Hi Johannes! On 16 Nov., 23:48, Johannes Huisman <johannes.huis...@gmail.com> wrote: > Does sage have a command for polynomial division by increasing powers? I > could not find such a command. Of course, one may use power series > division in order to compute the quotient, but it would be neat if one > could avoid all that.
What exactly do you expect? For example: sage: P.<x> = QQ[] sage: p = P.random_element() sage: q = P.random_element() sage: p 4/3*x^2 - x + 7 sage: q 2/7*x^2 - x 1. Apparently you do not want that the quotient of p and q lives in the fraction field, as it is currently the case: sage: p/q (4/3*x^2 - x + 7)/(2/7*x^2 - x) 2. Do you need the "quotient with remainder"? Then you could do sage: p.quo_rem(q) (14/3, 11/3*x + 7) 3. Or do you want that the quotient of p and q actually is a power series? So, like this: sage: p/q # not implemented -7*x^-1 - 1 - 34/21*x - 68/147*x^2 - 136/1029*x^3 - 272/7203*x^4 - 544/50421*x^5 - 1088/352947*x^6 - 2176/2470629*x^7 - 4352/17294403*x^8 - 8704/121060821*x^9 - 17408/847425747*x^10 - 34816/5931980229*x^11 - 69632/41523861603*x^12 - 139264/290667031221*x^13 - 278528/2034669218547*x^14 - 557056/14242684529829*x^15 - 1114112/99698791708803*x^16 - 2228224/697891541961621*x^17 - 4456448/4885240793731347*x^18 + O(x^19) Possibility 3. requires that Frac(P) does not return a formal fraction field (which is currently the case) but a power series ring. I am sure that it would require much persuasion and a poll on sage-devel if one wants such change. Also note that the term order in P and Q differs (with the additional complication that Q(p) does not have an attribute leading_coefficient, but p does). sage: p 4/3*x^2 - x + 7 sage: Q(p) 7 - x + 4/3*x^2 So, if what you want is 3., then currently you have to use the power series ring manually, such as: sage: Q = PowerSeriesRing(QQ,'x') sage: Q(p)/q # q is automatically coerced into Q -7*x^-1 - 1 - 34/21*x - 68/147*x^2 - 136/1029*x^3 - 272/7203*x^4 - 544/50421*x^5 - 1088/352947*x^6 - 2176/2470629*x^7 - 4352/17294403*x^8 - 8704/121060821*x^9 - 17408/847425747*x^10 - 34816/5931980229*x^11 - 69632/41523861603*x^12 - 139264/290667031221*x^13 - 278528/2034669218547*x^14 - 557056/14242684529829*x^15 - 1114112/99698791708803*x^16 - 2228224/697891541961621*x^17 - 4456448/4885240793731347*x^18 + O(x^19) Cheers, Simon -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
