Arithmetic.

 

• XFRC:
  Same as Q but handles quadratic irrationals (recognize a quadratic irrational if its expansion in contined fraction is ultimately periodic of period less or equal to 3) Examples:
  

  

• CAB: (Bezout identity)
  solve in the polynomials ring the equation c=ax+by Examples:
  

  * 1 'X^2+2*X+1' 'X^2+2*X+3' -> -1 1 1
  * 1 'X^2+2*X+1' 'X^2+2*X+3' -> 0

  This means for the first case that:

  

  as in the second case there is no solution because the gcd of x²+1*x+1 and x²+3*x+2 does not divide 1.

• EULER: Euler indicatrix
  Given an integer n, returns an integer e: the number of integers lower than and prime with n. Example for n=25, e=20 because 1,2,3,4,6,7,8,9,11,12,13,14,16,17,18,19,21,22,23,24 are prime together with 25.
• FCLI:
  converts a real into a rational, an integer, or a list (his development in continued fraction). Example:
  

  

• LIFC:
  continued fraction to fraction (or symbolic) For example { 3 7 15 1 292 } 103993 and 33102. You may type / to find approximatively ).
• ORND:
  round object at stack level 2, stack level 1 is the expected denominator of all rationals of the object. For example, .49999999999+.2000000001*x 10 ORND returns .5+.2*x.