Ali SeyedKavoosi asked . 2024-01-16

I have a 6x6 symbolic matrix A that I want to inverse?

I have a 6x6 symbolic matrix A full of Cos and Sins that I want to inverse. I am trying both inv(A) and A\I to do the inversion. However, it takes forever (more than a day) until I stop it. My hardware is also very good. Core i7, 16 Gb RAM. How can I do the invers matrix?

here is my matrix:

Q_m=[ (226815595159810653697779695616*cos(phi)^4*cos(theta)^3+(122729124939209*cos(phi)^4*cos(theta)^2*sin(theta)^3)/128-(122729124939209*cos(theta)^2*sin(phi)^4*sin(theta)^3)/128-176500710189829366671837495296*cos(phi)^4*cos(theta)^2*sin(theta)+226815595159810653697779695616*cos(phi)^2*sin(phi)^2*sin(theta)+176500710189829366671837495296*cos(theta)^2*sin(phi)^4*sin(theta))/(196062945931726816*cos(theta)^2*sin(phi)^2*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768))-2120697014133059/140737488355328 -(518289290378197257971428229120*cos(phi)^4*sin(theta)-291473695218386604273648533504*cos(phi)^4*cos(theta)+226815595159810653697779695616*cos(phi)^2*cos(theta)^2*sin(phi)^2*sin(theta))/(196062945931726816*sin(phi)^2*sin(theta)^2*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768))-1116218924199397/140737488355328 -9.1685 (1036578580756394515942856458240*cos(phi)^3*sin(theta)-582947390436773208547297067008*cos(phi)^3*cos(theta)+453631190319621307395559391232*cos(phi)*cos(theta)^2*sin(phi)^2*sin(theta))/(196062945931726816*sin(phi)*sin(theta)*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768)) -(453631190319621307395559391232*cos(phi)*sin(phi)^2*sin(theta)+453631190319621307395559391232*cos(phi)^3*cos(theta)^2*sin(theta))/(196062945931726816*cos(theta)*sin(phi)*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768)) (11378840434114016*cos(phi)^4*cos(theta)^2*sin(theta)^2-14622595356790864*cos(phi)^2*sin(phi)^2*sin(theta)^2-11378840434114016*cos(theta)^2*sin(phi)^4*sin(theta)^2+14622595356790864*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta))/(6320*cos(theta)*sin(phi)^2*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768)); -(12011166844429811712*cos(phi)^3*((353589694297967*cos(phi))/2097152-(353589694297967*cos(phi)*cos(theta)*sin(theta))/2097152))/(1750562017247561*sin(phi)^2*sin(theta)*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768))-1116218924199397/140737488355328 (226815595159810653697779695616*cos(phi)^2*cos(theta)^2*sin(phi)^2-291473695218386639458020622336*cos(phi)^4*sin(theta)^2-403316305349639950000873013248*cos(phi)^4*cos(theta)^2*sin(theta)^2+176500710189829366671837495296*cos(phi)^4*cos(theta)^2*sin(theta)^4-226815595159810653697779695616*cos(phi)^2*sin(phi)^2*sin(theta)^4+176500710189829366671837495296*cos(theta)^2*sin(phi)^4*sin(theta)^2-176500710189829366671837495296*cos(theta)^2*sin(phi)^4*sin(theta)^4+291473695218386639458020622336*cos(phi)^4*cos(theta)*sin(theta)+226815595159810653697779695616*cos(phi)^4*cos(theta)^3*sin(theta)-226815595159810653697779695616*cos(phi)^2*cos(theta)^2*sin(phi)^2*sin(theta)^2+226815595159810653697779695616*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^3)/(196062945931726816*sin(phi)^2*sin(theta)^3*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768))-2120697014133059/140737488355328 -9.1685 (23459310243026976*cos(phi)*((7802679563076885*cos(phi)^2*sin(theta)^2)/32768-(3035899015886451*cos(theta)^2*sin(phi)^2)/16384+(3035899015886451*cos(theta)^2*sin(phi)^2*sin(theta)^2)/16384-(7802679563076885*cos(phi)^2*cos(theta)*sin(theta))/32768))/(1878777008745185*sin(phi)*sin(theta)^2*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768)) (24022333688859623424*cos(phi)^3*((353589694297967*cos(theta))/2097152-(353589694297967*cos(theta)*sin(theta)^2)/2097152))/(1750562017247561*sin(phi)*sin(theta)*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768)) -(5923076600219083*cos(phi)^3*cos(theta)*(cos(phi)*cos(theta)-cos(phi)*sin(theta)))/(2560*sin(theta)*((7802679563076885*cos(phi)^4*cos(theta)^3*sin(phi)^2)/32768-(7802679563076885*cos(phi)^2*sin(phi)^4*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^6*sin(theta)^3)/16384+(3035899015886451*cos(theta)^2*sin(phi)^6*sin(theta))/16384+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(phi)^2*sin(theta)^3)/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^4*sin(theta)^2)/32768-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(phi)^2*sin(theta))/16384)); -9.1685 -9.1685 11729655121513488/(1878777008745185*cos(phi)^2)-2468866661864513/140737488355328 0 0 0; (24022333688859623424*cos(phi)^2*((353589694297967*cos(phi))/2097152-(353589694297967*cos(phi)*cos(theta)*sin(theta))/2097152))/(1750562017247561*sin(phi)*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768)) (23459310243026976*cos(phi)*((7802679563076885*cos(phi)^2*sin(theta)^2)/32768-(3035899015886451*cos(theta)^2*sin(phi)^2)/16384+(3035899015886451*cos(theta)^2*sin(phi)^2*sin(theta)^2)/16384-(7802679563076885*cos(phi)^2*cos(theta)*sin(theta))/32768))/(1878777008745185*sin(phi)*sin(theta)^2*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768)) 0 -(1281318364180027673672120608489472*cos(phi)^2*sin(theta)^2-997081356322527489540251466072064*cos(theta)^2*sin(phi)^2+997081356322527489540251466072064*cos(theta)^2*sin(phi)^2*sin(theta)^2-1281318364180027673672120608489472*cos(phi)^2*cos(theta)*sin(theta))/(215473177578967793664*sin(theta)*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768))-2200/619 -(5131724115662151*cos(phi)^2*((353589694297967*cos(theta))/2097152-(353589694297967*cos(theta)*sin(theta)^2)/2097152))/(44523515427081529851904*cos(phi)^4*cos(theta)^3+34646789112939027628032*cos(phi)^4*cos(theta)^2*sin(theta)^3-44523515427081529851904*cos(phi)^2*sin(phi)^2*sin(theta)^3-34646789112939027628032*cos(theta)^2*sin(phi)^4*sin(theta)^3-79170304540020557479936*cos(phi)^4*cos(theta)^2*sin(theta)+34646789112939027628032*cos(theta)^2*sin(phi)^4*sin(theta)+44523515427081529851904*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2) (60067132859724007391095431319005456239547121664*cos(phi)^2*cos(theta)*(cos(phi)*cos(theta)-cos(phi)*sin(theta)))/(3090959822350922421750773463860031455403966464*cos(phi)^4*cos(theta)^3*sin(phi)-2405287006075468939931671826555384286505074688*cos(theta)^2*sin(phi)^5*sin(theta)^3-3090959822350922421750773463860031455403966464*cos(phi)^2*sin(phi)^3*sin(theta)^3+2405287006075468939931671826555384286505074688*cos(theta)^2*sin(phi)^5*sin(theta)-5496246828426391678595095347472766116084842496*cos(phi)^4*cos(theta)^2*sin(phi)*sin(theta)+3090959822350922421750773463860031455403966464*cos(phi)^2*cos(theta)*sin(phi)^3*sin(theta)^2+2405287006075468939931671826555384286505074688*cos(phi)^4*cos(theta)^2*sin(phi)*sin(theta)^3); -(24022333688859623424*sin(phi)*((353589694297967*cos(phi)*sin(theta))/2097152-(353589694297967*cos(phi)*cos(theta)*sin(theta)^2)/2097152))/(1750562017247561*cos(theta)*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768)) -(640659182090013836836060304244736*cos(phi)^3*cos(theta)^2-1139199860251277653663780075208704*cos(phi)^3*cos(theta)*sin(theta)+498540678161263744770125733036032*cos(phi)^3*cos(theta)*sin(theta)^3)/(215473177578967793664*sin(phi)*sin(theta)^2*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768)) 0 (1281318364180027673672120608489472*cos(phi)^2*cos(theta)^2-2278399720502555307327560150417408*cos(phi)^2*cos(theta)*sin(theta)+997081356322527489540251466072064*cos(phi)^2*cos(theta)*sin(theta)^3)/(215473177578967793664*sin(theta)*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768)) (5131724115662151*sin(phi)^2*((353589694297967*sin(theta))/2097152-(353589694297967*sin(theta)^3)/2097152))/(44523515427081529851904*cos(phi)^4*cos(theta)^3+34646789112939027628032*cos(phi)^4*cos(theta)^2*sin(theta)^3-44523515427081529851904*cos(phi)^2*sin(phi)^2*sin(theta)^3-34646789112939027628032*cos(theta)^2*sin(phi)^4*sin(theta)^3-79170304540020557479936*cos(phi)^4*cos(theta)^2*sin(theta)+34646789112939027628032*cos(theta)^2*sin(phi)^4*sin(theta)+44523515427081529851904*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)-2200/619 -(35115176599067911854944413548544*sin(theta)*((1710574705220717*cos(phi)*cos(theta)*sin(phi))/134217728-(1710574705220717*cos(phi)*sin(phi)*sin(theta))/134217728))/(23029445278278905315330426870733733888*cos(phi)^4*cos(theta)^3+17920784697498894780365167756046237696*cos(phi)^4*cos(theta)^2*sin(theta)^3-23029445278278905315330426870733733888*cos(phi)^2*sin(phi)^2*sin(theta)^3-17920784697498894780365167756046237696*cos(theta)^2*sin(phi)^4*sin(theta)^3-40950229975777802456878836061602578432*cos(phi)^4*cos(theta)^2*sin(theta)+17920784697498894780365167756046237696*cos(theta)^2*sin(phi)^4*sin(theta)+23029445278278905315330426870733733888*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2); -(14622595356790864*cos(phi)^4*cos(theta)^2-11378840434114016*cos(phi)^4*cos(theta)^2*sin(theta)^2+14622595356790864*cos(phi)^2*sin(phi)^2*sin(theta)^2+11378840434114016*cos(theta)^2*sin(phi)^4*sin(theta)^2)/(6320*cos(theta)*((7802679563076885*cos(phi)^4*cos(theta)^3*sin(phi)^2)/32768-(7802679563076885*cos(phi)^2*sin(phi)^4*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^6*sin(theta)^3)/16384+(3035899015886451*cos(theta)^2*sin(phi)^6*sin(theta))/16384+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(phi)^2*sin(theta)^3)/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^4*sin(theta)^2)/32768-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(phi)^2*sin(theta))/16384)) ((5923076600219083*cos(phi)^2*cos(theta)^3*sin(phi)^2)/256+(5923076600219083*cos(phi)^4*cos(theta)*sin(theta)^2)/256)/(10*sin(theta)^2*((7802679563076885*cos(phi)^4*cos(theta)^3*sin(phi)^2)/32768-(7802679563076885*cos(phi)^2*sin(phi)^4*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^6*sin(theta)^3)/16384+(3035899015886451*cos(theta)^2*sin(phi)^6*sin(theta))/16384+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(phi)^2*sin(theta)^3)/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^4*sin(theta)^2)/32768-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(phi)^2*sin(theta))/16384)) 0 -((5923076600219083*cos(phi)*cos(theta)^3*sin(phi)^2)/256+(5923076600219083*cos(phi)^3*cos(theta)*sin(theta)^2)/256)/(5*sin(theta)*((7802679563076885*cos(phi)^4*cos(theta)^3*sin(phi))/32768-(3035899015886451*cos(theta)^2*sin(phi)^5*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^3*sin(theta)^3)/32768+(3035899015886451*cos(theta)^2*sin(phi)^5*sin(theta))/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(phi)*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^3*sin(theta)^2)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(phi)*sin(theta)^3)/16384)) ((5923076600219083*cos(phi)^3*cos(theta)^2)/256+(5923076600219083*cos(phi)*sin(phi)^2*sin(theta)^2)/256)/((4876674726923053*cos(phi)^4*cos(theta)^3*sin(phi))/4096-(7589747539716127*cos(theta)^2*sin(phi)^5*sin(theta)^3)/8192-(4876674726923053*cos(phi)^2*sin(phi)^3*sin(theta)^3)/4096+(7589747539716127*cos(theta)^2*sin(phi)^5*sin(theta))/8192-(8671548496781117*cos(phi)^4*cos(theta)^2*sin(phi)*sin(theta))/4096+(4876674726923053*cos(phi)^2*cos(theta)*sin(phi)^3*sin(theta)^2)/4096+(7589747539716127*cos(phi)^4*cos(theta)^2*sin(phi)*sin(theta)^3)/8192) -(11378840434114018*cos(phi)^4*cos(theta)^2*sin(theta)-11378840434114018*cos(theta)^2*sin(phi)^4*sin(theta))/((1504911341511411*cos(phi)^4*cos(theta)^3*sin(phi)^2)/2-(1504911341511411*cos(phi)^2*sin(phi)^4*sin(theta)^3)/2-(4684297309668547*cos(theta)^2*sin(phi)^6*sin(theta)^3)/8+(4684297309668547*cos(theta)^2*sin(phi)^6*sin(theta))/8+(4684297309668547*cos(phi)^4*cos(theta)^2*sin(phi)^2*sin(theta)^3)/8+(1504911341511411*cos(phi)^2*cos(theta)*sin(phi)^4*sin(theta)^2)/2-1337992834464274*cos(phi)^4*cos(theta)^2*sin(phi)^2*sin(theta))-31800/8911]

symbolic matrix , inverse matrix ,

Expert Answer

Neeta Dsouza answered . 2024-12-22 09:23:50

QM = sym('QM', [6 6]);
QMinv = inv(QM);   %takes a small number of seconds

syms phi
Q_m = [ (226815595159810653697779695616*cos(phi)^4*cos(theta)^3+(122729124939209*cos(phi)^4*cos(theta)^2*sin(theta)^3)/128-(122729124939209*cos(theta)^2*sin(phi)^4*sin(theta)^3)/128-176500710189829366671837495296*cos(phi)^4*cos(theta)^2*sin(theta)+226815595159810653697779695616*cos(phi)^2*sin(phi)^2*sin(theta)+176500710189829366671837495296*cos(theta)^2*sin(phi)^4*sin(theta))/(196062945931726816*cos(theta)^2*sin(phi)^2*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768))-2120697014133059/140737488355328 -(518289290378197257971428229120*cos(phi)^4*sin(theta)-291473695218386604273648533504*cos(phi)^4*cos(theta)+226815595159810653697779695616*cos(phi)^2*cos(theta)^2*sin(phi)^2*sin(theta))/(196062945931726816*sin(phi)^2*sin(theta)^2*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768))-1116218924199397/140737488355328 -9.1685 (1036578580756394515942856458240*cos(phi)^3*sin(theta)-582947390436773208547297067008*cos(phi)^3*cos(theta)+453631190319621307395559391232*cos(phi)*cos(theta)^2*sin(phi)^2*sin(theta))/(196062945931726816*sin(phi)*sin(theta)*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768)) -(453631190319621307395559391232*cos(phi)*sin(phi)^2*sin(theta)+453631190319621307395559391232*cos(phi)^3*cos(theta)^2*sin(theta))/(196062945931726816*cos(theta)*sin(phi)*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768)) (11378840434114016*cos(phi)^4*cos(theta)^2*sin(theta)^2-14622595356790864*cos(phi)^2*sin(phi)^2*sin(theta)^2-11378840434114016*cos(theta)^2*sin(phi)^4*sin(theta)^2+14622595356790864*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta))/(6320*cos(theta)*sin(phi)^2*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768)); -(12011166844429811712*cos(phi)^3*((353589694297967*cos(phi))/2097152-(353589694297967*cos(phi)*cos(theta)*sin(theta))/2097152))/(1750562017247561*sin(phi)^2*sin(theta)*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768))-1116218924199397/140737488355328 (226815595159810653697779695616*cos(phi)^2*cos(theta)^2*sin(phi)^2-291473695218386639458020622336*cos(phi)^4*sin(theta)^2-403316305349639950000873013248*cos(phi)^4*cos(theta)^2*sin(theta)^2+176500710189829366671837495296*cos(phi)^4*cos(theta)^2*sin(theta)^4-226815595159810653697779695616*cos(phi)^2*sin(phi)^2*sin(theta)^4+176500710189829366671837495296*cos(theta)^2*sin(phi)^4*sin(theta)^2-176500710189829366671837495296*cos(theta)^2*sin(phi)^4*sin(theta)^4+291473695218386639458020622336*cos(phi)^4*cos(theta)*sin(theta)+226815595159810653697779695616*cos(phi)^4*cos(theta)^3*sin(theta)-226815595159810653697779695616*cos(phi)^2*cos(theta)^2*sin(phi)^2*sin(theta)^2+226815595159810653697779695616*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^3)/(196062945931726816*sin(phi)^2*sin(theta)^3*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768))-2120697014133059/140737488355328 -9.1685 (23459310243026976*cos(phi)*((7802679563076885*cos(phi)^2*sin(theta)^2)/32768-(3035899015886451*cos(theta)^2*sin(phi)^2)/16384+(3035899015886451*cos(theta)^2*sin(phi)^2*sin(theta)^2)/16384-(7802679563076885*cos(phi)^2*cos(theta)*sin(theta))/32768))/(1878777008745185*sin(phi)*sin(theta)^2*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768)) (24022333688859623424*cos(phi)^3*((353589694297967*cos(theta))/2097152-(353589694297967*cos(theta)*sin(theta)^2)/2097152))/(1750562017247561*sin(phi)*sin(theta)*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768)) -(5923076600219083*cos(phi)^3*cos(theta)*(cos(phi)*cos(theta)-cos(phi)*sin(theta)))/(2560*sin(theta)*((7802679563076885*cos(phi)^4*cos(theta)^3*sin(phi)^2)/32768-(7802679563076885*cos(phi)^2*sin(phi)^4*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^6*sin(theta)^3)/16384+(3035899015886451*cos(theta)^2*sin(phi)^6*sin(theta))/16384+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(phi)^2*sin(theta)^3)/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^4*sin(theta)^2)/32768-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(phi)^2*sin(theta))/16384)); -9.1685 -9.1685 11729655121513488/(1878777008745185*cos(phi)^2)-2468866661864513/140737488355328 0 0 0; (24022333688859623424*cos(phi)^2*((353589694297967*cos(phi))/2097152-(353589694297967*cos(phi)*cos(theta)*sin(theta))/2097152))/(1750562017247561*sin(phi)*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768)) (23459310243026976*cos(phi)*((7802679563076885*cos(phi)^2*sin(theta)^2)/32768-(3035899015886451*cos(theta)^2*sin(phi)^2)/16384+(3035899015886451*cos(theta)^2*sin(phi)^2*sin(theta)^2)/16384-(7802679563076885*cos(phi)^2*cos(theta)*sin(theta))/32768))/(1878777008745185*sin(phi)*sin(theta)^2*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768)) 0 -(1281318364180027673672120608489472*cos(phi)^2*sin(theta)^2-997081356322527489540251466072064*cos(theta)^2*sin(phi)^2+997081356322527489540251466072064*cos(theta)^2*sin(phi)^2*sin(theta)^2-1281318364180027673672120608489472*cos(phi)^2*cos(theta)*sin(theta))/(215473177578967793664*sin(theta)*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768))-2200/619 -(5131724115662151*cos(phi)^2*((353589694297967*cos(theta))/2097152-(353589694297967*cos(theta)*sin(theta)^2)/2097152))/(44523515427081529851904*cos(phi)^4*cos(theta)^3+34646789112939027628032*cos(phi)^4*cos(theta)^2*sin(theta)^3-44523515427081529851904*cos(phi)^2*sin(phi)^2*sin(theta)^3-34646789112939027628032*cos(theta)^2*sin(phi)^4*sin(theta)^3-79170304540020557479936*cos(phi)^4*cos(theta)^2*sin(theta)+34646789112939027628032*cos(theta)^2*sin(phi)^4*sin(theta)+44523515427081529851904*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2) (60067132859724007391095431319005456239547121664*cos(phi)^2*cos(theta)*(cos(phi)*cos(theta)-cos(phi)*sin(theta)))/(3090959822350922421750773463860031455403966464*cos(phi)^4*cos(theta)^3*sin(phi)-2405287006075468939931671826555384286505074688*cos(theta)^2*sin(phi)^5*sin(theta)^3-3090959822350922421750773463860031455403966464*cos(phi)^2*sin(phi)^3*sin(theta)^3+2405287006075468939931671826555384286505074688*cos(theta)^2*sin(phi)^5*sin(theta)-5496246828426391678595095347472766116084842496*cos(phi)^4*cos(theta)^2*sin(phi)*sin(theta)+3090959822350922421750773463860031455403966464*cos(phi)^2*cos(theta)*sin(phi)^3*sin(theta)^2+2405287006075468939931671826555384286505074688*cos(phi)^4*cos(theta)^2*sin(phi)*sin(theta)^3); -(24022333688859623424*sin(phi)*((353589694297967*cos(phi)*sin(theta))/2097152-(353589694297967*cos(phi)*cos(theta)*sin(theta)^2)/2097152))/(1750562017247561*cos(theta)*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768)) -(640659182090013836836060304244736*cos(phi)^3*cos(theta)^2-1139199860251277653663780075208704*cos(phi)^3*cos(theta)*sin(theta)+498540678161263744770125733036032*cos(phi)^3*cos(theta)*sin(theta)^3)/(215473177578967793664*sin(phi)*sin(theta)^2*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768)) 0 (1281318364180027673672120608489472*cos(phi)^2*cos(theta)^2-2278399720502555307327560150417408*cos(phi)^2*cos(theta)*sin(theta)+997081356322527489540251466072064*cos(phi)^2*cos(theta)*sin(theta)^3)/(215473177578967793664*sin(theta)*((7802679563076885*cos(phi)^4*cos(theta)^3)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^2*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta)^3)/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(theta))/16384+(3035899015886451*cos(theta)^2*sin(phi)^4*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)/32768)) (5131724115662151*sin(phi)^2*((353589694297967*sin(theta))/2097152-(353589694297967*sin(theta)^3)/2097152))/(44523515427081529851904*cos(phi)^4*cos(theta)^3+34646789112939027628032*cos(phi)^4*cos(theta)^2*sin(theta)^3-44523515427081529851904*cos(phi)^2*sin(phi)^2*sin(theta)^3-34646789112939027628032*cos(theta)^2*sin(phi)^4*sin(theta)^3-79170304540020557479936*cos(phi)^4*cos(theta)^2*sin(theta)+34646789112939027628032*cos(theta)^2*sin(phi)^4*sin(theta)+44523515427081529851904*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2)-2200/619 -(35115176599067911854944413548544*sin(theta)*((1710574705220717*cos(phi)*cos(theta)*sin(phi))/134217728-(1710574705220717*cos(phi)*sin(phi)*sin(theta))/134217728))/(23029445278278905315330426870733733888*cos(phi)^4*cos(theta)^3+17920784697498894780365167756046237696*cos(phi)^4*cos(theta)^2*sin(theta)^3-23029445278278905315330426870733733888*cos(phi)^2*sin(phi)^2*sin(theta)^3-17920784697498894780365167756046237696*cos(theta)^2*sin(phi)^4*sin(theta)^3-40950229975777802456878836061602578432*cos(phi)^4*cos(theta)^2*sin(theta)+17920784697498894780365167756046237696*cos(theta)^2*sin(phi)^4*sin(theta)+23029445278278905315330426870733733888*cos(phi)^2*cos(theta)*sin(phi)^2*sin(theta)^2); -(14622595356790864*cos(phi)^4*cos(theta)^2-11378840434114016*cos(phi)^4*cos(theta)^2*sin(theta)^2+14622595356790864*cos(phi)^2*sin(phi)^2*sin(theta)^2+11378840434114016*cos(theta)^2*sin(phi)^4*sin(theta)^2)/(6320*cos(theta)*((7802679563076885*cos(phi)^4*cos(theta)^3*sin(phi)^2)/32768-(7802679563076885*cos(phi)^2*sin(phi)^4*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^6*sin(theta)^3)/16384+(3035899015886451*cos(theta)^2*sin(phi)^6*sin(theta))/16384+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(phi)^2*sin(theta)^3)/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^4*sin(theta)^2)/32768-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(phi)^2*sin(theta))/16384)) ((5923076600219083*cos(phi)^2*cos(theta)^3*sin(phi)^2)/256+(5923076600219083*cos(phi)^4*cos(theta)*sin(theta)^2)/256)/(10*sin(theta)^2*((7802679563076885*cos(phi)^4*cos(theta)^3*sin(phi)^2)/32768-(7802679563076885*cos(phi)^2*sin(phi)^4*sin(theta)^3)/32768-(3035899015886451*cos(theta)^2*sin(phi)^6*sin(theta)^3)/16384+(3035899015886451*cos(theta)^2*sin(phi)^6*sin(theta))/16384+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(phi)^2*sin(theta)^3)/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^4*sin(theta)^2)/32768-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(phi)^2*sin(theta))/16384)) 0 -((5923076600219083*cos(phi)*cos(theta)^3*sin(phi)^2)/256+(5923076600219083*cos(phi)^3*cos(theta)*sin(theta)^2)/256)/(5*sin(theta)*((7802679563076885*cos(phi)^4*cos(theta)^3*sin(phi))/32768-(3035899015886451*cos(theta)^2*sin(phi)^5*sin(theta)^3)/16384-(7802679563076885*cos(phi)^2*sin(phi)^3*sin(theta)^3)/32768+(3035899015886451*cos(theta)^2*sin(phi)^5*sin(theta))/16384-(6937238797424893*cos(phi)^4*cos(theta)^2*sin(phi)*sin(theta))/16384+(7802679563076885*cos(phi)^2*cos(theta)*sin(phi)^3*sin(theta)^2)/32768+(3035899015886451*cos(phi)^4*cos(theta)^2*sin(phi)*sin(theta)^3)/16384)) ((5923076600219083*cos(phi)^3*cos(theta)^2)/256+(5923076600219083*cos(phi)*sin(phi)^2*sin(theta)^2)/256)/((4876674726923053*cos(phi)^4*cos(theta)^3*sin(phi))/4096-(7589747539716127*cos(theta)^2*sin(phi)^5*sin(theta)^3)/8192-(4876674726923053*cos(phi)^2*sin(phi)^3*sin(theta)^3)/4096+(7589747539716127*cos(theta)^2*sin(phi)^5*sin(theta))/8192-(8671548496781117*cos(phi)^4*cos(theta)^2*sin(phi)*sin(theta))/4096+(4876674726923053*cos(phi)^2*cos(theta)*sin(phi)^3*sin(theta)^2)/4096+(7589747539716127*cos(phi)^4*cos(theta)^2*sin(phi)*sin(theta)^3)/8192) -(11378840434114018*cos(phi)^4*cos(theta)^2*sin(theta)-11378840434114018*cos(theta)^2*sin(phi)^4*sin(theta))/((1504911341511411*cos(phi)^4*cos(theta)^3*sin(phi)^2)/2-(1504911341511411*cos(phi)^2*sin(phi)^4*sin(theta)^3)/2-(4684297309668547*cos(theta)^2*sin(phi)^6*sin(theta)^3)/8+(4684297309668547*cos(theta)^2*sin(phi)^6*sin(theta))/8+(4684297309668547*cos(phi)^4*cos(theta)^2*sin(phi)^2*sin(theta)^3)/8+(1504911341511411*cos(phi)^2*cos(theta)*sin(phi)^4*sin(theta)^2)/2-1337992834464274*cos(phi)^4*cos(theta)^2*sin(phi)^2*sin(theta))-31800/8911] ;

tic;QMinvs = subs(QMinv, QM(:), Q_m(:)); toc

Elapsed time is 0.856434 seconds.

Just do not expect to be able to use the result in any non-trivial calculation. Even just vpa(QMinvs) takes a fair while.