Doing computation over the integers

[miky...@libero.it]

Hi,

if I want for example to use square roots over the rationals I can do something like this:

S=QQ[a]/(a^2-2)

S=toField S

R=S[x,y,z,w]

And now Macaulay 2 uses "a" as a constant and not as a variable. Without the second line of command we will get a ring with multi-degree....

Do you know how to do something similar if the base is not QQ but ZZ?

For example I would like to use 

S=ZZ[a]/(a^2-2)

S=????

R=S[x,y,z,w]

To make sure that "a" is again used as a constant not as a variable. Do you have any ideas/suggestions?

Thank you in advance.

Michele

[Trevor Karn]

Hi,

It might not be quite what you want, but you could set the degree of `a` to be `0`, so then it is technically a multidegree but should behave like a constant.

i21 : S=ZZ[a,Degrees=>{0}]/(a^2-2);

i22 : R=S[x,y,z,w];
i23 : degree(a*x) o23 = {1,0}

[Michele Torielli]

Hi Trevor,

thank you for the suggestion, I think that that might work. At the end of the day I want to compute groebner basis for ideals...

Best

Michele

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