florianwolz / construct

Software that allows to solve construction equations that determine the Langrangian of (so far linearized) physical theories

Construct

Software that allows to solve construction equations that determine the Langrangian of (so far linearized) physical theories.

Features

• Interactive console
• Generate tensors build from the totally antisymmetric tensor and a background metric
• Apply symmetries to tensors
• Determine the linear independent terms
• Simplify terms

Example

lambda = Arbitrary({\alpha \beta \gamma \delta})
#=> e_1 * \gamma_{\alpha\beta}\gamma_{\gamma\delta}  +
    e_2 * \gamma_{\alpha\gamma}\gamma_{\beta\delta}  +
    e_3 * \gamma_{\alpha\delta}\gamma_{\beta\gamma}
Symmetrize(lambda, {\alpha \beta}, {\gamma \delta})
# => e_1 * \gamma_{\alpha\beta}\gamma_{\gamma\delta}  +
     (e_2 + e3) * (\gamma_{\alpha\gamma}\gamma_{\beta\delta} + \gamma_{\beta\gamma}\gamma_{\alpha\delta})
RedefineVariables(lambda)
# => e_1 * \gamma_{\alpha\beta}\gamma_{\gamma\delta}  +
     e2 * (\gamma_{\alpha\gamma}\gamma_{\beta\delta} + \gamma_{\beta\gamma}\gamma_{\alpha\delta})

Disclaimer

(c) 2016 Constructive Gravity Group Erlangen

For private and educational use only.