ordinal, nonnegative integer, or polynomial with positive integer coefficients
ordinal data structure, nonnegative integer, polynomial with positive integer coefficients, or NULL.
The Dec(a) calling sequence decrements the ordinal number a, if possible. If a=0, then the return value is NULL. Otherwise, if the trailing term is ωe⋅c, where e is an ordinal and c is a positive integer, then exactly one of the following happens:
If e=0 then c is replaced by c−1.
If e≠0 and c≠1, then the trailing term is replaced by the sum of the two terms ωe⋅c−1+ωDec⁡e.
Otherwise, if e≠0 and c=1, then the trailing exponent is replaced by Dec⁡e.
Note that in general Dec⁡a is not the largest ordinal number smaller than a, because such an ordinal does not exist if a is a limit ordinal, which means its trailing degree is nonzero.
If a is a parametric ordinal number and c−1 is not a polynomial with nonnegative integer coefficients, an error is raised.
a ≔ Ordinal⁡ω,2,2,3,0,4
whilea≠0doa ≔ Dec⁡a;print⁡aend do:
b ≔ Ordinal⁡1,3,0,x2+x+2
Error, (in Ordinals:-Dec) cannot decrement, x^2+x
The Ordinals[Dec] command was introduced in Maple 2015.
For more information on Maple 2015 changes, see Updates in Maple 2015.
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