Use R ::= QQ[t,x,y,z];
HilbertSeries(R/Ideal(0));
(1) / (1-t)^4
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Q := R/Ideal(t^2, x, y^3); Poincare(Q);
(1 + 2t + 2t^2 + t^3) / (1-t)
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Poincare(R^2/Module([x^2,y^2],[z,y]));
(2 + t) / (1-t)^3
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Poincare(Module([x^2,y^2],[z,y]));
(t + t^2) / (1-t)^4
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Use R ::= QQ[t,x,y,z], Weights([1,2,3,4]);
Poincare(R/Ideal(t^2, x, y^3));
--- Non Simplified Pseries ---
(1 - 2t^2 + t^4 - t^9 + 2t^11 - t^13) / ( (1-t) (1-t^2) (1-t^3) (1-t^4) )
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Poincare(Ideal(t^2, x, y^3));
--- Non-simplified HilbertPoincare' Series ---
(2t^2 - t^4 + t^9 - 2t^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) )
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