5.8.8 Transform a continued fraction representation into a real: dfc2f
dfc2f takes as argument a list representing a continued
fraction, namely
-
a list of integers for a rational number
- a list whose last element is a list for an
ultimately periodic representation, i.e.
a quadratic number, that is a root of a second order equation with
integer coefficients.
- or a list with a remainder r as last element
(a=a0+1/....+1/an+1/r).
dfc2f returns the rational number or the quadratic number with the
argument as continued fraction representation.
Input:
dfc2f([1,2,[2]])
Output:
1/(1/(1+sqrt(2))+2)+1
After simplification with normal:
sqrt(2)
Input:
dfc2f([1,2,3])
Output:
10/7
Input:
normal(dfc2f([3,3,6,[3,6]]))
Output:
sqrt(11)
Input:
dfc2f([1,2,3,4,5,6,7])
Output:
9976/6961
Input to verify:
1+1/(2+1/(3+1/(4+1/(5+1/(6+1/7)))))
Output:
9976/6961
Input:
dfc2f([1,2,3,4,5,43/7])
Output:
9976/6961
Input to verify:
1+1/(2+1/(3+1/(4+1/(5+7/43))))
Output:
9976/6961