#5453: [with patch, needs review] Create a ring for working with polynomials in
countably infinitely many variables
---------------------------------+------------------------------------------
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 SimonKing):
Replying to [comment:9 SimonKing]:
> I suggest to use the method {{{change_ring()}}} of polynomial rings in
the background. Then, {{{stretch()}}} could be implemented along these
lines:
...
It seems that indeed the {{{while}}} loop that I gave above is both faster
and goes further when using my suggestion:
{{{
sage: R.<x1,y1>=QQ[]
sage: p=x1
sage: S=R.change_ring(names=['x2','y2'])
sage: n=2
sage: while(1):
....: p=S(p)
....: n=2*n
....: S=S.change_ring(names=['x%d'%(n),'y%d'%(n)])
....: print p
....:
x2
x4
x8
x16
x32
x64
x128
x256
x512
x1024
x2048
x4096
x8192
x16384
x32768
x65536
x131072
x262144
x524288
x1048576
x2097152
x4194304
x8388608
x16777216
x33554432
x67108864
x134217728
x268435456
x536870912
x1073741824
x2147483648
x4294967296
x8589934592
x17179869184
x34359738368
x68719476736
x137438953472
x274877906944
x549755813888
x1099511627776
x2199023255552
x4398046511104
x8796093022208
x17592186044416
x35184372088832
x70368744177664
x140737488355328
x281474976710656
x562949953421312
x1125899906842624
x2251799813685248
x4503599627370496
x9007199254740992
x18014398509481984
x36028797018963968
x72057594037927936
x144115188075855872
x288230376151711744
x576460752303423488
x1152921504606846976
x2305843009213693952
}}}
Only at that point was a type error, because the next number is not an
{{{int}}} anymore.
So, my suggestions are:
* An {{{InfinitePolynomialRing}}} should ''not'' have an underlying
polynomial ring by itself.
* Only the ''elements'' of an {{{InfinitePolynomialRing}}} should have an
underlying polynomial ring.
The advantage of my suggestion is that the rings become much smaller.
Cheers,
Simon
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5453#comment:10>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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