The routine returns true if the point f or the list/set of points f is on line l; false if it is not; and FAIL if it is unable to reach a conclusion.

In case of FAIL, if the third optional argument is given, the condition that makes f on line l is assigned to this argument. It will be either of the form $\mathrm{expr}=0$ or of the form $\&\mathrm{and}\left(\mathrm{expr\_1}=0,...,\mathrm{expr\_n}=0\right)$ where expr, expr_i are Maple expressions.

The command with(geometry,IsOnLine) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{geometry}\right)\:$

$\mathrm{line}\left(\mathrm{l1}\,y=0\,\left[x\,y\right]\right),\mathrm{line}\left(\mathrm{l2}\,x+y=1\,\left[x\,y\right]\right),\mathrm{point}\left(A\,\frac{1}{2}\,\frac{1}{2}\right)\:$

$\mathrm{IsOnLine}\left(A\,\mathrm{l1}\right)$

$\mathrm{false}$

$\mathrm{IsOnLine}\left(A\,\mathrm{l2}\right)$

$\mathrm{true}$

$\mathrm{point}\left(A\,a\,\frac{1}{2}\right),\mathrm{point}\left(B\,\frac{3}{5}\,b\right)\:$

$\mathrm{IsOnLine}\left(\left\{A\,B\right\}\,\mathrm{l2}\,'\mathrm{cond}'\right)$

IsOnLine:   "hint: the following conditions must be satisfied: {-2/5+b = 0, -1/2+a = 0}"

$\mathrm{FAIL}$

$\mathrm{cond}$

$\left(-\frac{2}{5}+b=0\right)\&and\left(-\frac{1}{2}+a=0\right)$

$\mathrm{assume}\left(\mathrm{op}\left(\mathrm{cond}\right)\right)$

$\mathrm{IsOnLine}\left(\left\{A\,B\right\}\,\mathrm{l2}\right)$

$\mathrm{true}$