REAL_POLY_POW_CONV : term -> thm

SYNOPSIS

Raise real polynomial to numeral power while retaining canonical form.

DESCRIPTION

For many purposes it is useful to retain polynomials in a canonical form. For more information on the usual normal form in HOL Light, see the function REAL_POLY_CONV, which converts a polynomial to normal form while proving the equivalence of the original and normalized forms. The function REAL_POLY_POW_CONV is a more delicate conversion that, given a term p1 pow n where p is a real polynomial in normal form and n a numeral, returns a theorem |- p pow n = p' where p' is in normal form.

FAILURE CONDITIONS

Fails if applied to a term that is not a real term raised to a numeral power. If the subterm is not a polynomial in normal form, the overall normalization is not guaranteed.

EXAMPLE

  # REAL_POLY_POW_CONV `(x + &1) pow 4`;;
  val it : thm =
    |- (x + &1) pow 4 = x pow 4 + &4 * x pow 3 + &6 * x pow 2 + &4 * x + &1

USES

More delicate polynomial operations that simply the direct normalization with REAL_POLY_CONV.