# degree(RingElement)

## Description

In Macaulay2, the degree of a polynomial is a list of integers. This is to accommodate polynomial rings having multigradings. The usual situation is when the ring has the usual grading: each variable has length 1.
 i1 : R = QQ[a..d]; i2 : degree (a^3-b-1)^2 o2 = {6} o2 : List
When not dealing with multigraded rings, obtaining the degree as a number is generally more convenient:
 i3 : first degree (a^3-b-1)^2 o3 = 6
 i4 : S = QQ[a..d,Degrees=>{1,2,3,4}]; i5 : first degree (a+b+c^3) o5 = 9
 i6 : T = QQ[a..d,Degrees=>{{0,1},{1,0},{-1,1},{3,4}}]; i7 : degree c o7 = {-1, 1} o7 : List
In a multigraded ring, the degree of a polynomial whose terms have different degrees is perhaps non-intuitive: it is the maximum (in each of the component degree) over each term:
 i8 : degree c^5 o8 = {-5, 5} o8 : List i9 : degree d o9 = {3, 4} o9 : List i10 : degree (c^5+d) o10 = {3, 5} o10 : List