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check for an algebraic extension in terms of radicals

Parameters

 expr - any expression K - (optional) type name for the coefficient domain

Description

 • The type(expr, radext) function checks if expr is a radical extension of the real numbers.  It is equivalent to type(expr, radical) or $\mathrm{expr}=I$.
 • The type(expr, radext(K)) function checks whether expr is a radical expression where the expression under the root sign belongs to the domain K.  For example, K could be integer or rational.
 • This function returns true if expr is such an expression. Otherwise, false is returned.

Examples

 > $\mathrm{type}\left(\sqrt{{x}^{2}+5},\mathrm{radext}\right)$
 ${\mathrm{true}}$ (1)
 > $\mathrm{type}\left({\left({x}^{2}+5\right)}^{\frac{4}{3}},\mathrm{radext}\left(\mathrm{polynom}\right)\right)$
 ${\mathrm{true}}$ (2)
 > $\mathrm{type}\left(5-{\left(\sqrt{3}\right)}^{\frac{5}{6}},\mathrm{radext}\left(\mathrm{rational}\right)\right)$
 ${\mathrm{false}}$ (3)
 > $\mathrm{type}\left({\left(5-\sqrt{3}\right)}^{\frac{5}{6}},\mathrm{radext}\left(\mathrm{radnum}\right)\right)$
 ${\mathrm{true}}$ (4)
 > $\mathrm{type}\left(\frac{2}{3},\mathrm{radext}\right)$
 ${\mathrm{false}}$ (5)