algfun - Maple Help
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type/algfun

check for an algebraic function

 Calling Sequence type(expr, algfun) type(expr, algfun(K)) type(expr, algfun(K, V))

Parameters

 expr - expression K - type name; for coefficient domain such as rational or anything V - (optional) name or list or set of names; variable(s)

Description

 • An expression expr is of type algfun (algebraic function) if it is an expression in the variable(s) V over the domain K extended by (polynomial) RootOfs.
 • The domain specification K must be a type name, such as rational or anything.  If K is omitted, then it defaults to type constant.
 • The optional argument V is an indeterminate or a list or set of indeterminates.  If V is not specified, then all the indeterminates of expr, which are names, are used.  That is, expr must be an algebraic function in all of its variables.

Examples

 > $\mathrm{type}\left(\frac{x}{1-x},\mathrm{algfun}\left(\mathrm{rational},x\right)\right)$
 ${\mathrm{true}}$ (1)
 > $f≔1+2\mathrm{RootOf}\left({x}^{3}-y,x\right)+yz$
 ${f}{≔}{1}{+}{2}{}{\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{3}}{-}{y}\right){+}{y}{}{z}$ (2)
 > $\mathrm{type}\left(f,\mathrm{algfun}\left(\mathrm{anything}\right)\right)$
 ${\mathrm{true}}$ (3)
 > $\mathrm{type}\left(f,\mathrm{algfun}\left(\mathrm{rational}\right)\right)$
 ${\mathrm{true}}$ (4)
 > $\mathrm{type}\left(f,\mathrm{algfun}\left(\mathrm{rational},y\right)\right)$
 ${\mathrm{false}}$ (5)
 > $\mathrm{type}\left(f,\mathrm{algfun}\left(\mathrm{rational},\left[y,z\right]\right)\right)$
 ${\mathrm{true}}$ (6)