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7.7.7.0. ivDimCheck
Procedure from library fpadim.lib (see fpadim_lib).
- Usage:
- ivDimCheck(L,n); L a list of intmats, n an integer
- Return:
- int, 0 if the dimension is finite, or 1 otherwise
- Purpose:
- Decides, whether the K-dimension is finite or not
- Assume:
- - basering is a Letterplace ring
- All rows of each intmat correspond to a Letterplace monomial
For the encoding of the variables see the overview.
- Note:
- - n is the number of variables
Example:
| | LIB "fpadim.lib";
ring r = 0,(x,y),dp;
def R = makeLetterplaceRing(5); // constructs a Letterplace ring
R;
==> // characteristic : 0
==> // 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
//some intmats, which contain monomials in intvec representation as rows
intmat I1 [2][2] = 1,1,2,2; intmat I2 [1][3] = 1,2,1;
intmat J1 [1][2] = 1,1; intmat J2 [2][3] = 2,1,2,1,2,1;
print(I1);
==> 1 1
==> 2 2
print(I2);
==> 1 2 1
print(J1);
==> 1 1
print(J2);
==> 2 1 2
==> 1 2 1
list G = I1,I2;// ideal, which is already a Groebner basis
list I = J1,J2; // ideal, which is already a Groebner basis and which
ivDimCheck(G,2); // invokes the procedure, factor is of finite K-dimension
==> 0
ivDimCheck(I,2); // invokes the procedure, factor is not of finite K-dimension
==> 1
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