852 appendix a: functions and instructions – Texas Instruments TITANIUM TI-89 User Manual

Page 852

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852

Appendix A: Functions and Instructions

part(

expression1

)

⇒

expression

Simplifies

expression1

and returns the

argument

or operand, where

is > 0 and

 the number of

top-level arguments or operands returned by

part(

expression1

)

. Otherwise, an error is returned.

part(cos(pùx+3),1) ¸ 3+pøx

Note: Simplification changed the order of the
argument.

By combining the variations of

part()

, you can

extract all of the sub-expressions in the simplified
result of

expression1

. As shown in the example to

the right, you can store an argument or operand
and then use

part()

to extract further sub-

expressions.

Note: When using

part()

, do not rely on any

particular order in sums and products.

part(cos(pùx+3)) ¸ 1

part(cos(pùx+3),0) ¸ "cos"

part(cos(pùx+3),1)!temp ¸

3+pøx

temp ¸

pø

x+3

part(temp,0) ¸ "+"

part(temp) ¸ 2

part(temp,2) ¸ 3

part(temp,1)!temp ¸

pø

part(temp,0) ¸

"ù"

part(temp) ¸ 2

part(temp,1) ¸

part(temp,2) ¸ x

Expressions such as (x+y+z) and (xì yì z) are
represented internally as (x+y)+z and (xì y)ì z.
This affects the values returned for the first and
second argument. There are technical reasons
why

part(

x+y+z,1

)

returns y+x instead of x+y.

part(x+y+z) ¸ 2

part(x+y+z,2) ¸ z

part(x+y+z,1) ¸ y+x

Similarly, xù yù z is represented internally as
(xù y)ù z. Again, there are technical reasons why
the first argument is returned as yøx instead of
xøy.

part(xùyùz) ¸ 2

part(xùyùz,2) ¸ z

part(xùyùz,1) ¸

yøx

When you extract sub-expressions from a matrix,
remember that matrices are stored as lists of lists,
as illustrated in the example to the right.

part([a,b,c;x,y,z],0) ¸ "{"

part([a,b,c;x,y,z]) ¸ 2

part([a,b,c;x,y,z],2)!temp ¸

{x y z}

part(temp,0) ¸ "{"

part(temp) ¸ 3

part(temp,3) ¸ z

delVar temp ¸ Done

The example Program Editor function to the right
uses

getType()

and

part()

to partially

implement symbolic differentiation. Studying and
completing this function can help teach you how
to differentiate manually. You could even include
functions that the cannot differentiate, such as
Bessel functions.

:d(y,x)

:Func

:Local f

:If getType(y)="VAR"

: Return when(y=x,1,0,0)

:If part(y)=0
: Return 0 ¦ y=p,ˆ,

,numbers

:part(y,0)!f

:If f="L" ¦ if negate

: Return ëd(part(y,1),x)
:If f="

−

" ¦ if minus

: Return d(part(y,1),x)

ìd(part(y,2),x)

:If f="+"

: Return d(part(y,1),x)

+d(part(y,2),x)

:If f="ù"

: Return part(y,1)ùd(part(y,2),x)

+part(y,2)ùd(part(y,1),x)

:If f="{"

: Return seq(d(part(y,k),x),

k,1,part(y))

:Return undef

:EndFunc

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