def make_constant(graphs, hyp, target, invariant):
"""
Parameters
----------
graphs : dictionary of graphs with precomputed graph properties
hyp : hypothesis object
target : graph invariant to conjecture on
invariant : graph invariant to compare with target
Returns
-------
[lower, upper] : list
lower : conjecture object
- 'If G satisfies hyp, then target(G) >= invariant(G) + m'
where m = min{target(G) - invariant(G): G is in the graph database}
upper : conjecture object
- 'If G satisfies hyp, then target(G) <= invariant(G) + M',
where M = max{target(G) - invariant(G): G is in the graph database}.
"""
constants = []
for G in graphs:
constants.append(G[target] - G[invariant])
if constants == []:
lower = None
upper = None
return lower, upper
else:
constants.sort()
m = min(constants)
M = max(constants)
if m == 0:
lower = Conjecture(hyp, target, " >= ", f"{invariant}")
elif m > -4 and m < 4:
lower = Conjecture(hyp, target, " >= ", f"{invariant} + {m}")
else:
lower = None
if M == 0:
upper = Conjecture(hyp, target, " <= ", f"{invariant}")
elif M > -4 and M < 4:
upper = Conjecture(hyp, target, " <= ", f"{invariant} + {M}")
else:
upper = None
return [lower, upper]
def make_ratio(graphs, hyp, target, invariant):
"""
Parameters
----------
graphs : dictionary of graphs with precomputed graph properties
hyp : hypothesis object
target : graph invariant to conjecture on
invariant : graph invariant to compare with target
Returns
-------
[lower, upper] : list
lower : conjecture object
- 'If G satisfies hyp, then target(G) >= m*invariant(G)'
where m = min{target(G)/invariant(G): G is in the graph database}
upper : conjecture object
- 'If G satisfies hyp, then target(G) <= M*invariant(G)',
where M = max{target(G)/invariant(G): G is in the graph database}.
"""
ratios = []
for G in graphs:
ratios.append(
Fraction(G[target] / G[invariant]).limit_denominator(1000))
if ratios == []:
lower = None
upper = None
return lower, upper
else:
ratios.sort()
m = min(ratios)
M = max(ratios)
if m == 1:
lower = Conjecture(hyp, target, " >= ", f"{invariant}")
elif m > -4 and m < 4:
lower = Conjecture(hyp, target, " >= ", f"{m} * {invariant}")
else:
lower = None
if M == 1:
upper = Conjecture(hyp, target, " <= ", f"{invariant}")
elif M > -4 and M < 4:
upper = Conjecture(hyp, target, " <= ", f"{M} * {invariant}")
else:
upper = None
return [lower, upper]
def make_ratio_five(graphs, hyp, target, invariant1, invariant2, invariant3):
ratios = []
for G in graphs:
if G[invariant1] != G[invariant2]:
ratios.append(
Fraction(
(G[target] * (G[invariant1]) /
(G[invariant2] + G[invariant3]))).limit_denominator(1000))
if ratios == []:
upper = None
lower = None
return lower, upper
else:
m = min(ratios)
M = max(ratios)
if m == 1:
upper = Conjecture(
hyp, target, " <= ",
f"( {invariant2} + {invariant3} ) / {invariant1}")
elif m > -4 and m < 4:
upper = Conjecture(
hyp, target, " <= ",
f"{m} * ( {invariant2} + {invariant3} ) / {invariant1} ")
else:
upper = None
if M == 1:
upper = Conjecture(
hyp, target, " <= ",
f"( {invariant2} + {invariant3} ) / {invariant1}")
elif M > -4 and M < 4:
upper = Conjecture(
hyp, target, " <= ",
f"{M} * ( {invariant2} + {invariant3} ) / {invariant1} ")
else:
upper = None
return [lower, upper]
def make_ratio_four(graphs, hyp, target, invariant1, invariant2):
"""
Parameters
----------
graphs : dictionary of graphs with precomputed graph properties
hyp : hypothesis object
target : graph invariant to conjecture on
invariant1 : graph invariant to compare with target
invariant2 : graph invariant to compare with target
Returns
-------
[lower, upper] : list
lower : conjecture object
- 'If G satisfies hyp, then target(G) >= m*(invariant1(G) - invariant2(G))'
where m = min{target(G)/ (invariant1(G) - invariant2(G)): G is in the graph database}
upper : conjecture object
- 'If G satisfies hyp, then target(G) <= M*(invariant1(G) - invariant2(G))'
where M = max{target(G)/ (invariant1(G) - invariant2(G)): G is in the graph database}
"""
ratios = []
for G in graphs:
if G[invariant1] != G[invariant2]:
ratios.append(
Fraction(
G[target] /
(G[invariant1] - G[invariant2])).limit_denominator(1000))
if ratios == []:
upper = None
lower = None
return lower, upper
else:
m = min(ratios)
M = max(ratios)
if m == 1:
lower = Conjecture(hyp, target, " >= ",
f"{invariant1} - {invariant2}")
elif m > -4 and m < 4:
lower = Conjecture(hyp, target, " >= ",
f"{m} * ( {invariant1} - {invariant2} )")
else:
lower = None
if M == 1:
upper = Conjecture(hyp, target, " <= ",
f"{invariant1} - {invariant2}")
elif M > -4 and M < 4:
upper = Conjecture(hyp, target, " <= ",
f"{M} * ( {invariant1} - {invariant2} )")
else:
upper = None
return [lower, upper]
def make_constant_two(graphs, hyp, target, invariant1, invariant2):
"""
Parameters
----------
graphs : dictionary of graphs with precomputed graph properties
hyp : hypothesis object
target : graph invariant to conjecture on
invariant1 : graph invariant to compare with target
invariant2 : graph invariant to compare with target
Returns
-------
[lower, upper] : list
lower : conjecture object
- 'If G satisfies hyp, then target(G) >= invariant1(G)/invariant2(G) + m'
where m = min{target(G) - invariant1(G)/invariant2(G): G is in the graph database}
upper : conjecture object
- 'If G satisfies hyp, then target(G) <= invariant1(G)/invariant2(G) + M',
where M = min{target(G) - invariant1(G)/invariant2(G): G is in the graph database}.
"""
constants = []
for G in graphs:
constants.append(
Fraction(G[target] -
(G[invariant1] / G[invariant2])).limit_denominator(1000))
if constants == []:
upper = None
lower = None
return lower, upper
else:
m = min(constants)
M = max(constants)
if m == 0:
lower = Conjecture(hyp, target, " >= ",
f"{invariant1} / {invariant2}")
elif m > -4 and m < 4:
lower = Conjecture(hyp, target, " >= ",
f"( {invariant1} / {invariant2} ) + {m}")
else:
lower = None
if M == 0:
upper = Conjecture(hyp, target, " <= ",
f"{invariant1} / {invariant2}")
elif M > -4 and M < 4:
upper = Conjecture(hyp, target, " <= ",
f"( {invariant1} / {invariant2} ) + {M}")
else:
upper = None
return lower, upper