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 BringIn

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

 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 functions QZP , ZPQ .

This function does not work on ideals because BringIn(Ideal(x-y, 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))).

 Example
 ``` RR ::= QQ[x[1..4],z,y]; SS ::= ZZ/(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 ::= 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 ------------------------------- ```