Another Example of Intermediate Expression Swell

• stages in the expression swell analysis of the computation of the characteristic polynomial of a general matrix containing ``prime'' 4-digit rational numbers (both the numerator and the denominator consist of 4 digits)
  1. Initial matrix.
     

     
     
     

  2. The sizes of the entries in the upper Hessenberg matrix H that is similar to A. For example, the (5,4) entry is a rational number with a 309-digit numerator and a 313-digit denominator!

     
     
     

  3. The sizes of the coefficients of the characteristic polynomial . For example, the coefficient of is a rational number with a 98-digit numerator and a 100-digit denominator. The numbers involved involved have decreased in size, but are still large!