groebner {qspray} | R Documentation |
Gröbner basis
Description
Returns a Gröbner basis following Buchberger's algorithm using the lexicographical order.
Usage
groebner(G, minimal = TRUE, reduced = TRUE)
Arguments
G |
a list of |
minimal |
Boolean, whether to return a minimal basis |
reduced |
Boolean, whether to return the reduced basis |
Value
A Gröbner basis of the ideal generated by G
, given as a list
of qspray
polynomials.
References
Cox, Little & O'Shea. Ideals, Varieties, and Algorithms. An Introduction to Computational Algebraic Geometry and Commutative Algebra. Fourth edition, Springer 2015.
Examples
library(qspray)
f <- qsprayMaker(string = "x^(3) - 2 x^(1,1)")
g <- qsprayMaker(string = "x^(2,1) - 2 x^(0,2) + x^(1)")
groebner(list(f, g), FALSE, FALSE)
# other example
x <- qlone(1); y <- qlone(2); z <- qlone(3)
f1 <- x^2 + y + z^2 - 1
f2 <- x^2 + y + z - 1
f3 <- x + y^2 + z - 1
groebner(list(f1, f2, f3))
[Package qspray version 3.1.0 Index]