/**/ use S ::= QQ[x,y,z];
/**/ I := ideal(x^3-y*z, y^2-x*z, z^2-x^2*y);
/**/ Q := ideal(y, z);
/**/ PS := PrimaryHilbertSeries(I, Q); PS;
/**/ use S ::= QQ[x,y,z,w];
/**/ I := ***Ideal(
/**/ x^5 - yz, y^4 - xz^2, xy^3 - zw, x^2z - yw,
/**/ y^2z^2 - w^3, y^3z - x^2w^2, x^3w - z^2, xyw^2 - z^3,
/**/ x^3y^2 - w^2, xz^4 - y^2w^3, yz^5 - xw^5, y^3w^5 - z^7,
/**/ x^2w^7 - z^8, z^9 - yw^8)***;
/**/ Q := ideal(x, y, z);
/**/ PS := PrimaryHilbertSeries(I, Q); PS;
/**/ $hp.PSerToHilbert(PS);
/**/ use S ::= ZZ/(32003)[x,y,z];
/**/ I := ideal(S, []); -- ideal in S with no generators
/**/ Q := ideal(x, y, z^2);
/**/ PS := PrimaryHilbertSeries(I, Q); PS;
/**/ $hp.PSerToHilbert(PS);
/**/ HV := $hp.PSerHVector(PS); -- the H-vector associated to PS
/**/ use S ::= ZZ/(32003)[x,y,z,w];
/**/ I := ***Ideal(-yz + xw, z^3 - yw^2, -xz^2 + y^2w, -y^3 + x^2z)***;
/**/ Q := ideal(x, y, z^2, w^3);
/**/ PS := PrimaryHilbertSeries(I, Q); PS;
/**/ $hp.PSerToHilbert(PS);
/**/ HV := $hp.PSerHVector(PS);
/**/ $primary.E(0, HV);
/**/ [ $primary.E(J,HV) | J in 0..($hp.PSerDim(PS)-2) ];
/**/ [ $primary.E(J,HV) | J in 0..(len(HV)-1) ];
/**/ use S ::= ZZ/(32003)[x,y,z,w];
/**/ I := ***Ideal(x^3-y^7, x^2y - xw^3-z^6)***;
/**/ Q := ideal(x, y, z, w);
/**/ PS := PrimaryHilbertSeries(I, Q); PS;
/**/ $hp.PSerToHilbert(PS);
/**/ HV := $hp.PSerHVector(PS);
/**/ [ $primary.E(J,HV) | J in 0..($hp.PSerDim(PS)-2) ];
/**/ [ $primary.E(J,HV) | J in 0..(len(HV)-1) ];
/**/ use S ::= ZZ/(32003)[x,y,z];
/**/ I := ideal(z^3);
/**/ Q := ideal(x^2, y^2, x*z, y*z);
/**/ PS := PrimaryHilbertSeries(I, Q); PS;
/**/ $hp.PSerToHilbert(PS);
/**/ HV := $hp.PSerHVector(PS);
/**/ [ $primary.E(J,HV) | J in 0..($hp.PSerDim(PS)-2) ];
/**/ [ $primary.E(J,HV) | J in 0..(len(HV)-1) ];
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