Texas Instruments TITANIUM TI-89 - Manual (Page 820)

820 Appendix A: Functions and Instructions
For the AUTO setting of the Exact/Approx mode,
including var permits approximation with floating-
point coefficients where irrational coefficients
cannot be explicitly expressed concisely in terms
of the built-in functions. Even when there is only
one variable, including
var might yield more
complete factorization.
Note: See also comDenom() for a fast way to
achieve partial factoring when factor() is not
fast enough or if it exhausts memory.
Note: See also cFactor() for factoring all the
way to complex coefficients in pursuit of linear
factors.
factor(x^5+4x^4+5x^3ì 6xì 3) ¸
x 5 + 4ø x 4 + 5ø x 3 м 6ш x ì 3
factor(ans(1),x) ¸
(xм.964…)ш (x +.611…)ø
(x + 2.125…)ø (xс + 2.227…ш
x + 2.392…)
factor( rationalNumber ) returns the rational
number factored into primes. For composite
numbers, the computing time grows
exponentially with the number of digits in the
second-largest factor. For example, factoring a
30-digit integer could take more than a day, and
factoring a 100-digit number could take more
than a century.
Note: To stop (break) a computation, press ´.
If you merely want to determine if a number is
prime, use
isPrime() instead. It is much faster,
particularly if rationalNumber is not prime and if
the second-largest factor has more than five
digits.
factor(152417172689) ¸
123457ø1234577
isPrime(152417172689) ¸ false
Fill MATH/Matrix menu
Fill expression, matrixVar
⇒
matrix
Replaces each element in variable matrixVar with
expression .
matrixVar must already exist.
[1,2;3,4]!amatrx ¸ [
1 2
3 4]
Fill 1.01,amatrx ¸ Done
amatrx ¸ [
1.01 1.01
1.01 1.01]
Fill expression, listVar ⇒ list
Replaces each element in variable listVar with
expression .
listVar must already exist.
{1,2,3,4,5}!alist ¸
{1 2 3 4 5}
Fill 1.01,alist ¸ Done
alist ¸
{1.01 1.01 1.01 1.01 1.01}
floor() MATH/Number menu
floor( expression )
⇒ ⇒ ⇒ ⇒ integer
Returns the greatest integer that is  the
argument. This function is identical to int() .
The argument can be a real or a complex number.
floor(л2.14) ¸ л 3.
floor( list1 )
⇒ ⇒ ⇒ ⇒ list
floor( matrix1 ) ⇒ ⇒ ⇒ ⇒ matrix
Returns a list or matrix of the floor of each
element.
Note: See also ceiling() and int() .
floor({3/2,0,л 5.3}) ¸
{1 0 л 6.}
floor([1.2,3.4;2.5,4.8]) ¸
[
1. 3.
2. 4.]