Casio ALGEBRA FX 2.0 Instruction and safety manual

19990401
Computer Algebra
System and Tutorial
Modes
7-1 Using the CAS (Computer Algebra System) Mode
7-2 Algebra Mode
7-3 Tutorial Mode
7-4 Algebra System Precautions
Chapter
7

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.
kk
kk
kInputting 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.
Calculation results appear in the lower part of the display, which is called the “output area.”
When a calculation produces an equation or inequality, the lower part of the display is
divided between a “natural result display area” for the result, and a “formula number area” for
the formula number as shown below.
REPLAY
COPY PASTE
H-COPY
i

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If all the result does not fit on the display, use the cursor keys to scroll it.
kk
kk
kPerforming 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
kk
kk
kMenu 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 ... {formula calculation menu}
•EQUA ... {equation, inequality menu}
•eqn ... {calls up an equation stored in Equation Memory in accordance with a specified
input value}
•CLR ... {variable/formula delete menu}
For details on commands and their formats, see the “Algebra Command Reference” on
page 7-1-7.
7-1-2
Using the CAS (Computer Algebra System) Mode

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kk
kk
kManual Formula and Parameter Input
You can use the function menus, Kkey, and Jkey in combination to input formulas and
parameters as described below.
•3(EQUA)b(INEQUA)
•{>}/{<}/{tt
tt
t}/{ss
ss
s} ... {inequality}
•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}... input of graph memory {Y}/{r}/{Xt}/{Yt}/{X}
kFormula Memory
The CAS Mode has 28 formula variables. Variable names are the letters A through Z, plus r,
and θ . CAS Mode formula variables are independent of standard value variables.*2
○○○○○
Example To assign a formula that differentiates sin(X) at X (cos(X)) to variable A
2(CALC)b(diff)sv,
v)aav(A)w
7-1-3
Using the CAS (Computer Algebra System) Mode
1 (real number, A> 0)
–1 (real number, A< 0)
*1signum (A)A(A= imaginary number)
|A|
Undefined (A= 0)
*2Use the approx command before inputting to
register a value to a general variable.
Example: approx 1 RA

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kFunction 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 Jkey and then input the
name of the graph.
○○○○○
Example To differentiate f1= cos(X), which is assigned to function memory f1,
at X
2(CALC)b(diff)K6(FMEM)
d(fn)b,v)w
○○○○○
Example To differentiate Y1 = cos(X), which is assigned to graph memory Y1,
at X
2(CALC)b(diff)
J1(Y) b,v)w
kEqn Memory
When a calculation result is an equation or inequality, its formula number is displayed in the
formula number area, and the equation is stored in Eqn memory.*1Stored equations can be
recalled with the eqn command, rclEqn command or rclAllEqn command.
7-1-4
Using the CAS (Computer Algebra System) Mode
*1Up to 99 formulas can be stored in Eqn
memory.
The error message “Memory ERROR” when
you try to store an equation when there are
already 99 equations in Eqn memory. When
this happens, execute the ALLEQU (Delete
All Equations) from the CLR menu.

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kAnswer (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)2and add the result to 2X
1(TRNS)b(expand)
(v+b)x)w
Continuing:
+cvw
kReplay Contents
Replay memory can be used in the input area. After a calculation is complete, pressing d
or ein the input area recalls the formula of the last calculation performed. After a
calculation or after pressing A, you can press for cto recall previous formulas.
kMoving the Cursor Between Display Areas
When ]'`$indicates a calculation result that does not fit on the display, the cursor
keys perform output area scrolling. To use the Replay Function from this condition, press
6(g)2(SW). ]'`$change to a dotted line display to indicate that cursor key
operations control the input area.
Pressing 2(SW) again moves the cursor back to the output area.
7-1-5
Using the CAS (Computer Algebra System) Mode
# Pressing 6(g)1(CLR)d(ALLEQU)
deletes Eqn memory, Ans memory, and
Replay memory contents.
#You can input up to 255 bytes of data into the
input area.

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SET UP Items
uu
uu
uAngle ... Unit of angular measurement specification
•{Deg}/{Rad} ... {degrees}/{radians}
uu
uu
uAnswer Type ... Result range specification
•{Real}/{Cplx}... {real number}/{complex number}
uu
uu
uDisplay ... Display format specification (for approx only)
•{Fix}/{Sci}/{Norm}... {number of decimal places}/{number of significant digits}/
{normal display format}
kGraph Function
Pressing 5(GRPH) displays the graph formula screen.You can execute
1(SEL) and 2(DEL) from this screen. Pressing 6(DRAW) graphs the
SET condition expressions.
kRECALL ANS Function
Pressing 6(g)3(R
•
ANS) recalls Ans Memory contents.
7-1-6
Using the CAS (Computer Algebra System) Mode

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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.
uexpand
Function: Expands an expression.
Syntax: expand ( {Exp/Eq/Ineq} [ ) ]
○○○○○
Example To expand (X+2)2
1(TRNS)b(expand)(v+c)xw X2+ 4X + 4
urFactor (rFctor)
Function: Factors an expression up to its root.
Syntax: rFactor ( {Exp/Eq/Ineq} [ ) ]
○○○○○
Example To factor the X2– 3
1(TRNS)c(rFctor)vx-dw(X – 3) (X + 3)
ufactor
Function: Factors an expression.
Syntax: factor ( {Exp/Eq/Ineq} [ ) ]
○○○○○
Example To factor X2– 4X + 4
1(TRNS)d(factor)vx-ev+ew(X – 2)2

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usolve
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+
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)!.(=)-i
!/( } ),!*( { )a+(X),X = – 1
a-(Y)!/( } )wY = 2
• X is the default when no variable is specified.
utExpand (tExpnd)
Function: Employs the addition theorem to expand a trigonometric function.
Syntax: tExpand( Exp [ ) ]
○○○○○
Example To employ the addition theorem to expand sin(A+B)
1(TRNS)f(TRIG)b(tExpnd)
s(av(A)+al(B)wcos(B) • sin(A) + sin(B) • cos(A)
utCollect (tCollc)
Function: Employs the addition theorem to transform the product of a trigonometric
function to a sum.
Syntax: tCollect( Exp [ ) ]
○○○○○
Example To employ the addition theorem to transform sin(A)cos(B) to
trigonometric sum.
1(TRNS)f(TRIG)c(tCollc)
sav(A)cal(B)w
7-1-8
Using the CAS (Computer Algebra System) Mode
sin (A + B)
2
sin (A – B)
2
+
– B
A
X =

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7-1-9
Using the CAS (Computer Algebra System) Mode
utrigToExp (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
uexpToTrig (expToT)
Function: Converts an exponential function to a trigonometric or hyperbolic function.
Syntax: expToTrig( Exp [ ) ]
○○○○○
Example To convert eix to a trigonometric function
1(TRNS)f(TRIG)e(expToT)
!I(ex)(!a(i)vw cos(X) + sin(X) •i
usimplify (smplfy)
Function: Simplifies an expression.
Syntax: simplify( {Exp/Eq/Ineq} [ ) ]
○○○○○
Example To simplify 2X + 3Y – X + 3 = Y + X – 3Y + 3 – X
1(TRNS)g(smplfy)ca+(X)+da-(Y)
-a+(X)+d!.(=)a-(Y)
+a+(X)-da-(Y)+d-
a+(X)w
X + 3Y + 3 = –2Y + 3
ex+ e
—
x
2

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ucombine (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
ucollect (collct)
Function: Rearranges an expression, focusing on a particular variable.
Syntax: collect( {Exp/Eq/Ineq} [,Exp-1/, variable] [ ) ]
○○○○○
Example To rearrange X2+ AX + BX, focusing on the variable X
1(TRNS)i(collct)vx+av(A)v+
al(B)vw X2+ (A + B)X
• X is the default when nothing is specified for [,Exp-1/, variable].
usubstitute (sbstit)
Function: Assigns an expression to a variable.
Syntax: substitute( {Exp/Eq/Ineq}, variable=expression [,..., variable=expression] [ ) ]
○○○○○
Example To assign 5 to X in 2X – 1
1(TRNS)j(sbstit)cv-b,
v!.(=)fw9
ucExpand (cExpnd)
Function: Expands xth root of imaginary number.
Syntax: cExpand( Exp [ ) ]
○○○○○
Example To expand 2i
1(TRNS)v(cExpnd)!x( )c!a(i)w1 + i
7-1-10
Using the CAS (Computer Algebra System) Mode
X3+ 5X2+ 7X + 1
X + 2

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uapprox
Function: Produces a numerical approximation for an expression.
Syntax: approx Exp
○○○○○
Example To obtain a numerical value for 2
1(TRNS)l(approx)!x( )cw1.414213562
kAbout 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.
With normal calculations (when approx is not used) in the CAS Mode, calculation results are
displayed in full, without using exponents. When you use approx in the CAS Mode, however,
results are displayed using the exponential format range specified by the Display item of the
SET UP screen.
This means approx displays results in the CAS Mode the same way they are displayed in the
RUN •MAT Mode.
○○○○○
Example 920
Normal:jMcaw12157665459056928801
approx: 1(TRNS)l(approx)jMcaw1. 215766546E+19 (Display: Norm1)
If you use approx to execute an expression that contains a variable, the value assigned to the
variable in general variable memory (variable memory recalled using RUN•MAT) is used for
the calculation.
○○○○○
Example 5A + 3, when A = 1.3
Normal:fav(A)+dw5A + 3
approx: 1(TRNS)l(approx)fav(A)+dw9.5
7-1-11
Using the CAS (Computer Algebra System) Mode
#ASyntax ERROR occurs if a calculation is
performed in front of (to the left of) the approx
command.
Example: 1+approx( 2 ) ... Syntax ERROR

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udiff
Function: Differentiates an expression.
Syntax: diff( Exp [, variable, order, derivative] [ ) ]
diff( Exp, variable [, order, derivative] [ ) ]
diff( Exp, variable, order [, derivative] [ ) ]
○○○○○
Example To differentiate X6with respect to X
2(CALC)b(diff)vMgw6X5
• X is the default when no variable is specified.
• 1 is the default when no order is specified.
u∫
Function: Integrates an expression.
Syntax: ∫( Exp [, variable, integration constant] [ ) ]
∫( Exp, variable [, integration constant] [ ) ]
∫( Exp, variable, lower limit, upper limit [ ) ]
○○○○○
Example To integrate X2with respect to X
2(CALC)c(∫)vxw
• X is the default when no variable is specified.
ulim
Function: Determines the limits of a function expression.
Syntax: lim( Exp, variable, point [, direction] [ ) ]
○○○○○
Example To determine the limits of sin(X)/X when X = 0
2(CALC)d(lim)sv/v,v,aw1
• Direction can be positive (from right) or negative (from left).
7-1-12
Using the CAS (Computer Algebra System) Mode
X3
3

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uΣ
Function: Calculates a sum.
Syntax: Σ( Exp, variable, start value, end value [ ) ]
○○○○○
Example To calculate the sum as the value of X in X2changes from X = 1
through X = 10
2(CALC)e(Σ)vx,v,b,baw385
uΠ
Function: Calculates a product.
Syntax: Π( Exp, variable, start value, end value [ ) ]
○○○○○
Example To calculate the product as the value of X in X2changes from X = 1
through X = 5
2(CALC)f(Π)vx,v,b,fw14400
utaylor
Function: Finds a Taylor polynomial.
Syntax: taylor( Exp, variable, order [, center point] [ ) ]
○○○○○
Example To find a 5th order Taylor polynomial for sin(X) with respect to X = 0
2(CALC)g(taylor)sv,v,f,aw
•The default center point is zero.
uarcLen
Function: Returns the arc length.
Syntax: arcLen( Exp, variable, start value, end value [ ) ]
○○○○○
Example To determine the arc length for X2from X = 0 to X = 1
2(CALC)h(arcLen)
vx,v,a,bw
7-1-13
Using the CAS (Computer Algebra System) Mode
X5
–X3+X
120 6
In (4 5 + 8) –In(2) + 5
422

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utanLine (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 X3when X = 2
2(CALC)i(tanLin)vMd,v,cw12X – 16
udenominator (den)
Function: Extracts the denominator of a fraction.
Syntax: denominator( Exp [ ) ]
○○○○○
Example To extract the denominator of the fraction (X + 2)/(Y – 1)
2(CALC)j(EXTRCT)b(den)
(a+(X)+c)/(a-(Y)-bwY – 1
unumerator (num)
Function: Extracts the numerator of a fraction.
Syntax: numerator( Exp [ ) ]
○○○○○
Example To extract the numerator of the fraction (X + 2)/(Y – 1)
2(CALC)j(EXTRCT)c(num)
(a+(X)+c)/(a-(Y)-bwX + 2
ugcd
Function: Returns the greatest common denominator.
Syntax: gcd( Exp, Exp [ ) ]
○○○○○
Example To determine the greatest common denominator of X + 1 and X2– 3X – 4
2(CALC)v(gcd)v+b,vx-
dv-ewX + 1
7-1-14
Using the CAS (Computer Algebra System) Mode

19990401
urclEqn
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,dw3X –Y = 7
3X + 6Y = 63
•The memory numbers of equations produced as the result of a recall are not updated.
urclAllEqn (rclAll)
Function: Recall all eqn memory contents.
Syntax: rclAllEqn
•The memory numbers of equations produced as the result of a recall are not updated.
urewrite (rewrit)
Function: Moves the right side element to the left side.
Syntax: rewrite( {Eq/Ineq} [ ) ]
○○○○○
Example To move the right side element of X + 3 = 5X – X2to the left side
3(EQUA)e(rewrit)v+d!.(=)
fv-vxw X2– 4X + 3 = 0
uexchange (exchng)
Function: Exchanges the right-side and left-side elements.
Syntax: exchange( {Eq/Ineq} [ ) ]
○○○○○
Example Exchange the left-side and right-side elements of 3 > 5X – 2Y
3(EQUA)f(exchng)d3(EQUA)b(INEQUA)b(>)
fa+(X)-ca-(Y)w5X – 2Y < 3
7-1-15
Using the CAS (Computer Algebra System) Mode

19990401
ueliminate (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)+dw4Y – 3 = 5
ugetRight (getRgt)
Function: Gets the right-side element.
Syntax: getRight( {Eq/Ineq} [ ) ]
○○○○○
Example To extract the right side element of Y = 2X2+ 3X + 5
3(EQUA)h(getRgt)a-(Y)!.(=)
ca+(X)x+da+(X)+fw2X2+ 3X + 5
ueqn
Function: Recalls eqn memory contents.
Syntax: eqn( memory number [ ) ]
○○○○○
Example To add 15 to both sides of the equation 6X – 15 = X – 7, which is stored
in equation memory 3
4(eqn)d)+bfw6X = X + 8
7-1-16
Using the CAS (Computer Algebra System) Mode

19990401
uclear (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
uclearVarAll (VarAll)
Function: Clears the contents of all 28 variables (A to Z, r, θ ).
Syntax: clearVarAll
7-1-17
Using the CAS (Computer Algebra System) Mode
{ }
{ }
{ }
*1When you start out with memories A, B, C,
and D, for example, and delete memories A
and B, the display shows only C,D because
they are the only memories remaining.

19990401
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. Also, the following commands are available in the Algebra Mode only.
uarrange (arrang)
Function: Arranges terms in sequence of their variables.
Syntax: arrange( {Exp/Eq/Ineq} [ ) ]
○○○○○
Example To arrange 2X + 3 – 5X + 8Y in sequence of its variables
1(TRNS)j(arrang)ca+(X)+d-
fa+(X)+ia-(Y)w– 5X + 2X + 8Y + 3
ureplace (replac)
Function: Replaces a variable with the expression assigned to the corresponding
expression variable.
Syntax: replace( {Exp/Eq/Ineq} [ ) ]
○○○○○
Example To replace S in the expression 3X + 2S, when the expression 2X + 1 is
assigned to S
1(TRNS)v(replac)dv+ca*(S)w3X + 2 (2X + 1)
7-2-1
Algebra Mode

19990401
uabsExpand (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)(
cv-d)!.(=)jw
7-2-2
Algebra Mode
2X – 3 = 9
or 2X – 3 = – 9 2
1