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7.10.6 ncrat_lib

Status: experimental
Framework for working with non-commutative rational functions

Ricardo Schnur, email: ricardo.schnur@math.uni-sb.de

This project has been funded by the SFB-TRR 195
'Symbolic Tools in Mathematics and their Application'.

This library provides a framework for working with
non-commutative rational functions (or rather, expressions) and their linearized representations

T. Mai: On the analytic theory of non-commutative distributions in free probability. Universitaet des Saarlandes, Dissertation, 2017

an almost self-explaining introduction to the posibilities of the framework can be achieved by running the example for the procedure ncrepGetRegularMinimal.

Procedures: ncInit  Set up framework, list contains nc variables ncVarsGet  List nc variables that are in use ncVarsAdd  Add variables from list to 'NCRING' ncratDefine  Define element of type ncrat ncratAdd  Addition of two ncrat's ncratSubstract  Substraction of two ncrat's ncratMultiply  Multiplication of two ncrat's ncratInvert  Invert an ncrat ncratSPrint  Print-to-string for ncrat ncratPrint  Print for ncrat ncratFromString  Reads string into ncrat ncratFromPoly  Converts poly to ncrat ncratPower  Raises ncrat to an integer power ncratEvaluateAt  Evaluate ncrat at scalar or matrix point ncrepGet  Calculate representation of ncrat ncrepAdd  Addition of two ncrep's ncrepSubstract  Substraction of two ncrep's ncrepMultiply  Multiplication of two ncrep's ncrepInvert  Invert an ncrep ncrepPrint  Print for ncrep ncrepDim  Return the size of ncrep ncrepSubstitute  Plug matrices into nc variables in ncrep ncrepEvaluate  Given (u, Q, v) calculate -u*Q^(-1)*v ncrepEvaluateAt  Evaluate ncrep at scalar or matrix point ncrepIsDefinedDim  Random matrix test if ncrep can be evaluated at size dim ncrepIsDefined  Random matrix test if domain of ncrep is not empty ncrepIsRegular  Random matrix test if ncrep can be evaluated at scalar point ncrepRegularZeroMinimize  Yields a minimal representation if regular at zero ncrepRegularMinimize  Yields a minimal representation if regular at scalar point ncrepGetRegularZeroMinimal  Get a minimal representation of ncrat regular at zero ncrepGetRegularMinimal  Get a minimal representation of ncrat regular at scalar point ncrepPencilGet  Given representation decompose its matrix in linear pencil ncrepPencilCombine  Given linear pencil add up its elements to single matrix