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Functions with operation (multiplication) as argument

asked 2021-01-29 16:18:57 +0200

SYLA gravatar image

updated 2021-02-05 23:39:41 +0200

slelievre gravatar image

Suppose I have functions $f$, $g_1$, $g_2$, $h$ and an operation $*$, which is not necessarily multiplication, satisfying the following relations:

$$ f(X * Y) = g_1(X) g_2(Y) + g_1(Y) g_2(X) + f(X) * f(Y) + h(X * Y) $$

$$ h(X * Y) = h^2(X) * g_1(Y) $$

How to find a symbolic expression for $f(X^7)$?

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I don't understand your question; f(X*Y) = ... does not seem to be valid Python syntax. Could you provide the full code of what you are trying to do?

eric_g gravatar imageeric_g ( 2021-01-30 12:48:11 +0200 )edit

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answered 2021-02-05 22:13:14 +0200

Max Alekseyev gravatar image

Define f(X*Y) as a function with 2 arguments, say f2(X,Y), and then compute f(X^7) recursively as f2(X,f2(X,f2(X,f2(X,f2(X,f2(X,f2(X,X)))))).

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Asked: 2021-01-29 16:18:57 +0200

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Last updated: Feb 05