numlib::contfrac
-- the domain
of continued fractionsnumlib::contfrac
(a, n)
creates a continued
fraction approximation for a
, using the first
n
digits of its floating-point evaluation.
numlib::contfrac(a <,n>)
n |
- | positive integer |
a |
- | numerical expression |
n
is not given, the value of the variable DIGITS
is used.approx(dom cf, positive
integer n)
n
coefficients coincide with those of cf
equals [a,b).unapprox(numerical expression a, numerical expression b)
_plus(dom a, dom
b)
a
and b
into
rationals, adds them, and returns the sum converted back into a
continued fraction._plus
of the system kernel._mult(dom a, dom
b)
a
and b
into
rationals, multiplies them, and returns the product converted back into
a continued fraction._mult
of the system kernel._invert(dom a)
_invert
of the system kernel._power(dom a, integer
n)
a
by itself n
times, or, if n
is negative, the inverse of a
by itself -n
times.numlib::contfrac
can also compute continued
fraction expansions of irrational numbers:
>> a:= numlib::contfrac(PI, 5): b:= numlib::contfrac(sqrt(7), 2): a, b
1 1 ---------------------- + 3, ------------------- + 2 1 1 ------------------ + 7 --------------- + 1 1 1 ------------- + 15 ----------- + 1 1 1 --------- + 1 ------- + 1 1 1 --- + 292 --- + 4 ... ...
All basic arithmetical operations are available:
>> a + b, a*b, a^3
1 1 1 --------------- + 5, ------- + 8, ------------- + 31 1 1 1 ----------- + 1 --- + 3 ------- + 159 1 ... 1 ------- + 3 --- + 3 1 ... --- + 1 ...
contfrac