'''
This file assumes that the conjecturing spkg is installed and that 'conjecturing.py' and
'matrixtheory.py' are loaded.
'''
def automatedMatrixSearch(objects, invariants, minimumSize, maximumSize, upperBound=True, steps=10, mainInvariant=1, verbose=False):
if verbose:
print("Starting with these objects:")
for m in objects:
print(" {}".format(m.rows()))
print("")
print("Available invariants:")
for pos, invariant in enumerate(invariants):
if type(invariant) == tuple:
name, _ = invariant
elif hasattr(invariant, '__name__'):
name = invariant.__name__
else:
name = 'invariant_{}'.format(pos)
if pos + 1 == mainInvariant:
print(" * {}".format(name))
else:
print(" {}".format(name))
print("")
for _ in range(steps):
l = conjecture(objects, invariants, mainInvariant, upperBound=upperBound)
if verbose:
print("Found the following conjectures:")
for c in l:
print(" {}".format(c))
print("")
noCounterExample = True
for i in range(minimumSize, maximumSize+1):
if verbose:
print("Looking for counterexamples of size {}".format(i))
for m in generateSymmetricMatrices(i):
try:
if any([not c.evaluate(m) for c in l]):
print("Adding {}".format(m.rows()))
objects.append(m)
noCounterExample = False
break
except:
print("Error while checking {}".format(m.rows()))
raise
if not noCounterExample: break
if noCounterExample:
print("No counterexample found")
break
if not noCounterExample:
l = conjecture(objects, invariants, mainInvariant, upperBound=upperBound)
if verbose:
print("Found the following conjectures:")
for c in l:
print(" {}".format(c))
print("")
return l
def inverseTriangularNumber(t):
n = int(sqrt(2*t))
assert n*(n+1)==2*t, "Not a triangular number: {}".format(t)
return n
def symmetricMatrixFromList(l):
n = inverseTriangularNumber(len(l))
m = [None] * n
end = 0
for i in range(n):
start = end
end += n - i
m[i] = [m[j][i] for j in range(i)] + l[start:end]
return matrix(m)
def int2base21(i, length):
if not i: return [0] * int(length)
l = []
while i:
l.append(i%21)
i//=21
l += [0]* (int(length)-len(l))
return l
def generateSymmetricMatrices(size):
length = ((size+1)*size/2)
count = 21**length
i = 0
while i < count:
yield symmetricMatrixFromList([n-10 for n in int2base21(i, length)])
i+=1
objects = [matrix([[1,1],[1,1]])]
def abs_determinant(m):
return abs(m.determinant())
invariants = [abs_determinant] + invariants
invariants.remove(determinant)
mainInvariant = invariants.index(abs_determinant)
conjectures = automatedMatrixSearch(objects, invariants, 2, 4, steps=100, verbose=True, mainInvariant=mainInvariant)
print("The conjectures are stored in the variable conjectures.")
