I recently started learning the computer algebra system Singular. Working through some early exercises of the book "A Singular introduction to Commutative Algebra" by Gert-Martin Greuel and Gerhard Pfister I wasn't able to find way to actually evaluate a polynomial defined in a arbitrary ring.
Using the online manual as well as looking through some Singular-libraries wasn't helpfull at all for me finding any procedure or way to evaluate a polynomial.
It seems that's either impossible or it is so obvious that there is no hint in the book and the manual how to do this.
I'm sure there must be a way to do such things in a computer algebra system like Singular?
An example what I'm aiming to do:
After defining a ring, such as
ring A = 0,(x,y),dp;
poly f = x2 + y;
Now calling
f(1,2);
leads to
? `f(1)` is undefined
? error occurred in or before STDIN line 3: `f(1,2);`
Any usual/intuitive way of setting values to the variables x and y like
x := 1;
with or without the dots causes the error:
? error occurred in or before STDIN line 4: `x:=1;`
skipping text from `1`
I think I figured it out. The way to go is using the function
substlike this:which will result in