-- -*- M2-comint -*- hash: 15822824056626816400

i1 : R = QQ[x,y,z]

o1 = R

o1 : PolynomialRing

i2 : I = ideal(random(4, R), random(4, R), random(4, R));

o2 : Ideal of R

i3 : betti res I

            0 1 2 3
o3 = total: 1 3 3 1
         0: 1 . . .
         1: . . . .
         2: . . . .
         3: . 3 . .
         4: . . . .
         5: . . . .
         6: . . 3 .
         7: . . . .
         8: . . . .
         9: . . . 1

o3 : BettiTally

i4 : degreeOfMap I

o4 = 16

i5 : upperBoundDegreeSingleGraded I

o5 = 16

i6 : A = matrix{ {x, x^2 + y^2},
                 {-y, y^2 + z*x},
                 {0, x^2}
               };

             3      2
o6 : Matrix R  <-- R

i7 : I = minors(2, A) -- a birational map

             2       2    3    2    3    2
o7 = ideal (x y + x*y  + y  + x z, x , -x y)

o7 : Ideal of R

i8 : degreeOfMap I

o8 = 1

i9 : upperBoundDegreeSingleGraded I

o9 = 2

i10 : A = matrix{ {x^2, x^2 + y^2},
                  {-y^2, y^2 + z*x},
                  {0, x^2}
                };

              3      2
o10 : Matrix R  <-- R

i11 : I = minors(2, A) -- a non birational map

               2 2    4    3    4    2 2
o11 = ideal (2x y  + y  + x z, x , -x y )

o11 : Ideal of R

i12 : degreeOfMap I

o12 = 2

i13 : upperBoundDegreeSingleGraded I

o13 = 4

i14 : A = matrix{ {x^3, x^2 + y^2},
                  {-y^3, y^2 + z*x},
                  {0, x^2}
                };

              3      2
o14 : Matrix R  <-- R

i15 : I = minors(2, A) -- a non birational map

              3 2    2 3    5    4    5    2 3
o15 = ideal (x y  + x y  + y  + x z, x , -x y )

o15 : Ideal of R

i16 : degreeOfMap I

o16 = 3

i17 : upperBoundDegreeSingleGraded I

o17 = 7

i18 : 
