If you just want to do simple arithmetic, you can use the FF class:
In [1]: FF(12)
Out[1]: ℤ₁₂
In [2]: FF(12)(4)
Out[2]: 4 mod 12
In [3]: FF(12)(4)/FF(12)(11)
Out[3]: 8 mod 12
Note that the name FF comes from finite field, so this may not work if
the modulus is not a power of a prime. For example:
In [4]: FF(12)(4)/FF(12)(2)
---------------------------------------------------------------------------
NotInvertible Traceback (most recent call last)
/Users/aaronmeurer/Documents/python/sympy/sympy/<ipython console> in <module>()
/Users/aaronmeurer/Documents/python/sympy/sympy/sympy/polys/domains/modularinteger.pyc
in __div__(self, other)
92
93 if val is not None:
---> 94 return self.__class__(self.val * self._invert(val))
95 else:
96 return NotImplemented
/Users/aaronmeurer/Documents/python/sympy/sympy/sympy/polys/domains/modularinteger.pyc
in _invert(cls, value)
160 @classmethod
161 def _invert(cls, value):
--> 162 return cls.dom.invert(value, cls.mod)
163
164 def invert(self):
/Users/aaronmeurer/Documents/python/sympy/sympy/sympy/polys/domains/ring.pyc
in invert(self, a, b)
39 return s % b
40 else:
---> 41 raise NotInvertible("zero divisor")
42
43 def revert(self, a):
NotInvertible: zero divisor
I'm not sure if you will get other errors if you use non-fields.
If you want to solve congruence relations, like x = 2 mod 3, then you
might look at this branch: https://github.com/sympy/sympy/pull/390.
It would be great if you could give that branch a complete review, as
I've only been able to comment on the code quality up to this point.
Aaron Meurer
On Fri, Sep 23, 2011 at 2:16 AM, smichr <smi...@gmail.com> wrote:
> I'm not sure where to look in sympy for support of things like solving
> congruence relationships (what number is 2 mod 3, 3 mod 5 and 2 mod 7;
> answer 23 mod 105) and operations modulo n, e.g., from
> http://tinyurl.com/3atamuj,
> the following question:
>
> In Z_12, divide 4 by 2, 3, 5, 7,8, and 11
>
> Do we have support for such things?
>
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