1521.sagews

Stein's trick

class integermodring:
    def __init__(self, modulus):
        self.modulus = modulus
    def eval(self, s, globals, locals):
        _temp = locals['Integer']
        locals['Integer'] = IntegerModRing(self.modulus)
        ans = python.eval(preparse(s),  globals, locals)
        locals['Integer'] = _temp
        return ans

%integermodring(23)
42 - 9 * 6

11

42 - 9 * 6

-12

class pyint:
    def eval(self, s, globals, locals):
        _temp = locals['Integer']
        locals['Integer'] = int
        ans = python.eval(preparse(s),  globals, locals)
        locals['Integer'] = _temp
        return ans
class myint:
    def eval(self, s, globals, locals):
        _temp = locals['Integer']
        locals['Integer'] = float
        ans = python.eval(preparse(s),  globals, locals)
        locals['Integer'] = _temp
        return ans

%pyint()
print type(45)
print 500 / 1000, 1000 / 1000
print 500 / 1000., 1000 / 1000.

<type 'int'> 0 1 0.500000000000000 1.00000000000000

%myint()
print type(45)
print 500 / 1000, 1000 / 1000
print 500 / 1000., 1000 / 1000.

<type 'float'> 0.5 1.0 0.500000000000000 1.00000000000000

print type(45)
print 500 / 1000, 1000 / 1000
print 500 / 1000., 1000 / 1000.

<type 'sage.rings.integer.Integer'> 1/2 1 0.500000000000000 1.00000000000000

import matplotlib.pyplot as plt

%pyint()
plt.plot([1, 1/2, 1/3, 1/4], [1, 1/4, 1/9, 1/16], 'ro')
plt.axis([0, 1/2, 0, 2/5])
plt.savefig('pyint.png')

(0,0) ?

%myint()
plt.plot([1, 1/2, 1/3, 1/4], [1, 1/4, 1/9, 1/16], 'ro')
plt.axis([0, 1/2, 0, 2/5])
plt.savefig('myint.png')

plt.plot([1, 1/2, 1/3, 1/4], [1, 1/4, 1/9, 1/16], 'ro')
plt.axis([0, 1/2, 0, 2/5])
plt.savefig('integer.png')

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/sage/sagenb/sage_notebook/worksheets/qed777/19/code/18.py", line 8, in <module> plt.axis([_sage_const_0 , _sage_const_1 /_sage_const_2 , _sage_const_0 , _sage_const_2 /_sage_const_5 ]) File "/home/sage/sage_install/sage-a/local/lib/python2.5/site-packages/matplotlib/pyplot.py", line 827, in axis v = ax.axis(*v, **kwargs) File "/home/sage/sage_install/sage-a/local/lib/python2.5/site-packages/matplotlib/axes.py", line 1250, in axis self.set_xlim([v[0], v[1]]) File "/home/sage/sage_install/sage-a/local/lib/python2.5/site-packages/matplotlib/axes.py", line 1944, in set_xlim xmin, xmax = mtransforms.nonsingular(xmin, xmax, increasing=False) File "/home/sage/sage_install/sage-a/local/lib/python2.5/site-packages/matplotlib/transforms.py", line 2237, in nonsingular if (not np.isfinite(vmin)) or (not np.isfinite(vmax)): TypeError: function not supported for these types, and can't coerce safely to supported types