Sample 1.  Real root of f(x) = x**5 - 3x**4 + x**3 - 4x**2 + x - 6 = 0.


 Iteration       Newton Approximation

         0       3.120000000000000000000000000000000000000000000000000000000000

         1       3.120656718532108533919391265947916793506741449899073468862023

         2       3.120656215327022122238354686569835883519704471397219749798884

         3       3.120656215326726500470956115551705969611230193197937042123082

         4       3.120656215326726500470956013523797484654623935599078168006617

         5       3.120656215326726500470956013523797484654623935599066014988828

         6       3.120656215326726500470956013523797484654623935599066014988828



 Sample 2.  Find the root above to 300 decimal places.

       3.12065621532672650047095601352379748465462393559906601498882843581902649995179546
      89783257450017151095811923431332682839420040840535954560118152245371792881305271951
      01711893889821240366205830730398354737691328200011005827350420283867070989561927541
      348452154928259189115694520078941581838752951201099960



 Sample 3.          109 terms were added in the Zeta sum

 Zeta(3) = 1.202056903159594285399738161511449990764986292340498881792272



 Sample 4.           57 values were checked before finding a prime p.

 p =  5468317884572019103692012212053793153845065543480825746529998049913561



 Sample 5.  Check that Gamma(1/2) = Sqrt(pi)

 Gamma(1/2) = 1.772453850905516027298167483341145182797549456122387128213808



 Sample 6.  Psi and Polygamma functions.

 Sum (n=1 to infinity) 1/(n**2 * (8n+1)**2) = 
             .013499486145413024755107829105035147950644978635837270816327



 Sample 7.  Incomplete gamma and Gamma functions.

 Probability =  .19373313011487144632751025918250599953472318607121386973066



 Sample 8.  Complex root of f(x) = x**5 - 3x**4 + x**3 - 4x**2 + x - 6 = 0.


 Iteration       Newton Approximation

     0     .560000000000000000000000000000 + 1.060000000000000000000000000000 i

     1     .561964780980333719745880263787 + 1.061135231152741154895778904059 i

     2     .561958308372772219534516409947 + 1.061134679566247415769456345141 i

     3     .561958308335403235495113920123 + 1.061134679604332556981397796290 i

     4     .561958308335403235498111195347 + 1.061134679604332556983391239059 i

     5     .561958308335403235498111195347 + 1.061134679604332556983391239059 i



 Sample 9.           44 terms were added to get Exp(1.23-2.34i)

 Result= -2.379681796854777515745457977697 - 2.458032970832342652397461908326 i



 Sample 10.  Exception handling.

             Iterate Exp(x) starting at 1.0 until overflow occurs.


 Iteration  1      2.718281828459045235360287471352662497757M+0

 Iteration  2      1.515426224147926418976043027262991190553M+1

 Iteration  3      3.814279104760220592209219594098203571024M+6

 Iteration  4      2.331504399007195462289689911012137666332M+1656520

 Iteration  5      + OVERFLOW

 Overflow was correctly detected.


 All results were ok.