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D.15.7.1 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:
==> (0),(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
==>
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