Processing a test ANLDE system

Web-SynDic can be used for solving test ANLDE system and showing report on solution to the user. The ANLDE system should be given manually by a user or generated automatically by a selected generator. Recently, only homogeneous ANLDE systems are supported by the Web-SynDic system.

Process an ANLDE system form is shown in Figure 4.

**Figure 4:** Process ANLDE System
$\begin{figure}\centering \epsfig{file=screenshots/process-ANLDE-main.eps, width=0.77\textwidth}\end{figure}$

Web-SynDic system checks each solution by substitution the solution into the given ANLDE system. Also if user uses alternative solver then the Web-SynDic system compares corresponding solutions.

Creating ANLDE system

The Web-SynDic system supports two ways for creating ANLDE system:

Manual input. User can input ANLDE system manually into the text area of the corresponding form (see Figure 4). The ANLDE system should be in ANLDE format (see section 3.1).
Automatic generation. The Web-SynDic system supports two generators called Gauss and Gordano. After generation user can modify produced ANLDE system.

The generation process consists of the following steps:

Set generator parameters using Algorithms configuration form (see section 3.2) or in the bottom of the current Process an ANLDE system form (see Figure 5).

Figure 5: Generator parameters
$\begin{figure}\centering \epsfig{file=screenshots/process-ANLDE-params.eps, width=0.77\textwidth}\end{figure}$
Choose desired generator and press Generate button. All generation queries are put into the Generator Spooler queue. The Web-SynDic displays the number of tasks in the Generator Spooler queue (see section 3.5.2). During generation time the Web-Syndic system shows the processing form (see Figure 6).

Figure 6: Web-SynDic wait page
$\begin{figure}\centering \epsfig{file=screenshots/process-ANLDE-process.eps, width=0.77\textwidth}\end{figure}$
In the case of successful generation produced ANLDE system will be placed in the text area of Process an ANLDE system form (see Figure 7).

Figure 7: Generated ANLDE system
$\begin{figure}\centering \epsfig{file=screenshots/process-ANLDE-generate.eps, width=0.77\textwidth}\end{figure}$
If generator is unable to produce an ANLDE system (for example if numbers of equations and unknowns are equal, see Figure 8) you may change generator or generator parameters and try again. In some cases you may try again without changing any parameters.

Figure 8: Generator failed
$\begin{figure}\centering \epsfig{file=screenshots/process-ANLDE-error.eps, width=0.77\textwidth}\end{figure}$

**Figure 5:** Generator parameters
$\begin{figure}\centering \epsfig{file=screenshots/process-ANLDE-params.eps, width=0.77\textwidth}\end{figure}$

**Figure 6:** Web-SynDic wait page
$\begin{figure}\centering \epsfig{file=screenshots/process-ANLDE-process.eps, width=0.77\textwidth}\end{figure}$

**Figure 7:** Generated ANLDE system
$\begin{figure}\centering \epsfig{file=screenshots/process-ANLDE-generate.eps, width=0.77\textwidth}\end{figure}$

**Figure 8:** Generator failed
$\begin{figure}\centering \epsfig{file=screenshots/process-ANLDE-error.eps, width=0.77\textwidth}\end{figure}$

Generated or manually inserted ANLDE system is stored by the Web-SynDic system as long as you work with it.

The Web-SynDic system may display the following generation errors:

``Number of equations is greater than number of unknowns''. Check that the number of equations is less than the number of unknowns.
``Numbers of equations and unknowns are equal''. The generator does not support this class of ANLDE systems. You can input the system manually.
``CPU time limit exceeded. Try to increase time limit''. Time limit is too small or generator parameters are too large. Try to increase time limit or change generator parameters.
``Algorithm cannot generate ANLDE system(s) or memory limit exceeded''. The generator is unable to generate ANLDE system with current parameters or memory limit is too small. Try to increase memory limit or change generator parameters.
``Generator failed''. The generator parameters are possibly wrong or the program itself failed to execute for some reason. We will be pleased if you will send note (see section 3.8) containing generator parameters in this case.
``Generator failure: parameter maximum value of coefficients for ANLDE system exceeded''. The maximum value of coefficients for ANLDE system is too small. Try to increase it.
``Generator failure: parameter maximum value of components in basis solutions exceeded''. The maximum value of components in basis solutions is too small. Try to increase it.
``Generator failure: parameter maximum number of basis solutions exceeded''. The maximum number of basis solutions is too small. Try to increase it.
``Generator failure: generated system is not correct''. The generator is unable to generate ANLDE system or generated ANLDE system is invalid. We will be pleased if you will send note (see section 3.8) containing generator parameters in this case.

Solving ANLDE system

The Web-SynDic system default solver is Syntactic. User can also use alternative solvers: Slopes and Lp_solve. The solving process consist of the following steps:

Insert valid ANLDE system into the text area of the Process an ANLDE system form. Alternatively, you can generate it automatically (see section 3.3.1). If ANLDE system is invalid or text area is empty then the Web-SynDic system prints error message (see Figure 9).

Figure 9: Syntax error message
$\begin{figure}\centering \epsfig{file=screenshots/process-ANLDE-incorrect.eps, width=0.77\textwidth}\end{figure}$
Set solver parameters using Algorithms configuration form (see section 3.2). You may also use default values.
Select alternative solver (if needed) and push button Solve (see Figure 10).

Figure 10: Alternative solvers
$\begin{figure}\centering \epsfig{file=screenshots/process-ANLDE-solvers.eps, width=0.77\textwidth}\end{figure}$

All solving queries are put into the Solver Spooler queue. The Web-SynDic displays the number of tasks in the Solver Spooler queue (see section 3.5.2). During solving time the Web-Syndic system shows the processing form (see Figure 6).

**Figure 9:** Syntax error message
$\begin{figure}\centering \epsfig{file=screenshots/process-ANLDE-incorrect.eps, width=0.77\textwidth}\end{figure}$

**Figure 10:** Alternative solvers
$\begin{figure}\centering \epsfig{file=screenshots/process-ANLDE-solvers.eps, width=0.77\textwidth}\end{figure}$

After processing the Web-SynDic system displays Solution Report form (see Figure 11).

**Figure 11:** Solution report for one ANLDE system
$\begin{figure}\centering \epsfig{file=screenshots/process-ANLDE-report.eps, width=0.77\textwidth}\end{figure}$

The Solution Report form contains the following information:

Test ANLDE system in traditional mathematical style and number of solutions. Current version of the Web-Syndic system obtains the number of solutions from the default solver.
Waiting time in Solver Spooler buffer. If buffer is empty then Solver Spooler executes new task immediately and waiting time equals to zero.
Performance metrics of the algorithms:

--

algorithm name;

--

summary CPU work time in seconds;

--

summary real work time in seconds;

--

maximum process virtual size in kilobytes;

--

solving result.

At the present the time unit for CPU work time is 0.001 second. If Solver uses CPU work time which is less than 0.001 second then `` 0.001'' is printed in the report page.
If the value is not available (for example Maximum process virtual size is not available when algorithm executes too fast) then ``N/A'' is displayed in the corresponding field.
The field Solving result contains "solved" if the system is solved successfully. Otherwise error message is displayed.
Solving machine characteristics like processor, core memory, operating system, Java version, Tomcat version, and Solver process nice value, if they are available.
Solutions of the test ANLDE system if the system is solved successfully.
Note on solution. You can simply press Agree with the result button or send more detailed message (see section 3.8).

The Web-SynDic system may display the following errors while solving given ANLDE system:

``Failed to solve the problem''. Solver process is abnormally terminated (for example, the process is killed). We will be pleased if you will send note (see section 3.8) containing the ANLDE system and the list of solvers in this case.
``Limit exceeded: maximum CPU time for solving''. Try to increase maximum CPU time for solving parameter.
``Algorithm failed''. The solver produces invalid solution (for example, the solver prints error message). We will be pleased if you will send note (see section 3.8) containing the ANLDE system and the list of solvers in this case.
``Internal solver error or memory limit exceeded''. Try to increase memory limit.
``CPU time limit exceeded''. Try to increase maximum CPU time for solving.
``Limit exceeded: maximum memory for solving''. Try to increase memory limit.
``Limit exceeded: maximum values of coefficients for basis solutions''. Try to increase maximum values of coefficients for basis solution.
``Limit exceeded: maximum number of unknowns''. The solver returns more unknowns than given ANLDE system contains. We will be pleased if you will send note (see section 3.8) containing the ANLDE system and the list of solvers in this case.
``Limit exceeded: maximum number of solutions''. Try to increase maximum number of basis solutions for ANLDE system.

Saving ANLDE system

The Web-SynDic has a feature, which allows user to save ANLDE system in a file. The saving process consists of the following steps:

Insert valid ANLDE system into the text area of the Process an ANLDE system form. Alternatively, you can generate it automatically (see section 3.3.1).
Press Save button to save the ANLDE system in a file. The Web-SynDic system opens new browser window containing the ANLDE system (see Figure 12).

Figure 12: Save ANLDE system
$\begin{figure}\centering \epsfig{file=screenshots/process-ANLDE-save.eps, width=0.77\textwidth}\end{figure}$
Using standard browser functions you can save the system in a file. The Web-SynDic system uses pop-up windows for saving ANLDE system. Your browser should support pop-up windows.

**Figure 12:** Save ANLDE system
$\begin{figure}\centering \epsfig{file=screenshots/process-ANLDE-save.eps, width=0.77\textwidth}\end{figure}$

Kirill Kulakov 2005-12-04