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# degrees(Ring) -- degrees of generators

- Function: degrees
- Usage:
    `degrees A`
- Inputs:
  - A, a ring, a ring, an ideal, a module, or a monoid
- Outputs:
  - a list, the list of multi-degrees for the generators of A

## Description

    i1 : R = ZZ/101[x,y,z];

    i2 : degrees R

    o2 = {{1}, {1}, {1}}

    o2 : List

    i3 : S = ZZ/101[x,y,z,Degrees => {{2,3},{1,2},{2,0}}];

    i4 : degrees S

    o4 = {{2, 3}, {1, 2}, {2, 0}}

    o4 : List

This function also applies to ideals, modules, and monoids.

    i5 : I = ideal"xy2,xyz,y3"

                   2          3
    o5 = ideal (x*y , x*y*z, y )

    o5 : Ideal of S

    i6 : degrees I

    o6 = {{4, 7}, {5, 5}, {3, 6}}

    o6 : List

    i7 : degrees R^5

    o7 = {{0}, {0}, {0}, {0}, {0}}

    o7 : List

    i8 : degrees R^{1,2,3,4}

    o8 = {{-1}, {-2}, {-3}, {-4}}

    o8 : List

## See also

- degreeLength -- the length of the degree vector
- degreesRing -- the ring or monoid of degrees

## Ways to use this method:

- `degrees(FractionField)`
- `degrees(Ideal)`
- `degrees(Module)`
- `degrees(Monoid)`
- `degrees(QuotientRing)`
- degrees(Ring) -- degrees of generators

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Macaulay2Doc/functions/degrees-doc.m2:39:0.