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user64494
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Maple 2017.3 helps you. For example,

convert(cos((1/7)*Pi), RootOf);
RootOf(8*_Z^3-4*_Z^2-4*_Z+1, .9009688679)
convert(cos((1/27)*Pi), RootOf)
RootOf(512*_Z^9-1152*_Z^7+864*_Z^5-240*_Z^3+18*_Z-1, .9932383577)

See convert and RootOf for info.

user64494
  • 3.5k
  • 14
  • 22