up previous next
Chinese Remainder Theorem on polynomial coefficients
CRTPoly(f1: RINGELEM, M1: INT, f2: RINGELEM, M2: INT): RECORD |
This function combines residue-modulus pairs
(f1,M1)
and
(f2,M2)
using the Chinese Remainder Theorem to produce a single
residue-modulus pair
(f,M)
such that
f
is a polynomial (with coefficients in
QQ
),
f = f1 mod M1
and
f = f2 mod M2
,
and all coefficients of
f
are smaller than
M
.
The moduli
M1
and
M2
must be coprime (hence
M = M1*M2
).
/**/ CRTPoly(x-y, 331, x+y, 10093);
record[modulus := 3340783, residue := x +676232*y]
/**/ mod(676232, 331);
330
/**/ mod(676232, 10093);
1
|