I made this function to test for the equivalence of two expressions. It
doesn't really prove anything, but if the tests are many, the probability
of it being wrong becomes negligible. Do such utility functions have a
place in SymPy?
def equiv(a, b, ntests=15):
""" Test if expression a is equivalent to b
by comparing the results of many random numeric tests """
# get the symbols
sb_a = filter(lambda x: x.is_Symbol, a.atoms())
sb_b = filter(lambda x: x.is_Symbol, b.atoms())
sb = list(set(sb_a + sb_b))
eq = True
for i in xrange(ntests):
k = dict(zip(sb, np.random.randn(len(sb))))
r_a = a.subs( k )
r_b = b.subs( k )
# prove there is a difference
if (r_a - r_b)**2 > 1e-30: # not the same? the expressions are
different
eq = False
break
return eq
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