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edited Dec 26, 2016 at 22:29

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How to apply ana rule to factors matching a certain form

Suppose we have many expressions involving irrational ArcTanArcTan expressions (such as ArcTan[Sqrt[3],5]) along with other irrational factors (such as 1/Sqrt[2]).

I want to simplify all of these ArcTansArcTans. For example, I might want to apply N@N to them to get their decimal approximation, or, I might want to apply Rationalize as in

N@ArcTan[Sqrt[3], 5] (* out: 1.23732 *) Rationalize[ArcTan[Sqrt[3], 5]/Pi, .0001] Pi (* out: 13 Pi/33 *)

However, I would like to be able to implement either of these options throughout large expressions involving many ArcTanArcTan functions and not act on any other forms.

Simple example would be:

m = 1/Sqrt[3]+ Sqrt[2] ArcTan[Sqrt[3], 5]

How can I apply a rule or something to mm that will allow me to implement one of these types of solutions to the ArcTanArcTan but not act on the other irrational factors?

How to apply an rule to factors matching a certain form

Suppose we have many expressions involving irrational ArcTan expressions (such as ArcTan[Sqrt[3],5]) along with other irrational factors (such as 1/Sqrt[2]).

I want to simplify all of these ArcTans. For example, I might want to apply N@ to them to get their decimal approximation, or, I might want to apply Rationalize as in

N@ArcTan[Sqrt[3], 5] (* out: 1.23732 *) Rationalize[ArcTan[Sqrt[3], 5]/Pi, .0001] Pi (* out: 13 Pi/33 *)

However, I would like to be able to implement either of these options throughout large expressions involving many ArcTan functions and not act on any other forms.

Simple example would be:

m = 1/Sqrt[3]+ Sqrt[2] ArcTan[Sqrt[3], 5]

How can I apply a rule or something to m that will allow me to implement one of these types of solutions to the ArcTan but not act on the other irrational factors?

How to apply a rule to factors matching a certain form

Suppose we have many expressions involving irrational ArcTan expressions (such as ArcTan[Sqrt[3],5]) along with other irrational factors (such as 1/Sqrt[2]).

I want to simplify all of these ArcTans. For example, I might want to apply N to them to get their decimal approximation, or I might want to apply Rationalize as in

N@ArcTan[Sqrt[3], 5] (* out: 1.23732 *) Rationalize[ArcTan[Sqrt[3], 5]/Pi, .0001] Pi (* out: 13 Pi/33 *)

However, I would like to be able to implement either of these options throughout large expressions involving many ArcTan functions and not act on any other forms.

Simple example would be:

m = 1/Sqrt[3]+ Sqrt[2] ArcTan[Sqrt[3], 5]

How can I apply a rule or something to m that will allow me to implement one of these types of solutions to the ArcTan but not act on the other irrational factors?

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asked Mar 12, 2014 at 20:59

Steve

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How to apply an rule to factors matching a certain form

Suppose we have many expressions involving irrational ArcTan expressions (such as ArcTan[Sqrt[3],5]) along with other irrational factors (such as 1/Sqrt[2]).

I want to simplify all of these ArcTans. For example, I might want to apply N@ to them to get their decimal approximation, or, I might want to apply Rationalize as in

N@ArcTan[Sqrt[3], 5] (* out: 1.23732 *) Rationalize[ArcTan[Sqrt[3], 5]/Pi, .0001] Pi (* out: 13 Pi/33 *)

However, I would like to be able to implement either of these options throughout large expressions involving many ArcTan functions and not act on any other forms.

Simple example would be:

m = 1/Sqrt[3]+ Sqrt[2] ArcTan[Sqrt[3], 5]

How can I apply a rule or something to m that will allow me to implement one of these types of solutions to the ArcTan but not act on the other irrational factors?