/**/ Use R ::= QQ[t,x,y,z]; -- standard weights
/**/ HilbertSeries(R/ideal(R,[]));
(1) / (1-t)^4
/**/ HilbertSeries(R/ideal(t^2, x, y^3));
(1 + 2*t + 2*t^2 + t^3) / (1-t)
/**/ R2 := NewFreeModule(R, 2); -- MODULE
/**/ M := SubmoduleRows(R2, matrix(R, [[x^2,0], [0,z^3]]));
/**/ HilbertSeries(M);
(t^2 + t^3) / (1-t)^4
-- /**/ HilbertSeries(R2/M); --***WORK IN PROGRESS***
/**/ Ws := RowMat([1,2,3,4]); -- weights and multigradings
/**/ P := NewPolyRing(QQ, "t,x,y,z", MakeTermOrd(Ws), 1);
/**/ Use P;
/**/ HilbertSeries(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) )
/**/ HilbertSeries(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) )
/**/ Ws := mat([[1,2,3,4],[0,0,5,8]]);
/**/ P := NewPolyRing(QQ, "t,x,y,z", MakeTermOrd(Ws), 2);
/**/ Use P;
/**/ HilbertSeries(P/ideal(t^2, x, y^3));
--- Non Simplified Pseries ---
(1 - 2*t[1]^2 + t[1]^4 - t[1]^9*t[2]^15 + 2*t[1]^11*t[2]^15 - t[1]^13*t[2]^15) / ( (1-t[1])^1*(1-t[1]^2)*(1-t[1]^3*t[2]^5)*(1-t[1]^4*t[2]^8) )
/**/ Ws := mat([[1,2,3,4],[0,0,5,8]]);
/**/ P := NewPolyRing(QQ, "t,x,y,z", MakeTermOrd(Ws), 2);
/**/ Use P;
/**/ HilbertSeries(P/ideal(t^2, y^3));
--- Non-simplified HilbertPoincare' Series ---
(1 - t[1]^2 - t[1]^9*t[2]^15 + t[1]^11*t[2]^15) /
((1-t[1])^1*(1-t[1]^2)*(1-t[1]^3*t[2]^5)*(1-t[1]^4*t[2]^8) )
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