Mathematica Globally Define Variable as Real

[teroenza]

I want to write a line of code at the top of my .nb and have Mathematica treat the specified variables as real only. I've tried using "Assumptions" and "Assuming", but it just won't work. I still get back answers where the entire expression is returned inside the Re[ ] command, like it is confused over which variables might have imaginary parts.

Can it just be defined somehow globally that {x,y,z} are real only?

 

[DrClaude]

Using $Assumptions should work. You will need to give a specific example if you want more help.

 

[teroenza]

Assuming[x \[Element] Reals && y \[Element] Reals && \[Theta] \[Element] Reals,Re[(x + I y)^2 Sin[\[Theta]/2]^2]]

Simplify[Re[(x + I y)^2 Sin[\[Theta]/2]^2],Assumptions ->  x \[Element] Reals &&   y \[Element] Reals && \[Theta] \[Element] Reals]

returns

Re[(x + I y)^2 Sin[\[Theta]/2]^2]

Re[(x + I y)^2] Sin[\[Theta]/2]^2

 

[DrClaude]

I see. You need to do also a ComplexExpand:

Assuming[x \[Element] Reals && y \[Element] Reals && \[Theta] \[Element] Reals, 
Simplify[ComplexExpand[Re[(x + I y)^2 Sin[\[Theta]/2]^2]]]]

 

[alphy]

I understand the frustration of trying to get Mathematica to treat variables as real only. However, there is a way to globally define variables as real in Mathematica.

One way to do this is by using the "Set" command. For example, if you want to define x, y, and z as real variables, you can type the following at the top of your .nb file:

Set[x, Element[x, Reals]]
Set[y, Element[y, Reals]]
Set[z, Element[z, Reals]]

This will tell Mathematica that x, y, and z are elements of the set of real numbers, and it will treat them as such in any calculations or expressions.

Another option is to use the "Assuming" command, but you need to specify the variables you want to be treated as real within the command. For example:

Assuming[{x, y, z} \[Element] Reals, expression]

This will tell Mathematica to assume that x, y, and z are real variables only when evaluating the expression.

I hope this helps and allows you to effectively use real variables in your Mathematica code.