"Source: Text/Commut/GB.text";
"Line: 428";
"Date: Thu Sep 25 14:47:46 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Commut/GB.text, line: 428
// Example: H115E1 ()
print "Example: H115E1";
ei := GetEchoInput();
SetEchoInput(true);
Z := IntegerRing();
// Construct polynomial ring with DEFAULT lex order
P<a,b,c,d> := PolynomialRing(Z, 4);
MonomialOrder(P);
MonomialOrderWeightVectors(P);
// Construct polynomial ring with grevlex order
P<a,b,c,d> := PolynomialRing(Z, 4, "grevlex");
MonomialOrder(P);
MonomialOrderWeightVectors(P);
// Construct polynomial ring with block elimination and a > d > b > c
P<a,b,c,d> := PolynomialRing(Z, 4, "elim", [1, 4], [2, 3]);
MonomialOrder(P);
MonomialOrderWeightVectors(P);
a + b + c + d;
a + d^10 + b + c^10;
a + d^10 + b + c;   
// Construct polynomial ring with weight order and x > y > z
P<x, y, z> := PolynomialRing(Z, 3, "weight", [100,10,1, 1,10,100, 1,1,1]);
MonomialOrder(P);
MonomialOrderWeightVectors(P);
x + y + z;
(x+y^2+z^3)^4;
SetEchoInput(ei);
