Singular Manual: teach_lpSickleDim

| #### 7.10.1.6 teach_lpSickleDim Procedure from library `fpadim.lib` (see fpadim_lib). Usage: teach_lpSickleDim(G[,degbound,n]); G an ideal, degbound, n optional integers Return: list Purpose: Compute the K-dimension and the mistletoes of K<X>/<G> Assume: - basering is a Letterplace ring. - if you specify a different degree bound degbound, degbound <= attrib(basering,uptodeg) holds. Note: - If L is the list returned, then L[1] is an integer, the K-dimension, L[2] is an ideal, the mistletoes. - 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; // G is a monomial Groebner basis
    teach_lpSickleDim(G); // invokes the procedure with ring parameters
    ==> [1]:
    ==>    6
    ==> [2]:
    ==>    _[1]=x*y
    ==>    _[2]=y*x*y
    // the factor algebra is finite, so the degree bound, given
    // by the Letterplace ring is not necessary
    teach_lpSickleDim(G,0); // procedure without any degree bound
    ==> [1]:
    ==>    6
    ==> [2]:
    ==>    _[1]=x*y
    ==>    _[2]=y*x*y

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