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Solution Set of Interval Linear System

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Plot the solution set of a 2-dimensional square interval linear system A.x = b, where each element of the matrix A and the right-hand side vector b can be either a number (floating-point, integer, rational, exact singleton, or a numeric valued expression) or a numeric valued interval.

Usually, the solution set of the interval linear system A.x = b has a complicated shape (in general not necessarily convex, connected, or bounded). It is connected and bounded if the matrix A is regular. In this case it constitutes a two-dimensional polyhedron which is a sum of at most 4 convex polyhedrons obtained as intersections of the solution set with every of the four orthants of the solution space.

Cases in which the solution set cannot be plotted:
1. Point linear system;
2. The system involves only one interval. (In this case the solution set is a line and can be drown as a Parametric Solution Set.);
3. The system has not a solution;
4. Invalid input data.

Enter the elements of the matrix: (each element can be either an interval or a number)

a(1,1) = Interval[ ]    a(1,2) = Interval[ ]

a(2,1) = Interval[ ]    a(2,2) = Interval[ ]

Enter the elements of the right hand side vector: (each element can be either an interval or a number)

b(1) = Interval[ ]    b(2) = Interval[ ]

Show the solution set in the range: (obligatory for unbounded solution sets)
The specified solution set range can change the view of the solution set, only if the specified range is contained in the Exact Hull of the solution set.

< = x(1) < =   ,   < = x(2) < =

Color of the filling (RGBColor): red part : green part : blue part :

To download the generated graphics, click here.
To specify more 2D graphics options, click here.

Show combinatorial points:
Points of the solution set obtained as solutions to point linear systems generated by all possible combinations of the interval end-points involved in the system.

Point size:

Point color (RGBColor): red part : green part : blue part :

Show Rohn's points:
Vertices of the solution set that determine its exact hull. These points are obtained by a sign-accord algorithm of J. Rohn.

Point size:

Point color (RGBColor): red part : green part : blue part :

Show interval boxes:

Enter a 2D Interval Box as, e.g., {IntVal[-2.5, 1], IntVal[-1/2, 1+Sqrt[4]]} :

Thickness: Dashing: RGB Color: red: green: blue: