niceq's profile - activity

I understand. Thanks for looking though. You probably wont like the other question I just posted then. I prefer to use built in functions rather that make them myself.

Is there a built in sage command to get values of the Hilbert function of an ideal? Of course for for large enough integers the value of the Hilbert function is equal to the value of the Hilbert polynomial, and there is a command to in sage for the Hilbert polynomial. But I need the values of the Hilbert function for small integers. Also, I could use the command for Hilbert series but the output is a rational function that I have to expand in a power series in order to see the values of the Hilbert function. Is there a built in command to give me the value directly?

Yes, that is right. I just need a function that checks if all the generators of A are contained in the ideal B. Easy enough, and I think your costom function does work but I am wondering if there is a predefined sage function(command) that does this or if I have to define one.

Oh no, that does not seem useful. Thank you for your response. Now I am doubting that A==B being True even means that the ideals are equal, which I was assuming. Does sage have built in functions for ideal equality and ideal containment? I would like to have a function like equality(A,B) and containment(A,B) whose value being true means A=B as ideal and A is contained in B, respectively? Does such a function exist? I know I can compute reduced Grob bases of both ideals and visually check if they are the same but I would like have a sage function that will check that for me.

What does the output mean when you type A<=B where A and B are ideals in a polynomial ring?