The command evalindets is a particular combination of calls to eval and indets that allows you to efficiently transform all subexpressions of a given type by some algorithm. It encapsulates a common "pattern" used in expression manipulation and transformation.

Each subexpression of type atype is transformed by the supplied transformer procedure. Then, each subexpression is replaced in the original expression, using eval, with the corresponding transformed expression.

If the flat option is supplied as an index to the evalindets command, then Maple will not recursively look inside any subexpressions of the given atype for further (nested) subexpressions of that type. This provides a hint to Maple that it can use a somewhat faster algorithm in this special case.

If the flat option is not supplied, then subexpressions of type atype at deeper levels of nesting are processed and replaced before subexpressions at shallower levels of nesting. This is illustrated in an example below.

By default, evalindets uses a cache to avoid repetitive type checking and repeated calls to transformer for multiple instances of the same subexpression (this cache is limited in size, so repeated calls may occur, but there is no guarantee that they will). The nocache option, specified as an index to the evalindets command, prevents the use of this cache, and guarantees that transformer will be called once for each instance of any common subexpression matching atype. Note that using the nocache option can dramatically lower the performance of evalindets on expressions containing many common subexpressions.

If evalindets is called with an integer index, N, then each subexpression to be processed by transformer will be passed as the N-th argument to transformer. The sequence of N-1 arguments of evalindets between atype and transformer will be passed as the first N-1 arguments to transformer.

A numeric index may be combined with the flat option, and they can be specified in either order.

$\mathrm{evalindets}\left(F\left(G\left(x\right)\,F\left(x\,y\right)\right)\,'\mathrm{specfunc}\left(\mathrm{anything}\,F\right)'\,f\mapsto \mathrm{subsop}\left(0=H\,f\right)\right)$

$H\left(G\left(x\right)\,H\left(x\,y\right)\right)$

$\mathrm{evalindets}\left[\mathrm{flat}\right]\left(F\left(2.3\right)+G\left(4\,1.1\right)\,'\mathrm{float}'\,\mathrm{trunc}\right)$

$F\left(2\right)+G\left(4\,1\right)$

$\mathrm{evalindets}\left[\mathrm{flat}\right]\left(F\left(G\left(x\right)\,F\left(x\,y\right)\right)\,'\mathrm{specfunc}\left(\mathrm{anything}\,F\right)'\,f\mapsto \mathrm{subsop}\left(0=H\,f\right)\right)$

$H\left(G\left(x\right)\,F\left(x\,y\right)\right)$

$\mathrm{evalindets}\left(F\left(G\left(x\right)\,F\left(x\,y\right)\right)\,'\mathrm{specfunc}\left(\mathrm{symbol}\,F\right)'\,f\mapsto \mathrm{subsop}\left(0=H\,f\right)\right)$

$F\left(G\left(x\right)\,H\left(x\,y\right)\right)$

$\mathrm{evalindets}\left(\left[\sin \left(x\right)\,\cos \left(y\right)\,\tan \left(z\right)\right]\,'\mathrm{symbol}'\,y\mapsto y+\mathrm{\pi }\right)$

$\left[-\sin \left(x\right)\,-\cos \left(y\right)\,\tan \left(z\right)\right]$

$\mathrm{expr}≔\sin \left(x+y\right)+x\left(x+1\right)+\left(x+1\right)\left(x+2\right)$

$\mathrm{expr}≔\sin \left(x+y\right)+x\left(x+1\right)+\left(x+1\right)\left(x+2\right)$

$\mathrm{evalindets}\left(\mathrm{expr}\,'\mathrm{`*`}'\,\mathrm{expand}\right)$

$\sin \left(x+y\right)+2x^2+4x+2$

$\mathrm{expand}\left(\mathrm{expr}\right)$

$\sin \left(x\right)\cos \left(y\right)+\cos \left(x\right)\sin \left(y\right)+2x^2+4x+2$

$\mathrm{evalindets}\left(\sin \left(\left(3+\mathrm{I}\right)\mathrm{\pi }\right)+{\left(x+y\right)}^{100}\,'\sin \left(\mathrm{anything}\right)'\,\mathrm{expand}\right)$

$-\mathrm{I}\sinh \left(\mathrm{\pi }\right)+{\left(x+y\right)}^{100}$

$\mathrm{expr}≔\sin \left(x+y\right)+x\left(x+3\right)+\exp \left(x+1\right)\left(y+2\right)$

$\mathrm{expr}≔\sin \left(x+y\right)+x\left(x+3\right)+{\ⅇ}^{x+1}\left(y+2\right)$

$\mathrm{evalindets}\left(\mathrm{expr}\,'\mathrm{`*`}'\,\mathrm{expand}\right)$

$\sin \left(x+y\right)+x^2+3x+{\ⅇ}^x\ⅇy+2{\ⅇ}^x\ⅇ$

$\mathrm{evalindets}\left(\mathrm{expr}\,'\mathrm{`*`}'\,\mathrm{expand}\,\exp \right)$

$\sin \left(x+y\right)+x^2+3x+{\ⅇ}^{x+1}y+2{\ⅇ}^{x+1}$

$\mathrm{expr}≔x^2+3x+f\left(x\right)\:$

$\mathrm{count}≔0\:$

evalindets(expr,symbol,proc(s) global count; count:=count+1; cat(s,count) end);

${\mathrm{x1}}^2+3\mathrm{x1}+f\left(\mathrm{x1}\right)$

$\mathrm{count}≔0\:$

evalindets['nocache'](expr,symbol,proc(s) global count; count:=count+1; cat(s,count) end);

${\mathrm{x1}}^2+3\mathrm{x2}+f\left(\mathrm{x3}\right)$

$\mathrm{expr}≔{f\left(x\,y\right)}^2+3f\left(x\,y\right)+3\;$$\mathrm{evalindets}\left[2\right]\left(\mathrm{expr}\,\mathrm{specfunc}\left(f\right)\,1\,\mathrm{op}\right)$

$\mathrm{expr}≔{f\left(x\,y\right)}^2+3f\left(x\,y\right)+3$

$x^2+3x+3$

$\mathrm{evalindets}\left(\mathrm{expr}\,\mathrm{specfunc}\left(f\right)\,x\mapsto \mathrm{op}\left(1\,x\right)\right)$

$x^2+3x+3$

$\mathrm{expr}≔2+f\left(4\,g\left(h\left(6\right)\right)\right)$

$\mathrm{expr}≔2+f\left(4\,g\left(h\left(6\right)\right)\right)$

$\mathrm{evalindets}\left(\mathrm{expr}\,\mathrm{function}\,\mathrm{fn}\mapsto \mathrm{evalindets}\left(\mathrm{fn}\,\mathrm{integer}\,i\mapsto \mathrm{cat}\left(i\,''in''\,\mathrm{op}\left(0\,\mathrm{fn}\right)\right)\right)\right)$

$2+f\left(\mathrm{4\; in\; f}\,g\left(h\left(\mathrm{6\; in\; h}\right)\right)\right)$

The evalindets command was updated in Maple 2015.

The N parameter was introduced in Maple 2015.

The preargs parameter was updated in Maple 2015.

The nocache option was introduced in Maple 2015.

For more information on Maple 2015 changes, see Updates in Maple 2015.