Singular

With execute the polynomial will just be displayed but you can't work with it.
Even an assignment afterwards like [i] poly g = _; [/i]is not possible.

To have access, you must enclose the string (variable) [i]nameofpoly[/i] into
the backticks ` ` . These are the delimiter for name substitution

See [b]Special characters[/b]:
http://www.singular.uni-kl.de/Manual/latest/sing_36.htm#SEC63

Modified solution:
[code]
> ring R = 0, (x,y,z), dp;
> poly f = x+y+z;
> string s = "f";
> `s`;
x+y+z

> proc p1mod(def R, string nameofpoly)
{
setring(R);
poly g = `nameofpoly`;
g = g+1;
g;
}

> ring S = 0, x, dp;
> p1mod(R, "f");
x+y+z+1
[/code]

One possibility is to define a procedure which takes the ring R as a parameter. Objects inside this ring can then be accessed by their names:

[code]
proc p1(def R, string nameofpoly)
{
setring(R);
execute(nameofpoly);
}

ring R = 0, (x,y,z), dp;
poly f = x+y+z;
ring S = 0, x, dp;
p1(R, "f");
x+y+z
[/code]

Note that
[code]
proc p1(ring R, ...)
[/code]
does [b]not[/b] work, see http://www.singular.uni-kl.de/Manual/latest/sing_44.htm#SEC81.

Another possibility is to use user defined types ("newstructs"), see http://www.singular.uni-kl.de/Manual/latest/sing_176.htm#SEC216.

How can one define a procedure which may be called with parameters not in the current ring, such as "imap(R,f)", where the polynomial "f" belongs to the ring "R"?