Chapter 3: Symbolic Manipulation 61
03SYMBOL.DOC TI-89/TI-92 Plus: Symbolic Manipulation (English) Susan Gullord Revised: 02/23/01 10:52 AM Printed: 02/23/01 2:12 PM Page 61 of 24
When Exact/Approx = EXACT, the TI-89 / TI-92 Plus uses exact rational
arithmetic with up to 614 digits in the numerator and 614 digits in the
denominator. The EXACT setting:
¦ Transforms irrational numbers to standard forms as much as
possible without approximating them. For example, 12
transforms to 2 3 and ln(1000) transforms to 3 ln(10).
¦ Converts floating-point numbers to rational numbers. For
example, 0.25 transforms to 1/4.
The functions solve, cSolve, zeros, cZeros, factor,
∫
, fMin, and fMax
use only exact symbolic algorithms. These functions do not compute
approximate solutions in the EXACT setting.
¦ Some equations, such as 2–x = x, have solutions that cannot all be
finitely represented in terms of the functions and operators on the
TI-89 / TI-92 Plus.
¦ With this kind of equation, EXACT will not compute approximate
solutions. For example, 2–x = x has an approximate solution
x ≈ 0.641186, but it is not displayed in the EXACT setting.
Advantages Disadvantages
Results are exact. As you use more complicated rational
numbers and irrational constants,
calculations can:
¦ Use more memory, which may
exhaust the memory before a solution
is completed.
¦ Take more computing time.
¦ Produce bulky results that are harder
to comprehend than a floating-point
number.
Using Exact, Approximate, and Auto Modes
The Exact/Approx mode settings, which are described briefly
in Chapter 2, directly affect the precision and accuracy with
which the TI-89 / TI-92 Plus calculates a result. This section
describes these mode settings as they relate to symbolic
manipulation.
EXACT
Setting