Chapter 7 Computer Algebra System and Tutorial Modes 7-1 7-2 7-3 7-4 Using the CAS (Computer Algebra System) Mode Algebra Mode Tutorial Mode Algebra System Precautions 19990401
7-1-1 Using the CAS (Computer Algebra System) Mode 7-1 Using the CAS (Computer Algebra System) Mode On the Main Menu, select the CAS icon to enter the CAS Mode. The following table shows the keys that can be used in the CAS Mode. COPY H-COPY PASTE REPLAY i k Inputting and Displaying Data Input in the Algebra Mode is performed in the upper part of the display, which is called the “ input area.” You can input commands and expressions at the current cursor location.
7-1-2 Using the CAS (Computer Algebra System) Mode If all the result does not fit on the display, use the cursor keys to scroll it. k Performing an Algebra Mode Operation There are two methods that you can use for input in the Algebra Mode. • Function menu command input • Manual formula and parameter input k Menu Command Input Press a function menu key to display the menu of functions for the type of operation you are trying to perform. • TRNS ... {formula transformation menu} • CALC ...
7-1-3 Using the CAS (Computer Algebra System) Mode k Manual Formula and Parameter Input You can use the function menus, K key, and J key in combination to input formulas and parameters as described below. • 3(EQUA)b(INEQUA) t}/{s s } ... {inequality} • {>}/{<}/{t •Kkey • {∞}/{Abs}/{ x!}/{sign} ... {infinity}/{absolute value}/{factorial}/{signum function*1} • {HYP} ... {hyperbolic}/{inverse hyperbolic} functions • {sinh}/{cosh}/{tanh}/{sinh–1}/{cosh–1}/{tanh–1 } •Jkey • {Y}/{ r}/{Xt}/{Yt}/{X} ...
7-1-4 Using the CAS (Computer Algebra System) Mode k Function Memory and Graph Memory Function memory lets you store functions for later recall when you need them. With graph memory, you can store graphs in memory. Press the J key and then input the name of the graph.
7-1-5 Using the CAS (Computer Algebra System) Mode k Answer (Ans) Memory and Continuous Calculation Answer (Ans) memory and continuous calculation can be used just as with standard calculations. In the Algebra Mode, you can even store formulas in Ans memory. ○ ○ ○ ○ ○ Example To expand (X+1)2 and add the result to 2X 1(TRNS)b(expand) (v+b)x)w Continuing: +cvw k Replay Contents Replay memory can be used in the input area.
-1-6 Using the CAS (Computer Algebra System) Mode SET UP Items u Angle ... Unit of angular measurement specification • {Deg}/{Rad} ... {degrees}/{radians} u Answer Type ... Result range specification • {Real}/{Cplx} ... {real number}/{complex number} u Display ... Display format specification (for approx only) • {Fix}/{Sci}/{Norm} ... {number of decimal places}/{number of significant digits}/ {normal display format} k Graph Function Pressing 5(GRPH) displays the graph formula screen.
7-1-7 Using the CAS (Computer Algebra System) Mode Algebra Command Reference The following are the abbreviations used in this section. • Exp ... Expression (value, formula, variable, etc.) • Eq ... Equation • Ineq ... Inequality Anything enclosed within square brackets can be omitted. u expand Function: Expands an expression. Syntax: expand ( {Exp/Eq/Ineq} [ ) ] ○ ○ ○ ○ ○ Example To expand (X+2)2 X2 + 4X + 4 1(TRNS)b(expand)(v+c)xw u rFactor (rFctor) Function: Factors an expression up to its root.
7-1-8 Using the CAS (Computer Algebra System) Mode u solve Function: Solves an equation. Syntax: solve( Exp [,variable] [ ) ] solve( {Exp-1,..., Exp-n}, {variable-1,...,variable-n} [ ) ] ○ ○ ○ ○ ○ Example To solve AX + B = 0 for X 1(TRNS)e(solve)av(A)v+ X=–B A al(B)!.(=)aw ○ ○ ○ ○ ○ Example To solve simultaneous linear equation 3X + 4Y = 5, 2X – 3Y = – 8 1(TRNS)e(solve)!*( { ) da+(X)+ea-(Y)!.(=)f, ca+(X)-da-(Y)!.
7-1-9 Using the CAS (Computer Algebra System) Mode u trigToExp (trigToE) Function: Transforms a trigonometric or hyperbolic function to an exponential function. Syntax: trigToExp( Exp [ ) ] ○ ○ ○ ○ ○ Example To convert cos(iX) to an exponential function 1(TRNS)f(TRIG)d(trigToE)c!a(i)vw ex+ e— x 2 u expToTrig (expToT) Function: Converts an exponential function to a trigonometric or hyperbolic function.
7-1-10 Using the CAS (Computer Algebra System) Mode u combine (combin) Function: Reduces a fraction. Syntax: combine( {Exp/Eq/Ineq} [ ) ] ○ ○ ○ ○ ○ Example To reduce the fraction (X + 1) / (X + 2) + X (X + 3) 1(TRNS)h(combin)(v+b)/ (v+c)+v(v+dw X3 + 5X2 + 7X + 1 X+2 u collect (collct) Function: Rearranges an expression, focusing on a particular variable.
7-1-11 Using the CAS (Computer Algebra System) Mode u approx Function: Produces a numerical approximation for an expression. Syntax: approx Exp ○ ○ ○ ○ ○ Example To obtain a numerical value for 1(TRNS)l(approx)!x( 2 )cw 1.414213562 k About approx Using approx affects the number of digits used to display a calculation result and the way calculations that include variables are performed in the CAS Mode.
7-1-12 Using the CAS (Computer Algebra System) Mode u diff Function: Differentiates an expression. Syntax: diff( Exp [, variable, order, derivative] [ ) ] diff( Exp, variable [, order, derivative] [ ) ] diff( Exp, variable, order [, derivative] [ ) ] ○ ○ ○ ○ ○ Example To differentiate X6 with respect to X 2(CALC)b(diff)vMgw 6X5 • X is the default when no variable is specified. • 1 is the default when no order is specified. u∫ Function: Integrates an expression.
7-1-13 Using the CAS (Computer Algebra System) Mode uΣ Function: Calculates a sum. Syntax: Σ( Exp, variable, start value, end value [ ) ] ○ ○ ○ ○ ○ Example To calculate the sum as the value of X in X 2 changes from X = 1 through X = 10 2(CALC)e(Σ)vx,v,b,baw 385 uΠ Function: Calculates a product.
7-1-14 Using the CAS (Computer Algebra System) Mode u tanLine (tanLin) Function: Returns the expression for a tangent line. Syntax: tanLine( Exp, variable, variable value at point of tangency [ ) ] ○ ○ ○ ○ ○ Example To determine the expression for a line tangent with X3 when X = 2 2(CALC)i(tanLin)vMd,v,cw 12X – 16 u denominator (den) Function: Extracts the denominator of a fraction.
7-1-15 Using the CAS (Computer Algebra System) Mode u rclEqn Function: Recalls multiple eqn memory contents. Syntax: rclEqn( memory number [ , ..., memory number] [ ) ] ○ ○ ○ ○ ○ Example To recall the contents of equation memory 2 and equation memory 3 3(EQUA)c(rclEqn)c,dw 3X – Y = 7 3X + 6Y = 63 • The memory numbers of equations produced as the result of a recall are not updated. u rclAllEqn (rclAll) Function: Recall all eqn memory contents.
7-1-16 Using the CAS (Computer Algebra System) Mode u eliminate (elim) Function: Assigns an expression to a variable. Syntax: eliminate( {Eq/Ineq} -1, variable, Eq-2 [ ) ] ○ ○ ○ ○ ○ Example To transform Y = 2X + 3 to X= and then substitute 2X + 3Y = 5 3(EQUA)g(elim)ca+(X)+da-(Y)!.(=) f,a+(X),a-(Y)!.(=) ca+(X)+dw 4Y – 3 = 5 u getRight (getRgt) Function: Gets the right-side element.
7-1-17 Using the CAS (Computer Algebra System) Mode u clear (clrVar) Function: Clears the contents of specific equation (A to Z, r, θ ).* 1 Syntax: clear( variable [ ) ] clear( {variable list} [ ) ] ○ ○ ○ ○ ○ Example To clear the contents of variable A 6(g)1(CLR)b(clrVar)av(A)w ○ ○ ○ ○ ○ Example { } To clear the contents of variables X, Y, and Z 6(g)1(CLR)b(clrVar)!*( { )a+(X), a-(Y),aa(Z)!/( } )w { } u clearVarAll (VarAll) Function: Clears the contents of all 28 variables (A to Z, r, θ ).
7-2-1 Algebra Mode 7-2 Algebra Mode The CAS Mode automatically provides you with the final result only. The Algebra Mode, on the other hand, lets you obtain intermediate results at a number of steps along the way. On the Main Menu, select the ALGEBRA icon to enter the Algebra Mode. The screens in this mode are the same as those in the CAS Mode. Operations in the Algebra Mode are identical to those in the CAS Mode, except for a number of limitations.
7-2-2 Algebra Mode u absExpand (absExp) Function: Divides an expression that contains an absolute value into two expressions. Syntax: absExpand( {Eq/Ineq} [ ) ] ○ ○ ○ ○ ○ Example To strip the absolute value from | 2X – 3 | = 9 3(EQUA)i(absExp)K1(Abs)( 2X – 3 = 9 cv-d)!.
7-3-1 Tutorial Mode 7-3 Tutorial Mode On the Main Menu, select the TUTOR icon to enter the Tutorial Mode. k Tutorial Mode Flow 1. Specify the expression type. 2. Define the expression. 3. Specify the solve mode. k Specifying the Expression Type Entering the Tutorial Mode displays a menu of the following expression types. • Linear Equation • Linear Inequality • Quadratic Equation • Simul (Simultaneous) Equation Use the cursor keys to highlight the expression type you want to specify, and then press w.
7-3-2 Tutorial Mode The following shows the formulas available for each type of expression.
7-3-3 Tutorial Mode k Defining the Expression In this step, you specify coefficients and define the expression. You can select any of the three following methods for specifying coefficients. • {RAND} ... {random generation of coefficients} • {INPUT} ... {key input of coefficients} • {SMPL} ... {selection of coefficients from samples} • {SEED} ...
7-3-4 Tutorial Mode k Specifying the Solve Mode You can select one of the following three solve modes for the displayed expression. • {VRFY} ... {Verify Mode} In this mode, you input a solution for verification of whether or not it is correct. It provides a good way to check solutions you arrive at manually. • {MANU} ... {Manual Mode} In this mode, you manually input algebra commands, transform the expression, and calculate a result. • {AUTO} ...
7-3-5 Tutorial Mode You can press 4(MANU) to change to the Manual Mode or 5(AUTO) to change to the Auto Mode.
7-3-6 Tutorial Mode k Manual Mode Press 5(MANU) to enter the Manual Mode. As with the Algebra Mode, the screen is divided between an input area and a display area. This means you can select Algebra Mode commands from the function menu, transform the expression, and solve it. Operation is the same as that in the Algebra Mode. After you obtain a result, you can press 5(JUDG) to determine whether or not it is correct. • {DISP} ... Determines whether the expression in the display area is a correct solution.
7-3-7 Tutorial Mode ○ ○ ○ ○ ○ Example 4X2 = 16 True (X = 2, X = – 2) Besides “TRUE” the messages shown below can also appear as the result of verification. “CAN NOT JUDGE” appears in the Manual Mode, while the other messages appear in both the Verify Mode and Manual Mode. u andConnect (andCon) Function: Connects two inequalities into a single expression.
7-3-8 Tutorial Mode k Auto Mode Press 6(AUTO) to enter the Auto Mode. In the Simultaneous Equation Mode, you must also select SBSTIT (Substitution Method) or ADD-SU (Addition/Subtraction Method). The Substitution Method first transforms the equation to the format Y = aX + b, and substitutes the other expression to Y.*1 The Addition/Subtraction Method multiplies both sides of the expression by the same value to isolate the coefficient X (or Y).
7-4-1 Algebra System Precautions 7-4 Algebra System Precautions • If an algebraic operation cannot be performed for some reason, the original expression remains on the display. • It may take considerable time to perform an algebraic operation. Failure of a result to appear immediately does not indicate malfunction of the computer. • Any expression can be displayed in various different formats.
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