, Ao = A.integer_ring(

, Ao Out: Q 2 {x, } ? We can now create and manipulate elements: In: f = 2*x^2 + 5*x*y^2 g = 4 + 2*x^2*y f + g Out: ...00101x 2 + ...000010x 2 + ...000010x 2 + ...0000100 In: (1+g)

, The big-oh appearing on the last line hides terms which are multiple of 2 5, We observe that, in the outputs, terms are ordered with respect to the term order on T {X}, the greatest one coming rst

, Ideals of K {X} can be dened and manipulated as follows

.. }-?-), J

, *g in J Out: True In: log(1+g) in J Out: True And similarly for ideals of K {X} ? (observe that no losses of precision occur this time

;. Jo, .. .. , and .. , 000010x 2 + ...000100 + O (2 6 Q 2 {x

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