Continued fraction/Arithmetic
By popular demand, see Talk:Continued fraction#creating_a_continued_fraction and Talk:Continued fraction#Arithmetics.3F.3F, or be careful what you ask for.
This page is a placeholder for several subtasks which will eventually implement a function:
- G(matrix NG, Continued Fraction N1, Continued Fraction N2)
which will perform basic mathmatical operations on continued fractions.
For these tasks continued fractions will be of the form:
so each may be described by the notation []
Continued fraction arithmetic/Continued fraction r2cf(Rational N)
During these tasks I shall use the function described in this task to create continued fractions from rational numbers.
Matrix NG
Consider a matrix NG:
and a function G(matrix NG, Number N1, Number N2) which returns:
- Convince yourself that NG = :
- adds N1 to N2
- subtracts N2 from N1
- multiplies N1 by N2
- divides N1 by N2
- calculates (3*N1 + 4) * (7*N2 - 5)
- Note that with N1 = 22, N2 = 7, and NG = :
- I could define the solution to be N1 = 1, N2 = 1 and NG = :
- So I can define arithmetic as operations on this matrix which make a12, a1, a2, b12, b1, b2 zero and read the answer from a and b. This is more interesting when N1 and N2 are continued fractions, which is the subject of the following tasks.
- Investigate G(matrix NG, Contined Fraction N)
- The complete solution G(matrix NG, Continued Fraction N1, Continued Fraction N2)
- Compare two continued fractions