A torus-invariant Weil divisor is effective if all the coefficients of the torus-invariant prime divisors are nonnegative.
The canonical divisor is not effective, but the anticanonical divisor is.
i1 : PP3 = projectiveSpace 3;
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i2 : K = toricDivisor PP3
o2 = - PP3 - PP3 - PP3 - PP3
0 1 2 3
o2 : ToricDivisor on PP3
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i3 : isEffective K
o3 = false
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i4 : isEffective(-K)
o4 = true
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The torus-invariant prime divisors generate the cone of effective divisors.