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7.7.7.0. ivMis2Dim
Procedure from library fpadim.lib (see fpadim_lib).
- Usage:
- ivMis2Dim(M); M a list of intvecs
- Return:
- int, the K-dimension of the given algebra
- Purpose:
- Computing the K-dimension out of given mistletoes
- Assume:
- - The mistletoes have to be ordered lexicographically -> OrdMisLex.
Otherwise the returned value may differ from the K-dimension.
- basering is a Letterplace ring.
Example:
| | LIB "fpadim.lib";
ring r = 0,(x,y),dp;
def R = makeLetterplaceRing(5); // constructs a Letterplace ring
R;
==> // coefficients: QQ
==> // number of vars : 10
==> // block 1 : ordering a
==> // : names x(1) y(1) x(2) y(2) x(3) y(3) x(4) y(4) x(\
5) y(5)
==> // : weights 1 1 1 1 1 1 1 1 \
1 1
==> // block 2 : ordering dp
==> // : names x(1) y(1)
==> // block 3 : ordering dp
==> // : names x(2) y(2)
==> // block 4 : ordering dp
==> // : names x(3) y(3)
==> // block 5 : ordering dp
==> // : names x(4) y(4)
==> // block 6 : ordering dp
==> // : names x(5) y(5)
==> // block 7 : ordering C
setring R; // sets basering to Letterplace ring
intvec i1 = 1,2; intvec i2 = 2,1,2;
// the mistletoes are xy and yxy, which are already ordered lexicographically
list L = i1,i2;
ivMis2Dim(L); // returns the dimension of the factor algebra
==> 6
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