Hello,
i would like to add that commutative variables in supercommutative
algebras may be local (whereas non-commutative variables must be
global), e.g:
{{{
LIB "nctools.lib";
ring r=0,(x,y,z), (ds(1), dp(2)); // x is local!
def E = superCommutative(2,3);setring E; E;
// characteristic : 0
// number of vars : 3
// block 1 : ordering ds
// : names x
// block 2 : ordering dp
// : names y z
// block 3 : ordering C
// noncommutative relations:
// zy=-yz
// quotient ring from ideal
_[1]=y2
_[2]=z2
> y*y; // SCA!
0
> 1+ x + y + z; // y > z > 1 > x !
y+z+1+x
}}}
This functionality was initially intended to support computation of
direct images of sheaves in certain cases but by no means limited to
that.
The Singular's "std" uses a modified Mora variant of BBA in such a
"local" case.
Feel free to experiment with this feature :)
Please do let us know about your favorite and yet missing non-
commutative features!
Any feedback is greatly appreciated!
Cheers,
Oleksandr
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