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.