Number theory MOC

Simple continued fraction

A (simple) continued fraction for a real number is an expression of the form

where , More precisely, , where the convergent

where there are defined by the recurrence relations

Sage

The methods .p and .q correspond to the notation given above

K.<α> = QuadraticField(223)
continued_fraction(α) 
# [14; (1, 13, 1, 28)*]
continued_fraction(α).p(1) 
# 209
continued_fraction(α).q(1) 
# 14
continued_fraction(α).convergent(2) 
# 209/14

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