CoCoA:Coefficients
From ApCoCoAWiki
Coefficients
list of coefficients of a polynomial or vector
Description
This function returns the coefficients of F. In the first form, a
list of the (non-zero) coefficients is returned; the order being
decreasing on the terms in F as determined by the term-ordering of the ring to which F belongs.
In the second form, the function views F as a polynomial in X, and
returns a list of coefficients which are polynomials in the remaining
variables; their order is decreasing in powers of X, and a zero value is given for those powers of X absent from F.
In the third form, the coefficients of the specified terms are
returned; their order is determined by the list S.
Example
Use R ::= Q[x,y,z]; F := 3x^2y+5y^3-xy^5; Coefficients(F); [-1, 3, 5] ------------------------------- ScalarProduct(Coefficients(F), Support(F)) = F; TRUE ------------------------------- V := Vector(3x^2+y, x-5z^3); Coefficients(V); [-5, 3, 1, 1] ------------------------------- ScalarProduct(Coefficients(V), Support(V)) = V; TRUE ------------------------------- Coefficients(x^3z+xy+xz+y+2z, x); [z, 0, y + z, y + 2z] ------------------------------- F := (1+2*x+3*y^4+5*z^6)^7; Skeleton := [1, x^3, y^12, z^19, x^2*y^8*z^12]; Coefficients(F, Skeleton); [1, 280, 945, 0, 567000] -------------------------------
Syntax
Coefficients(F:POLY or VECTOR):LIST Coefficients(F:POLY,X:INDET):LIST Coefficients(F:POLY,S:LIST):LIST
<type>polynomial</type>
