toCoordinates -- coordinates of a point from its ideal

i1 : S = ZZ/5[x,y,z]

o1 = S

o1 : PolynomialRing

i2 : I = ideal(x- y, z)

o2 = ideal (x - y, z)

o2 : Ideal of S

i3 : L = toCoordinates I

o3 = {1, 1, 0}

o3 : List

i4 : I == fromCoordinates(L,S)

o4 = true

i5 : S = GF(5,2,Variable => a)[x,y,z]/(ideal "x3-y3+z3")

o5 = S

o5 : QuotientRing

i6 : a^24 == 1

o6 = true

i7 : (a^8)^3

o7 = 1

o7 : GF 25

i8 : (a^16)^3

o8 = 1

o8 : GF 25

i9 : p = {a^8, a^16, 0}

o9 = {2a + 1, - 2a - 2, 0}

o9 : List

i10 : fromCoordinates (p,S)

o10 = ideal ((- 2a - 1)x + y, z)

o10 : Ideal of S

i11 : L = toCoordinates fromCoordinates ({a^8,1,0}, S)

o11 = {2a + 1, 1, 0}

o11 : List