ptosfp
, sfptop
ptosfp()
converts coefficients of a polynomial to
elements in a small finite field GF(p^n) set as a ground field.
If a coefficient is already an element of the field,
no conversion is done. If a coefficient is a positive integer,
then its residue modulo p^n is expanded as p-adic integer,
then p is substituted by x, finally the polynomial
is converted to its correspoding logarithmic representation
with respect to the primitive element.
For example, GF(3^5) is represented as F(3)[x]/(x^5+2*x+1),
and each element of the field is represented as @_k
by its exponent k with respect to the primitive element x.
23 = 2*3^2+3+2 is represented as 2*x^2+x+2 and
it is equivalent to x^17 modulo x^5+2*x+1.
Therefore an integer 23 is conterted to @_17.
sfptop()
is the inverse of ptosfp()
.
[196] setmod_ff(3,5); [3,x^5+2*x+1,x] [197] A = ptosfp(23); @_17 [198] 9*2+3+2; 23 [199] x^17-(2*x^2+x+2); x^17-2*x^2-x-2 [200] sremm(@,x^5+2*x+1,3); 0 [201] sfptop(A); 23
setmod_ff
, section simp_ff
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