#### UserFunction Sum

`Sum(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.

$C$: Type of coefficients.

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

$O=LEX|GRLEX|GREVLEX$: Term order.

**Specification. ** Generators for the sum ideal of $u$ and $v$ are returned. In general they are not a Groebner basis.

**Examples.** The input for the examples is given in *Reduce* algebraic mode syntax. The output for each minisession

is returned in a separate window.

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

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

`Sum(I,J|DPOLID(RATF Q,{x,y},GRLEX)|); `

$<xy+2x-3,x^{2}+3x+y>,$

$<3xy+y^{2}-x-1,x+3y-1>$

The sum ideal:

$<xy+2x-3,x^{2}+3x+y>,3xy+y^{2}-x-1,x+3y-1>$

**Related Functions.** Product, 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.