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# classicalReesAlgebra -- computes the flattened Rees algebra

- Usage:
    `S = classicalReesAlgebra(J)`
- Inputs:
  - J, an ideal,
- Outputs:
  - S, a ring,

## Description

This function calls the function reesAlgebra from the package ReesAlgebras and formats it for our purposes.

The difference is this ring is flattened, and there are certain keys added for obtaining information about this Rees algebra, as demonstrated in the example below.

    i1 : R = QQ[x,y,z];

    i2 : J= ideal(x^2,y);

    o2 : Ideal of R

    i3 : S1 = reesAlgebra J;

    i4 : describe S1

          R[w ..w ]
             0   1
    o4 = -----------
          2
         x w  - y*w
            0      1

    i5 : S2 = classicalReesAlgebra J;

    i6 : describe S2

         QQ[x..z, ly ..ly ]
                    0    1
    o6 = ------------------
             2
            x ly  - y*ly
                0       1

    i7 : degrees S2

    o7 = {{0, 1}, {0, 1}, {0, 1}, {1, 1}, {1, 2}}

    o7 : List

BaseRing provides the ring where we blew up the ideal. Degree1 is the generators of the degree 1 part of the Rees algebra. BaseRingList is the list of generators of the ideal we blew up.

## Caveat

Currently, this only works for singly graded base rings.

## See also

- reesAlgebra -- Compute the defining ideal of the Rees Algebra
- extendedReesAlgebra -- computes the flattened extended Rees algebra

## Ways to use classicalReesAlgebra:

- `classicalReesAlgebra(Ideal)`

## For the programmer

The object classicalReesAlgebra is a method function with options.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/NonPrincipalTestIdeals.m2:1043:0.