left logarithm of ordinals
ordinals, nonnegative integers, or polynomials with positive integer coefficients
All calling sequences return an expression sequence l, q, r such that a=bl⋅q+r, where l, q and r are ordinals, nonnegative integers, or polynomials with positive integer coefficients, and q and r are as small as possible.
The Log(a,b) calling sequence computes the unique ordinal numbers l, q, and r such that a=bl⋅q+r, 0≺q≺b and r≺bl, where ≺ is the strict ordering of ordinals.
If b=0 or b=1, a division by zero error is raised.
The log[b](a) and Log(a,b) calling sequences are equivalent. The log(a) calling sequence is equivalent to Log(a,ω).
If one of a and b is a parametric ordinal and the logarithm cannot be taken, an error is raised.
The log command overloads the corresponding top-level routine log. The top-level command is still accessible via the :- qualifier, that is, as :-log.
a ≔ Ordinal⁡4,1,2,2,1,3,0,5
b ≔ Ordinal⁡2,1,0,2
l,q,r ≔ Log⁡a,b
l,q,r ≔ Log⁡a,b+1
Error, (in Ordinals:-Sub) unable to subtract 2+x from 2
When the base is constant:
l,q,r ≔ Log⁡a,x+2
When both arguments are integers, the first return value is the integer part of the logarithm over the real numbers:
l,q,r ≔ Log⁡100,3
Example with a nonconstant logarithm:
b ≔ `.`⁡ω,2+3
a ≔ Dec⁡+x
The Ordinals[Log] and Ordinals[log] commands were introduced in Maple 2015.
For more information on Maple 2015 changes, see Updates in Maple 2015.
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