/**/ Use R ::= QQ[t,x,y,z];
/**/ HilbertSeries(R/Ideal(R,[]));
(1) / (1-t)^4
/**/ Q := R/Ideal(t^2, x, y^3); Poincare(Q);
(1 +2*t +2*t^2 +t^3) / (1-t)
/**/ Poincare(R^2/Module([x^2,y^2],[z,y])); --***OBSOLETE MANUAL: WORK IN PROGRESS***
(2 + t) / (1-t)^3
/**/ Poincare(Module([x^2,y^2],[z,y])); ***Obsolete manual: work in progress**
(t + t^2) / (1-t)^4
/**/ Ws := RowMat([1,2,3,4]);
/**/ P := NewPolyRing(QQ,["t","x","y","z"],CompleteToOrd(Ws),1);
/**/ Use P;
/**/ Poincare(P/ideal(t^2, x, y^3));
--- Non-simplified HilbertPoincare' Series ---
(1 - 2*t^2 + t^4 - t^9 + 2*t^11 - t^13) / ( (1-t)*(1-t^2)*(1-t^3)*(1-t^4) )
Poincare(Ideal(t^2, x, y^3));
--- Non-simplified HilbertPoincare' Series ---
(2*t^2 - t^4 + t^9 - 2*t^11 + t^13) / ( (1-t)*(1-t^2)*(1-t^3)*(1-t^4) )
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Use R ::= QQ[t,x,y,z], Weights(Mat([[1,2,3,4],[0,0,5,8]]));
Poincare(R/Ideal(t^2, x, y^3));
--- Non Simplified Pseries ---
( - t^13x^15 + 2t^11x^15 - t^9x^15 + t^4-2t^2 + 1) / ( (1-t) (1-t^2) (1-t^3x^5) (1-t^4x^8) )
/**/ Ws := Mat([[1,2,3,4],[0,0,5,8]]);
/**/ P := NewPolyRing(QQ, ["t","x","y","z"], CompleteToOrd(Ws), 2);
/**/ Use P;
/**/ Poincare(P/Ideal(t^2, y^3));
--- Non-simplified HilbertPoincare' Series ---
(1 - t^2 - t^9*x^15 + t^11*x^15) / ( (1-t)*(1-t^2)*(1-t^3*x^5)*(1-t^4*x^8) )
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