# topCoefficients -- first variable and its coefficient of a polynomial or matrix

## Synopsis

• Usage:
(lf, cf) = topCoefficients f
• Inputs:
• f, or
• Outputs:
• lf, , or , the power of the lowest index variable occurring in f, if f is a ring element, or the one row matrix of these powers for each column, if f is a matrix.
• cf, , or , the cofficient of lf in f, if f is a ring element, or the matrix of these coefficients for each column of f

## Description

 i1 : A = ZZ[x] o1 = A o1 : PolynomialRing i2 : (lf,cf) = topCoefficients (7*x^4-13*x^3+x+1) 4 o2 = (x , 7) o2 : Sequence i3 : v = first support lf o3 = x o3 : A i4 : e = first degree lf o4 = 4
The polynomial ring may have more variables.
 i5 : B = ZZ[x,y,z] o5 = B o5 : PolynomialRing i6 : f = y^4*(3*z^3-z^2-1) - y^3*z^7 + y + z^12 12 3 7 4 3 4 2 4 o6 = z - y z + 3y z - y z - y + y o6 : B i7 : (lf,cf) = topCoefficients f 4 3 2 o7 = (y , 3z - z - 1) o7 : Sequence

## Caveat

If the polynomial ring B of f has a polynomial coefficient ring A, and no variables of B occur in f, then this 'drills down' into A and finds the top variable and coefficient there, but as elements of B