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6

I suspect that the reason why your simplifications work differently lies in the LeafCount of their outputs, which is a major contributor to the complexity function that the *Simplify functions use by default. Consider for instance: FullSimplify[Conjugate[a] a b] (* Out: a b Conjugate[a]*) % // LeafCount (* Out: 5 *) Abs[a^2] b //...


4

TL;DR Use HeavisideTheta's properties before integration. This is my strategy. First the HeavisideTheta gives you the following integration limits: $$0\leq y \leq 1-x \qquad \& \qquad 0\leq x \leq 1$$ $$0\leq x \leq 1-y \qquad \& \qquad 0\leq y \leq 1$$ In both cases I used Integrate first then NIntegrate. In the first case I could not ...


2

Clear your variables before you run and "cosine" isn't recognized by Mathematica. You need to use Cos[]. ClearAll["Global`*"] Integrate[1/(1 + 3 Cos[x] Cos[x]), {x, -Pi, Pi}] Pi In regard to your follow-up question in the comments about the following equation: $$1/(1 - Cos[x] - I (1/3) Sin[x])$$ The integral doesn't converge with the region {x,-Pi,...


2

Use Simplify with Assuming: m = {{E^(I*β1 + I*β3) Cos[β2], E^(I β1 - I*β3) Sin[β2]}, {(-E^((-I) β1 + I*β3)) Sin[β2], E^((-I) β1 - I*β3)*Cos[β2]}}; MatrixForm[ Assuming[{β1, β2, β3} ∈ Reals, Simplify@ConjugateTranspose[m]]] $$\left( \begin{array}{cc} e^{i \text{$\beta $1}+i \text{$\beta $3}} \cos (\text{$\beta $2}) & e^{i \text{$\...



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