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

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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