Exporting Nonlinear Equations from Polymath to Excel

See Also: Exporting from Polymath to Excel  Nonlinear Equations Solver  Variables and Expressions 

The "Export to Excel"  function of Polymath is found in the drop-down Program menu at the top of the Nonlinear Equations problem screen.  A problem should be exported after it has been completely entered successfully into Polymath and ready for solution. The desired Excel Workbook must be opened on the desktop before the problem is exported to Excel.  It is good practice to also solve the problem in Polymath so that the solution in Excel can be compared and verified.  Upon export, the problem in Polymath will be completely transferred into Excel to a new Worksheet in the current Excel Workbook.  This transfer automatically includes the translation of logical statements and the intrinsic functions from Polymath into equivalent functions within Excel.  This transfer is conveniently illustrated by using Example 3 of the Nonlinear Problem Solver.  The export can be initiated by either clicking on the Excel icon or selecting 'Export to Excel' from the Problem menu: 

The resulting problem is opened up in a new worksheet within Excel as shown below:

Note that all of the information from Polymath has been transferred including the variable names, the values, the Polymath equations, and the comments.  The Sum of Squares cell, which is highlighted in red, is created from the sum of the squares of the errors in the nonlinear equations of the problem.  This cell value should become very small during the Excel solution.

The solution of the problem within Excel must utilize the "Solver" Add-In which is a part of the Excel software package, but you must be sure that it is installed.  This is accomplished from the Tools/Add-In menu of Excel where Solver should be checked.  The solution is initiated by going to Tools/Solver... and then filling out the Solver window as shown below:

Note that the target cell for minimization is cell $C$16, the Min of this cell is set, and the cells to be changed are $C$12 to $C$13 (indicated in pink).  Pressing the Solve button gives the Solver solution.  Note that the function that is minimized is the sum of squares of the nonlinear equations which should be very close to zero at the desired solution.

Click "OK" to keep the Solver solution.  Note that this Excel solution with Solver calculates D = .03952 and fF = .004927 which compares well with the Polymath solution of  D = .03897 and fF = .004591.