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7.5.20.0. Exterior
Procedure from library nctools.lib (see nctools_lib).
- Usage:
- Exterior();
- Return:
- qring
- Purpose:
- create the exterior algebra of a basering
- Note:
- activate this qring with the "setring" command
- Theory:
- given a basering, this procedure introduces the anticommutative relations x(j)x(i)=-x(i)x(j) for all j>i,
moreover, creates a factor algebra modulo the two-sided ideal, generated by x(i)^2 for all i
Example:
| | LIB "nctools.lib";
ring R = 0,(x(1..3)),dp;
def ER = Exterior();
setring ER;
ER;
==> // coefficients: QQ considered as a field
==> // number of vars : 3
==> // block 1 : ordering dp
==> // : names x(1) x(2) x(3)
==> // block 2 : ordering C
==> // noncommutative relations:
==> // x(2)x(1)=-x(1)*x(2)
==> // x(3)x(1)=-x(1)*x(3)
==> // x(3)x(2)=-x(2)*x(3)
==> // quotient ring from ideal
==> _[1]=x(3)^2
==> _[2]=x(2)^2
==> _[3]=x(1)^2
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