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bring in objects from another ring
BringIn(E: OBJECT): OBJECT 
This function maps a polynomial (or a list, matrix of these) into the
current ring, preserving the names of the indeterminates.
This function is not implemented on ideals because might be
misleading: one might expect that bringing an ideal from
R[x,y]
into
R[x]
means eliminating
y
, while others might
expect the ideal generated by mapping the generators.
For example in the first case
(xy, x+y) returns the
ideal
(x), in the second case returns an error.
So, if you want to map the generators of the ideal type
ideal(BringIn(gens(I)))
.
 Changing characteristic from non0 to 0 is NOT YET IMPLEMENTED in CoCoA5
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).
/**/ RR ::= QQ[x[1..4],z,y];
/**/ SS ::= ZZ[z,y,x[1..2]];
/**/ use RR;
/**/ F := (x[1]yz)^2; F;
x[1]^2 2*x[1]*z +z^2 2*x[1]*y +2*z*y +y^2
/**/ use SS;
/**/ BringIn(F);
z^2 +2*z*y +y^2 2*z*x[1] 2*y*x[1] +x[1]^2
/**/ use R ::= QQ[x,y,z];
/**/ F := (1/2)*x^3 + (34/567)*x*y*z  890;  poly with rational coefficients
/**/ use S ::= ZZ/(101)[x,y,z];
/**/ BringIn(F);
50*x^3 19*x*y*z +19
