def upper_bound(min_length, max_length, floor, ceiling, min_slope, max_slope):
"""
Compute a coarse upper bound on the size of a vector satisfying the
constraints.
TESTS::
sage: import sage.combinat.integer_list as integer_list
sage: f = lambda x: lambda i: x
sage: integer_list.upper_bound(0,4,f(0), f(1),-infinity,infinity)
4
sage: integer_list.upper_bound(0, infinity, f(0), f(1), -infinity, infinity)
inf
sage: integer_list.upper_bound(0, infinity, f(0), f(1), -infinity, -1)
1
sage: integer_list.upper_bound(0, infinity, f(0), f(5), -infinity, -1)
15
sage: integer_list.upper_bound(0, infinity, f(0), f(5), -infinity, -2)
9
"""
from sage.functions.all import floor as flr
if max_length < float('inf'):
return sum([ceiling(j) for j in range(max_length)])
elif max_slope < 0 and ceiling(1) < float('inf'):
maxl = flr(-ceiling(1) / max_slope)
return ceiling(1) * (maxl + 1) + binomial(maxl + 1, 2) * max_slope
#FIXME: only checking the first 10000 values, but that should generally
#be enough
elif [ceiling(j) for j in range(10000)] == [0] * 10000:
return 0
else:
return float('inf')
def upper_bound(min_length, max_length, floor, ceiling, min_slope, max_slope):
"""
Compute a coarse upper bound on the size of a vector satisfying the
constraints.
TESTS::
sage: import sage.combinat.integer_list as integer_list
sage: f = lambda x: lambda i: x
sage: integer_list.upper_bound(0,4,f(0), f(1),-infinity,infinity)
4
sage: integer_list.upper_bound(0, infinity, f(0), f(1), -infinity, infinity)
inf
sage: integer_list.upper_bound(0, infinity, f(0), f(1), -infinity, -1)
1
sage: integer_list.upper_bound(0, infinity, f(0), f(5), -infinity, -1)
15
sage: integer_list.upper_bound(0, infinity, f(0), f(5), -infinity, -2)
9
"""
from sage.functions.all import floor as flr
if max_length < float('inf'):
return sum( [ ceiling(j) for j in range(max_length)] )
elif max_slope < 0 and ceiling(1) < float('inf'):
maxl = flr(-ceiling(1)/max_slope)
return ceiling(1)*(maxl+1) + binomial(maxl+1,2)*max_slope
#FIXME: only checking the first 10000 values, but that should generally
#be enough
elif [ceiling(j) for j in range(10000)] == [0]*10000:
return 0
else:
return float('inf')