Question: Dividing a multivatiate polynomial

March 30 2012 by Ronan 15
false
Maple 15

0


I have a rather large multivatiate polynomial "Dtest"  I need to divie it by a cubic poly "DGm" using rem and quo. Both are determinants multiplied out,  both given below. Have spent the past 2 nights trying to sort, collect, expand, equate coefficients plex groebner etc. Am trying to collect up all the powers of c3 but cant anything to work. even expand doesn't fully expand "Dtest". If I set c1 and c2 to 1 things are ok but that was just a test. Would appreciate any help.

Dtest := Expand(2.9067425*10^67*Typesetting:-delayDotProduct(9.081648558*10^7*c[3]^3-2.771891978*10^15*c[3]^2*c[2]^2+7.497466392*10^7*c[3]^2*c[2]*c[1]-5.525292690*10^16*c[3]^2*c[2]+2.304580504*10^6*c[3]^2*c[1]+2.771892150*10^15*c[3]^2+1.562627708*10^16*c[3]*c[2]^3-1.490066642*10^7*c[3]*c[2]^2*c[1]+6.237481561*10^17*c[3]*c[2]^2+4.114300799*10^6*c[3]*c[2]*c[1]^2+7.0000000*10^7*c[3]*c[2]*c[1]+6.208843377*10^18*c[3]*c[2]+1.09327727*10^8*c[3]*c[1]^2+2.109933358*10^7*c[3]*c[1]-3.122650608*10^17*c[3]-5.525292510*10^16*c[2]^3+3.121342300*10^16*c[2]^2*c[1]-2.08421231*10^8*c[2]^2-5.525292160*10^16*c[2]*c[1]^2+3.107011295*10^17*c[2]*c[1]-5.525292350*10^16*c[2]+2.771891940*10^15*c[1]^2-1.562627711*10^16*c[1]+2.771891974*10^15, c[2])*c[3]^3-3.687801369*10^86*c[2]^2*c[1]^2+1.270856084*10^87*c[3]^2*c[2]*c[1]^2+1.286351265*10^86*c[3]*c[2]^2*c[1]^2+4.615678303*10^83*c[3]^4*c[2]*c[1]^2-4.122576584*10^81*c[3]^5*c[2]*c[1]^2-7.295074980*10^75*c[3]^3*c[2]*c[1]^3+1.610276627*10^82*c[3]^3*c[2]^2*c[1]^2+2.324063303*10^82*c[3]^4*c[2]^2*c[1]^2-2.425998043*10^78*c[3]^2*c[2]*c[1]^3-1.154918687*10^85*c[3]^3*c[2]*c[1]^2+1.997563707*10^75*c[3]^4*c[2]*c[1]^3-3.720590534*10^86*c[3]^2*c[2]^3*c[1]-4.787141101*10^87*c[3]^2*c[2]^2*c[1]+1.899934303*10^79*c[3]*c[2]^3*c[1]+1.186323320*10^85*c[3]^4*c[2]^2*c[1]-4.048186940*10^77*c[3]^5*c[2]^2*c[1]-6.689867818*10^85*c[3]^3*c[2]^3*c[1]+2.279625276*10^78*c[3]^4*c[2]^3*c[1]-7.326275290*10^87*c[3]*c[2]^2*c[1]+7.423112636*10^87*c[3]*c[2]*c[1]^2+6.541665162*10^85*c[2]^2*c[1]-6.599829040*10^85*c[2]*c[1]^2-4.615678141*10^83*c[3]^3*c[1]^3-3.177879794*10^83*c[3]^2*c[1]^3-1.610853527*10^82*c[3]*c[1]^4+4.122576967*10^81*c[3]^4*c[1]^3+3.375629923*10^73*c[3]^3*c[1]^4+1.350694476*10^74*c[3]^5*c[1]^3+3.427554079*10^72*c[3]^4*c[1]^4+7.392273582*10^87*c[3]^2*c[2]^3-2.324063304*10^82*c[3]^2*c[1]^4+3.687801390*10^86*c[3]^2*c[2]^4+8.464374435*10^77*c[3]*c[2]^4+2.239705767*10^85*c[3]^4*c[2]^3-1.286351443*10^86*c[3]^3*c[2]^4-3.28*10^62*Typesetting:-delayDotProduct(9.081648558*10^7*c[3]^3-2.771891978*10^15*c[3]^2*c[2]^2+7.497466392*10^7*c[3]^2*c[2]*c[1]-5.525292690*10^16*c[3]^2*c[2]+2.304580504*10^6*c[3]^2*c[1]+2.771892150*10^15*c[3]^2+1.562627708*10^16*c[3]*c[2]^3-1.490066642*10^7*c[3]*c[2]^2*c[1]+6.237481561*10^17*c[3]*c[2]^2+4.114300799*10^6*c[3]*c[2]*c[1]^2+7.0000000*10^7*c[3]*c[2]*c[1]+6.208843377*10^18*c[3]*c[2]+1.09327727*10^8*c[3]*c[1]^2+2.109933358*10^7*c[3]*c[1]-3.122650608*10^17*c[3]-5.525292510*10^16*c[2]^3+3.121342300*10^16*c[2]^2*c[1]-2.08421231*10^8*c[2]^2-5.525292160*10^16*c[2]*c[1]^2+3.107011295*10^17*c[2]*c[1]-5.525292350*10^16*c[2]+2.771891940*10^15*c[1]^2-1.562627711*10^16*c[1]+2.771891974*10^15, c[2])+4.719135687*10^79*c[1]^4-6.531220102*10^76*c[2]^4-8.371113761*10^78*c[1]^3-1.293256947*10^87*c[3]^3*c[2]^2*c[1]+4.30972352*10^69*Typesetting:-delayDotProduct(9.081648558*10^7*c[3]^3-2.771891978*10^15*c[3]^2*c[2]^2+7.497466392*10^7*c[3]^2*c[2]*c[1]-5.525292690*10^16*c[3]^2*c[2]+2.304580504*10^6*c[3]^2*c[1]+2.771892150*10^15*c[3]^2+1.562627708*10^16*c[3]*c[2]^3-1.490066642*10^7*c[3]*c[2]^2*c[1]+6.237481561*10^17*c[3]*c[2]^2+4.114300799*10^6*c[3]*c[2]*c[1]^2+7.0000000*10^7*c[3]*c[2]*c[1]+6.208843377*10^18*c[3]*c[2]+1.09327727*10^8*c[3]*c[1]^2+2.109933358*10^7*c[3]*c[1]-3.122650608*10^17*c[3]-5.525292510*10^16*c[2]^3+3.121342300*10^16*c[2]^2*c[1]-2.08421231*10^8*c[2]^2-5.525292160*10^16*c[2]*c[1]^2+3.107011295*10^17*c[2]*c[1]-5.525292350*10^16*c[2]+2.771891940*10^15*c[1]^2-1.562627711*10^16*c[1]+2.771891974*10^15, c[1])*c[3]^2-1.46*10^62*Typesetting:-delayDotProduct(9.081648558*10^7*c[3]^3-2.771891978*10^15*c[3]^2*c[2]^2+7.497466392*10^7*c[3]^2*c[2]*c[1]-5.525292690*10^16*c[3]^2*c[2]+2.304580504*10^6*c[3]^2*c[1]+2.771892150*10^15*c[3]^2+1.562627708*10^16*c[3]*c[2]^3-1.490066642*10^7*c[3]*c[2]^2*c[1]+6.237481561*10^17*c[3]*c[2]^2+4.114300799*10^6*c[3]*c[2]*c[1]^2+7.0000000*10^7*c[3]*c[2]*c[1]+6.208843377*10^18*c[3]*c[2]+1.09327727*10^8*c[3]*c[1]^2+2.109933358*10^7*c[3]*c[1]-3.122650608*10^17*c[3]-5.525292510*10^16*c[2]^3+3.121342300*10^16*c[2]^2*c[1]-2.08421231*10^8*c[2]^2-5.525292160*10^16*c[2]*c[1]^2+3.107011295*10^17*c[2]*c[1]-5.525292350*10^16*c[2]+2.771891940*10^15*c[1]^2-1.562627711*10^16*c[1]+2.771891974*10^15, c[1])*c[3]^3+2.36*10^70*Typesetting:-delayDotProduct(9.081648558*10^7*c[3]^3-2.771891978*10^15*c[3]^2*c[2]^2+7.497466392*10^7*c[3]^2*c[2]*c[1]-5.525292690*10^16*c[3]^2*c[2]+2.304580504*10^6*c[3]^2*c[1]+2.771892150*10^15*c[3]^2+1.562627708*10^16*c[3]*c[2]^3-1.490066642*10^7*c[3]*c[2]^2*c[1]+6.237481561*10^17*c[3]*c[2]^2+4.114300799*10^6*c[3]*c[2]*c[1]^2+7.0000000*10^7*c[3]*c[2]*c[1]+6.208843377*10^18*c[3]*c[2]+1.09327727*10^8*c[3]*c[1]^2+2.109933358*10^7*c[3]*c[1]-3.122650608*10^17*c[3]-5.525292510*10^16*c[2]^3+3.121342300*10^16*c[2]^2*c[1]-2.08421231*10^8*c[2]^2-5.525292160*10^16*c[2]*c[1]^2+3.107011295*10^17*c[2]*c[1]-5.525292350*10^16*c[2]+2.771891940*10^15*c[1]^2-1.562627711*10^16*c[1]+2.771891974*10^15, c[1])+3.737915722*10^81*c[3]^5*c[2]^3-2.107214404*10^82*c[3]^4*c[2]^4-2.635971526*10^87*c[3]^3*c[2]^3+8.239656631*10^69*Typesetting:-delayDotProduct(9.081648558*10^7*c[3]^3-2.771891978*10^15*c[3]^2*c[2]^2+7.497466392*10^7*c[3]^2*c[2]*c[1]-5.525292690*10^16*c[3]^2*c[2]+2.304580504*10^6*c[3]^2*c[1]+2.771892150*10^15*c[3]^2+1.562627708*10^16*c[3]*c[2]^3-1.490066642*10^7*c[3]*c[2]^2*c[1]+6.237481561*10^17*c[3]*c[2]^2+4.114300799*10^6*c[3]*c[2]*c[1]^2+7.0000000*10^7*c[3]*c[2]*c[1]+6.208843377*10^18*c[3]*c[2]+1.09327727*10^8*c[3]*c[1]^2+2.109933358*10^7*c[3]*c[1]-3.122650608*10^17*c[3]-5.525292510*10^16*c[2]^3+3.121342300*10^16*c[2]^2*c[1]-2.08421231*10^8*c[2]^2-5.525292160*10^16*c[2]*c[1]^2+3.107011295*10^17*c[2]*c[1]-5.525292350*10^16*c[2]+2.771891940*10^15*c[1]^2-1.562627711*10^16*c[1]+2.771891974*10^15, c[2])*c[3]^2+6.689866671*10^85*c[3]*c[2]*c[1]^3+2.098943865*10^82*c[3]^2*c[2]^2*c[1]^2-2.364586293*10^70*Typesetting:-delayDotProduct(9.081648558*10^7*c[3]^3-2.771891978*10^15*c[3]^2*c[2]^2+7.497466392*10^7*c[3]^2*c[2]*c[1]-5.525292690*10^16*c[3]^2*c[2]+2.304580504*10^6*c[3]^2*c[1]+2.771892150*10^15*c[3]^2+1.562627708*10^16*c[3]*c[2]^3-1.490066642*10^7*c[3]*c[2]^2*c[1]+6.237481561*10^17*c[3]*c[2]^2+4.114300799*10^6*c[3]*c[2]*c[1]^2+7.0000000*10^7*c[3]*c[2]*c[1]+6.208843377*10^18*c[3]*c[2]+1.09327727*10^8*c[3]*c[1]^2+2.109933358*10^7*c[3]*c[1]-3.122650608*10^17*c[3]-5.525292510*10^16*c[2]^3+3.121342300*10^16*c[2]^2*c[1]-2.08421231*10^8*c[2]^2-5.525292160*10^16*c[2]*c[1]^2+3.107011295*10^17*c[2]*c[1]-5.525292350*10^16*c[2]+2.771891940*10^15*c[1]^2-1.562627711*10^16*c[1]+2.771891974*10^15, c[2])*c[3]+1.450211*10^66*Typesetting:-delayDotProduct(-2.771891958*10^15*c[3]^3+2.771891958*10^15*c[3]^2*c[2]*c[1]+1.562627709*10^16*c[3]^2*c[2]-7.497466392*10^7*c[3]^2*c[1]^2+5.525292590*10^16*c[3]^2*c[1]+3.122650607*10^17*c[3]^2-1.562627709*10^16*c[3]*c[2]^2*c[1]-2.771892067*10^15*c[3]*c[2]^2+1.490066642*10^7*c[3]*c[2]*c[1]^2-6.229661904*10^17*c[3]*c[2]*c[1]+3.590066642*10^7*c[3]*c[2]-4.114300799*10^6*c[3]*c[1]^3-2.771891698*10^15*c[3]*c[1]^2-6.208843376*10^18*c[3]*c[1]-2.771891908*10^15*c[3]+5.525292500*10^16*c[2]^2*c[1]-3.850332996*10^7*c[2]^2-3.121342300*10^16*c[2]*c[1]^2+2.771891868*10^15*c[2]*c[1]-2.767466146*10^6*c[2]+5.525292170*10^16*c[1]^3-3.114830954*10^17*c[1]^2+5.525292330*10^16*c[1]-4.326128906*10^7, c[1])*c[3]^2-1.020966422*10^78*c[2]^3+1.487279023*10^66*Typesetting:-delayDotProduct(-2.771891958*10^15*c[3]^3+2.771891958*10^15*c[3]^2*c[2]*c[1]+1.562627709*10^16*c[3]^2*c[2]-7.497466392*10^7*c[3]^2*c[1]^2+5.525292590*10^16*c[3]^2*c[1]+3.122650607*10^17*c[3]^2-1.562627709*10^16*c[3]*c[2]^2*c[1]-2.771892067*10^15*c[3]*c[2]^2+1.490066642*10^7*c[3]*c[2]*c[1]^2-6.229661904*10^17*c[3]*c[2]*c[1]+3.590066642*10^7*c[3]*c[2]-4.114300799*10^6*c[3]*c[1]^3-2.771891698*10^15*c[3]*c[1]^2-6.208843376*10^18*c[3]*c[1]-2.771891908*10^15*c[3]+5.525292500*10^16*c[2]^2*c[1]-3.850332996*10^7*c[2]^2-3.121342300*10^16*c[2]*c[1]^2+2.771891868*10^15*c[2]*c[1]-2.767466146*10^6*c[2]+5.525292170*10^16*c[1]^3-3.114830954*10^17*c[1]^2+5.525292330*10^16*c[1]-4.326128906*10^7, c[1])*c[3]^3+3.720590789*10^86*c[2]*c[1]^3-2.768451361*10^78*c[2]^3*c[1]+3.800478587*10^81*c[3]*c[1]^3-6.541664867*10^85*c[3]*c[2]^3+4.28145306*10^69*Typesetting:-delayDotProduct(-2.771891958*10^15*c[3]^3+2.771891958*10^15*c[3]^2*c[2]*c[1]+1.562627709*10^16*c[3]^2*c[2]-7.497466392*10^7*c[3]^2*c[1]^2+5.525292590*10^16*c[3]^2*c[1]+3.122650607*10^17*c[3]^2-1.562627709*10^16*c[3]*c[2]^2*c[1]-2.771892067*10^15*c[3]*c[2]^2+1.490066642*10^7*c[3]*c[2]*c[1]^2-6.229661904*10^17*c[3]*c[2]*c[1]+3.590066642*10^7*c[3]*c[2]-4.114300799*10^6*c[3]*c[1]^3-2.771891698*10^15*c[3]*c[1]^2-6.208843376*10^18*c[3]*c[1]-2.771891908*10^15*c[3]+5.525292500*10^16*c[2]^2*c[1]-3.850332996*10^7*c[2]^2-3.121342300*10^16*c[2]*c[1]^2+2.771891868*10^15*c[2]*c[1]-2.767466146*10^6*c[2]+5.525292170*10^16*c[1]^3-3.114830954*10^17*c[1]^2+5.525292330*10^16*c[1]-4.326128906*10^7, c[1])*c[3]+2.380983517*10^70*Typesetting:-delayDotProduct(-2.771891958*10^15*c[3]^3+2.771891958*10^15*c[3]^2*c[2]*c[1]+1.562627709*10^16*c[3]^2*c[2]-7.497466392*10^7*c[3]^2*c[1]^2+5.525292590*10^16*c[3]^2*c[1]+3.122650607*10^17*c[3]^2-1.562627709*10^16*c[3]*c[2]^2*c[1]-2.771892067*10^15*c[3]*c[2]^2+1.490066642*10^7*c[3]*c[2]*c[1]^2-6.229661904*10^17*c[3]*c[2]*c[1]+3.590066642*10^7*c[3]*c[2]-4.114300799*10^6*c[3]*c[1]^3-2.771891698*10^15*c[3]*c[1]^2-6.208843376*10^18*c[3]*c[1]-2.771891908*10^15*c[3]+5.525292500*10^16*c[2]^2*c[1]-3.850332996*10^7*c[2]^2-3.121342300*10^16*c[2]*c[1]^2+2.771891868*10^15*c[2]*c[1]-2.767466146*10^6*c[2]+5.525292170*10^16*c[1]^3-3.114830954*10^17*c[1]^2+5.525292330*10^16*c[1]-4.326128906*10^7, c[1])+1.560520911*10^70*Typesetting:-delayDotProduct(9.081648558*10^7*c[3]^3-2.771891978*10^15*c[3]^2*c[2]^2+7.497466392*10^7*c[3]^2*c[2]*c[1]-5.525292690*10^16*c[3]^2*c[2]+2.304580504*10^6*c[3]^2*c[1]+2.771892150*10^15*c[3]^2+1.562627708*10^16*c[3]*c[2]^3-1.490066642*10^7*c[3]*c[2]^2*c[1]+6.237481561*10^17*c[3]*c[2]^2+4.114300799*10^6*c[3]*c[2]*c[1]^2+7.0000000*10^7*c[3]*c[2]*c[1]+6.208843377*10^18*c[3]*c[2]+1.09327727*10^8*c[3]*c[1]^2+2.109933358*10^7*c[3]*c[1]-3.122650608*10^17*c[3]-5.525292510*10^16*c[2]^3+3.121342300*10^16*c[2]^2*c[1]-2.08421231*10^8*c[2]^2-5.525292160*10^16*c[2]*c[1]^2+3.107011295*10^17*c[2]*c[1]-5.525292350*10^16*c[2]+2.771891940*10^15*c[1]^2-1.562627711*10^16*c[1]+2.771891974*10^15, c[1])*c[3]):
  NULL

``

NULL

DGm := -9.40120030876993*10^75*c[3]^3+1.63887663817259*10^78*c[3]^2-2.55902590396600*10^78*c[3]+1.74949694317927*10^79

-0.9401200309e76*c[3]^3+0.1638876638e79*c[3]^2-0.2559025904e79*c[3]+0.1749496943e80

 (1)

NULL


Download sort_poly2.mw
polynomial collect expand groebner sort coeff
 
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