# parseTriplet -- Parses the output from LRtriple into Macaulay2 objects.

## Synopsis

• Usage:
(R, pols, sols, fixedFlags, movedFlag, solutionPlanes) = parseTriplet(f, p, s)
• Inputs:
• f, , represents the fixed flag.
• p, , represents a polynomial system.
• s, , solutions to the polynomial system.
• Optional inputs:
• Verbose => ..., default value false, request verbose feedback
• Outputs:
• R, a ring, a polynomial ring with complex floating-point coefficients and in the variables used in the systems p.
• pols, a list, list of polynomial equations in the ring R.
• sols, a list, list of solutions of the system pols.
• fixedFlags, a list, list of the fixed flags, as matrices of complex numbers.
• movedFlag, a list, the moved flag, the flag not listed here is the identity matrix.
• solutionPlanes, a list, list of complex matrices which store the solution planes.

## Description

parseTriplet processes the output of LRtriple for other methods in NumericalSchubertCalculus.

 i1 : (f, p, s) = LRtriple(6,matrix{{3, 2, 4, 6}}); i2 : (R, pols, sols, fixedFlags, movedFlag, solutionPlanes) = parseTriplet(f, p, s) o2 = (R, {(- .471646 - .9954*ii)x11*x32*x53 + (- .869072 - .43886*ii)x11*x32 ------------------------------------------------------------------------ + (- .642276 - .265166*ii)x11*x53 + (- .0603964 - .67823*ii)x32*x53 + (- ------------------------------------------------------------------------ .570235 + .128313*ii)x11 + (- .326867 - .382885*ii)x32 + (- .372724 - ------------------------------------------------------------------------ .222037*ii)x53 - .257401 + .0316447*ii, (.303734 + ------------------------------------------------------------------------ .744526*ii)x11*x32*x53 + (.226972 + .768298*ii)x11*x32 + (.58282 + ------------------------------------------------------------------------ .162737*ii)x11*x53 + (.653127 + .0849658*ii)x32*x53 + (.495139 + ------------------------------------------------------------------------ .229682*ii)x11 + (.394523 - .0167605*ii)x32 + (.732801 - .173069*ii)x53 ------------------------------------------------------------------------ + .533122 - .274907*ii, (- .18661 + .215089*ii)x11*x32*x53 + (- .309351 ------------------------------------------------------------------------ - .428333*ii)x11*x32 + (- .486815 + .161359*ii)x11*x53 + (- .108247 + ------------------------------------------------------------------------ .194965*ii)x32*x53 + (- .104537 - 1.0865*ii)x11 + (- .218615 - ------------------------------------------------------------------------ .108011*ii)x32 + (- .256078 + .0243888*ii)x53 - .0177934 - .584684*ii, ------------------------------------------------------------------------ (.0273895 + .39522*ii)x11*x32*x53 + (- .214911 - .111125*ii)x11*x32 + (- ------------------------------------------------------------------------ .196011 + .290367*ii)x11*x53 + (.128298 + .248982*ii)x32*x53 + (- ------------------------------------------------------------------------ .0382901 - .376232*ii)x11 + (.0344195 - .0337692*ii)x32 + (- .109889 + ------------------------------------------------------------------------ .131053*ii)x53 + .225794 - .302136*ii, (.590816 - .318487*ii)x11*x32*x53 ------------------------------------------------------------------------ + (.241664 + .375667*ii)x11*x32 + (.372265 - .302125*ii)x11*x53 + ------------------------------------------------------------------------ (.282047 - .0565437*ii)x32*x53 + (.674057 + .0595601*ii)x11 + (.167211 + ------------------------------------------------------------------------ .52667*ii)x32 + (.207793 - .0873171*ii)x53 + .553026 + .33979*ii, (- ------------------------------------------------------------------------ .723798 - .592262*ii)x11*x32*x53 + (- .979458 - .326772*ii)x11*x32 + (- ------------------------------------------------------------------------ .335332 - .569444*ii)x11*x53 + (- .469315 - .297852*ii)x32*x53 + (- ------------------------------------------------------------------------ .897371 - .453343*ii)x11 + (- .610368 - .132587*ii)x32 + (- .114415 - ------------------------------------------------------------------------ .317184*ii)x53 - .487613 - .267875*ii}, {{-.773649-.235132*ii, ------------------------------------------------------------------------ -.685693+.132902*ii, 2.03196-.198652*ii}, {-.657506+.065900*ii, ------------------------------------------------------------------------ -1.98322+1.12022*ii, -.838731+.4121*ii}}, {| -.408248-1.85037e-17ii | .180737-.366061ii | .204436-.353373ii | .404559+.054759ii | .405591+.0465072ii | .115491-.391572ii ------------------------------------------------------------------------ .346052-.235876ii .346313-.221297ii -.366469-.1354ii -.335789+.120226ii .156047-.744019ii -.0241166-.0405615ii -.236226-.281874ii -.170674+.00529615ii -.389476-.0297145ii -.11808+.446968ii .0949265+.270728ii -.582255+.145386ii .179121-.323089ii -.252619+.0363794ii .194702+.406084ii .341526-.308728ii -.250639+.117292ii -.3062-.189305ii ------------------------------------------------------------------------ -.24813+.426481ii .296902+.0692881ii |}, | 1 1 1 1 1 1 |, {| -.0778119-.250394ii .229291+.0682375ii | | -1 -1 -1 -1 -1 0 | | -.180344+.315664ii -.599576+.157119ii | | 1 1 1 1 0 0 | | -.084651+.114781ii .309664-.246811ii | | -1 -1 -1 0 0 0 | | -.438495+.0295669ii .352732+.333672ii | | 1 1 0 0 0 0 | | .504883-.295341ii .266274+.0466155ii | | -1 0 0 0 0 0 | | ------------------------------------------------------------------------ -.773649-.235132ii 0 0 |, | 1 0 0 | | 0 -.685693+.132902ii 0 | | 0 1 0 | | 0 0 2.03196-.198652ii | | 0 0 1 | | ------------------------------------------------------------------------ -.657506+.0659003ii 0 0 |}) 1 0 0 | 0 -1.98322+1.12022ii 0 | 0 1 0 | 0 0 -.838731+.4121ii | 0 0 1 | o2 : Sequence i3 : vars(R) o3 = | x11 x32 x53 | 1 3 o3 : Matrix R <--- R i4 : peek sols o4 = {Point{ConditionNumber => 32.7011 }, Point{ConditionNumber => 15.6446 }} Coordinates => {-.773649-.235132*ii, -.685693+.132902*ii, 2.03196-.198652*ii} Coordinates => {-.657506+.065900*ii, -1.98322+1.12022*ii, -.838731+.4121*ii} LastT => 1 LastT => 1 SolutionStatus => Regular SolutionStatus => Regular i5 : peek solutionPlanes o5 = {Matrix{cache => CacheTable{} }, Matrix{cache => CacheTable{} }} RawMatrix => -.773649-.235132i 0 0 RawMatrix => -.657506+.065900i 0 0 1 0 0 1 0 0 0 -.685693+.132902i 0 0 -1.98322+1.12022i 0 0 1 0 0 1 0 0 0 2.03196-.198652i 0 0 -.838731+.4121i 0 0 1 0 0 1 ring => CC ring => CC 53 53 3 3 source => CC source => CC 53 53 6 6 target => CC target => CC 53 53

## Ways to use parseTriplet :

• "parseTriplet(String,String,String)"

## For the programmer

The object parseTriplet is .