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bring in objects from another ring
BringIn(E:OBJECT):OBJECT
where E
is a polynomial, a rational function, or a list/matrix/vector of
these.

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 functions
QZP
,
ZPQ
.
This function does not work on ideals because
BringIn(Ideal(xy, x+y))
into
R[x] is ambiguous: one might expect
Ideal(2x),
whereas just mapping the generators would return an error.
So, if you want to map the generators of the ideal type
Ideal(BringIn(Gens(I))).
RR ::= QQ[x[1..4],z,y];
SS ::= ZZ/(101)[z,y,x[1..2]];
Use RR;
F := (x[1]yz)^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 ::= 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) = BringIn(F);
TRUE

