    Fig. 85. Work of the built-in function Maple in Mathcad

As we have told several times in this book calculus mathematics of Mathcad is not development of the firm MathSoft, Inc., but it is the purchasing of the firm Waterloo Maple, Inc. Who is developer of Maple. Calculus mathematics of Mathcad is (we have to use trite comparison) … top of an iceberg. But the “iceberg” is calculus mathematics of Maple: only ~ 10%  functions of Maple are accessible in Mathcad. And it is obvious. If the firm Waterloo Maple, Inc. passed (sold) MathSoft, Inc. All function, then it would be the end of Maple itself.

This and next (Tip 86) tip are the original attempts to dive from Mathcad to Maple and to look at “underwater part of the iceberg”.

Undocumented way of call the function solve is showed in the fig. 85. This function “fires” both sides: on the right through the operator “→” and gives analytical solution of the algebraic equations f(x), but on the left through the operator “:=” – numerical solution. This method we have already used in tip 3, when we combine analytical with numerical derivations  of the calculation’s results by the formulas. In the fig. 85 new is Maple’ s address to the function solve.

The operator solve is well-known for users of Mathcad (see, for example, the figures in Tips 10, 44, 74 and other). If we add to it the prefix l, then built-in Mathcad-function lsolve is obtained, aimed for solution systems of linear algebraic equations.

The work of “thoroughbred” Maple-function fsolve is showed in the fig. 85. It returns the solution of an algebraic equation in the form of floating-point  number (float – from this it follows the prefix f), but not in the form of analytical solution.

Main point of the tip: it is worth sometimes to call the Maple-functions directly. At that it is not worth to forget that undocumented method is fraught with complication.

 Such illusion appears when you look at the third operator in the fig. 85. In fact the analytical solution is carried in the variable Roots. Then this analytical solution is quantified”, i.е. outputted by the operator “=” in the form of floating-point  number.