Arithmetic (integers, reals and complexes or polynomials)

 

• FACTO (integer): gives the list of prime factors. Example:
  3150 -> { 2 3 3 5 5 7 }
  You can forget levels 2 and 3
• DIVIS: gives a list of divisors. Example:
  21 -> { 1 7 3 21 }
• SQRT: formal square root of an integer or complex integer or polynomial. Examples:

  

• GCD1: greatest common divisor (integers or polynomials). 'X^2+2*X+1' 'X^2+3*X+2' GCD1 -> 'X+1'
25 15 GCD1 -> 5
  If flag 12 is clear returns 1.
• LCM: lowest common multiple (GCD LCM ). Examples:
  'X^2+2*X+1' 'X^2+3*X+2' LCM -> '(X^2+2*X+1)*(X+2)'
25 15 LCM -> 75
• GCD3: extended gcd algorithm, given x and y returns d , u and v s.t.:

  

  (d is a multiple of the GCD of x and y by an invertible, i.e. an integer in the univariate case)

• re: real part of a fraction, global names are always considered as reals
• im: imaginary part of a fraction,
• conj: conjugate of a fraction,