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--- status: DRAFT
--- author(s): MES
--- notes:
document {
Key => {topCoefficients,
(topCoefficients, RingElement),
(topCoefficients, Matrix)},
Headline => "first variable and its coefficient of a polynomial or matrix",
Usage => "(lf, cf) = topCoefficients f",
Inputs => {
"f" => Nothing => {ofClass RingElement, " or ", ofClass Matrix}
},
Outputs => {
"lf" => Nothing => {ofClass RingElement, ", or ", ofClass 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" => Nothing => {ofClass RingElement, ", or ", ofClass Matrix,
", the coefficient of lf in f, if f is a ring element,
or the matrix of these coefficients for each column of f"}
},
EXAMPLE lines ///
A = ZZ[x]
(lf,cf) = topCoefficients (7*x^4-13*x^3+x+1)
v = first support lf
e = first degree lf
///,
"The polynomial ring may have more variables.",
EXAMPLE lines ///
B = ZZ[x,y,z]
f = y^4*(3*z^3-z^2-1) - y^3*z^7 + y + z^12
(lf,cf) = topCoefficients f
///,
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"
},
SeeAlso => {pseudoRemainder}
}
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