Singular Manual: ncrat_lib

> | ### 7.7.22 ncrat_lib Status: experimental Library: ncrat.lib Purpose: Framework for working with nc rational functions Author: Ricardo Schnur, email: ricardo.schnur@math.uni-sb.de Support: This project is funded by the SFB-TRR 195 'Symbolic Tools in Mathematics and their Application'. Overview: This library provides a framework for working with non-commutative rational functions (or rather, expressions) and their representations References: T. Mai: On the analytic theory of non-commutative distributions in free probability. Universitaet des Saarlandes, Dissertation, 2017 Procedures:
> 7.7.22.0. ncInit |  | Set up framework, list contains nc variables
> 7.7.22.0. ncVarsGet |  | List nc variables that are in use
> 7.7.22.0. ncVarsAdd |  | Add variables from list to 'NCRING'
> 7.7.22.0. ncratDefine |  | Define element of type ncrat
> 7.7.22.0. ncratAdd |  | Addition of two ncrat's
> 7.7.22.0. ncratSubstract |  | Substraction of two ncrat's
> 7.7.22.0. ncratMultiply |  | Multiplication of two ncrat's
> 7.7.22.0. ncratInvert |  | Invert an ncrat
> 7.7.22.0. ncratSPrint |  | Print-to-string for ncrat
> 7.7.22.0. ncratPrint |  | Print for ncrat
> 7.7.22.0. ncratFromString |  | Reads string into ncrat
> 7.7.22.0. ncratFromPoly |  | Converts poly to ncrat
> 7.7.22.0. ncratPower |  | Raises ncrat to an integer power
> 7.7.22.0. ncratEvaluateAt |  | Evaluate ncrat at scalar or matrix point
> 7.7.22.0. ncrepGet |  | Calculate representation of ncrat
> 7.7.22.0. ncrepAdd |  | Addition of two ncrep's
> 7.7.22.0. ncrepSubstract |  | Substraction of two ncrep's
> 7.7.22.0. ncrepMultiply |  | Multiplication of two ncrep's
> 7.7.22.0. ncrepInvert |  | Invert an ncrep
> 7.7.22.0. ncrepPrint |  | Print for ncrep
> 7.7.22.0. ncrepDim |  | Return the size of ncrep
> 7.7.22.0. ncrepSubstitute |  | Plug matrices into nc variables in ncrep
> 7.7.22.0. ncrepEvaluate |  | Given (u, Q, v) calculate -u*Q^(-1)*v
> 7.7.22.0. ncrepEvaluateAt |  | Evaluate ncrep at scalar or matrix point
> 7.7.22.0. ncrepIsDefinedDim |  | Random matrix test if ncrep can be evaluated at size dim
> 7.7.22.0. ncrepIsDefined |  | Random matrix test if domain of ncrep is not empty
> 7.7.22.0. ncrepIsRegular |  | Random matrix test if ncrep can be evaluated at scalar point
> 7.7.22.0. ncrepRegularZeroMinimize |  | Yields a minimal representation if regular at zero
> 7.7.22.0. ncrepRegularMinimize |  | Yields a minimal representation if regular at scalar point
> 7.7.22.0. ncrepGetRegularZeroMinimal |  | Get a minimal representation of ncrat regular at zero
> 7.7.22.0. ncrepGetRegularMinimal |  | Get a minimal representation of ncrat regular at scalar point
> 7.7.22.0. ncrepPencilGet |  | Given representation decompose its matrix in linear pencil
> 7.7.22.0. ncrepPencilCombine |  | Given linear pencil add up its elements to single matrix

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