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Divide - Division of polynomials over algebraic extension fields
Calling Sequence
evala(Divide(P, Q, 'p'))
Parameters
P, Q
-
polynomials over an algebraic number or function field
p
(optional) a name
Description
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 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.
Examples
The second argument below is not a polynomial. Therefore, an error is returned:
Error, (in evala/Divide/preproc0) invalid arguments
See Also
Divide, divide, evala, Quo, RootOf
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