# python generators and infinite power series

So I found an interesting paper describing how to use lazy lists to represent infinite series and i thought I’d try to do the same thing in python using generators, which are similar.

It’s cool but kind of a mess. I assume with more thought this could be tweaked into a clear thing. The thunking is especially gross. Maybe totally unnecessary? At some point I felt like it was the right thing to do for some reason and then I stuck with it.

The obvious simpler way would be to truncate the series at n=100 or something and just use lists. Why would I ever want terms higher than that anyhow? Interesting exercise though.

```
# lazy evaluation
# sometimes a problem can be simple if we're working in an insanely huge space.
# if you can proceed thorugh the space lazily, this might be an acceptable strategy
# decorator to convert function into a function that returns a thunk that will evelauted to the original function
def thunkify(func):
def func_wrapper(*args, **kwargs):
return lambda: func(*args, **kwargs)
return func_wrapper
#geometric series
def geo():
while True:
yield 1
#exponential expansion
def exp():
num = 0.
fact = 1.
yield 1.
while True:
num += 1.
fact = fact * num
yield 1./fact
@thunkify
def const(c):
yield c
while True:
yield 0
def oneX():
yield 0
yield 1
while True:
yield 0
@thunkify
def convertArray(myarray):
for i in myarray:
yield i
while True:
yield 0
# oneX = convertArray([0,1])
myexp = exp()
print next(myexp)
print next(myexp)
print next(myexp)
''' #an old unthunked approach. I need to instantiate all generators before passing them.
def add(a, b):
while True:
yield next(a) + next(b)
mysum = add(oneX(), const(3))
print next(mysum)
print next(mysum)
print next(mysum)
'''
#If i do this way, need to always returns thunks for all constructors.
# such as const(3): def thunk
@thunkify
def add(a, b):
#could this be lazier? # do I want egnerator combinators to instantiate the genereators?
a = a()
b = b()
while True:
yield next(a) + next(b)
mysum = add(oneX, const(3))
mysum = mysum()
print next(mysum)
print next(mysum)
print next(mysum)
#I fear rethunking will lead to weird bugs. rehtunked guys might be linked to each other in ways you might not expect
def rethunk(a):
return lambda: a
@thunkify
def constmult(c, a):
a = a()
while True:
yield c * next(a)
@thunkify
def mult(a,b):
abar = a()
bbar =b()
a0 = next(abar)
b0 = next(bbar)
bbar = rethunk(bbar)
abar = rethunk(abar)
yield a0 * b0
remainprod = add(constmult(a0, bbar), mult(abar,b))
remainprod = remainprod()
while True:
yield next(remainprod)
@thunkify
def integrate(C, a):
num = 0.
a = a()
yield C
while True:
num += 1.
yield next(a)/num
@thunkify
def differentiate(a):
a = a()
num = 0.
next(a) #toss away constant
while True:
num += 1.
yield num * next(a)
def evalseries(x, n, series):
pass
def take(n, gen):
gen = gen()
arr = []
for i in range(n):
arr.append(next(gen))
return arr
print take(5, exp)
print take(5, mult(oneX, exp))
print take(5, integrate(0,oneX))
print take(5, differentiate(oneX))
print take(5, differentiate(exp))
```