CoCoA:BringIn

BringIn

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 functions <ttref>QZP</ttref>, <ttref>ZPQ</ttref>.

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 ::= 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
-------------------------------
```

Syntax

```BringIn(E:OBJECT):OBJECT

where E
is a polynomial, a rational function, or a list/matrix/vector of
these.
```

```   <type>list</type>
<type>matrix</type>
<type>polynomial</type>
<type>ratfun</type>
<type>vector</type>
```