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Colon, :, HColon
Syntax
Colon(M:IDEAL,N:IDEAL):IDEAL
Colon(M:MODULE,N:MODULE):IDEAL
M : N
HColon(M:IDEAL,N:IDEAL):IDEAL
Summary
ideal or module quotient
Description
These functions return the quotient of M by N: the ideal of
polynomials F in R such that FG is in M for all G in N. The command
M : N
is a shortcut for
Colon(M,N)
.
The function
HColon
calculates the ideal quotient using a
Hilbert-driven algorithm. It differs from
Colon
only when the input
is inhomogeneous, in which case,
HColon
may be faster.
example
Use R ::= Q[x,y];
Ideal(xy,x^2) : Ideal(x);
Ideal(y, x)
-------------------------------
Colon(Ideal(x^2,xy),Ideal(x,x-y^2));
Ideal(x)
-------------------------------
HColon(Ideal(x^2,xy),Ideal(x,x-y^2));
Ideal(x)
-------------------------------
See Also