Here's a different approach, which is more efficient, but poses its own challenges:
sage: I = R.ideal(x^2) sage: Q = R.quo(I) sage: f = Q(x^3*y^3 + x^2*y^4 + x*y + x + y + 1) sage: f xbar*ybar + xbar + ybar + 1 So, the variables look different, and with reason. But: sage: %timeit g*g 625 loops, best of 3: 3.4 µs per loop sage: %timeit f*f 625 loops, best of 3: 30.5 µs per loop sage: %timeit g+g 625 loops, best of 3: 2.39 µs per loop sage: %timeit f+f 625 loops, best of 3: 27.2 µs per loop Multiplication is faster than Simon's solution, but addition is (curiously) much slower. regards john perry On Monday, June 3, 2013 7:12:34 PM UTC-5, Sam math wrote: > > I have a multivariate polynomial and want to keep only up to a certain > degree. I already know how to do this for the univariate case. > > For 1 variable, I'd do: > > R.<x> = PolynomialRing(QQ) > > f = x^4 + x^2 + x^3 + x + 1 > > f = f + O(x^3) > > print f > > #output would be 1 + x + x^2... which is what I want. > > How do I do this for a multivariate polynomial? It says O(.) is not > defined... > > R.<x,y> = PolynomialRing(QQ) > > f = x^3*y^3 + x^2 * y^4 + x*y + x + y + 1 > > How can I chop this polynomial up to a certain degree of x and y? I.e. I > want to keep up until the second degree of x only (regardless of y). > > I know one way I could go about this is to just redefine the polynomial by > looping through the first few coefficients, but I'm looking for a more > efficient/easier way. > > Thanks! > > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
