"Common ring not found" when creating an ideal

[signedout]

Hi, I hope this time around I'm asking in the right place :)

In the course of some manipulations, I end up with the list P={x^2,xy^3,y^4}, all of the elements belonging to Q[t,x,y]. However, when I make ideal(P), I get a "common ring not found". What's going on? How can I create the ideal I want?

[Secondary question: is there a way to have M2 give the output in the same format that I give the input? i.e. like x*y^3 instead of the two-line formatting with a 3 on the top line.]

i35: P

o35 = {x^2 , x*y^3 , y^4}

o35 : List

i36 : P#0

            
o36 = x^2

o36 : QQ[t, x..y]

i37 : P#1

              
o37 = x*y^3

o37 : QQ[t, x..y]

i38 : P#2

            
o38 = y^4

o38 : QQ[t, x..y]

i39 : ideal(P)
stdio:75:1:(3): error: common ring not found

[DanGrayson]

Yes, this is the right place, but I don't know how many other people are hanging out here. There's also the google group.

Try checking the hash codes of the rings to see if the rings are really identical.

i11 : {(QQ[t]; t), (QQ[t]; t)}

o11 = {t, t}

o11 : List

i12 : class \ oo

o12 = {QQ[t], QQ[t]}

o12 : List

i13 : hash \ oo

o13 = {1170809, 1170823}

o13 : List

[DanGrayson]

It's better to construct a list whose elements are in the same ring. Probably somewhere you are creating that ring, and then you create it again, and again a third time. Investigate your code and make that ring only once.

[signedout]

Thanks. Seems like that was the case, so I created a ring S outside of the routine. But now here's the problem I run into, duly isolated from all the rest:

S=QQ[t,x,y];

K=frac(QQ[t]);

R=K[y,x, MonomialOrder=>GLex];

f=t*x;

g=sub(f,S);

sub(g,t=>1)

stdio:11:1:(3): error: expected t to be a generator of S

I don't understand. Surely t is a generator of QQ[ŧ,x,y] !

[d-torrance]

At this point, t is considered an element of the coefficient field K:

i7 : t

o7 = t

o7 : K

To get back to doing this in terms of S, you could use use:

i8 : use S

o8 = S

o8 : PolynomialRing

i9 : sub(g,t=>1)

o9 = x

o9 : S

[DanGrayson]

You have created two ring elements named t, and the second one is the one found when you type t:

i14 : S=QQ[t,x,y];

i15 : K=frac(QQ[t]);

i16 : t

o16 = t

o16 : K

[signedout]

Thanks a lot, that explains it, and using "use" did it!