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# twodimToricIrrationalPoincare -- Produces the example of a two-dimensional toric ideal whose Poincar\'e series is irrational.

## Synopsis

• Usage:
I = twodimToricIrrationalPoincare ()
• Outputs:

## Description

Returns the example from Roos and Sturmfels' "A toric ring with irrational Poincar\'e-Betti series" (1998) of a toric ideal whose quotient ring has an irrational Poincar\'e series. It is the toric ideal of the numerical subsemigroup of $\mathbb{N}^2$ generated by ${(36,0), (33,3), (30,6), (28,8), (26,10), (25,11), (24,12), (18,18), (0,36)}.$

 i1 : I = onedimToricIrrationalPoincare 2 2 2 3 o1 = ideal (w - w w , w - w w , w w - w w , w - w w , w w - w w , w - 2 1 6 3 2 4 3 4 1 7 4 2 5 4 5 2 6 1 ------------------------------------------------------------------------ 2 2 2 2 2 2 w w , w - w w , w w - w w , w w - w , w w - w w , w w - w , w w w 2 6 5 4 6 5 6 3 7 1 2 6 1 3 5 7 1 6 7 2 3 5 ------------------------------------------------------------------------ 2 2 2 2 3 - w w w , w w w - w w w , w w - w w , w w - w w w , w w - w w w , w 1 4 7 2 3 6 1 5 7 2 6 1 7 3 6 2 5 7 4 6 3 5 7 6 ------------------------------------------------------------------------ 2 - w w ) 2 7 o1 : Ideal of QQ[w ..w ] 1 7

## For the programmer

The object twodimToricIrrationalPoincare is an ideal.