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7.7.8.0. lpGlDimBound
Procedure from library fpaprops.lib (see fpaprops_lib).
- Usage:
- lpGlDimBound(I); I an ideal
- Return:
- int, an upper bound for the global dimension, -1 means infinity
- Purpose:
- computing an upper bound for the global dimension
- Assume:
- - basering is a Letterplace ring, G is a reduced Groebner Basis
- Note:
- if I = LM(I), then the global dimension is equal the Gelfand
Kirillov dimension if it is finite
Global dimension should be 0 for A/G = K and 1 for A/G = K<x1...xn>
Example:
| LIB "fpaprops.lib";
ring r = 0,(x,y),dp;
def R = makeLetterplaceRing(5); // constructs a Letterplace ring
setring R; // sets basering to Letterplace ring
ideal G = x(1)*x(2), y(1)*y(2),x(1)*y(2)*x(3); // ideal G contains a
//Groebner basis
lpGlDimBound(G); // invokes procedure with Groebner basis G
==> 0
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