#8342: Efficient Arbitrary Sequence Generator
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Reporter: colah | Owner: jkantor
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.3.4
Component: numerical | Keywords: sequence, generator
Author: colah | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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{{{
def construct_sequence(base,f):
"""
Returns a function that gives sequence terms, building off past calls.
Input:
- `base` -- the base case(s) of the sequence.
- `f` -- the recursive description of the sequence; it takes a
sequence referencing function and returns a function that will, given n,
return the nth term.
Output:
A function that, given n, returns the nth term in the sequence.
Examples:
sage: fib = construct_sequence([1,1], lambda t: lambda n : t(n-1) +
t(n-2)) #The Fibonacci sequence
sage: hof = construct_sequence([1,1], lambda t: lambda n :
t(n-t(n-1)) + t(n-t(n-2))) #The Hofstadter Q sequence
sage: [hof(n) for n in range(100)] # List of 100 terms
"""
b = {}
for i in range(len(base)):
b[i] = base[i]
def get_term(n):
if n in b.keys(): return b[n]
else:
b[n] = f(get_term)(n)
return b[n]
return get_term
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8342>
Sage <http://www.sagemath.org>
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