Divide
division of polynomials over algebraic extension fields
Calling Sequence
Parameters
Description
Examples
evala(Divide(P, Q, 'p'))
P, Q
-
polynomials over an algebraic number or function field
p
(optional) a name
This function returns true if the polynomial Q divides P and false otherwise. The coefficients of P and Q must be algebraic functions or algebraic numbers.
Algebraic functions and algebraic numbers may be represented by radicals or with the RootOf notation (see type,algnum, type,algfun, type,radnum, type,radfun).
When Q divides P, the optional argument p is assigned the quotient P/Q.
The division property is meant in the domain Kx where:
x is the set of names in P and Q which do not appear inside a RootOf or a radical,
K is a field generated over the rational numbers by the coefficients of P and Q.
The arguments P and Q must be polynomials in x.
Algebraic numbers and functions occurring in the results are reduced modulo their minimal polynomial (see Normal).
If a or b contains functions, their arguments are normalized recursively and the functions are frozen before the computation proceeds.
Other objects are frozen and considered as variables.
aliasα=RootOfx3+x+1
α
evalaDividex3+x+1,x−α,a1
true
a1
α2+αx+x2+1
evalaDividex3+x+1,x−α+1,a2
false
a2
P1≔expandx−sqrttysqrttx+12
P1≔tx3+2tx2+x−t32yx2−2tyx−ty
Q1≔ty−sqrttx
Q1≔ty−tx
evalaDivideP1,Q1,a3
a3
−tx2−2x−1t
The second argument below is not a polynomial. Therefore, an error is returned:
evalaDivideP1,Q1+1x,a3
Error, (in `evala/Divide/preproc0`) invalid arguments
See Also
divide
evala
Quo
RootOf
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