Macaulay2 » Documentation
Packages » NonPrincipalTestIdeals :: extendedReesAlgebra
next | previous | forward | backward | up | index | toc

extendedReesAlgebra -- computes the flattened extended Rees algebra

Description

This function creates an extended Rees algebra. Unlike the reesAlgebra command, this function creates a flattened ring with certain other keys added for the convenience of other functions in this package.

i1 : R = QQ[x,y,z];
 
i2 : J= ideal(x^2,y);

o2 : Ideal of R
 
i3 : S2 = extendedReesAlgebra J;
 
i4 : describe S2

               QQ[x..z, ly ..ly , ti]
                          0    1
o4 = ------------------------------------------
       2                             2
     (x ly  - y*ly , - y + ly ti, - x  + ly ti)
          0       1          0             1
 
i5 : degrees S2

o5 = {{0, 1}, {0, 1}, {0, 1}, {1, 1}, {1, 2}, {-1, 0}}

o5 : List

Caveat

Currently, this only works for singly graded base rings.

See also

Ways to use extendedReesAlgebra:

  • extendedReesAlgebra(Ideal)

For the programmer

The object extendedReesAlgebra is a method function with options.

The source of this document is in NonPrincipalTestIdeals.m2:1071:0.