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
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
// 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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