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7.10.6 ncrat_lib
Status: experimental- 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