In[]:=

Basic Examples

Find the parity of a basic power function:
In[]:=
[◼]
FunctionParity
[x^2,x]
Out[]=
1
Test another power function:
In[]:=
[◼]
FunctionParity
[x^3,x]
Out[]=
-1
Show that a constant function has even parity:
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[◼]
FunctionParity
[1,x]
Out[]=
1
Find the parity of a rational function:
In[]:=
[◼]
FunctionParity
[x/(x^2+1),x]
Out[]=
-1
Find the parity of the absolute value function:
In[]:=
[◼]
FunctionParity
[Abs[x],x]
Out[]=
1
Find the parity of a trigonometric function:
In[]:=
[◼]
FunctionParity
[Sin[x+Pi/4]+Cos[x+Pi/4],x]
Out[]=
1
Find the parity of a gaussian function:
In[]:=
[◼]
FunctionParity
[Exp[-x^2],x]
Out[]=
1
Test a signed gaussian function:
In[]:=
[◼]
FunctionParity
[Sign[x]Exp[-x^2],x]
Out[]=
-1
Find the parity of the hyperbolic tangent function:
In[]:=
[◼]
FunctionParity
[Tanh[x],x]
Out[]=
-1
Find the parity of the error function:
In[]:=
[◼]
FunctionParity
[Erf[x],x]
Out[]=
-1
Find the parity of a Fresnel integral:
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[◼]
FunctionParity
[FresnelC[x],x]
Out[]=
-1
Find the parity of a shifted Fresnel integral:
In[]:=
[◼]
FunctionParity
[FresnelC[x]+1,x]
Out[]=
Undefined
In[]:=

Scope

Show that an implicitly-defined circle is even in both
x
and
y
:
In[]:=
[◼]
FunctionParity
[x^2+y^2,{x,y}]
Out[]=
1
Find the parity of a function of two variables:
In[]:=
[◼]
FunctionParity
[Sinh[x+y],{x,y}]
Out[]=
1
Find the parity of a function of three variables:
In[]:=
[◼]
FunctionParity
[Sin[xyz],{x,y,z}]
Out[]=
1
In[]:=

Properties and Relations

FunctionParity returns
Undefined
for functions that are neither even nor odd:
In[]:=
[◼]
FunctionParity
[1+x,x]
Out[]=
Undefined
The constant function
f(x)=0
is both even and odd:
In[]:=
[◼]
FunctionParity
[0,x]
Out[]=
0