Singular

7.10.6 ncrat_lib

Library:

ncrat.lib

Purpose:

Framework for working with non-commutative rational functions

Author:

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

Support:

This project has been 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 linearized representations

References:

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

Note:

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

Procedures:

7.10.6.1 ncInit		Set up framework, list contains nc variables
7.10.6.2 ncVarsGet		List nc variables that are in use
7.10.6.3 ncVarsAdd		Add variables from list to 'NCRING'
7.10.6.4 ncratDefine		Define element of type ncrat
7.10.6.5 ncratAdd		Addition of two ncrat's
7.10.6.6 ncratSubstract		Subtraction of two ncrat's
7.10.6.7 ncratMultiply		Multiplication of two ncrat's
7.10.6.8 ncratInvert		Invert an ncrat
7.10.6.9 ncratSPrint		Print-to-string for ncrat
7.10.6.10 ncratPrint		Print for ncrat
7.10.6.11 ncratFromString		Reads string into ncrat
7.10.6.12 ncratFromPoly		Converts poly to ncrat
7.10.6.13 ncratPower		Raises ncrat to an integer power
7.10.6.14 ncratEvaluateAt		Evaluate ncrat at scalar or matrix point
7.10.6.15 ncrepGet		Calculate representation of ncrat
7.10.6.16 ncrepAdd		Addition of two ncrep's
7.10.6.17 ncrepSubstract		Subtraction of two ncrep's
7.10.6.18 ncrepMultiply		Multiplication of two ncrep's
7.10.6.19 ncrepInvert		Invert an ncrep
7.10.6.20 ncrepPrint		Print for ncrep
7.10.6.21 ncrepDim		Return the size of ncrep
7.10.6.22 ncrepSubstitute		Plug matrices into nc variables in ncrep
7.10.6.23 ncrepEvaluate		Given (u, Q, v) calculate -u*Q^(-1)*v
7.10.6.24 ncrepEvaluateAt		Evaluate ncrep at scalar or matrix point
7.10.6.25 ncrepIsDefinedDim		Random matrix test if ncrep can be evaluated at size dim
7.10.6.26 ncrepIsDefined		Random matrix test if domain of ncrep is not empty
7.10.6.27 ncrepIsRegular		Random matrix test if ncrep can be evaluated at scalar point
7.10.6.28 ncrepRegularZeroMinimize		Yields a minimal representation if regular at zero
7.10.6.29 ncrepRegularMinimize		Yields a minimal representation if regular at scalar point
7.10.6.30 ncrepGetRegularZeroMinimal		Get a minimal representation of ncrat regular at zero
7.10.6.31 ncrepGetRegularMinimal		Get a minimal representation of ncrat regular at scalar point
7.10.6.32 ncrepPencilGet		Given representation decompose its matrix in linear pencil
7.10.6.33 ncrepPencilCombine		Given linear pencil add up its elements to single matrix