Division of polynomials over algebraic extension fields
evala(Divide(P, Q, 'p'))
polynomials over an algebraic number or function field
(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.
P1 ≔ expand⁡x−t⁢y⁢t⁢x+12
P1 ≔ t⁢x3+2⁢t⁢x2+x−t3/2⁢y⁢x2−2⁢t⁢y⁢x−t⁢y
Q1 ≔ t⁢y−t⁢x
The second argument below is not a polynomial. Therefore, an error is returned:
Error, (in evala/Divide/preproc0) invalid arguments
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