Polynomial modulus in QuotientRing

asked 2014-08-27 10:36:29 -0600

kekx gravatar image

updated 2015-01-14 07:37:04 -0600

FrédéricC gravatar image

I am trying to perform a polynomial modulus between elements in a QuotientRing, more or less like so:

sage: R = QuotientRing(ZZ[x], x**8+1)
sage: t = R.gen()
sage: g = 3*t^5 + 3*t^4 + 2*t^3 + 3*t^2 + t + 2
sage: a = -14*t^7 - t^6 + t^4 - 9*t^2 + 5*t + 1
sage: a.mod(g)
-14*xbar^7 - xbar^6 + xbar^4 - 9*xbar^2 + 5*xbar + 1

As you can see the modulus is not doing anything. I am not very well versed in this kind of maths, but I still believe that it should be possible to compute that modulus. Thus my question is, if it is possible to compute that modulus in sage, possibly via some kind of workaround.

I would be glad about any hints!

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What would you expect from such a command? In order for mod to makes sense the domain needs to have a well defined division, doesn't it?

vdelecroix gravatar imagevdelecroix ( 2014-08-28 10:29:12 -0600 )edit