9.5.13 `algtodalg', `dalgtoalg', `dptodalg', `dalgtodp'
-------------------------------------------------------

algtodalg(ALG)
     :: Converts an algebraic number ALG to a `DAlg'.

dalgtoalg(DALG)
     :: Converts a `DAlg' `dalg' to an algebraic number.

dptodalg(DP)
     :: Converts an algebraic number ALG to a `DAlg'.

dalgtodp(DALG)
     :: Converts a `DAlg' `dalg' to an algebraic number.

RETURN
     An algebraic number, a `DAlg' or a list [distributed
     polynomial,denominator]

ALG
     an algebraic number containing `root'

DP
     a distributed polynomial over Q

   * These functions are converters between `DAlg' and an algebraic
     number containing `root', or a distributed polynomial.

   * A ground field to which a `DAlg' belongs must be set by
     `set_field()' in advance.

   * `dalgtodp()' returns a list containing the numerator (a
     distributed polynomial) and the denominator (an integer).

   * `algtodalg()', `dptodalg()' return the simplified result.

     [0] A=newalg(x^2+1);
     (#0)
     [1] B=newalg(x^3+A*x+A);
     (#1)
     [2] set_field([B,A]);
     0
     [3] C=algtodalg((A+B)^10);
     ((408)*<<2,1>>+(103)*<<2,0>>+(-36)*<<1,1>>+(-446)*<<1,0>>
     +(-332)*<<0,1>>+(-218)*<<0,0>>)
     [4] dalgtoalg(C);
     ((408*#0+103)*#1^2+(-36*#0-446)*#1-332*#0-218)
     [5] D=dptodalg(<<10,10>>/10+2*<<5,5>>+1/3*<<0,0>>);
     ((-9)*<<2,1>>+(57)*<<2,0>>+(-63)*<<1,1>>+(-12)*<<1,0>>
     +(-60)*<<0,1>>+(1)*<<0,0>>)/30
     [6] dalgtodp(D);
     [(-9)*<<2,1>>+(57)*<<2,0>>+(-63)*<<1,1>>+(-12)*<<1,0>>
     +(-60)*<<0,1>>+(1)*<<0,0>>,30]

Reference
     *Note `set_field': set_field.

