Wolfram Function Repository
Instantuse addon functions for the Wolfram Language
Function Repository Resource:
Determine the parity of a function, even or odd, with respect to one or more variables
ResourceFunction["FunctionParity"][expr,x] gives an integer indicating the parity of expr with respect to x, or Undefined. 

ResourceFunction["FunctionParity"][expr,{x_{1},x_{2},…}] gives the overall parity of expr with respect to multiple variables x_{i}. 
1  expr is an odd function of x 
1  expr is an even function of x 
0  expr is both an even and an odd function of x 
Undefined  none of the above is true 
Find the parity of a basic power function:
In[1]:= 

Out[1]= 

Test another power function:
In[2]:= 

Out[2]= 

Show that a constant function has even parity:
In[3]:= 

Out[3]= 

Find the parity of a rational function:
In[4]:= 

Out[4]= 

Find the parity of the absolute value function:
In[5]:= 

Out[5]= 

Find the parity of a trigonometric function:
In[6]:= 

Out[6]= 

Find the parity of a gaussian function:
In[7]:= 

Out[7]= 

Test a signed gaussian function:
In[8]:= 

Out[8]= 

Find the parity of the hyperbolic tangent function:
In[9]:= 

Out[9]= 

Find the parity of the error function:
In[10]:= 

Out[10]= 

Find the parity of a Fresnel integral:
In[11]:= 

Out[11]= 

Find the parity of a shifted Fresnel integral:
In[12]:= 

Out[12]= 

For a function of multiple variables, parity is determined based on the behavior of the function under the transformation {x,y,..}→{x,y,..}. Find the parity of a function of two variables:
In[13]:= 

Out[13]= 

Find the parity of a function of three variables:
In[14]:= 

Out[14]= 

Wrapping z in Abs converts this to an even function:
In[15]:= 

Out[15]= 

Show that an implicitlydefined circle is even in both x and y:
In[16]:= 

Out[16]= 

FunctionParity returns Undefined for functions that are neither even nor odd:
In[17]:= 

Out[17]= 

The constant function f(x)=0 is both even and odd:
In[18]:= 

Out[18]= 

This work is licensed under a Creative Commons Attribution 4.0 International License