#1956: implement multivariate truncated power series arithmetic
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Reporter: was
| Owner: pernici
Type: enhancement
| Status: needs_review
Priority: major
| Milestone: sage-4.6.2
Component: commutative algebra
| Keywords: multivariate power series
Author: Niles Johnson
| Upstream: N/A
Reviewer: Martin Albrecht, Simon King
| Merged:
Work_issues: multivariate series on 1 generator should remain different from a
univariate series |
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Comment(by pernici):
The method sqrt of MPowerSeries does not work because sqrt does not
currently work for series on polynomial rings.
In ticket #10720 nth_root is added;
applying trac_10720_power_series_nth_root_2.patch
the definition of nth_root for MPowerSeries is
{{{
sage: def nth_root(self, n):
....: return self.parent(self._bg_value.nth_root(n))
....:
}}}
Examples:
{{{
sage: R.<x,y> = QQ[[]]
sage: p = 1 + 2*x + 3*y + R.O(20)
sage: nth_root(p^10,2) - p^5
0 + O(x, y)^20
sage: nth_root(p^10,5) - p^2
0 + O(x, y)^20
sage: nth_root(p^-10,2) - p^-5
0 + O(x, y)^20
sage: nth_root(p^-10,5) - p^-2
0 + O(x, y)^20
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/1956#comment:84>
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