#1956: implement multivariate truncated power series arithmetic
-------------------------------------------+--------------------------------
Reporter: was | Owner: pernici
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.7
Component: commutative algebra | Keywords: multivariate power
series
Author: Niles Johnson | Upstream: N/A
Reviewer: Martin Albrecht, Simon King | Merged:
Work_issues: |
-------------------------------------------+--------------------------------
Changes (by hlaw):
* cc: hlaw (added)
Comment:
First, thanks for all your work Niles, what you've done has already saved
me hours of pain!
There seems to be a problem with how coercion/evaluation works between two
multivariate power series rings when the number of variables in each
differs. For example:
{{{
sage: A.<a, b, c> = PowerSeriesRing(QQ)
sage: B.<s, t> = PowerSeriesRing(QQ)
sage: s(a, b)
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
/home/hlaw/Dropbox/org/<ipython console> in <module>()
/home/hlaw/src/sage-src/local/lib/python2.6/site-
packages/sage/rings/multi_power_series_ring_element.pyc in __call__(self,
*x, **kwds)
419 for i in range(len(x)):
420 try:
--> 421 xi = self.parent(x[i])
422 except AttributeError:
423 raise AttributeError(str(x[i])+" does not coerce
to parent ring.")
/home/hlaw/src/sage-src/local/lib/python2.6/site-
packages/sage/structure/element.so in
sage.structure.element.Element.parent (sage/structure/element.c:4069)()
/home/hlaw/src/sage-src/local/lib/python2.6/site-
packages/sage/rings/power_series_ring.pyc in __call__(self, f, prec,
check)
604 v = sage_eval(f.Eltseq())
605 return self(v) * (self.gen(0)**f.Valuation())
--> 606 return self.__power_series_class(self, f, prec,
check=check)
607
608 def construction(self):
/home/hlaw/src/sage-src/local/lib/python2.6/site-
packages/sage/rings/multi_power_series_ring_element.pyc in __init__(self,
parent, x, prec, is_gen, check)
352 self._bg_value =
parent._bg_ps_ring(x._bg_value)
353 except TypeError:
--> 354 raise TypeError("Unable to coerce into
background ring.")
355
356 elif xparent == parent._bg_ps_ring():
TypeError: Unable to coerce into background ring.
}}}
I would expect this to print `a`. Similar permutations with `s^2`, `s +
t`, etc. produce the same result.
Another problem, possibly related, is the following:
{{{
sage: B.<s, t> = PowerSeriesRing(QQ)
sage: C.<z> = PowerSeriesRing(QQ)
sage: s(z, z) # expect z
1
sage: s(z, z^2) # expect z
1
sage: s(0, z^2) # expect 0
0
sage: s(z^2, 0) # expect z^2
1
sage: (2*s^2)(z, z) # expect 2*z^2
2
sage: (2*s^2 + 3*t)(z, z) # expect 3*z + 2*z^2
5
sage: t(0, z) # expect z
1
sage: t(z, z) # expect z
1
sage: z(s + t) # expect s + t
s + t
sage: z(s) # expect s
s
sage: z(t) # expect t
t
}}}
Clearly `z` is being sent to 1 (one) somehow when going from `QQ[[s,t]]`
to `QQ[[z]]`, but the maps in the other direction work fine.
Both of these problems (assuming they're distinct) disappear when one does
the analogous calculations directly with multivariate ''polynomial''
rings.
Cheers, Hamish.
(Using Sage 4.6.2 +power series patches, on Ubuntu 10.10 64bit, Macbook
5.1.)
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/1956#comment:96>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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