Useful facilities for standard forms

4.10 Useful facilities for standard forms

4.10.1 Kernel list

The function kernels extracts all kernels from a standard form and returns them as list.

kernels numr simp ’(plus (expt x 3)(expt y 4));

will result in (xy).

4.10.2 Greatest common divisor

The greatest common divisor of two polynomials is computed by the function *gcdf. It takes as arguments two standard forms and returns a standard form or a 1 if there is no non trivial common divisor.

4.10.3 Factorization

The function fctrf is the interface for calling the factorizer. It takes a standard form as parameter and returns a list which contains

as first element the content of the polynomial - that is the gcd of the coefficients or the “common numeric factor”,
as second and following elements the factors in the form (SF.m) where SF is the factor as standard form and m is its multiplicity.

So calling fctrf for 2x² - 2 will result in

(2 ((((X . 1) . 1) . 1) . 1) ((((X . 1) . 1) . -1) . 1))

Here you see the common domain factor 2 and the two factors x + 1 and x- 1 as standard forms paired with their multiplicity 1.

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