I'm trying to understand how Cases work in Mathematica, and I'm a bit curios why i't wont pick up the Sqrt function?
Consider the following expressions
Cases[Erfc[b], _Erfc, Infinity]
Cases[a*Erfc[b], _Erfc, Infinity]
Cases[a*Sqrt[b], _Sqrt, Infinity]
Cases[a*Sqrt[b], _Sqrt, Infinity]
Cases[a*Sqrt[a]*Erfc[b], _Erfc, Infinity]
Cases[a*Sqrt[a]*Erfc[b], _Sqrt, Infinity]
they give respectively
{}
{Erfc[b]}
{}
{}
{Erfc[b]}
{}
Why does Cases fail in the cases that give {}?
In the first case:
Cases[Erfc[b], _Erfc, Infinity]
"Infinity" means: {1,Infinity}. But Erfc[b] is at level 0. Therefore, you need:
Cases[Erfc[b], _Erfc, {0,Infinity}]
Further, the next problem:
Cases[a*Sqrt[b], _Sqrt, Infinity]
The full form of Sqrt[b] is Power[..] (You may use "FullForm" to see the full form). Therefore, you need:
Cases[a*Sqrt[b], _Power, Infinity]
To get:
{Sqrt[b]}
Then the case of:
Cases[a*Sqrt[a]*Erfc[b], _Sqrt, Infinity]
Because arguments are evaluated before sending them to functions, a*Sqrt[a] is simplified to a^(3/2) and by:
Cases[a*Sqrt[a]*Erfc[b], _Power, Infinity]
you get:
{a^(3/2)}
Check FullForm, arg of Cases is evaluated before matching:
FullForm[a*Sqrt[b]]
Cases[HoldForm[a*Sqrt[b]], _Sqrt, Infinity]
MatchQ[f[x], f[x]]
Symbol === Head[f]
Cases[f[x], _f, Infinity]
Cases[{f[x]}, _f, Infinity]
Cases[Erfc[b], _Erfc, Infinity] gives {}?
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Commented
Apr 30, 2021 at 13:31
Head being a symbol, see the edit, not sure why
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Cases[Erfc[b], _Erfc, {0, Infinity}]. The level spec Infinity is equivalent to {1, Infinity}.
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Commented
Apr 30, 2021 at 16:46
Try HoldForm
Cases[HoldForm[ Erfc[b]], _Erfc, Infinity]
Cases[HoldForm[ a*Erfc[b]], _Erfc, Infinity]
Cases[HoldForm[ a*Sqrt[b]], _Sqrt, Infinity]
Cases[HoldForm[ a*Sqrt[b]], _Sqrt, Infinity]
Cases[HoldForm[ a*Sqrt[a]*Erfc[b]], _Erfc, Infinity]
Cases[HoldForm[ a*Sqrt[a]*Erfc[b]], _Sqrt, Infinity]
FullForm[Sqrt[x]]. It returnsPower[x, Rational[1, 2]]which corresponds tox^(1/2), and either you have to prevent evaluation or match this form. $\endgroup$