### D.8.2 interval_lib

Library:
  interval.lib
Purpose:
  implements interval arithmetic on polynomials
Authors:
  Dominik Bendle
  Clara Petroll

Overloads:
  // intervals
  [ intervalGet indexing
  = intervalAssign assigning
  == intervalEqual equality
  print intervalPrint pretty print
  + intervalAdd addition
  - intervalNegate negation (unary)
  - intervalSubtract subtraction
  * intervalMultiply multiplication
  / intervalDivide division
  ^ intervalPotentiate potentiation

  // boxes
  = boxSet assigning
  [ boxGet indexing
  == boxEqual equality
  print boxPrint printing
  - boxSubtract subtraction
  intersect boxIntersect intersection

  // intervalmatrices
  [ ivmatGet indexing
  print ivmatPrint printing
  nrows ivmatNrows number of rows
  ncols ivmatNcols number of columns
  det determinant determinant
  * ivmatMultiply matrix multiplication

Procedures:

> D.8.2.1 length2 |  | length/size if interval
> D.8.2.2 bounds2 |  | construct interval for given bounds.
> D.8.2.3 intervalmatrixInit |  | initialises an interval matrix
> D.8.2.4 unitMatrix2 |  | unit matrix
> D.8.2.5 applyMatrix |  | apply matrix to box
> D.8.2.6 ivmatGaussian2 |  | Gaussian elimination on matrices
> D.8.2.7 evalPolyAtBox2 |  | evaluate interval extension of polynomial
> D.8.2.8 exclusionTest |  | first version of our exclusion test

See also: rootisolation_lib.

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