support -- list of variables occurring in a polynomial or matrix

Synopsis

• Usage:
support f
• Inputs:
• f, , or over a polynomial ring
• Outputs:

Description

 i1 : R = QQ[a..g] o1 = R o1 : PolynomialRing i2 : f = a^3+b^2*c+3*f^10*d-1+e-e 10 3 2 o2 = 3d*f + a + b c - 1 o2 : R i3 : support f o3 = {a, b, c, d, f} o3 : List
 i4 : M = matrix"a+b2,c+g2;c,a-1" o4 = | b2+a g2+c | | c a-1 | 2 2 o4 : Matrix R <--- R i5 : support M o5 = {a, b, c, g} o5 : List
If the ring is a polynomial ring over another polynomial ring, then the support contains all of the variables, even the ones in the coefficient ring. The ring of each of these is the ring of f.
 i6 : A = ZZ[a,b]; B = A[r,s,t]; C = B[x,y,z,w]; i9 : f = (a+r+z+1)^2+y 2 2 2 o9 = z + y + (2r + 2a + 2)z + r + (2a + 2)r + a + 2a + 1 o9 : C i10 : S = support f o10 = {y, z, r, a} o10 : List i11 : ring S_2 === ring f o11 = true
Here is one way to select only the top level variables.
 i12 : select(S, x -> index x < numgens C) o12 = {y, z} o12 : List
To obtain a list of the integer indices of the variables one can use either indices(RingElement) or apply index to each variable.
 i13 : indices f o13 = {1, 2, 4, 7} o13 : List i14 : apply(support f, index) o14 = {1, 2, 4, 7} o14 : List

Ways to use support :

• "support(Matrix)"
• "support(RingElement)"
• support(Ideal) -- list of variables occurring in the generators of an ideal

For the programmer

The object support is .