-- -*- M2-comint -*- hash: 1582306734251052790

i1 : R = QQ[t];

i2 : X = polyPath({t,2*t^2,3*t^3})

o2 = Path in 3-dimensional space with 1 polynomial segment:

            2    3
     {{t, 2t , 3t }}

o2 : Path

i3 : Y = polyPath({{({1},1)},{({2},2)},{({3},3)}})

o3 = Path in 3-dimensional space with 1 polynomial segment:

            2    3
     {{t, 2t , 3t }}

o3 : Path

i4 : R = QQ[a][t]; --QQ[a,t] will not work!

i5 : X = polyPath({t,2*a*t^2,3*a^2*t^3})

o5 = Path in 3-dimensional space with 1 polynomial segment:

              2    2 3
     {{t, 2a*t , 3a t }}

o5 : Path

i6 : Y = linPath({2,3,4})

o6 = Path in 3-dimensional space with 1 polynomial segment:

     {{2t, 3t, 4t}}

o6 : Path

i7 : Z = X ** Y

o7 = Path in 3-dimensional space with 2 polynomial segments:

              2    2 3
     {{t, 2a*t , 3a t }, {2t, 3t, 4t}}

o7 : Path

i8 : A = matrix {{1,2,3},{2,3,4},{4,5,6}};

              3       3
o8 : Matrix ZZ  <-- ZZ

i9 : W = pwLinPath(A)

o9 = Path in 3-dimensional space with 3 polynomial segments:

     {{t, 2t, 4t}, {2t, 3t, 5t}, {3t, 4t, 6t}}

o9 : Path

i10 : getDimension(Z) --The ambient dimension of the path

o10 = 3

i11 : getPieces(Z) --The polynomial pieces of the path, in listForm

                                          2
o11 = {{{({1}, 1)}, {({2}, 2a)}, {({3}, 3a )}}, {{({1}, 2)}, {({1}, 3)},
      -----------------------------------------------------------------------
      {({1}, 4)}}}

o11 : List

i12 : getCoefficientRing(Z) -- The coefficient ring of the polynomial components of the path

o12 = QQ[a]

o12 : PolynomialRing

i13 : getNumberOfPieces(Z) -- The number of polynomial pieces of the path

o13 = 2

i14 : Z_0

o14 = Path in 3-dimensional space with 1 polynomial segment:

               2    2 3
      {{t, 2a*t , 3a t }}

o14 : Path

i15 : Z2 = Z^2

o15 = Path in 3-dimensional space with 4 polynomial segments:

               2    2 3                         2    2 3
      {{t, 2a*t , 3a t }, {2t, 3t, 4t}, {t, 2a*t , 3a t }, {2t, 3t, 4t}}

o15 : Path

i16 : Z2_{0,-1}

o16 = Path in 3-dimensional space with 2 polynomial segments:

               2    2 3
      {{t, 2a*t , 3a t }, {2t, 3t, 4t}}

o16 : Path

i17 : X^4

o17 = Path in 3-dimensional space with 4 polynomial segments:

               2    2 3           2    2 3           2    2 3           2    2 3
      {{t, 2a*t , 3a t }, {t, 2a*t , 3a t }, {t, 2a*t , 3a t }, {t, 2a*t , 3a t }}

o17 : Path

i18 : X^(-1)

o18 = Path in 3-dimensional space with 1 polynomial segment:

                2             2 3     2 2     2
      {{-t, 2a*t  - 4a*t, - 3a t  + 9a t  - 9a t}}

o18 : Path

i19 : 
