#### UserFunction Power

`Power(u:DPOLID(C,v,O),n:Z)`

The arguments $u$ has type $DPOLID$ which abbreviates * Distributive Polynomial Ideal, $n$ is a natural number.
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.

$n$: Nonnegative integer.

**Specification.** Generators for $n-$th power of ideal of $u$ are returned. In general they are not a Groebner basis.

**Examples.** The input is given in {\em 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};}`

`Power(I|DPOLID(Q,{x,y},GRLEX),2);`

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

The power ideal:

$<x^2y^2+4x^2y+4x^2-6xy-12x+9,$

$x^3y+2x^3+3x^2y+3x^2-xy^2-2xy-9x+3y,$

$x^4+6x^3-2x^2y+9x^2-6xy+y^2>

**Related Functions.** Product.

**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* and * 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.