Sqrt[Matrix[( {
{0, 1},
{-1, 0}
} )]] /. f_[Matrix[x__]] :> Matrix[MatrixFunction[f, x]]
Matrix is an undefined symbol but I want to define some substitutions with it.
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$\begingroup$ For those searching for a similar question in the future please make the title more informative. For example " function substitution not matching with Sqrt" $\endgroup$– userrandrandNov 2, 2022 at 19:51
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3 Answers
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I assume this is related to that other question you recently posted--maybe merge them? Anyway, I'm going to change MatrixFunction for now to hopefully get a clearer answer. Your pattern matched an expression whose body only had one argument. You need to add something to the pattern to match more arguments. Try something like this:
Sqrt[Matrix[({{0, 1}, {-1, 0}})]] /.
f_[Matrix[mat_], args___] :> Matrix[MatrixFunction[f[#, args] &, mat]]
Matrix[MatrixFunction[Sqrt[#1] & , {{0, 1}, {-1, 0}}]]
(Thanks BobHanlon)
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2$\begingroup$ The RHS of the rule should be
Matrix[MatrixFn[f[#, args]&, mat]]$\endgroup$ Nov 2, 2022 at 19:01 -
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$\begingroup$ @Anixx, I don't know what to expect from MatrixFunction, so I chose something else to make verifying the result easier. As it turns out, I still screwed that up because I forgot it was the f that needed to be applied. $\endgroup$– lericrNov 2, 2022 at 19:19
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If you look at the FullForm of Sqrt, you see that it is silently converted to a Power, a function taking two arguments, not one. Your pattern only matches functions of a single argument.
FullForm[Sqrt[x]]
(* Power[x, Rational[1, 2]]*)
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As explained by @Mikado Sqrt is converted to Power which takes two arguments. One solution is to define:
sqrt=Inactive[Sqrt]
and then use sqrt instead like
sqrt[Matrix[({{0, 1}, {-1, 0}})]] /.
f_[Matrix[x__]] :> Matrix[MatrixFunction[Activate@f, x]]
If it is too late and you already used Sqrt at multiple parts in the notebook then you can use:
Hold[Sqrt[Matrix[({{0, 1}, {-1, 0}})]]] /.
f_[Matrix[x__]] :> Matrix[MatrixFunction[f, x]] // ReleaseHold
Or
Sqrt[Matrix[({{0, 1}, {-1, 0}})]] /. Sqrt[s_] -> Inactive[Sqrt][s] /.
f_[Matrix[x__]] :> Matrix[MatrixFunction[Activate@f, x]]
Notice that I used Sqrt[s_] -> Inactive[Sqrt][s] instead of Sqrt -> Inactive[Sqrt] because I am allowing Sqrt[s_] to be converted to
Power[Pattern[s,Blank[]],Rational[1,2]]
If I had a bad idea and used HoldPattern :
Sqrt[Matrix[({{0, 1}, {-1, 0}})]] /.
HoldPattern[Sqrt[s_]] -> Inactive[Sqrt][s]
Then it would not work because It would not convert to Power. If the Sqrt was a Cos then HoldPattern would work :
Cos[Matrix[({{0, 1}, {-1, 0}})]] /.
HoldPattern[Cos[s_]] -> Inactive[Cos][s]
because there is nothing to worry about concerning hidden transformations in that case (there can be in other cases because of the parity of Cos which leads to argument reordering).
