# Limit comparison test

Hi! I want to define a function to do limit comparison test. I want the function that can be given one or three arguments. First argument should be the formula for n-th element of sequence I want to put to the test - a. Second, optional, argument should be the formula for n-th element of sequence I want to compare with - b. Third argument should be the letters 'k' or 'd' wether the given sequence b is convergent or divergent.

I have problem to define a function with optional number of arguments. I don't know how to make the program differentiate the number of arguments. I used the nargs command but it does not work.

var('n,b,L')
def limzk(a, *args):
if nargs==0:
b=1/n^2
L=lim(a/b, n=Infinity)
if L<Infinity:
print('convergent')
else:
b=1/n
L=lim(a/b, n=Infinity)
if L>0:
print('divergent')
else:
print('cannot be decided by this test')
elif nargs==2:
if args==('k'):
b=args
L=lim(a/b, n=Infinity)
if L<Infinity:
print('convergent')
else:
print('cannot be decided by this test')
elif args==('d'):
b=args
L=lim(a/b, n=Infinity)
if L>0:
print('divergent')
else:
print('cannot be decided by this test')
else:
print('ERROR: wrong number of parameters given')


Thank you for help.

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Your problem seems to be the use of arguments in a Python function rather than Sage-specific. A few notes :

• Your code defines b and L variables local to limzk ; globals b and L won't be used by this code.

• Are you sanguine about the order of your arguments ?

• What about keyword arguments ?

• Why distinct behaviour for the no-argument case (which returns either "convergent","divergent" or "undecidable") and the two-arguments case ?

• the catchall print("ERROR"...) code would be avanteageously replaced by raising an exception. Or, even better,

• you could enclose the body of your code in a try...except statement.