Casio CFX-9970G User manual

Algebraic Expressions

The ALGBR Mode (Algebraic Mode) provides tools for expansion of

algebraic expressions, factoring, etc. In this mode, differential and

integration calculation results are displayed as mathematical

expressions instead of decimal values.

20-1 Before Using the Algebraic Mode

20-2 Inputting and Executing Calculations

20-3 ALGBR Mode Commands

20-4 Signum Function

20-5 Natural Display Notation

20-6 ALGBR Mode Error Messages

20-7 ALGBR Mode Precautions

Chapter

350

20-1 Before Using the Algebraic Mode

In the Main Menu, select the ALGBR icon to enter the ALGBR Mode and display

its initial screen, which contains the following items.

•{expn} ... {expansion}

•{fctor} ... {factorization}

•{diff} ... {differential}

•{

∫

(} ... {integration}

•{SOLV} ... {Solve function}

•{tExp} ... {expression transformation using the addition theorem}

•{tColl} ... {product-to-sum transformation using the addition theorem}

•{comb} ... {combination}

•{PTS

} ... {function for line passing through specific points}

•{CPLX} ... {complex function transformation}

•{appr} ... {convert to numeric value}

•{collc} ... {collection}

•{tanL} ... {tangent expression}

The following table shows the keys that can be used in the ALGBR Mode.

• The Mkey performs its screen shot send function only. It does not perform its

fraction-decimal conversion function.

351

20-2 Inputting and Executing Calculations

The ALGBR Mode display is divided into three areas: an input area, a solution

area, and a message area (used for display of menus and error messages).

Example X + X2 + 3X – 2X2

v+vx+dv-cvx

• Solutions are displayed in natural display notation.

• Solutions produced in the ALGBR Mode are also stored inAns memory and

can be recalled by pressing !K.

• You can input up to 255 bytes of data for eachALGBR Mode calculation.

• If a solution does not fit within the solution area, use f, c, d, and eto

scroll the screen.

• Inputting more data while there is data in the input area and solution area

causes the previous data to be cleared from two areas automatically.

• If you clear the display by pressing A, you can recall the previous operation

by pressing dor e(Replay Function).

• The Angle item of the set up screen can be set to either "Deg" or "Rad" for

ALGBR Mode operations.

• The Display item of the set up screen can be set to "Fix", "Sci", or "Norm" for

ALGBR Mode operations. Note, however, that this setting is applied for the

approx command only.

• A displayed solution can be stored in function memory by pressing

K6(FMEM)1(STO). Next, press a function 1(f1) to 6(f6) to select a

specific function memory.

Input area

Solution area

Messages area

P.361

P.356

352

20-3 ALGBR Mode Commands

In theALGBR Mode, results are calculated in accordance with commands and

expressions you input. This section describes each of the commands available in

the ALGBR Mode.

kConventions Used in this Section

The following conventions are used in the command descriptions of this section.

Item Description

<expression> This item indicates a mathematical expression input by you.

The actual expression you should input depends on the type of

operation you are performing. One example of an expression

is: X+1.

<variable> This item indicates a variable input by you. The actual variable

you should input depends on the type of operation you are

performing. One example of a variable is: A.

[ ] Anything enclosed within square brackets is optional, which

means you can skip it if you want. Note the following:

expand (<expression>[)]

The above example means that the final closed parenthesis to

the right of <expression> does not need to be input for the

command to execute properly.

kCommands

uExpansion —— (expn)

This command expands an expression.

Syntax: expand (<expression>[)]

Example To expand the expression (X + 2)2

1(expn)(v+c)xw X2+ 4X + 4

uFactorization —— (fctor)

This command factorizes an expression.

Syntax: factor (<expression>[)]

353

Example To factorize the expression X2 - 4X + 4

2(fctor)vx-ev

+ew(X – 2)2

• You can also factorize a value into its prime factors.

Example To factorize 64 into its prime factors

2(fctor)gew26

uAddition Theorems —— (tExp)

This command uses trigonometric addition theorems to transform an expression.

Syntax: tExpand (<expression>[)]

Example To transform sin(A+B) using addition theorems

6(g)1(tExp)

s(aA+aBwcos(B) • sin(A) + sin(B) • cos(A)

uProduct-to-Sum Transformation —— (tColl)

This command uses addition theorems to perform product-to-sum transformation.

Syntax: tCollect (<expression>[)]

Example To perform product-to-sum transformation on sin(A)cos(B)

using addition theorems

6(g)2(tColl)

saAcaBw

ALGBR Mode Commands 20 - 3

sin(A + B) sin(A – B)

2 2

354

uIntegration —— ( ()

This command can be used to determine the primitive function or calculate the

definite integral for an expression.

Syntax 1: ∫(<expression>, <variable> [, <integration constant>] [)]

Syntax 2: ∫(<expression>[, <variable>, <integration constant>] [)]

Syntax 3: ∫(<expression>, <variable> , <start>, <end> [)]

<integration constant>...........Integration constant

<start> ............ Start point of the integration interval

<end> ............. End point of the integration interval

• A default variable of X is used when specification of a variable is skipped in

Syntax 2.

• Syntax 3 calculates the definite interval in accordance with the specified

integration interval.

• Multiple integral calculations can also be performed.

Example To integrate the expression X2for variable X

4(∫( )vx,vw

• A default value of 0 is automatically assumed for the integration constant.

Inputting a symbol name such as C for the integration constant produces a

result in a form that is the same as the indefinite integral.

uDifferential —— (diff)

This command can be used to determine the derivative or calculate the value of

the derivative for an expression.

Syntax 1: diff (<expression>, <variable>, <nth>[, <differential coefficient>] [)]

Syntax 2: diff (<expression>, <variable>[, <nth>, <differential coefficient>] [)]

Syntax 3: diff (<expression>[, <variable>, <nth>, <differential coefficient>] [)]

<nth> .............. Specifies differential of nth order. nmust be a positive integer.

....................... Any value specified as the differential coefficient is substituted

in the function for calculation of the result.

20- 3 ALGBR Mode Commands

355

• Syntax 1 determines the derivative in accordance with a specified expression,

variable and order. Specifying a differential coefficient calculates a result in

accordance with the input value.

• A default order of 1 is used when specification of the order is skipped in Syntax

• A default variable of X is used when specification of a variable is skipped in

Syntax 3.

Example To differentiate the expression X6for variable X

3(diff)vMgw6X5

uTangent Expression —— (tanL)

This command calculates the tangent expression of another expression.

Syntax: tanLine (<expression>, <variable>, <contact point>[)]

....................... The contact point is specified using the <variable> name.

Example To calculate the tangent expression when X = 2 for the

expression X3

6(g)6(g)3(tanL)

vMd,v,cw12X – 16

uSolve —— (solve)

This command calculate solutions for an expression. Solutions are displayed as

mathematical expressions.

Syntax: solve (<expression> [ =<expression>] [, <variable>] [)]

The second expression can be preceded by any of the following operators: =

(equals), < (less than), > (greater than), H(less than or equal to), or I(greater

than or equal to).

• A default variable of X is used when specification of a variable is skipped.

ALGBR Mode Commands 20 - 3

356

Example To solve AX+B = 0 for X

5(SOLV)1(solve)aA

v+aB,vw

• Other solve functions are available that produce numeric calculation results .

uConvert to Numeric Value —— (appr)

This command converts an expression to a numeric value.

Syntax: approx <expression>

Example To convert the expression 2 to a numeric value

6(g)6(g)1(appr)

!9cw1.414213562

• Any command to the left of approx causes an error.

Example 1+ approx ( 2 ) (Causes an error.)

• Inputting anotherALGBR Mode command or the signum( function into the

approx command causes an error.

Example approx approx 2 (Causes an error.)

kDifference Between "approx" and Standard Calculations

approx differs from standard calculations (calculations that do not use natural

display notation) in the number of display digits and handling of variables. With

standard calculations, calculation results are displayed without using exponential

notation.

Example jMcaw12157665459056928801

When part of the expression includes a variable, the variable is processed as a

variable regardless of whether or not it has been assigned a value.

Example f*aA+dw5A + 3

20- 3 ALGBR Mode Commands

{–B }

X =

P.107

357

With approx, calculation results are displayed using exponential notation. As with

the RUN Mode, the mantissa can have up to 10 digits and the exponent up to two

digits. The number of digits that can be input for approx depends on the setting of

the set up screen's Display item.

Example 6(gg

g)6(gg

g)1(appr)jMcaw(Display: Norm1)

1.215766546E + 19

When part of the expression includes a variable, the calculation is performed by

substituting the value for the variable. The following shows the calculation whenA

= 0.

Example 6(gg

g)6(gg

g)1(appr)f*aA+dw

uCollection —— (collc)

This command arranges the terms of an expression, focusing on a particular

variable.

Syntax: collect (<expression>[, <variable>] [)]

• A default variable of X is used when specification of a variable is skipped.

Example To arrange the terms of the expression X2+ AX + BX, focusing

on the variable X

6(g)6(g)2(collc)vx+

aAv+aBvw X2+ (A + B)X

uCombine —— (comb)

This command produces a fraction made up of a fully expanded numerator over a

fully expanded denominator.

Syntax: combine (<expression>[)]

Example To combine the expressions (X+1) / (X+2) + X × (X+3)

6(g)3(comb)(v+b)

/(v+c)+v*

(v+d)w

ALGBR Mode Commands 20 - 3

X3+ 5X2+ 7X + 1

X + 2

358

20- 3 ALGBR Mode Commands

N353N

– N2++15

6 6

uSequence —— (sequ)

This command creates the function that describes the relationship between the

variable and the value of the expression, if the value of the expression is entered

when the variable is assigned the first specified <value>, the second specified

<value>, and so on.

• The function is a linear algebra expression.

Syntax 1: sequence ({<value>, <value>, ...} [,<variable>] [)]

• A default variable of X is used when specification of a variable is skipped.

Example To obtain the expression when 1 through 4 is {23, 30, 37, 45}

6(g)4(PTS

)1(sequ)

!{cd,da,dh,

ef!},aNw

• If List 1 = {23, 30, 37, 45}, the same result can be obtained by inputting the

following: sequence(List 1, N).

Syntax 2: sequence ({<value>, <value>, ...},{<value>, <value>, ...} [,<variable>] [)]

The values input with this syntax are handled as lists, with the first value of the

first list paired with the first value of the second list, the second value with the

second value, and so on. This syntax creates a function using this relationship.

Example To obtain an expression for variable values {2, 4, 6, 8} and

expression values {23, 30, 37, 44}

6(g)4(PTS

)1(sequ)

!{c,e,g,i

!},!{cd,da

,dh,ee!},

aNw

• If List 1 = {2, 4, 6, 8} and List 2 = {23, 30, 37, 44}, the same result can be

obtained by inputting the following: sequence(List 1, List 2, N).

uSum of Sequence —— (smSq)

This command obtains a function that expresses the sum up to the nth term of a

sequence of numbers.

• The function is a linear algebra expression.

7N +16

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