#### UserFunction In?

In?(u,v:DPOLID(C,v,O))

The arguments $u$ and $v$ have the type $DPOLID$ which abbreviates
Distributive Polynomial Ideal. The meaning of its parameters is as follows.

$C$: Coefficient type.

$v=\{v_1,v_2,\ldots \}$: Distributive variables in decreasing order.

$O:LEX|GRLEX|GREVLEX$: Term ordering.

Specification. Returns $true$ if $u\subseteq v$ and $false$ otherwise.

Examples.} The input is given in Reduce algebraic mode syntax. The output for each
minisession is returned in a separate window.

I:={x**2+y+1,x*y+2\};

J:={x**4+2*x**2*y+2*x**2+y**2+2*y+1,

x**3*y+2*x**2+x*y**2+x*y+2*y+2,x**2*y**2+4*x*y+4};

T==|DPOLID(Q,{x,y},GRLEX)|;

In?(I,J|T|);

false

In?(I,J|T|);

true

References.

W.W. Adams, P. Loustaunau, An Introduction to Groebner Bases, American Mathematical Society, 1994.

D. Cox, J. Little, D. O'Shea, Ideals, Varieties and Algorithms Using Algebraic Geometry,
Undergraduate Texts in Mathematics, Springer, 1992 and 1998.

G.M. Greuel, G. Pfister, A Singular Introduction to Commutative Algebra, Springer, 2002.

M. Kreuzer, L. Robbiano, Using Computational Commutative Algebra I and II, Springer, 2000.