The convert function is used to convert an expression from one form to another.  Some of the conversions are data-type conversions, for example convert([x, y], set)  Others are form or function conversions, for example convert(x^3-3*x^2+7*x+9, horner, x)  yields  9+(7+(-3+x)*x)*x and convert(a*x!, GAMMA) yields a*GAMMA(x+1).

For function conversions, a set of optional arguments to perform the conversion in different manners are described in convert/to_special_function.

The types of known conversions are (the second argument form must be one of these):

Further information is available under help pages convert/form where form is one of the forms from the above list.

A user can make custom conversions known to the convert function by defining a Maple procedure in the following way.  If the procedure `convert/f` is defined, then the function call convert(a, f, x, y, ...) will invoke `convert/f`(a, x, y, ...); Note that the procedure may be indexed, for example convert([1,2,3], Vector[row]);

$\mathrm{convert}\left(9\,\mathrm{binary}\right)$

$1001$

$\mathrm{convert}\left(\mathrm{\pi }\,\mathrm{degrees}\right)$

$180\mathrm{degrees}$

$\mathrm{convert}\left(1.23456\,\mathrm{rational}\right)$

$\frac{3858}{3125}$

$\mathrm{convert}\left(\frac{1}{8}\,\mathrm{float}\,3\right)$

$0.125$

$\mathrm{convert}\left(22\,\mathrm{units}\,\mathrm{inches}\,m\right)$

$\frac{1397}{2500}$

$\mathrm{convert}\left(''XI''\,\mathrm{arabic}\right)$

$11$

$\mathrm{convert}\left(\left[1\,2\,3\,4\right]\,\mathrm{`+`}\right)$

$10$

$f≔\mathrm{seq}\left({x\left[i\right]}^i\,i=1..4\right)$

$f≔x_1,x_2^2,x_3^3,x_4^4$

$\mathrm{convert}\left(\left[f\right]\,\mathrm{`*`}\right)$

$x_1{x}_2^2{x}_3^3{x}_4^4$

$\mathrm{convert}\left(\left[x\,y\right]\,\mathrm{`and`}\right)$

$x\mathbf{and}y$

$f≔\frac{x^3+x}{x^2-1}$

$f≔\frac{x^3+x}{x^2-1}$

$\mathrm{convert}\left(f\,\mathrm{parfrac}\,x\right)$

$x+\frac{1}{x+1}+\frac{1}{x-1}$

$s≔\mathrm{series}\left(f\,x\,4\right)$

$s≔-x-2x^3+O\left(x^5\right)$

$\mathrm{convert}\left(s\,\mathrm{polynom}\right)$

$-2x^3-x$

$\mathrm{convert}\left(\frac{1}{2}+\frac{\mathrm{I}}{2}\,\mathrm{polar}\right)$

$\mathrm{polar}\left(\frac{\sqrt{2}}{2}\,\frac{\mathrm{\pi }}{4}\right)$

$g≔\sinh \left(x\right)+\sin \left(x\right)$

$g≔\sinh \left(x\right)+\sin \left(x\right)$

$\mathrm{convert}\left(g\,\exp \right)$

$\frac{{\ⅇ}^x}{2}-\frac{{\ⅇ}^{-x}}{2}-\frac{\mathrm{I}\left({\ⅇ}^{\mathrm{I}x}-{\ⅇ}^{\mathrm{-I}x}\right)}{2}$

$h≔\mathrm{BesselJ}\left(a\,z\right)$

$h≔\mathrm{BesselJ}\left(a\,z\right)$

$j≔\mathrm{convert}\left(h\,\mathrm{hypergeom}\right)$

$j≔\frac{z^a\mathrm{hypergeom}\left(\left[\right]\,\left[a+1\right]\,-\frac{z^2}{4}\right)}{\mathrm{\Gamma }\left(a+1\right)2^a}$

$\mathrm{convert}\left(j\,\mathrm{Bessel}\right)$

$\mathrm{BesselJ}\left(a\,z\right)$