796 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
ì 6ø x
ì 3
factor(ans(1),x)
¸
(xì.964…)ø (x
+.611…)ø
(x
+
2.125…)ø (xñ +
2.227…ø
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
c
the argument.
This function is identical to
int()
.
The argument can be a real or a complex number.
floor(ë 2.14)
¸ ë 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,ë 5.3})
¸
{1 0 ë 6.}
floor([1.2,3.4;2.5,4.8])
¸
[
1. 3.
2. 4.
]
fMax() MATH/Calculus menu
fMax(
expression, var
) ⇒
Boolean expression
Returns a Boolean expression specifying candidate
values of
var
that maximize
expression
or locate its
least upper bound.
fMax(1ì (xì a)^2ì (xì b)^2,x)
¸
x =
a+b
2
fMax(.5x^3ì xì 2,x)
¸ x = ˆ
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