i1 : R = ZZ/101[x, Degrees => {2}]; |
i2 : M = module ideal x^2 o2 = image | x2 | 1 o2 : R-module, submodule of R |
i3 : s = hilbertSeries M 4 T o3 = -------- 2 (1 - T ) o3 : Expression of class Divide |
i4 : numerator s 4 o4 = T o4 : ZZ [T, MonomialOrder => RevLex, Inverses => true] |
i5 : poincare M 4 o5 = T o5 : ZZ [T, MonomialOrder => RevLex, Inverses => true] |
i6 : R=ZZ/101[x, Degrees => {{1,1}}]; |
i7 : M = module ideal x^2; |
i8 : s = hilbertSeries M 2 2 T T 0 1 o8 = ---------- (1 - T T ) 0 1 o8 : Expression of class Divide |
i9 : numerator s 2 2 o9 = T T 0 1 o9 : ZZ [T , T , MonomialOrder => RevLex, Inverses => true] 0 1 |
i10 : poincare M 2 2 o10 = T T 0 1 o10 : ZZ [T , T , MonomialOrder => RevLex, Inverses => true] 0 1 |