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7.10.1.3 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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