The numboccur(f, x) function returns the number of times that x is found in f.

If x is a sum or a product, the counted expressions are those where the sum or product appear with no extra terms or factors in f.  If x is a list or a set, then every element in the list or set is counted.

If x is a list or set, numboccur counts and adds together the number of times each member of the list or set occurs in f. In other words, numboccur(f,{x,y}) is equivalent to numboccur(f,x) + numboccur(f,y). Note that if x is a list and contains a given element more than once, it is counted more than once each time it appears in f.

If the item that you want numboccur to count is itself a list or set, you must enclose it in a list or set. Otherwise, numboccur will count occurrences of the items in the list or set as described above.

The numboccur command is thread-safe as of Maple 15.

For more information on thread safety, see index/threadsafe.

$\mathrm{numboccur}\left(x^3+x-1\,x\right)$

$2$

$\mathrm{big\_expr}≔\mathrm{expand}\left(\sin \left(7x\right)\right)$

$\mathrm{big\_expr}≔64\sin \left(x\right){\cos \left(x\right)}^6-80\sin \left(x\right){\cos \left(x\right)}^4+24\sin \left(x\right){\cos \left(x\right)}^2-\sin \left(x\right)$

$\mathrm{numboccur}\left(\mathrm{big\_expr}\,\sin \left(x\right)\right)$

$4$

$\mathrm{numboccur}\left(\frac{\left(a+b\right)\left(a+b+1\right)}{a+b+c}\,a+b\right)$

$1$

$\mathrm{numboccur}\left(ax+x^2+b\,\left[a\,x\,x^2\,b\right]\right)$

$5$

$\mathrm{numboccur}\left(ax+x^2+b\,\left[a\,a\,x\,x^2\,b\right]\right)$

$6$

$\mathrm{numboccur}\left(\left\{\left[1\right]\,\left[3\right]\,\left[2\,3\right]\right\}\,\left[3\right]\right)$

$2$

$\mathrm{numboccur}\left(\left\{\left[1\right]\,\left[3\right]\,\left[2\,3\right]\right\}\,\left\{\left[3\right]\right\}\right)$

$1$