## Not run:
#
#
# polys <- mp(c(
# "x^2 - y^2 - z^2 - .5",
# "x^2 + y^2 + z^2 - 9",
# ".25 x^2 + .25 y^2 - z^2"
# ))
# variety(polys)
#
# # algebraic solution :
# c(sqrt(19)/2, 7/(2*sqrt(5)), 3/sqrt(5)) # +/- each ordinate
#
#
#
# # character vectors can be taken in; they're passed to mp
# variety(c("y - x^2", "y - x - 2"))
#
#
#
# # an example of how varieties are invariant to the
# # the generators of the ideal
# variety(c("2 x^2 + 3 y^2 - 11", "x^2 - y^2 - 3"))
#
# # the following takes a few seconds to initialize, feel free to them
# # gb <- grobner(mp(c("2 x^2 + 3 y^2 - 11", "x^2 - y^2 - 3")))
# # variety(gb)
#
# m2("
# R = QQ[x,y]
# gens gb ideal(2*x^2 + 3*y^2 - 11, x^2 - y^2 - 3)
# ")
# variety(c("y^2 - 1", "x^2 - 4"))
# variety(c("x^2 - 4", "y^2 - 1"))
#
#
#
# # variable order is by default equal to vars(mpolyList)
# # (this finds the zeros of y = x^2 - 1)
# variety(c("y", "y - x^2 + 1")) # y, x
# vars(mp(c("y", "y - x^2 + 1")))
# variety(c("y", "y - x^2 + 1"), c("x", "y")) # x, y
#
#
#
# # complex solutions
# variety("x^2 + 1")
# variety(c("x^2 + 1 + y", "y"))
#
#
# # multiplicities
# variety("x^2")
# variety(c("2 x^2 + 1 + y", "y + 1"))
# variety(c("x^3 - x^2 y", "y + 2"))
#
#
# #
# p <- mp(c("2 x - 2 - 3 x^2 l - 2 x l",
# "2 y - 2 + 2 l y",
# "y^2 - x^3 - x^2"))
# variety(p)
#
# ## End(Not run)
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