up previous next
change field for polynomials and ideals
QZP(F: RINGELEM): RINGELEM
QZP(F: LIST of POLY): LIST of POLY
QZP(I: IDEAL): IDEAL 
***** NOT YET IMPLEMENTED *****
The functions
QZP
and
ZPQ
map polynomials and
ideals of other rings into ones of the current ring.
When mapping from one ring to another, one of the rings must have
coefficients in the rational numbers and the other must have
coefficients in a finite field. The indeterminates in both
rings must be identical.
The function
QZP
maps polynomials with rational coefficients to
polynomials with coefficients in a finite field; the function
ZPQ
does the reverse, mapping a polynomial with finite field coefficients
into one with rational (actually, integer) coefficients. The function
ZPQ
is not uniquely defined mathematically, and currently for each
coefficient the least nonnegative equivalent integer is chosen.
Users should not rely on this choice, though any change will be
documented.
use R ::= QQ[x,y,z];
F := 1/2*x^3 + 34/567*x*y*z  890;  a poly with rational coefficients
use S ::= ZZ/(101)[x,y,z];
QZP(F);  compute its image with coeffs in ZZ/(101)
50x^3  19xyz + 19

G := It;
use R;
ZPQ(G);  now map that result back to QQ[x,y,z]
 it is NOT the same as F...
51x^3 + 82xyz + 19

H := It;
F  H;  ... but the difference is divisible by 101
101/2x^3  46460/567xyz  909

use S;
QZP(H)  G;  F and H have the same image in ZZ/(101)[x,y,z]
0

