Home Online Manual
Top
Back: graal_lib
Forward: dimensionOfLocalization
FastBack:
FastForward:
Up: graal_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

D.15.15.1 graalMixed

Procedure from library graal.lib (see graal_lib).

Usage:
graalMixed(L,t); L ideal, t int (optional)

Return:
graalBearer with all the necessary structures for our machinery if t specified and t>0, puts an upper time limit
on finding a necessary transformation to map an intermediate ideal into general position.

Note:
assumes that the current basering is a domain and that L is a prime ideal.

Example:
 
LIB "graal.lib";
// see [Mora] Example 6.5
ring Q = 0,(x,y,z),dp;
ideal H = y2-xz;
qring A = std(H);
ideal L = x3-yz,x2y-z2;
graalBearer Gr = graalMixed(L); Gr;
==> affine coordinate ring: 
==>    (QQ),(x,y,z),(dp(3),C)
==>      mod <y2-xz>
==> 
==> ideal defining the subvariety: 
==>    <x3-yz,x2y-z2>
==> 
==> Al: 
==>    (0,z),(Y(1),Y(2),x,y),(ds(2),c,dp(2))
==>      mod <x^3+(-z)*y-Y(1),x^2*y+(-z^2)-Y(2),y^2+(-z)*x,(z)*Y(1)-Y(2)*y>
==> graal: 
==>    (0,z),(Y(1),Y(2),y),(c,dp(2),lp(1))
==>      mod <(z)*Y(1)-Y(2)*y,y^5+(-z^4)>
==>    where 
==>      Y(1) represents generator x3-yz
==>      Y(2) represents generator x2y-z2
==>    and x,y in Al are mapped to 1/(z)*y^2,y in Graal
==>