CoCoA:ZPQ

ZPQ

change field for polynomials and ideals

Description

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 <ttref>QZP</ttref> for more details.

Example

  Use R ::= Q[x,y,z];
  F := 1/2*x^3 + 34/567*x*y*z - 890; -- a poly with rational coefficients
  Use S ::= Z/(101)[x,y,z];
  QZP(F);                            -- compute its image with coeffs in Z/(101)
-50x^3 - 19xyz + 19
-------------------------------
  G := It;
  Use R;
  ZPQ(G);     -- now map that result back to Q[x,y,z] it is NOT the same as F...
51x^3 + 82xyz + 19
-------------------------------

Syntax

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

Accessing Other Rings

BringIn

Image

   <type>ideal</type>
   <type>polynomial</type>
   <type>ring</type>