On Feb 21, 2:18 am, Simon King <[EMAIL PROTECTED]> wrote:
> Dear John,
>
> i think i figured out how to form a tensor product of several copies
> of a (non-commutative) ring with itself...
>
> On Feb 20, 9:47 pm, "William Stein" <[EMAIL PROTECTED]> wrote:
> <snip>> No, that would not be reasonable. [[woah, John Palmieri just appeared
> > in my office... chat for a while...] Anyway, copy should return an exact
> > copy since that's the semantics of __copy__ in Python. However,
> > I strongly encourage you to write a method like you describe and
> > just call it something slightly different, e.g.,
> > def change_names(self, ...):
>
> <snip>
>
> ... and i can also demonstrate how "change_names" could work.
>
> The idea is as follows.
> Singular describes a ring by means of a "ringlist". It provides the
> variable names, the characteristic, the ordering, and also (if it
> applies) the non-commutative relations or quotients by an ideal.
>
> Now, we simply change the variable names in the ringlist and form a
> new ring by the altered ringlist. Eventually, we sum up the copies of
> the ring.
> I've put the following into a file tensorpower.spyx:
>
> import sage
> import sage.all
> from sage.interfaces.singular import singular
>
> def tensorpower(R,n):
> R.set_ring()
> L=R.ringlist()
> OutR=R
> for nr from 0<=nr<n-1:
> R.set_ring()
> for i from 1<=i<=len(L[2]):
> singular.eval('%s[2][%d] = "%s"'%(L.name(),i,"'"+str(L[2]
> [i])))
> OutR=OutR+L.ring()
> return OutR
I'm having problems with this: if I call this tensorpower.spyx (or use
the one you emailed to me), I get this:
sage: attach tensorpower.spyx
Loading of file "/Users/palmieri/.sage/tensorpower.spy" has type not
implemented.
If I rename it to tensor.sage (not sure if this is a good idea), I
get:
sage: attach tensor.sage
line 10
for nr from Integer(0)<=nr<n-Integer(1):
The same thing happens if I type the function definition directly into
Sage.
This is with Sage 2.10.1 on Mac OS X (although I can test it on a
linux machine tomorrow). I'm probably doing something stupid,
though...
I have one question about the results of your computation; see below.
> Now, i get the following sage session:
>
> sage: attach tensorpower.spyx
> Compiling /home/king/Projekte/Plural/tensorpower.spyx...
> sage: R=singular.ring(0,'(x1,x12,x2)','dp')
> sage: C=singular.matrix(3,3,'1,-1,-1, -1,1,-1, -1,-1,1')
> sage: D=singular.matrix(3,3,'0,0,-x12, 0,0,0, 0,0,0')
> sage: singular.LIB('ncall.lib')
> sage: S=C.nc_algebra(D)
> sage: X=tensorpower(S,3)
> sage: X.set_ring()
> sage: X
>
> // characteristic : 0
> // number of vars : 6
Shouldn't this be 9?
> // block 1 : ordering dp
> // : names x1 x12 x2
> // block 2 : ordering dp
> // : names 'x1 'x12 'x2
> // block 3 : ordering dp
> // : names ''x1 ''x12 ''x2
> // block 4 : ordering C
> // noncommutative relations:
> // x12x1=-x1*x12
> // x2x1=-x1*x2-x12
> // x2x12=-x12*x2
> // 'x12'x1=-'x1*'x12
> // 'x2'x1=-'x1*'x2-'x12
> // 'x2'x12=-'x12*'x2
> // ''x12''x1=-''x1*''x12
> // ''x2''x1=-''x1*''x2-''x12
> // ''x2''x12=-''x12*''x2
>
> So, after tax declaration and adding a doc-string and doc-tests, i
> think this might be a patch.
>
> Yours
> Simon
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