

We start with examining the area between 0 and pi We start with examining the area between 0 and pi 
2.5333470746795834 2.5333470746795834 
Okay, we found a root in [0,pi] equal to that, so we look from zero to that root, and from there to pi. Okay, we found a root in [0,pi] equal to that, so we look from zero to that root, and from there to pi. 
1.5707963267948966 1.5707963267948966 
1.57079632679490 1.57079632679490 
Traceback (click to the left of this block for traceback) ... RuntimeError: f appears to have no zero on the interval Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_16.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# * coding: utf8 *\\n" + _support_.preparse_worksheet_cell(base64.b64decode("ZmluZF9yb290KCBmKHgpID09IGcoeCksIDIuNTMzMzUsIHBpKQ=="),globals())+"\\n"); execfile(os.path.abspath("___code___.py")) File "", line 1, in <module> File "/tmp/tmpgT6I9s/___code___.py", line 3, in <module> exec compile(u'find_root( f(x) == g(x), _sage_const_2p53335 , pi) File "", line 1, in <module> File "/home/sageserver/sage/sage5.0stock/local/lib/python2.7/sitepackages/sage/numerical/optimize.py", line 72, in find_root return f.find_root(a=a,b=b,xtol=xtol,rtol=rtol,maxiter=maxiter,full_output=full_output) File "expression.pyx", line 8316, in sage.symbolic.expression.Expression.find_root (sage/symbolic/expression.cpp:31805) File "/home/sageserver/sage/sage5.0stock/local/lib/python2.7/sitepackages/sage/numerical/optimize.py", line 104, in find_root raise RuntimeError, "f appears to have no zero on the interval" RuntimeError: f appears to have no zero on the interval 
We did not find a root in the second subdivision, but we found one in the first. Now we'll look between 0 and the new root, and between the new root and the old root. We did not find a root in the second subdivision, but we found one in the first. Now we'll look between 0 and the new root, and between the new root and the old root. 
0.6082455789102097 0.6082455789102097 
Traceback (click to the left of this block for traceback) ... RuntimeError: f appears to have no zero on the interval Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_21.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# * coding: utf8 *\\n" + _support_.preparse_worksheet_cell(base64.b64decode("ZmluZF9yb290KCBmKHgpID09IGcoeCksIDEuNTcwODAsIDIuNTMzMzQp"),globals())+"\\n"); execfile(os.path.abspath("___code___.py")) File "", line 1, in <module> File "/tmp/tmpuzSd9D/___code___.py", line 3, in <module> exec compile(u'find_root( f(x) == g(x), _sage_const_1p57080 , _sage_const_2p53334 ) File "", line 1, in <module> File "/home/sageserver/sage/sage5.0stock/local/lib/python2.7/sitepackages/sage/numerical/optimize.py", line 72, in find_root return f.find_root(a=a,b=b,xtol=xtol,rtol=rtol,maxiter=maxiter,full_output=full_output) File "expression.pyx", line 8316, in sage.symbolic.expression.Expression.find_root (sage/symbolic/expression.cpp:31805) File "/home/sageserver/sage/sage5.0stock/local/lib/python2.7/sitepackages/sage/numerical/optimize.py", line 90, in find_root raise RuntimeError, "f appears to have no zero on the interval" RuntimeError: f appears to have no zero on the interval 
Okay, now we are almost done. We have to check between 0 and 0.608245... Okay, now we are almost done. We have to check between 0 and 0.608245... 
Traceback (click to the left of this block for traceback) ... RuntimeError: f appears to have no zero on the interval Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_23.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# * coding: utf8 *\\n" + _support_.preparse_worksheet_cell(base64.b64decode("ZmluZF9yb290KCBmKHgpID09IGcoeCksIDAsIDAuNjA4MjQ1KQ=="),globals())+"\\n"); execfile(os.path.abspath("___code___.py")) File "", line 1, in <module> File "/tmp/tmpevdkmH/___code___.py", line 3, in <module> exec compile(u'find_root( f(x) == g(x), _sage_const_0 , _sage_const_0p608245 ) File "", line 1, in <module> File "/home/sageserver/sage/sage5.0stock/local/lib/python2.7/sitepackages/sage/numerical/optimize.py", line 72, in find_root return f.find_root(a=a,b=b,xtol=xtol,rtol=rtol,maxiter=maxiter,full_output=full_output) File "expression.pyx", line 8316, in sage.symbolic.expression.Expression.find_root (sage/symbolic/expression.cpp:31805) File "/home/sageserver/sage/sage5.0stock/local/lib/python2.7/sitepackages/sage/numerical/optimize.py", line 90, in find_root raise RuntimeError, "f appears to have no zero on the interval" RuntimeError: f appears to have no zero on the interval 
Now we are done. Now we are done. 




0.997494986604054 0.997494986604054 
0.997494986604054 0.997494986604054 
