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bring in objects from another ring


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 (x-y, 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 non-0 to 0 is NOT YET IMPLEMENTED in CoCoA-5 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]-y-z)^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

See Also