Singular Manual: lpMonomialBasis

| #### 7.10.1.4 lpMonomialBasis Procedure from library `fpadim.lib` (see fpadim_lib). Usage: lpMonomialBasis(d, donly, J); d, donly integers, J an ideal Return: ideal Purpose: computes a list of free monomials in a Letterplace basering R of degree at most d and not contained in <LM(J)> if donly <> 0, only monomials of degree d are returned Assume: - basering is a Letterplace ring. - d <= attrib(basering,uptodeg) holds. - J is a Groebner basis Note: will be replaced with reduce(maxideal(d), J); soon Example:
    LIB "fpadim.lib";
    ring r = 0,(x,y),dp;
    def R = freeAlgebra(r, 7); setring R;
    ideal J = x*y*x - y*x*y;
    option(redSB); option(redTail);
    J = letplaceGBasis(J);
    J;
    ==> J[1]=x*y*x-y*x*y
    ==> J[2]=y*x*y*y*x-x*y*y*x*y
    ==> J[3]=y*x*y*y*y*x-x*x*y*y*x*y
    ==> J[4]=y*x*y*y*y*y*x-x*x*x*y*y*x*y
    //monomials of degree 2 only in K<x,y>:
    lpMonomialBasis(2,1,ideal(0));
    ==> _[1]=x*x
    ==> _[2]=y*x
    ==> _[3]=x*y
    ==> _[4]=y*y
    //monomials of degree <=2 in K<x,y>
    lpMonomialBasis(2,0,ideal(0));
    ==> _[1]=1
    ==> _[2]=x
    ==> _[3]=y
    ==> _[4]=x*x
    ==> _[5]=y*x
    ==> _[6]=x*y
    ==> _[7]=y*y
    //monomials of degree 3 only in K<x,y>/J
    lpMonomialBasis(3,1,J);
    ==> _[1]=x*x*x
    ==> _[2]=y*x*x
    ==> _[3]=y*y*x
    ==> _[4]=x*x*y
    ==> _[5]=y*x*y
    ==> _[6]=x*y*y
    ==> _[7]=y*y*y
    //monomials of degree <=3 in K<x,y>/J
    lpMonomialBasis(3,0,J);
    ==> _[1]=1
    ==> _[2]=x
    ==> _[3]=y
    ==> _[4]=x*x
    ==> _[5]=y*x
    ==> _[6]=x*y
    ==> _[7]=y*y
    ==> _[8]=x*x*x
    ==> _[9]=y*x*x
    ==> _[10]=y*y*x
    ==> _[11]=x*x*y
    ==> _[12]=y*x*y
    ==> _[13]=x*y*y
    ==> _[14]=y*y*y

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