webComputing

Parametric AE Solution Set of 2D Interval Linear System

Math Cocktail

Expand
Integrate
Differentiate
Bessel Zeros
To MathML
Animate
Integral Curves

IntervalComputations

Calculator
Polynomial Expansion
Differentiation
Plot Functions
Solution Set
AE Solution Set
3D Solution Set
Parametric EE SSet
Parametric AE SSet

Parametric LinSolver:
Linear Dependencies
Any Dependencies

General Info

Technology
Why to use?
Contacts

Consider a 2-dimensional parametric linear system A(p,q).x = b(p,q), where the elements of the matrix A(p,q) and the right-hand side vector b(p,q) are afine-linear functions of some parameters, e.g. p1, p2, ..., pk and q1,q1,...,qm.
By this page you can obtain explicit representation of the parametric AE solution set to the system A(p,q).x = b(p,q), that is SpAE := {x | (for all p in [p])(there exist q in [q])such that A(p,q)x=b(p,q)} by a set of inequalities.
You can also plot the parametric AE solution sets which are not empty and non-degenerate (point or curve).

Enter the elements of the parametric matrix:

a(1,1) =    a(1,2) =

a(2,1) =    a(2,2) =

Enter the elements of the parametric right hand side vector:

b(1) =    b(2) =

Enter the interval values for the universally quantified parameters by a list of rules:
Rules have the form rule[parameter_name, IntVal[numeric_value, numeric_value]].

Enter the interval values for the existentially quantified parameters by a list of rules:
Rules have the form rule[parameter_name, IntVal[numeric_value, numeric_value]].

Show the explicit representation of the parametric AE solution set.
YES NO

Solve the describing inequalities with respect to the coordinate variables x1, x2.
Use this option only if the graphics visualizing the parametric AE solution set is empty.

Plot the parametric AE solution set.

Show the parametric AE 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 parametric solution (RGB color): red part : green part : blue part :

To specify some 2D graphics options, click here.

To download the generated graphics, click here.