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#### 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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