I would like to solve a system of polynomial equations
to do this in Macaulay2, I wrote it as an ideal, and compute its dimension which is given as $5$.
R = CC[sa,sb,sc,sd,se,ca,cb,cc,cd,ce];
I = ideal {-cb*sa - cc*sa + ca*sb + ca*sc, cb*sa - ca*sb - cc*sb + cb*sc,
cc*sa + cc*sb - ca*sc - cb*sc, -1 + ca^2 + sa^2, -1 + cb^2 +
sb^2, -1 + cc^2 + sc^2}
dim I
However, all solutions to this equations are finite isolated points, which contradicts with the dimension of the ideal dim I = 5.
Could anyone help me to solve this confusion? I will appreciate any help to clarify my confusion. Many thanks in advance!