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Macaulay2Doc > basic commutative algebra > M2SingularBook > Singular Book 1.5.10

Singular Book 1.5.10 -- realization of rings

We define the rings of example 1.5.3, in the Singular book.
i1 : (n,m) = (2,3);
i2 : A1 = QQ[x_1..x_n,y_1..y_m,MonomialOrder=>{n, RevLex=>m},Global=>false];
i3 : f = x_1*x_2^2 + 1 + y_1^10 + x_1*y_2^5 + y_3

        2      5             10
o3 = x x  + x y  + 1 + y  + y
      1 2    1 2        3    1

o3 : A1
i4 : 1_A1 > y_1^10

o4 = true

The second monomial order has the first block local, and the second block polynomial.

i5 : A2 = QQ[x_1..x_n,y_1..y_m,MonomialOrder=>{RevLex=>n, m},Global=>false];
i6 : substitute(f,A2)

      10               5      2
o6 = y   + y  + 1 + x y  + x x
      1     3        1 2    1 2

o6 : A2
i7 : x_1*y_2^5 < 1_A2

o7 = true

The third example has three blocks of variables.

i8 : A3 = QQ[x_1..x_n,y_1..y_m,MonomialOrder=>{n, RevLex=>2, m-2},Global=>false];
i9 : substitute(f,A3)

        2      5             10
o9 = x x  + x y  + y  + 1 + y
      1 2    1 2    3        1

o9 : A3