To test containments of symbolic and ordinary powers of ideals defining monomial curves, we can skip the step where we define the ideals.
For example, if I is the ideal defining the monomial curve defined by t3, t4, t5 over ℤ/101, we can ask whether I(3) ⊆I2:
i1 : symbolicContainmentMonomialCurve(ZZ/101,{3,4,5},3,2)
o1 = true
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Or we simply ask for the symbolic powers of these ideals. For example, here is the third of the same ideal:
i2 : symbolicPowerMonomialCurve(ZZ/101,{3,4,5},3)
6 4 2 2 2 3 3 2 5 3 3 4 2 4 2
o2 = ideal (c - 3b*c d + 3b c d - b d , b c - 2b c d + b c*d - c d +
------------------------------------------------------------------------
2 3 2 4 3 4 4 2 5 2 5 3 2 2 3 5 2
2b*c d - b d , b c - 2b c d + b d - c d + 2b*c d - b c*d , b c -
------------------------------------------------------------------------
6 5 2 3 3 2 2 3 4 7 4 2 5 2 5
b d + b*c - 4b c d + 3b c*d + c d - b*d , b c - b c d - 2b d + c d -
------------------------------------------------------------------------
3 2 2 3 5 8 4 3 5 4 2 2 2 3 3
3b*c d + 5b c*d - d , b + b c - 4b c*d - b*c d + 3b c d + b d -
------------------------------------------------------------------------
4
c*d )
ZZ
o2 : Ideal of ---[b, c, d]
101
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