ZPQ

ZPQ

change field for polynomials and ideals

Syntax

ZPQ(F: RINGELEM): RINGELEM
ZPQ(F: LIST of RINGELEM): LIST of RINGELEM
ZPQ(I: IDEAL): IDEAL

Description

***** NOT YET IMPLEMENTED *****

The function ZPQ maps a polynomial with finite field coefficients into one with rational (actually, integer) coefficients. It is not uniquely defined mathematically, and currently for each coefficient the least non-negative equivalent integer is chosen. Users should not rely on this choice, though any change will be documented.

See QZP for more details.

Example

  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
-------------------------------

See Also

BringIn