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Review variance relation

step inference rule input feed output step validity (as per SymPy)
1
  • 111299: declare identity
  • number of inputs: 0; feeds: 0; outputs: 1
  • Eq.~\\ref{eq:#1} is an identity.
  1. 3585845894
    \(\langle \left(x-\langle x \rangle\right)^2 \rangle=\langle x^2 \rangle-\langle x \rangle^2\)
 no validation is available for declarations
2
  • 111457: simplify
  • number of inputs: 1; feeds: 0; outputs: 1
  • Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.
  1. 3585845894
    \(\langle \left(x-\langle x \rangle\right)^2 \rangle=\langle x^2 \rangle-\langle x \rangle^2\)
  1. 8399484849
    \(\langle x^2 - 2 x \langle x \rangle + \langle x \rangle^2 \rangle=\langle x^2 \rangle-\langle x \rangle^2\)
 invalid syntax (<string>, line 0)
3
  • 111457: simplify
  • number of inputs: 1; feeds: 0; outputs: 1
  • Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.
  1. 8399484849
    \(\langle x^2 - 2 x \langle x \rangle + \langle x \rangle^2 \rangle=\langle x^2 \rangle-\langle x \rangle^2\)
  1. 2404934990
    \(\langle x^2\rangle -2\langle x \rangle\langle x \rangle+\langle x \rangle^2=\langle x^2 \rangle-\langle x \rangle^2\)
 invalid syntax (<string>, line 0)
4
  • 111457: simplify
  • number of inputs: 1; feeds: 0; outputs: 1
  • Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.
  1. 2404934990
    \(\langle x^2\rangle -2\langle x \rangle\langle x \rangle+\langle x \rangle^2=\langle x^2 \rangle-\langle x \rangle^2\)
  1. 4949359835
    \(\langle x^2\rangle -2\langle x^2 \rangle+\langle x \rangle^2=\langle x^2 \rangle-\langle x \rangle^2\)
 invalid syntax (<string>, line 0)
5
  • 111457: simplify
  • number of inputs: 1; feeds: 0; outputs: 1
  • Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.
  1. 4949359835
    \(\langle x^2\rangle -2\langle x^2 \rangle+\langle x \rangle^2=\langle x^2 \rangle-\langle x \rangle^2\)
  1. 2494533900
    \(\langle x^2\rangle -\langle x \rangle^2=\langle x^2 \rangle-\langle x \rangle^2\)
 invalid syntax (<string>, line 0)
6
  • 111345: claim LHS equals RHS
  • number of inputs: 1; feeds: 0; outputs: 0
  • Thus we see that LHS of Eq.~\\ref{eq:#1} is equal to RHS.
  1. 2494533900
    \(\langle x^2\rangle -\langle x \rangle^2=\langle x^2 \rangle-\langle x \rangle^2\)
 invalid syntax (<string>, line 0)


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