So, simply enough:

full-exp[op,n] |x>

maps to: (1 + op/1 + op^2/2 + ... + op^n/n! ) |x>

No point giving the python.

Anyway, a quick example:

-- define our X operator: sa: X |*> #=> algebra(|x>,|*>,|_self>) -- the previous exp operator: sa: exp[X,6] |1> |1> + |x> + |x*x> + |x*x*x> + |x*x*x*x> + |x*x*x*x*x> + |x*x*x*x*x*x> -- the new exp operator: sa: full-exp[X,6] |1> |1> + |x> + 0.5|x*x> + 0.167|x*x*x> + 0.042|x*x*x*x> + 0.008|x*x*x*x*x> + 0.001|x*x*x*x*x*x>And I guess that is it. We see the standard Taylor series for exp(x) as expected.

Update: and we can use exp as a "smear" operator, to expand a single point into a range of points. So, in a way, a little like the range function.

In the console:

-- define a translation operator: T |*> #=> arithmetic(|_self>,|+>,|x: 1>) -- a test case (translate by 1): sa: T |x: 0> |x: 1> -- another test case (translate by 7): sa: T^7 |x: 0> |x: 7> -- use exp[op,n] as a smear operator: sa: exp[T,7] |x: 0> |x: 0> + |x: 1> + |x: 2> + |x: 3> + |x: 4> + |x: 5> + |x: 6> + |x: 7>

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updated: 19/12/2016

by Garry Morrison

email: garry -at- semantic-db.org