>
> Good idea. The ability to generate random expressions is very useful. We
> should make this more general and add it to sympy/utilities/iterables.py.
>
It's mesmerizing...may make the thing into a screen saver ;).
I had to make a few modifications to your script. First off, you were
> testing if integral(function.diff(x)) == function, which has two problems:
> first, you don't even pass it to simplify(). As I said, the integral will
> usually not look like the original function.
>
Ahh, right. Does it make sense to simplify the original formula before
returning it from build_func? Attached is a copy that simplifies that
equation, as well as the diff.
> Fourth, I also regular print the original expression, which makes it easier
> to copy and paste it if it is wrong and I need to debug it.
>
> I attached an improved script. Thanks for taking the time to look into
> this.
>
So the attached alteration (which is just a few edits to yours...we should
invent a system to control versions of files or something ;)) also makes the
seed explicit. You can copy the printed seed into the source to repeat the
same tests.
Cheers
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#! /usr/bin/env python
from sympy import (exp, log, risch_integrate, cancel, pretty_print, Symbol,
diff, simplify)
import random
import time
# Seed this test
seed = int(time.time())
random.seed(seed)
print "Random Seed Used %d" % seed
# Uncomment this with a proper seed if you wish to reproduce results
# random.seed(1234)
x = Symbol('x')
unops = [exp, log, lambda x: -x]
binops = [lambda x,y: x+y, lambda x,y: x-y, lambda x,y: x*y, lambda x,y: x/y]
TRIALS = 5
def build_func(starting_vars = 2, starting_nums = 4, prob_unary = 0.5):
parts = [x] * starting_vars
for i in range(starting_nums):
parts.append(random.randrange(1,10))
#print "Working with the following building blocks: %s" % str(parts)
while len(parts) > 1:
if random.random() < prob_unary:
index = random.randrange(0,len(parts))
parts[index] = random.choice(unops)(parts[index])
else:
random.shuffle(parts)
parts.append(random.choice(binops)(parts.pop(), parts.pop()))
return simplify(parts[0])
for i in range(TRIALS):
eq = build_func()
print "\n\n------------------------------\nTesting the following equation {%s}:\n" % str(eq)
pretty_print(eq)
print "\n\nDiff:\n"
d = simplify(diff(eq, x))
pretty_print(d)
print "\n\nIntegral of Diff:\n"
try:
res = risch_integrate(d, x)
except NotImplementedError, detail:
print "\nNotImplemented (%s)" % detail
else:
pretty_print(res)
print "\nDifference (should be constant): %s" % str(cancel(res - eq))
print "\nDiff difference (should be 0): %s" % str(cancel(diff(res, x) - d))
print "------------------------------"
