-- -*- M2-comint -*- {* hash: 214800591 *}

i1 : S = QQ[x_0..x_4]

o1 = S

o1 : PolynomialRing

i2 : i = monomialCurveIdeal(S,{2,3,5,6})

                          2                       3      2     2      2     2
o2 = ideal (x x  - x x , x  - x x , x x  - x x , x  - x x , x x  - x x , x x 
             2 3    1 4   2    0 4   1 2    0 3   3    2 4   1 3    0 4   0 3
     ------------------------------------------------------------------------
        2     2              3    2
     - x x , x x  - x x x , x  - x x )
        1 4   1 3    0 2 4   1    0 4

o2 : Ideal of S

i3 : isLinearType i

o3 = false

i4 : isLinearType(i, i_0)

o4 = false

i5 : I = reesIdeal i

                                                                            
o5 = ideal (x w  - x w  + x w , x w  - x w  - w , x w  - x w  + x w , x w  -
             2 0    3 1    4 2   1 0    3 2    5   0 0    1 1    2 2   0 4  
     ------------------------------------------------------------------------
                                       2                                 
     x w  - x w , x w  - x w  - x w , x w  + x w  - x w , x x w  + x w  -
      1 5    4 7   0 3    3 5    4 6   4 2    1 3    3 4   0 4 2    1 6  
     ------------------------------------------------------------------------
            2                          2                                   
     x w , x w  - x w  + x w  + x w , x w  + x w  - x w , x x w  - x x w  -
      3 7   3 2    2 4    3 5    4 6   1 2    0 6    2 7   1 4 1    2 4 2  
     ------------------------------------------------------------------------
                                                         2      2           
     x w  + x w , x x w  - x x w  - x w  + x w  - x w , x w  - x w  - x w  +
      1 4    3 6   0 4 1    1 3 2    1 5    2 6    4 7   3 0    4 1    2 3  
     ------------------------------------------------------------------------
                                      2    2                            
     x w , x w w  + w w  - w w , x x w  - w  - x w w  + w w , x x w w  -
      4 4   4 2 5    4 6    3 7   1 4 2    6    4 1 7    4 7   3 4 0 2  
     ------------------------------------------------------------------------
               2
     x w w  + w  - w w )
      4 1 4    4    3 6

o5 : Ideal of S[w , w , w , w , w , w , w , w ]
                 0   1   2   3   4   5   6   7

i6 : select(I_*, f -> first degree f > 1)

                                 2    2                                     
o6 = {x w w  + w w  - w w , x x w  - w  - x w w  + w w , x x w w  - x w w  +
       4 2 5    4 6    3 7   1 4 2    6    4 1 7    4 7   3 4 0 2    4 1 4  
     ------------------------------------------------------------------------
      2
     w  - w w }
      4    3 6

o6 : List

i7 : S = ZZ/101[x,y,z]

o7 = S

o7 : PolynomialRing

i8 : for p from 1 to 5 do print isLinearType (ideal vars S)^p
true
false
false
false
false

i9 :