import scas.base.
import scas.power.Lexicographic
import scas.polynomial.tree.Polynomial
import .given

val r = Polynomial(using , Lexicographic[Int]("x", "y", "z"))
val xyz = r.generators
import r.given

assert(x + 1 >< 1 + x)
assert(x + BigInteger("1") >< BigInteger("1") + x)

val s = Polynomial(using xyz, Lexicographic[Int]("a"))
val a = s.generators
import s.given

assert(a + 1 >< 1 + a)
assert(a + BigInteger("1") >< BigInteger("1") + a)
assert(a + x >< x + a)
assert((a + x).show == "xa")