반복리스트 명령

GeoGebra Manual
이동: 둘러보기, 검색
Accessories dictionary.png
이 페이지는 공식 매뉴얼에서 출력과 pdf를 위한 부분입니다. 일반 사용자들은 이 페이지를 편집할 수 없습니다. 만일 이 페이지에서 오류를 발견하였으면, 연락하여 주시기 바랍니다.사용자에 의해 편집 가능한 버전으로 이동
IterationList( <Function>, <Start Value>, <Number of Iterations> )
Gives you a list of length n+1 (n = number of iterations) whose elements are iterations of the function starting with the start value.
예: After defining f(x) = x^2 the command IterationList(f, 3, 2) gives you the list {3, 9, 81}.
You can also use this command to define a sequence where ak+1 depends on ak and k. If the input function f is a function of two variables and start value is a list of two numbers {s, as}, then the output list consists of numbers as,as+1,....,as+n where for k>s we have ak+1=f(k, ak).
예: Define f(k,a)=(k+1)*a, which corresponds to the recursive definition of factorial. The command IterationList(f, {3, 6}, 4) gives you the list {6, 24, 120, 720, 5040}.
IterationList( <Expression>, <Variable Name>, ..., <Start Values>, <Number of Iterations> )
Gives you a list of length n+1 (n = number of iterations) whose elements are iterations of the expression starting with the given start value. In each iteration the variables in the expression are substituted by last elements of the list. There should be at least as many start values as there are variables, otherwise the result is undefined.
예: Let A, B be points. The command IterationList(Midpoint(A, C), C, {B}, 3) internally computes values C0 = B,   C1 = Midpoint(A, C0),   C2 = Midpoint(A, C1),   C3 = Midpoint(A, C2) and yields {C0, C1, C2, C3}. Hence for A = (0,0) and B = (8,0) the result will be {(8,0), (4,0), (2,0), (1,0)}.
예: Let f_0, f_1 be numbers. IterationList(a + b, a, b, {f_0, f_1}, 5) fills the first 2 values of the resulting list from the start values. Afterwards the values are computed as f2 = f0 + f1,   f3 = f1 + f2,   f4 = f2 + f3,   f5 = f3 + f4. Hence for f_0 = f_1 = 1 the result will be {1, 1, 2, 3, 5, 8}.
노트: See also Iteration_Command.
© 2021 International GeoGebra Institute