Singular

How do I define a numerical semigroup ring in Singular. For example

k[[t^5,t^7]]

or something like

k[[t^6,t^8 + t^9,t^11]] ?

I would simply write it as an affine ring. You can use eliminate to get the ring relations.

Mohamed

Yes, this would do it. But how can we use eliminate to get the defining ideal? I am surprised that there is not a procedure that would take a map, say x to t^5 and y to t^7, and produce the defining ideal.

A procedure for two lines would be overkill since one has to specify the map anyway.
Here is the SINGULAR input:

ring r = 0,(t,x,y),dp;
ideal i = x-t5, y-t7;
eliminate(i,t);