algstat (version 0.0.2)

polySolve: Solve a System of Polynomial Equations

Description

polySolve solves a system of polynomial equations, specifiable in any of several ways.

Usage

polySolve(lhs, rhs, varOrder, ...)

Arguments

lhs

a mpolyList or character vector of left hand sides

rhs

a mpolyList or character vector of right hand sides

varOrder

variable order (see examples)

...

stuff to pass to bertini

Value

an object of class bertini

See Also

variety, bertini

Examples

## Not run: 
# 
# # it can solve linear systems
# # (here where the line y = x intersects y = 2 - x)
# polySolve(c("y", "y"), c("x", "2 - x"), c("x", "y"))
# 
# # or nonlinear systems
# polySolve(c("y", "y"), c("x^2", "2 - x^2"), c("x", "y"))
# 
# # perhaps an easier specification is equations themselves
# # with either the " = " or " == " specifications
# # varOrder is used to order the solutions returned
# polySolve(c("y = x^2", "y = 2 - x^2"), varOrder = c("x", "y"))
# polySolve(c("y == x^2", "y == 2 - x^2"), varOrder = c("x", "y"))
# 
# 
# # mpoly objects can be given instead of character strings
# lhs <- mp(c("y - (2 - x)", "x y"))
# rhs <- mp(c("0","0"))
# polySolve(lhs, rhs, varOrder = c("x", "y"))
# 
# # if no default right hand side is given, and no "=" or "==" is found,
# # rhs is taken to be 0's.
# # below is where the lines y = x and y = -x intersect the unit circle
# polySolve(c("(y - x) (y + x)", "x^2 + y^2 - 1"))
# 
# # the output object is a bertini object
# out <- polySolve(c("(y - x) (y + x)", "x^2 + y^2 - 1"))
# str(out,1)
# 
# # here is the code that was run :
# cat(out$bertiniCode)
# 
# # the finite and real solutions:
# out$finite_solutions
# out$real_finite_solutions
# 
# 
# 
# 
# # example from Riccomagno (2008), p. 399
# polySolve(c(
#   "x (x - 2) (x - 4) (x - 3)",
#   "(y - 4) (y - 2) y",
#   "(y - 2) (x + y - 4)",
#   "(x - 3) (x + y - 4)"
# ))
# 
# ## End(Not run)