UserFunction Intersection

Intersection}(u,v:DPOLID(C,vs,O))

The arguments $u$ and $v$ have the type $DPOLID$ which abbreviates
{\em 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 order.

Specification.
Generators for the intersection ideal of $u$ and $v$ are returned.

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

f:={x*y+2*x-3,x**2+3*x+y};

g:={3*x*y-x+y**2-1,x+3*y-1};

s:=Intersection(f,g|DPOLID(RATF Q,{x,y},GRLEX)|);

The given ideals:
$<xy+2x-3,x^{2}+3x+y>$
$<3xy+y^{2}-x-1,x+3y-1>$
The intersection ideal:
$<y^{5}+ \frac{13}{4}y^{4}+\frac{41}{4}y^{3} +\frac{73}{4}y^{2}-17y+ \frac{27}{4},$

$x+\frac{22592}{201333}y^{4}+\frac{63388}{201333}y^{3} +\frac{252887}{201333}y^{2}+ \frac{393466}{201333}y -\frac{41487}{67111}>$

Related Functions. Lcm

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.