radaar

I am trying to solve system consisting of two equations and two unknowns. I tried solve but it gives back unevaluated then I tried fsolve which gives an error.

$restart; x := 2.891022275*`ε`^4*sin(phi)^5*cos(phi)+1.080128320*`ε`^8*sin(phi)^11*cos(phi)+.1742483217*`ε`^10*sin(phi)^9*cos(phi)+3.293959886*`ε`^4*sin(phi)^15*cos(phi)+0.1414814731e-3*`ε`^12*sin(phi)*cos(phi)+0.1186386550e-1*`ε`^10*sin(phi)^3*cos(phi)+4.689119196*`ε`^2*sin(phi)^11*cos(phi)+.2775645236*`ε`^8*sin(phi)^5*cos(phi)+2.242139502*`ε`^6*sin(phi)^7*cos(phi)+6.170463035*`ε`^4*sin(phi)^9*cos(phi)+.2212715683*`ε`^2*sin(phi)*cos(phi)+.2565381358*`ε`^4*sin(phi)*cos(phi)+6.282275004*`ε`^4*sin(phi)^11*cos(phi)+0.9582543506e-5*`ε`^14*sin(phi)*cos(phi)+1.375810863*`ε`^2*sin(phi)^3*cos(phi)+0.4588193106e-1*`ε`^10*sin(phi)^5*cos(phi)+.6194422970*`ε`^8*sin(phi)^7*cos(phi)+0.1249753779e-2*`ε`^12*sin(phi)^3*cos(phi)+3.258184644*`ε`^6*sin(phi)^9*cos(phi)+3.520102051*`ε`^2*sin(phi)^13*cos(phi)+0.9608710101e-4*`ε`^14*sin(phi)^3*cos(phi)+5.222697446*`ε`^4*sin(phi)^13*cos(phi)+0.4740690151e-6*`ε`^16*sin(phi)*cos(phi)+.1124269022*`ε`^10*sin(phi)^7*cos(phi)+0.5349926002e-2*`ε`^12*sin(phi)^5*cos(phi)+.9885168554*`ε`^8*sin(phi)^9*cos(phi)+3.656113028*`ε`^6*sin(phi)^11*cos(phi)+2.252753163*`ε`^2*sin(phi)^15*cos(phi)+0.1562649478e-2*`ε`^10*sin(phi)*cos(phi)+0.8234222560e-1*`ε`^8*sin(phi)^3*cos(phi)+0.1277730241e-1*`ε`^12*sin(phi)^7*cos(phi)+1.148250169*`ε`^6*sin(phi)^5*cos(phi)+0.4933078791e-5*`ε`^16*sin(phi)^3*cos(phi)+4.857729947*`ε`^4*sin(phi)^7*cos(phi)+5.282506255*`ε`^2*sin(phi)^9*cos(phi)+0.1560418629e-7*`ε`^18*sin(phi)*cos(phi)-.6257226193*sin(phi)*cos(phi)+.6645139802*sin(phi)^11*cos(phi)+0.4077214292e-3*`ε`^14*sin(phi)^5*cos(phi)+.1265580305*sin(phi)^17*cos(phi)+.2494189998*sin(phi)^15*cos(phi)+.4337136311*sin(phi)^13*cos(phi)-.1331733921*sin(phi)^3*cos(phi)+.5467360220*sin(phi)^5*cos(phi)+.8861408610*sin(phi)^7*cos(phi)+4.820745909*`ε`^2*sin(phi)^7*cos(phi)+1.134364300*`ε`^2*sin(phi)^17*cos(phi)+0.7437311918e-1*`ε`^6*sin(phi)*cos(phi)+0.1283200926e-1*`ε`^8*sin(phi)*cos(phi)+1.168884099*`ε`^4*sin(phi)^3*cos(phi)+.3981616844*`ε`^6*sin(phi)^3*cos(phi)+3.270035435*`ε`^2*sin(phi)^5*cos(phi)+.8667852062*sin(phi)^9*cos(phi)+0.5208654259e-1*sin(phi)^19*cos(phi)+2.975771526*`ε`^6*sin(phi)^13*cos(phi); y := 2.891022275*`ε`^4*sin(phi)^5*cos(phi)+1.080128320*`ε`^8*sin(phi)^11*cos(phi)+.1742483217*`ε`^10*sin(phi)^9*cos(phi)+3.293959886*`ε`^4*sin(phi)^15*cos(phi)+0.1414814731e-3*`ε`^12*sin(phi)*cos(phi)+0.1186386550e-1*`ε`^10*sin(phi)^3*cos(phi)+4.689119196*`ε`^2*sin(phi)^11*cos(phi)+.2775645236*`ε`^8*sin(phi)^5*cos(phi)+2.242139502*`ε`^6*sin(phi)^7*cos(phi)+6.170463035*`ε`^4*sin(phi)^9*cos(phi)+.2212715683*`ε`^2*sin(phi)*cos(phi)+.2565381358*`ε`^4*sin(phi)*cos(phi)+6.282275004*`ε`^4*sin(phi)^11*cos(phi)+0.9582543506e-5*`ε`^14*sin(phi)*cos(phi)+1.375810863*`ε`^2*sin(phi)^3*cos(phi)+0.4588193106e-1*`ε`^10*sin(phi)^5*cos(phi)+.6194422970*`ε`^8*sin(phi)^7*cos(phi)+0.1249753779e-2*`ε`^12*sin(phi)^3*cos(phi)+3.258184644*`ε`^6*sin(phi)^9*cos(phi)+3.520102051*`ε`^2*sin(phi)^13*cos(phi)+0.9608710101e-4*`ε`^14*sin(phi)^3*cos(phi)+5.222697446*`ε`^4*sin(phi)^13*cos(phi)+0.4740690151e-6*`ε`^16*sin(phi)*cos(phi)+.1124269022*`ε`^10*sin(phi)^7*cos(phi)+0.5349926002e-2*`ε`^12*sin(phi)^5*cos(phi)+.9885168554*`ε`^8*sin(phi)^9*cos(phi)+3.656113028*`ε`^6*sin(phi)^11*cos(phi)+2.252753163*`ε`^2*sin(phi)^15*cos(phi)+0.1562649478e-2*`ε`^10*sin(phi)*cos(phi)+0.8234222560e-1*`ε`^8*sin(phi)^3*cos(phi)+0.1277730241e-1*`ε`^12*sin(phi)^7*cos(phi)+1.148250169*`ε`^6*sin(phi)^5*cos(phi)+0.4933078791e-5*`ε`^16*sin(phi)^3*cos(phi)+4.857729947*`ε`^4*sin(phi)^7*cos(phi)+5.282506255*`ε`^2*sin(phi)^9*cos(phi)+0.1560418629e-7*`ε`^18*sin(phi)*cos(phi)-.6257226193*sin(phi)*cos(phi)+.6645139802*sin(phi)^11*cos(phi)+0.4077214292e-3*`ε`^14*sin(phi)^5*cos(phi)+.1265580305*sin(phi)^17*cos(phi)+.2494189998*sin(phi)^15*cos(phi)+.4337136311*sin(phi)^13*cos(phi)-.1331733921*sin(phi)^3*cos(phi)+.5467360220*sin(phi)^5*cos(phi)+.8861408610*sin(phi)^7*cos(phi)+4.820745909*`ε`^2*sin(phi)^7*cos(phi)+1.134364300*`ε`^2*sin(phi)^17*cos(phi)+0.7437311918e-1*`ε`^6*sin(phi)*cos(phi)+0.1283200926e-1*`ε`^8*sin(phi)*cos(phi)+1.168884099*`ε`^4*sin(phi)^3*cos(phi)+.3981616844*`ε`^6*sin(phi)^3*cos(phi)+3.270035435*`ε`^2*sin(phi)^5*cos(phi)+.8667852062*sin(phi)^9*cos(phi)+0.5208654259e-1*sin(phi)^19*cos(phi)+2.975771526*`ε`^6*sin(phi)^13*cos(phi); evalf(solve({x = 0, y = 0}, {phi, `ε`})); fsolve({x = 0, y = 0}, {phi, `ε`})$

${phi = 0., `ε` = `ε`}, {phi = 1.570796327, `ε` = `ε`}, {phi = phi, `ε` = RootOf(1560418629*_Z^18+(47406901510+493307879100*sin(phi)^2)*_Z^16+(40772142920000*sin(phi)^4+9608710101000*sin(phi)^2+958254350600)*_Z^14+(14148147310000+124975377900000*sin(phi)^2+534992600200000*sin(phi)^4+1277730241000000*sin(phi)^6)*_Z^12+(11242690220000000*sin(phi)^6+1186386550000000*sin(phi)^2+17424832170000000*sin(phi)^8+156264947800000+4588193106000000*sin(phi)^4)*_Z^10+(8234222560000000*sin(phi)^2+61944229700000000*sin(phi)^6+98851685540000000*sin(phi)^8+108012832000000000*sin(phi)^10+27756452360000000*sin(phi)^4+1283200926000000)*_Z^8+(7437311918000000+114825016900000000*sin(phi)^4+297577152600000000*sin(phi)^12+325818464400000000*sin(phi)^8+365611302800000000*sin(phi)^10+224213950200000000*sin(phi)^6+39816168440000000*sin(phi)^2)*_Z^6+(485772994700000000*sin(phi)^6+628227500400000000*sin(phi)^10+522269744600000000*sin(phi)^12+329395988600000000*sin(phi)^14+25653813580000000+617046303500000000*sin(phi)^8+116888409900000000*sin(phi)^2+289102227500000000*sin(phi)^4)*_Z^4+(22127156830000000+137581086300000000*sin(phi)^2+468911919600000000*sin(phi)^10+352010205100000000*sin(phi)^12+225275316300000000*sin(phi)^14+528250625500000000*sin(phi)^8+327003543500000000*sin(phi)^4+113436430000000000*sin(phi)^16+482074590900000000*sin(phi)^6)*_Z^2-62572261930000000-13317339210000000*sin(phi)^2+12655803050000000*sin(phi)^16+54673602200000000*sin(phi)^4+86678520620000000*sin(phi)^8+43371363110000000*sin(phi)^12+66451398020000000*sin(phi)^10+88614086100000000*sin(phi)^6+24941899980000000*sin(phi)^14+5208654259000000*sin(phi)^18)}$

Error, (in fsolve) number of equations, 1, does not match number of variables, 2

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Solving an equation analytically...

Asked: radaar 202 Product: Maple

fsolve + Manage Tags

June 30 2017

1 11

I am trying to evaluate the following equation analytically but it gives back unevaluated then I tried fsolve which giving me the answer but I need phi greater than zero. How can I avoid negative values. Also Is there any ways to solve it analytically.

Please see the attachment

Download ANALYTIC.mw

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Maple giving back double integral uneval...

Asked: radaar 202 Product: Maple 13

integral numeric + Manage Tags

June 12 2017

0 18

I am trying to evaluate the following double integral where hypergeom([x,1/2],[3/2],C) is gauss hypergeometric function 2f1. maple gives back it unevaluated. I doubt it may be due to slow convergence of hypergeometric function.

restart; x := (1/6)*Pi; evalf(int(evalf(int(cos(x)*hypergeom([x, 1/2], [3/2], sin(x)/(r*cos(x)+k-2*r*sin(x))^2)/(r*sin(x)^2+r*cos(x)+k)^4, k = 0 .. 10)), r = 1 .. 2))

Int(Int(.8660254040*hypergeom([.5000000000, .5235987758], [1.500000000], .5000000000/(-.1339745960*r+k)^2)/(1.116025404*r+k)^4, k = 0. .. 10.), r = 1. .. 2.)