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9.1.6 Simplification of expressions involving Dirac delta distribution

The simplifyDirac command simplifies expressions involving Dirac delta distribution (see Section 6.3.10).

Examples

Since δ(x)=−xδ′(x):

simplifyDirac(Dirac(x,1)*x)
     
δ
x
          

(x−2)3δ(3)(1−x/2) simplifies to:

simplifyDirac((x-2)^3*Dirac(1-x/2,3))
     
12 δ
x−2
          

If f(x)=p(x)/q(x) is rational with p(x)=(xx1)(xx2)⋯(xxn), xixj for ij, and q(x)≠ 0 ∀ x∈ℝ, then δ(f(x)) expands to ∑k=1nδ(xxk)/f′(xk). For example:

simplifyDirac(Dirac(x^2-x-6))
     
δ
x+2
5
+
δ
x−3
5
          

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