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Review Euler equation to e^(i pi) + 1 = 0

step inference rule input feed output validity (as per SymPy)
3
  • ID: 111457; simplify
  • number of inputs: 1; feeds: 0; outputs: 1
  • Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.
  1. 8332931442
    \(\exp(i \pi)=\cos(\pi)+i \sin(\pi)\)
  1. 6885625907
    \(\exp(i \pi)=-1 + i 0\)
LHS diff is 0 RHS diff is pdg0004621*sin(pdg0003141) + cos(pdg0003141) + 1
2
  • ID: 111886; change variable X to Y
  • number of inputs: 1; feeds: 2; outputs: 1
  • Change variable $#1$ to $#2$ in Eq.~\\ref{eq:#3}; yields Eq.~\\ref{eq:#4}.
  1. 4938429483
    \(\exp(i x)=\cos(x)+i \sin(x)\)
  1. 3268645065
    \(x\)
  1. 9350663581
    \(\pi\)
  1. 8332931442
    \(\exp(i \pi)=\cos(\pi)+i \sin(\pi)\)
valid
1
  • ID: 111981; declare initial expression
  • number of inputs: 0; feeds: 0; outputs: 1
  • Eq.~\\ref{eq:#1} is an initial equation.
  1. 4938429483
    \(\exp(i x)=\cos(x)+i \sin(x)\)
no validation is available for declarations
5
  • ID: 111530; add X to both sides
  • number of inputs: 1; feeds: 1; outputs: 1
  • Add $#1$ to both sides of Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.
  1. 3331824625
    \(\exp(i \pi)=-1\)
  1. 4901237716
    \(1\)
  1. 2501591100
    \(\exp(i \pi) + 1=0\)
valid
4
  • ID: 111457; simplify
  • number of inputs: 1; feeds: 0; outputs: 1
  • Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.
  1. 6885625907
    \(\exp(i \pi)=-1 + i 0\)
  1. 3331824625
    \(\exp(i \pi)=-1\)
valid
6
  • ID: 111341; declare final expression
  • number of inputs: 1; feeds: 0; outputs: 0
  • Eq.~\\ref{eq:#1} is one of the final equations.
  1. 2501591100
    \(\exp(i \pi) + 1=0\)
no validation is available for declarations


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