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Question: Bug in abs/Heaviside

Question:Bug in abs/Heaviside

chrisc 111 Maple
convert abs heaviside
April 29 2021
2

Hi folks, here's a bug in converting abs to Heavisides:

Converting the derivative of the abs function to a piecewise function is fine: 
convert(abs(1,x),piecewise);
returns
piecewise(x < 0, -1, x = 0, undefined, 0 < x, 1);

Whereas, 
convert(abs(1,x),Heaviside);
returns 1.

abs_problem.mw


 

> 

restart;
interface(version);

`Standard Worksheet Interface, Maple 2020.2, Mac OS X, November 11 2020 Build ID 1502365`

 (1)
> 

convert(abs(1,x),piecewise);
convert(abs(1,x),Heaviside);

convert(%%,Heaviside);

piecewise(x < 0, -1, x = 0, undefined, 0 < x, 1)

  

1

  

-1+2*Heaviside(x)+undefined*Dirac(x)

 (2)
> 

abs(x)=convert(abs(x),Heaviside);
diff(%,x);
strange:=convert(%,Heaviside);
eval(subs(x=-1,%));

abs(x) = -x+2*x*Heaviside(x)

  

abs(1, x) = -1+2*Heaviside(x)+2*x*Dirac(x)

  

1 = -1+2*Heaviside(x)

  

1 = -1

 (3)
> 

plot([(abs(x)),lhs(strange),rhs(strange)],x=-5..5,colour=[black,red,blue]);

 
> 

 

> 

 


 

Download abs_problem.mw
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