-- -*- M2-comint -*- {* hash: -687253909 *}

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

i2 : I = ideal(x*y^2+2*x^2*y, z^3);

o2 : Ideal of R

i3 : J = janetBasis I;

i4 : N1 = invNoetherNormalization J

o4 = {{x, - x + y, z}, {y}}

o4 : List

i5 : N2 = invNoetherNormalization(J, PermuteVariables => true)

o5 = {{x, - x + z, y}, {z}}

o5 : List

i6 : R = QQ[w,x,y,z];

i7 : I = ideal(w*x-y^2, y*z-x^2)

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

o7 : Ideal of R

i8 : J = janetBasis I;

i9 : N1 = invNoetherNormalization J

o9 = {{w, x, y, z}, {z, w}}

o9 : List

i10 : J1 = janetBasis substitute(gens I, for i in toList(0..numgens(R)-1) list R_i => N1#0#i);

i11 : F1 = factorModuleBasis(J1)

      +----+------+
o11 = |1   |{z}   |
      +----+------+
      |y   |{z}   |
      +----+------+
      | 2  |      |
      |y   |{z}   |
      +----+------+
      | 3  |      |
      |y   |{z}   |
      +----+------+
      |x   |{z}   |
      +----+------+
      |x*y |{z}   |
      +----+------+
      |w   |{z, w}|
      +----+------+
      |w*y |{z, w}|
      +----+------+
      |   2|      |
      |w*y |{z, w}|
      +----+------+
      |   3|      |
      |w*y |{z, w}|
      +----+------+

o11 : FactorModuleBasis

i12 : N2 = invNoetherNormalization(J, PermuteVariables => true)

o12 = {{y, x, w, z}, {z, y}}

o12 : List

i13 : J2 = janetBasis substitute(gens I, for i in toList(0..numgens(R)-1) list R_i => N2#0#i);

i14 : F2 = factorModuleBasis(J2)

      +---+------+
o14 = |1  |{z, y}|
      +---+------+
      |x  |{z, y}|
      +---+------+
      |w  |{z, y}|
      +---+------+
      |w*x|{z, y}|
      +---+------+

o14 : FactorModuleBasis

i15 :