exponents. Coefficients and exponents may be any real number. Radian measure of the angle x is assumed. F7: INTEGRATE. After a function is defined this option selects numerical integration to compute the definite integral of a function. You select which function to integrate of the (potential) four on the function stack (see note below). The lower and upper limits of integration must be entered as well as the number of sub-intervals over which the integration is to be done. After the integral is computed a calculation summary is displayed in the Small Window Area. For a typical integration the calculation summary looks like this: Most recent results: Function integrated: number 1 Method used: Gaussian quadrature. Lower limit: 5 Upper limit: 6 Intervals : 3 Integral : 5.500000020489097 There are two choices of integration method: 20 point Gaussian quadrature and the Trapezoidal Rule. The calculated integral is placed in the x-register. NOTE: the capability to view the function before manipulating it is provided within the Integrate and Solve options. View the function first to confirm you are dealing with the desired function. This is a good practice for this reason: up to four different functions are retained in memory at any given moment. As functions are defined they are pushed onto a function stack. Assume this stack is empty and you define (and save) a function. This function is now the first function on the stack. Imagine another function is defined and saved. This most recently defined function MathPad Version 1.0, page 10 is now function #1 on the stack. The first function is now function #2 on the stack. Imagine that eventually a fifth function is defined. As that fifth function is saved, the function that was defined first is lost, since it had occupied position #4 prior to saving the fifth function and is now pushed off the stack with this as the fifth function is saved. Thus it is a good practice to view your function before you Integrate or Solve it. F8: SOLVE. You select which function to solve of the potential four on the function stack. View the function before solving. You should make your best guess as to interval in which a root may lie. The search involves evaluating the function at random points within the interval and checking for a change of sign. The prompts guide you through entering the lower and upper limits of the interval. When a sign change is found a root is then approximated. If no sign change is found the assumption is made that no root lies in the specified interval and you are asked to input a new interval. Found roots are put in the x-register. F9: LINEAR SYSTEM. You may solve a system of up to eight simultaneous linear equations. You are asked to specify how many equations your system has. The number of equations must be equal to the number of unknowns. You then enter the coefficient matrix from top row to bottom and left column to right. For example, consider this system of equations: 2∙x1 + 3∙x2 - .5∙x3 - 12∙x4 = 9 5∙x2 + 3∙x3 + 4∙x4 = -3 3∙x1 - 2∙x3 = 0 x1 - x2 - x3 = 1 (x1,x2,x3,x4 are all linear variables. The maximum number of equations solvable in MathPad is eight; in this case, MathPad expects eight unknown linear variables.) This is the coefficient This is the constant matrix for this system: matrix for this system: 2 3 -.5 -12 9 0 5 3 4 -3 3 0 -2 0 0 1 -1 -1 0 1 Put together, these matrices look like this: 2 3 -.5 -12 9 0 5 3 4 -3 3 0 -2 0 0 1 -1 -1 0 1 Enter these values in order from left to right and top to bottom. For the top equation you will input the COEFFICIENTS 2,3,-.5,12 and then, immediately after, the CONSTANT 9. Do this now if you wish. Then, for the second equation enter the COEFFICIENTS 0,5,3,4 and then the CONSTANT -3. You will do the same for the third and fourth equations. (Notice the displayed keywords COEFFICIENT and CONSTANT as you enter numbers.) Here is what MathPad then calculates: (a) the determinant of the coefficient matrix (automatically put into the MathPad Version 1.0, page 11 x-register). (b) the solution to this system, if it exists. You are given the option of storing solutions in Storage Registers you specify. (c) the inverse matrix of the coefficient matrix. This matrix is available for viewing if desired. F10: VECTOR MATH. You are asked to enter the x-, y-, and z- coordinates of two vectors. Then these items are calculated: (a) the magnitude of each vector. (b) the angle in degrees between the vectors. (c) the angle in degrees between each vector and the x, y, and z axes. (d) the vector sum. (e) the vector difference. (f) the vector dot product. (g) the vector cross product. ──────────────────────────────────────────────────────────────────────────────── ARITHMETIC MENU ┌───────────────────────────────────────────┐ │ F1 Add: y+x F2 Subtract: y-x │ │ F3 Multiply: y∙x F4 Divide: y/x │ │ F5 x factorial F6 Reciprocal of x │ │ F7 Store F8 Recall │ │ F9 Interchange x,y F10 Roll the stack │ └───────────────────────────────────────────┘ Pressing F2 from the Main Menu calls up the Arithmetic Menu. F1: Add. The value in the x-register is added to the value in the y-register. The result is placed in the x-register. The stack is "pulled up" so that the y-register contains what was in z-register, the z-register contains what was in t-register, the t-register remains unchanged. F2: Subtract. The value in the x-register is subtracted from the value in the y-register. The result is placed in the x-register. The stack is pulled up. F3: Multiply. The value in the x-register is multiplied by the value in the y-register. The result is placed in the x-register. The stack is pulled up. F4: Divide. The value in the x-register is divided into the value in the y-register. The result is placed in the x-register. The stack is pulled up. F5: x factorial. The factorial of the number in the x-register is calculated and pushed onto the stack. F6: Reciprocal. The reciprocal of the number in the x-register is calculated and replaces the value in the x-register. The stack is not pushed. F7: Store F8: Recall F9: Interchange x,y F10: Roll the stack MathPad Version 1.0, page 12 TRIG MENU ┌───────────────────────────────────────────┐ │ F1 Utilities F2 Toggle deg/rad │ │ F3 Sin F4 Cos │ │ F5 Tan F6 Hyper & Inverse │ │ F7 Store F8 Recall │ │ F9 Interchange x,y F10 Roll the stack │ └───────────────────────────────────────────┘ Pressing F4 from the Main Menu calls up the Trig Menu. F1: Utilities. See above. F2: Toggle deg/rad. This changes the trigonometric mode from degrees to radians. Notice the Mode Indicator on the same line as the Trig Menu title. This indicator is displayed on all three trig Menus. Toggling here is global, i.e., the mode in coordinate conversion (F3 on Operations Menu) is also toggled. F3: Sin: Trigonometric sine. F4: Cos: Trigonometric cosine. F5: Tan: Trigonometric tangent. Sin, Cos, and Tan all replace the value in the x-register; there is no stack push. F6: Hyper and Inverse. Pressing F6 here invokes the hyperbolic and inverse trig functions Menu, explained. F7: Store F8: Recall F9: Interchange x,y F10: Roll the stack ──────────────────────────────────────────────────────────────────────────────── HYPERBOLIC TRIG MENU ┌───────────────────────────────────────────┐ │ F1 Utilities F2 Toggle deg/rad │ │ F3 Hyperbolic Sin F4 Hyperbolic Cos │ │ F5 Hyperbolic Tan F6 Inverse Trig │ │ F7 Store F8 Recall │ │ F9 Interchange x,y F10 Roll the stack │ └───────────────────────────────────────────┘ This Menu is called up by pressing F6 from the Trig Menu. F1: Utilities. See above. F2: Toggle deg/rad. This performs as explained under F2 in the Trig Menu section above. F3: Hyperbolic Sin: Hyperbolic sine. F4: Hyperbolic Cos: Hyperbolic cosine. F5: Hyperbolic Tan: Hyperbolic tangent. Hyperbolic Sin, Cos, and Tan all replace the value in the x-register; there is MathPad Version 1.0, page 13 no stack push. Hyperbolic functions are defined exponentially. For detail see: CRC Standard Mathematical Tables 27th Edition (c) Copyright 1984 by the CRC Press, Inc. Edited by William H. Beyer Page 172 F6: Inverse Trig. Pressing F6 here calls up the Inverse Trig Menu. F7: Store F8: Recall F9: Interchange x,y F10: Roll the stack ──────────────────────────────────────────────────────────────────────────────── INVERSE TRIG MENU ┌───────────────────────────────────────────┐ │ F1 Inverse Sin F2 Inv Hyper Sin │ │ F3 Inverse Cos F4 Inv Hyper Cos │ │ F5 Inverse Tan F6 Inv Hyper Tan │ │ F7 Store F8 Recall │ │ F9 Interchange x,y F10 Roll the stack │ └───────────────────────────────────────────┘ This Menu is called up by pressing F6 from the Hyperbolic and Inverse Trig Menu. F1: Inverse Sin or Arcsin. This function places into the x-register the quadrant I or IV angle (measured in degrees or radians as selected) whose sine is the value in the x-register. F3: Inverse Cos or Arcsin. This function places into the x-register the quadrant I or II angle (measured in degrees or radians) whose cosine is the value in the x-register. F5: Inverse Tan or Arctangent. This function places into the x-register the angle (measured in degrees or radians) whose tangent is the value in the x-register. Inverse Hyperbolic functions are defined logarithmically. For detail see: CRC Standard Mathematical Tables, 27th Edition (complete reference above). Page 181. F2: Inv Hyper Sin (Arcsinh). Inverse hyperbolic sine. F4 Inv Hyper Cos (Arccosh). Inverse hyperbolic cosine. Only the principal value of Arccosh is returned. F6 Inv Hyper Tan (Arctanh). Inverse hyperbolic tangent. F7: Store F8: Recall F9: Interchange x,y F10: Roll the stack MathPad Version 1.0, page 14 INTEGER, FRACTION, ROOTS AND POWERS MENU ┌───────────────────────────────────────────┐ │ F1 Integer of x F2 Fraction of x │ │ F3 Square root of x F4 x squared │ │ F5 x to the y F6 x cubed │ │ F7 Store F8 Recall │ │ F9 Interchange x,y F10 Roll the stack │ └───────────────────────────────────────────┘ This Menu is called up by pressing F5 from the Main Menu. All the functions below act without stack push or pull. F1: Integer. Replaces the value in the x-register with the integer portion of the value in the x-register. F2: Fraction. Replaces the value in the x-register with the decimal portion of the value in the x-register. F3: Square root of x. Replaces the value in the x-register with the square root of the value in the x-register. F4: x squared. Replaces the value in the x-register with the square of the value in the x-register. F5: x to the y. Calculates x-register value exponentiated to the y-register value and places this value in the x-register. F6: x cubed. Replaces the value in the x-register with the cube of the value in the x-register. F7: Store F8: Recall F9: Interchange x,y F10: Roll the stack ──────────────────────────────────────────────────────────────────────────────── LOGARITHMIC FUNCTIONS MENU ┌───────────────────────────────────────────┐ │ F1 Utilities F2 Log base 2 of x │ │ F3 Log base 10 of x F4 10 to the x │ │ F5 Natural log of x F6 e to the x │ │ F7 Store F8 Recall │ │ F9 Interchange x,y F10 Roll the stack │ └───────────────────────────────────────────┘ This Menu is called up by pressing F6 from the Main Menu. F1: Utilities. See above. All the functions below act without stack push or pull. F2: Log base 2 of x. The result of this calculation is the power to which the number 2 must be raised in order to equal the value in the x-register. F3: Log base 10 of x. The result of this calculation is the power to which the number 10 must be raised in order to equal the value in the x-register. MathPad Version 1.0, page 15 F4: 10 to the x. The result of this calculation is the number 10 exponentiated to the x-register value. F5 Natural log of x. The result of this calculation is the power to which the base of natural logarithms (e) must be raised in order to equal the value in the x-register. The value for e used in MathPad is 2.718281828459045 F6: e to the x. The result of this calculation is the base of natural logarithms (e) exponentiated to the x-register value. F7: Store F8: Recall F9: Interchange x,y F10: Roll the stack ──────────────────────────────────────────────────────────────────────────────── NAVIGATION Below is a tree diagram depicting access routes, via described function keys, to MathPad Menus. All Menus except those boxed provide direct access to the Utilities Menu. A carriage return at the diamond input prompt in any Menu returns MathPad to the immediately preceding Menu, as shown in the tree diagram. A carriage return at the Main Menu has no effect. To leave MathPad, type an "x" or an "X" at the Main Menu (only). You are asked for confirmation to quit. Main Menu ───┬─── Operations Menu │ │ ┌──────────────────────────────────────────┐ ├───┤ Integer, Fraction, Roots and Powers Menu │ │ └──────────────────────────────────────────┘ │ ┌─────────────────┐ ├───┤ Arithmetic Menu │ │ └─────────────────┘ │ ┌───────────────────┐ ├─── Trig Menu ─┬───┤ Inverse Trig Menu │ │ │ └───────────────────┘ │ │ │ └─── Hyperbolic Trig Menu │ └─── Logarithmic Functions Menu MathPad Version 1.0, page 16 Below are Menu function key guides which may be printed and kept handy while learning to use MathPad. Main Menu Operations Menu ┌───────────────────────────────────────────┐ ┌───────────────────────────────────────────┐ │ F1 Utilities F2 Operations │ │ F1 Utilities F2 Statistics │ │ F3 Arithmetic F4 Trig functions │ │ F3 (x,y) to (r,Θ) F4 Deg to rad │ │ F5 Int, Frac, Roots F6 Log functions │ │ F5 P(y,x), C(y,x) F6 Define function │ │ F7 Store F8 Recall │ │ F7 Integrate F8 Solve │ │ F9 Interchange x,y F10 Roll the stack │ │ F9 Linear system F10 Vector math │ └───────────────────────────────────────────┘ └───────────────────────────────────────────┘ Arithmetic Menu Trig Menu ┌───────────────────────────────────────────┐ ┌───────────────────────────────────────────┐ │ F1 Add: y+x F2 Subtract: y-x │ │ F1 Utilities F2 Toggle deg/rad │ │ F3 Multiply: y∙x F4 Divide: y/x │ │ F3 Sin F4 Cos │ │ F5 x factorial F6 Reciprocal of x │ │ F5 Tan F6 Hyper & Inverse │ │ F7 Store F8 Recall │ │ F7 Store F8 Recall │ │ F9 Interchange x,y F10 Roll the stack │ │ F9 Interchange x,y F10 Roll the stack │ └───────────────────────────────────────────┘ └───────────────────────────────────────────┘ Inverse Trig Menu Hyperbolic Trig Menu ┌───────────────────────────────────────────┐ ┌───────────────────────────────────────────┐ │ F1 Inverse Sin F2 Inv Hyper Sin │ │ F1 Utilities F2 Toggle deg/rad │ │ F3 Inverse Cos F4 Inv Hyper Cos │ │ F3 Hyperbolic Sin F4 Hyperbolic Cos │ │ F5 Inverse Tan F6 Inv Hyper Tan │ │ F5 Hyperbolic Tan F6 Inverse Trig │ │ F7 Store F8 Recall │ │ F7 Store F8 Recall │ │ F9 Interchange x,y F10 Roll the stack │ │ F9 Interchange x,y F10 Roll the stack │ └───────────────────────────────────────────┘ └───────────────────────────────────────────┘ Integer, Fraction, Roots and Powers Menu Logarithmic Functions Menu ┌───────────────────────────────────────────┐ ┌───────────────────────────────────────────┐ │ F1 Integer of x F2 Fraction of x │ │ F1 Utilities F2 Log base 2 of x │ │ F3 Square root of x F4 x squared │ │ F3 Log base 10 of x F4 10 to the x │ │ F5 x to the y F6 x cubed │ │ F5 Natural log of x F6 e to the x │ │ F7 Store F8 Recall │ │ F7 Store F8 Recall │ │ F9 Interchange x,y F10 Roll the stack │ │ F9 Interchange x,y F10 Roll the stack │ └───────────────────────────────────────────┘ └───────────────────────────────────────────┘ Utilities ┌───────────────────────────────────────────┐ │ 1. Toggle register contents. │ │ 2. Erase stack. │ │ 3. Erase registers. │ │ 4. Fix decimal point. │ │ 5. DOS shell. │ │ 6. Redraw screen. │ └───────────────────────────────────────────┘