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BringIn
Syntax
BringIn(E:OBJECT):OBJECT

where E is a polynomial, a rational function, or a list/matrix/vector of
these.
Summary
bring in objects from another ring
Description
This function maps a polynomial or rational function (or a list,
matrix, or vector of these) into the current ring, preserving the
names of the indeterminates.  When mapping from a ring of finite
characteristic to one of zero characteristic then consistent choices
of image for the coefficients are made (i.e. if two coefficients are
equal mod p then their images will be equal).

If the two polynomial rings differ only in characteristic then it
is faster to use the function QZP or ZPQ.

Example

RR ::= Q[x[1..4],z,y];
SS ::= Z/(101)[z,y,x[1..2]];
Use RR;
F := (x[1]-y-z)^2;
F;
x[1]^2 - 2x[1]z + z^2 - 2x[1]y + 2zy + y^2
-------------------------------
Use SS;
B := BringIn(F);
B;
z^2 + 2zy + y^2 - 2zx[1] - 2yx[1] + x[1]^2
-------------------------------

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) = BringIn(F);
TRUE
-------------------------------