Construct a real interval by specifying a center and a radius:

Construct a complex interval by specifying a center and a radius:

Construct centered intervals by specifying arbitrary-precision numbers:

Convert a bounded Interval object to a centered interval:

Binary Gaussian rationals are exactly representable as intervals with radius zero:

Other exact numbers are converted to intervals with nonzero radii:

Nonzero machine-precision numbers are treated as numbers with $MachinePrecision precise digits:

Convert machine-precision zero to a center-radius interval:

Use arithmetic operations with centered interval arguments:

Use centered intervals as arguments of mathematical functions:

Operations with centered interval and numeric arguments yield centered intervals:

The returned interval contains all values of the function in the input interval:

Interval arithmetic operations return Indeterminate if the set of values is unbounded:

Extract the properties of a real interval:

The center and the radius are binary rational numbers:

Find rational bounds for the elements of the interval:

Convert the interval to an arbitrary-precision number:

Extract the center and the radius of a complex interval:

The center and the radius are binary Gaussian rational numbers:

Find Gaussian rational bounds for the elements of the interval:

Convert the interval to an arbitrary-precision number:

Test interval membership:

Test inclusion of intervals:

Visualize the intervals:

Compare real intervals:

If the intervals intersect, the comparison cannot be resolved:

Use IntervalIntersection to compute the intersection:

The empty interval is expressed as Interval[]:

Product of CenteredInterval matrices:

Find random representatives mrep and nrep of m and n:

Verify that mn contains the product of mrep and nrep:

Raise a CenteredInterval matrix to an integer power:

Find a random representative mrep of m:

Verify that mpow contains MatrixPower[mrep,17]:

The exponential of a CenteredInterval matrix:

Find a random representative mrep of m:

Verify that mexp contains the exponential of mrep:

Determinant of a CenteredInterval matrix:

Find a random representative mrep of m:

Verify that mdet contains the determinant of mrep:

Inverse of a CenteredInterval matrix:

Find a random representative mrep of m:

Verify that minv contains the inverse of mrep:

Solve for CenteredInterval matrices:

Find random representatives mrep and brep of m and b:

Verify that sol contains LinearSolve[mrep,brep]:

Eigensystem of a CenteredInterval matrix:

Find an eigensystem for a random representative mrep of m:

Verify that, after reordering and scaling of vectors, vals contain rvals and vecs contain rvecs:

LU decomposition for a CenteredInterval matrix:

Cholesky decomposition for a real symmetric positive definite CenteredInterval matrix:

Characteristic polynomial of a CenteredInterval matrix:

Find a random representative mrep of m:

Verify that the coefficients of p contain the coefficients of the characteristic polynomial of mrep: