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## Transform a continued fraction representation into a real : dfc2f

dfc2f takes as argument a list, a continued fraction representation
• 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

suivant: The n-th Bernoulli number monter: Rationals précédent: Continued fraction representation of   Table des matières   Index
giac documentation written by Renée De Graeve and Bernard Parisse