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D.4.14.3 modIntersect
Procedure from library modstd.lib (see modstd_lib).
- Usage:
- modIntersect(I,J); I,J ideal/module
- Return:
- a generating set of the intersection of I and J
- Note:
- The procedure computes a the intersection of I and J
(over the rational numbers) by using modular methods
with high probability.
No additional tests are performed.
Example:
| | LIB "modstd.lib";
ring R1 = 0, (x,y,z,t), dp;
ideal I = 3x3+x2+1, 11y5+y3+2, 5z4+z2+4;
ideal J = maxideal(2);
modIntersect(I,J);
==> _[1]=z4-12/5x3-4/5x2+1/5z2
==> _[2]=x3t2+1/3x2t2+1/3t2
==> _[3]=x3zt+1/3x2zt+1/3zt
==> _[4]=x3yt+1/3x2yt+1/3yt
==> _[5]=x4t+1/3x3t+1/3xt
==> _[6]=x3z2+1/3x2z2+1/3z2
==> _[7]=x3yz+1/3x2yz+1/3yz
==> _[8]=x4z+1/3x3z+1/3xz
==> _[9]=y5-6/11x3+1/11y3-2/11x2
==> _[10]=x3y2+1/3x2y2+1/3y2
==> _[11]=x4y+1/3x3y+1/3xy
==> _[12]=x5+1/3x4+1/3x2
simplify(intersect(I,J),1);
==> _[1]=z4-12/5x3-4/5x2+1/5z2
==> _[2]=x3t2+1/3x2t2+1/3t2
==> _[3]=x3zt+1/3x2zt+1/3zt
==> _[4]=x3yt+1/3x2yt+1/3yt
==> _[5]=x4t+1/3x3t+1/3xt
==> _[6]=x3z2+1/3x2z2+1/3z2
==> _[7]=x3yz+1/3x2yz+1/3yz
==> _[8]=x4z+1/3x3z+1/3xz
==> _[9]=y5-6/11x3+1/11y3-2/11x2
==> _[10]=x3y2+1/3x2y2+1/3y2
==> _[11]=x4y+1/3x3y+1/3xy
==> _[12]=x5+1/3x4+1/3x2
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See also:
modular.
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