#5453: [with patch, needs review] Create a ring for working with polynomials in
countably infinitely many variables
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Reporter: mhansen | Owner: mhansen
Type: enhancement | Status: assigned
Priority: major | Milestone: sage-3.4.1
Component: commutative algebra | Keywords:
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Comment(by mhansen):
Replying to [comment:4 SimonKing]:
> But how? Perhaps it would be better if the f.g. polynomial rings were
more hidden. For example, the elements of an infinite polynomial ring
could be described not simply as a polynomial (say, {{{x100*x101+x90}}})
but as a pair formed by a polynomial in a smaller ring and an offset, say
{{{(90,x10*x11+x0)}}}, or perhaps by an even smaller polynomial and a
permutation, say {{{(((0,90),(1,100),(2,101)), x1*x2+x0)}}}.
>
> I think a compromise between speed and size makes sense. Or perhaps even
concurrent models, similar to dense vs. sparse matrices.
Yes, I even mention this in the documentation that the current
implementation is definitely tailored to what I needed and that it would
be a good project to have different backends.
The primary problem will be doing the arithmetic efficiently. This is not
my area of expertise though.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5453#comment:5>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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