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);

The given ideal:
$<xy+2x-3,x^{2}+3x+y>$
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.