substitute values for parameters in an ordinal
integer or polynomial with integer coefficients
list or set of equations of type x=v
The Eval(o, x=v) calling sequence substitutes the value v for the parameter x in the ordinal o, returning either an ordinal data structure, a nonnegative integer, or a polynomial with positive integer coefficients.
It is possible for v to be a negative integer or a polynomial with some negative integer coefficients, provided that the result is a valid ordinal, which means it does not have any negative integer coefficients.
The resulting ordinal is simplified, namely, any coefficients that become zero are removed, and if only a single term with exponent 0 is left after that, a nonnegative integer or a polynomial with positive integer coefficients is returned.
The Eval(o, l) calling sequence performs all the substitutions in l simultaneously.
This command can also be applied to a polynomial with positive integer coefficients representing a nonnegative integer ordinal.
o1 ≔ Ordinal⁡ω,x,2,3,1,y+1,0,4
Several substitutions can be done at once. It is also possible to substitute a polynomial for a parameter and not just an integer.
The result need not be an ordinal data structure.
o2 ≔ Ordinal⁡2,x2+x,1,x,0,4
The attempt to substitute a negative integer or a polynomial with negative coefficients may result in an error if the result has negative coefficients.
o3 ≔ Ordinal⁡1,2⁢x+2,0,3
Error, (in Ordinals:-Eval) invalid substitution; result is not a valid ordinal
The Eval command can also be applied to a polynomial with positive integer coefficients representing a constant ordinal.
The Ordinals[Eval] command was introduced in Maple 2015.
For more information on Maple 2015 changes, see Updates in Maple 2015.
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