Singular Manual: teach_lpKDim

| #### 7.10.1.3 teach_lpKDim Procedure from library `fpadim.lib` (see fpadim_lib). Usage: teach_lpKDim(G[,degbound, n]); G an ideal, degbound, n optional integers Return: int, the K-dimension of the factor algebra Purpose: Compute the K-dimension of a factor algebra, given via an ideal Assume: - basering is a Letterplace ring - if you specify a different degree bound degbound, degbound <= attrib(basering,uptodeg) holds. Note: - If degbound is set, there will be a degree bound added. 0 means no degree bound. Default: attrib(basering, uptodeg). - n is the number of variables, which can be set to a different number. Default: attrib(basering, lV). - If the K-dimension is known to be infinite, a degree bound is needed Example:
    LIB "fpadim.lib";
    ring r = 0,(x,y),dp;
    def R = freeAlgebra(r, 5); // constructs a Letterplace ring
    setring R; // sets basering to Letterplace ring
    ideal G = x*x, y*y,x*y*x;
    // ideal G contains a Groebner basis
    teach_lpKDim(G); //procedure invoked with ring parameters
    ==> 6
    // the factor algebra is finite, so the degree bound given by the Letterplace
    // ring is not necessary
    teach_lpKDim(G,0); // procedure without any degree bound
    ==> 6

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