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BringIn --
bring in objects from another ring
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BringIn(E: OBJECT): OBJECT
BringIn(R: RING, E: OBJECT): OBJECT |
This function maps a polynomial (or a list, matrix of these) into the
current ring, or the ring
R, preserving the names of the indeterminates.
Honestly, this is not-so-clean shortcut for creating and calling a
homomorphism. (
Introduction to RINGHOM
)
NOTE: this function is not implemented on IDEAL because might be
misleading: one might expect that bringing an ideal from
K[x,y]
into
K[x] means eliminating
y. For this operation
call
elim
.
Instead, if you want to map the generators of the ideal type
ideal(BringIn(R, 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
/**/ BringIn(SS, 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
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