isEffective DA torus-invariant Weil divisor is effective if all the coefficients of the torus-invariant irreducible divisors are nonnegative.
The canonical divisor is not effective, but the anticanonical divisor is.
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The torus-invariant irreducible divisors generate the cone of effective divisors.
The source of this document is in /__w/M2/M2/macaulay2-1.26.05+ds/M2/Macaulay2/packages/NormalToricVarieties/DivisorsDocumentation.m2:1598:0.