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Continued fraction representation of a real : dfc

dfc takes as argument a real or a rational or a floating point number a and an integer n (or a real epsilon).
dfc returns the list of the continued fraction representation of a of order n (or with precision epsilon i.e. the continued fraction representation which approachs a or evalf(a) with precision epsilon, by default epsilon is the value of the epsilon defined in the cas configuration with the menu Cfg $ \blacktriangleright$Cas Configuration).
convert with the option confrac has a similar functionnality: in that case the value of epsilon is the value of the epsilon defined in the cas configuration with the menu Cfg $ \blacktriangleright$Cas Configuration (see 1.21.23) and the answer may be stored in an optionnal third argument.

Remarks

If dfc(a)=[a0,a1,a2,[b0,b1] that means :

a = a0 + $\displaystyle {\frac{{1}}{{a1+\frac{1}{a2+\frac{1}{b0+\frac{1}{b1+\frac{1}{b0+...}}}}}}}$

If dfc(a)=[a0,a1,a2,r] that means :

a = a0 + $\displaystyle {\frac{{1}}{{a1+\frac{1}{a2+\frac{1}{r}}}}}$

Input :
dfc(sqrt(2),5)
Output :
[1,2,[2]]
Input :
dfc(evalf(sqrt(2)),1e-9)
Or :
dfc(sqrt(2),1e-9)
Output :
[1,2,2,2,2,2,2,2,2,2,2,2,2]
Input :
convert(sqrt(2),confrac,'dev'
Output (if in the cas configuration epsilon=1e-9) :
[1,2,2,2,2,2,2,2,2,2,2,2,2]
and [1,2,2,2,2,2,2,2,2,2,2,2,2] is stored in dev.
Input :
dfc(9976/6961,5)
Output :
[1,2,3,4,5,43/7]
Input to verify:
1+1/(2+1/(3+1/(4+1/(5+7/43))))
Output :
9976/6961
Input :
convert(9976/6961,confrac,'l')
Output (if in the cas configuration epsilon=1e-9) :
[1,2,3,4,5,6,7]
and [1,2,3,4,5,6,7] is stored in l
Input :
dfc(pi,5)
Output :
[3,7,15,1,292,(-113*pi+355)/(33102*pi-103993)]
Input :
dfc(evalf(pi),5)
Output (if floats are hardware floats, e.g. for Digits=12) :
[3,7,15,1,292,1.57581843574]
Input :
dfc(evalf(pi),1e-9)
Or :
dfc(pi,1e-9)
Or (if in the cas configuration epsilon=1e-9) :
convert(pi,confrac,'ll')
Output :
[3,7,15,1,292]


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suivant: Transform a continued fraction monter: Rationals précédent: Simplification of a pair   Table des matières   Index
giac documentation written by Renée De Graeve and Bernard Parisse