Divide - Division of polynomials over algebraic extension fields
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Calling Sequence
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evala(Divide(P, Q, 'p'))
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Parameters
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P, Q
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polynomials over an algebraic number or function field
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p
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(optional) a name
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Description
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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.
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When Q divides P, the optional argument p is assigned the quotient P/Q.
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The division property is meant in the domain where:
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x is the set of names in P and Q which do not appear inside a RootOf or a radical,
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K is a field generated over the rational numbers by the coefficients of P and Q.
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Algebraic numbers and functions occurring in the results are reduced modulo their minimal polynomial (see Normal).
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If a or b contains functions, their arguments are normalized recursively and the functions are frozen before the computation proceeds.
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Other objects are frozen and considered as variables.
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Examples
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The second argument below is not a polynomial. Therefore, an error is returned:
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