ASKSAGE: Sage Q&A Forum - Latest question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 06 Dec 2017 17:09:09 -0600How to truncate a power series in two variables?http://ask.sagemath.org/question/39983/how-to-truncate-a-power-series-in-two-variables/I would like to truncate power-series by setting $y$ to 0, in order to express $y = x^3 - xy^2$ as a power series in $x$ by recursively plugging in the equation for $y$, then truncating.
R.<x, y> = PowerSeriesRing(QQ, default_prec = 20)
f = x^3 + x*y^2
j = f(x, f(x, f(x, f(x, f(x,y))))).expand()
j + O(y)
---------------------------------------------------------------------------
ArithmeticError Traceback (most recent call last)
<ipython-input-20-fe9380f2a091> in <module>()
----> 1 j + O(y)
/usr/lib/sagemath/local/lib/python2.7/site-packages/sage/rings/big_oh.py in O(*x, **kwds)
154 elif hasattr(x, 'O'):
155 return x.O(**kwds)
--> 156 raise ArithmeticError("O(%s) not defined" % (x,))
ArithmeticError: O(y) not defined
I have found that other variants, such as` j + O(x, y)^{31}`, `j.truncate(31)`, and `j + R.O(31)` also do not work. masseygirlWed, 06 Dec 2017 17:09:09 -0600http://ask.sagemath.org/question/39983/