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

Synopsis

Usage:
(lf, cf) = topCoefficients f
Inputs:
- f, a ring element or a matrix
Outputs:
- lf, a ring element, or a matrix, 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, a ring element, or a matrix, 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

See also

pseudoRemainder -- compute the pseudo-remainder

Ways to use `topCoefficients` :

topCoefficients(Matrix)
topCoefficients(RingElement)