
norm - norm of a polynomial

Calling sequence:
norm(poly [ , number ])
norm(expr [ , indets ]  [ , number ])
indets  ---> [ expr_1 ...]

Parameter:
poly           --  polynomial
expr, expr_1   --  expressions
number         --  number not equal to 0

Overloading:

1

Summary:

norm calculates numerically the norm of a polynomial whose coefficientsare
numbers or expressions which may be converted to numbers via float or
domain elements.

 o  norm(p) returns the maximum norm of the polynomial p.  This is
    defined as max( abs(c[i]) $ i=1..nterms(p) ), where the c[i] are
    the coefficients of p.

  o  norm(p,n) returns the n-norm of the polynomial p. This is defined as

        sum( abs(c[i])^n, i=1..nterms(p) )^(1/n)

     where the c[i] are the coefficients of p. n may be any complex number
     not equal to 0.

If the coefficient ring of the polynomial is a domain , then this must have the
method norm. The method must return the norm of a domain element as a
number or an expression which may be converted to a number via float.

The first argument of norm is allowed to be a polynomial or an expression
and optionally a listof indeterminates.  An expression is converted into a
polynomial in the specified indeterminates (see function poly). norm returns
FAIL if the expression cannot be converted into a polynomial. norm returns
an error if the argument number is not a number or is zero. norm is a kernel
function.

>>  norm(6*x*y+9*y^2+2, [x,y]);

      9

>>  p := poly(2*x^3+2*y, [x,y]): norm(p, 2);

      2.828427124

See also:  float , poly

