i1 : R = QQ[x,y,z]; |
i2 : I = monomialIdeal(x*y^3*z, x*y^2*z^2, y^3*z^2, y^2*z^3) 3 2 2 3 2 2 3 o2 = monomialIdeal (x*y z, x*y z , y z , y z ) o2 : MonomialIdeal of R |
i3 : standardPairs I 2 2 2 o3 = {{1, {x, z}}, {y, {x, z}}, {1, {x, y}}, {z, {y}}, {y z, {x}}, {y z , ------------------------------------------------------------------------ {}}} o3 : List |
The standard pairs are computed with Algorithm 3.2.5 in GrÃ¶bner Deformations of Hypergeometric Differential Equations, by Mutsumi Saito, Bernd Sturmfels and Nobuki Takayama; Algorithms and Computation in Mathematics 6, Springer-Verlag, 2000. Implemented by Gregory G. Smith.
For more information, see the Monomial ideals chapter in Computations in algebraic geometry with Macaulay2, edited by David Eisenbud, Daniel R. Grayson, Michael E. Stillman, and Bernd Sturmfels, Algorithms and Computations in Mathematics 8, Springer-Verlag, 2001.
The object standardPairs is a method function.