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I think there is another problem with the dirac_delta in Sage:

(previous problem is discussed in the thread Integration of dirac_delta)

Here is the problem:

var('a',"real")
f=integrate_delta(dirac_delta(a*x),x,-oo,oo);show(f)

returns 1/|a| as expected.

But

var('a',"real")
f1=integral(dirac_delta(x^2-a^2),x,-oo,oo);show(f1)

gives the result 1/|a|, where it should be 1/(2|a|)

I think there is another problem with the dirac_delta in Sage:

(previous problem is discussed in the thread Integration of dirac_delta)

Here is the problem:

var('a',"real")
f=integrate_delta(dirac_delta(a*x),x,-oo,oo);show(f)
f=integral(dirac_delta(a*x),x,-oo,oo);show(f)

returns 0 where it should return 1/|a| as expected.

But and

var('a',"real")
f1=integral(dirac_delta(x^2-a^2),x,-oo,oo);show(f1)
f=integral(dirac_delta(x^2-a^2),x,-oo,oo);show(f)

gives the result returns 1/|a|, where it should be 1/(2|a|)

I think there is another problem with the dirac_delta in Sage:

(previous problem is discussed in the thread Integration of dirac_delta)

Here is the problem:

var('a',"real")
f=integral(dirac_delta(a*x),x,-oo,oo);show(f)

returns 01 where it should return 1/|a|

and

var('a',"real")
f=integral(dirac_delta(x^2-a^2),x,-oo,oo);show(f)

returns 1/|a|, where it should be 1/(2|a|)

I think there is another problem with the dirac_delta in Sage:

(previous problem is discussed in the thread Integration of dirac_delta)

Here is the problem:

var('a',"real")
f=integral(dirac_delta(a*x),x,-oo,oo);show(f)

returns 1 where it should return 1/|a|

and

var('a',"real")
f=integral(dirac_delta(x^2-a^2),x,-oo,oo);show(f)

returns 1/|a|, where it should be 1/(2|a|)

I think there is another problem with the integration of the dirac_delta in Sage:

(previous problem is discussed in the thread Integration of dirac_delta)

Here is the problem:

var('a',"real")
f=integral(dirac_delta(a*x),x,-oo,oo);show(f)

returns 1 where it should return 1/|a|

and

var('a',"real")
f=integral(dirac_delta(x^2-a^2),x,-oo,oo);show(f)

returns 1/|a|, where it should be 1/(2|a|)

I think there is another problem with the integration of the dirac_delta in Sage:

(previous problem is discussed in the thread Integration of dirac_delta)

Here is the problem:

var('a',"real")
f=integral(dirac_delta(a*x),x,-oo,oo);show(f)

returns 1 where it should return 1/|a|

and

var('a',"real")
f=integral(dirac_delta(x^2-a^2),x,-oo,oo);show(f)

returns 1/|a|, where it should be 1/(2|a|)