radaar

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2 years, 136 days

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These are replies submitted by radaar

@Markiyan Hirnyk 

   I have already stated that I have two equations 1) integral equation 2) the corresponding analytical equation. The integral equation gives me converged result where as analytical (posted) equation shows divergence. There is no typo too.

@Carl Love 

   The integral equation for the same is converging. So this must converge.

@Kitonum 

  I tried approximate int option and got the following result

integral7.mw

@Kitonum 

The last step is not evaluated even with numerical integration in the following code


 

restart; a := 2; Q := 5.48; d := 6.48; chi := (1/4)*Pi; phi := 0.; p := 5/2; x := freeze((a*sin(CHI)*sin(phi)+d*cos(chi))^2+(a*cos(CHI)+d*sin(chi))^2); y := freeze(2*Q*((a*sin(CHI)*sin(phi)+d*cos(chi))^2+(a*cos(CHI)+d*sin(chi))^2)^(1/2)); int(1/(Q^2+x+y*cos(beta))^p, beta)

qq := int(1/(Q^2+x+y*cos(beta))^p, beta = 0 .. 2*Pi):

qqq := evalf(Int(zz, CHI = 0 .. Pi))

Warning,  computation interrupted

 

NULL

NULL


 

Download INTEGRAL_NEW3.mw

@vv how to check integral exist or not

@Mariusz Iwaniuk 

But i am running a loop over epsilon and this sum is not converged at m=35. I need much more fast.

@Rouben Rostamian  

I only need ee thats why I put colon for yy. yy is pair of differential equation. Please help me to solve this problem.

@acer 

How to use student calculus command for two variable function say f(x,y)

@one man 

How to get all the possible solutions for f(\epsilon,\phi). fsolve gives only one solution.

@one man 

Please see below file. I need \phi and \epsilon at a particular range. fsolve then gives back unevaluated

equation_solve(1).mw
 

fsolve({0.2800309790e-2*`ε`^5*sin(phi)^14+0.1808179723e-2*`ε`^3*sin(phi)^16+0.1800064143e-2*`ε`^5+0.9975458560e-5*`ε`^9+2.695613387*10^(-11)*`ε`^17+5.719268841*10^(-7)*`ε`^11+2.715095888*10^(-8)*`ε`^13+4.363704318*10^(-13)*`ε`^19+4.332726974*10^(-8)*`ε`^15*sin(phi)^4+3.083663044*10^(-10)*`ε`^17*sin(phi)^2+2.449307251*10^(-7)*`ε`^13*sin(phi)^2+1.010054487*10^(-9)*`ε`^15+0.1472851728e-3*`ε`^7+1.058921279*10^(-8)*`ε`^15*sin(phi)^2+9.837894806*10^(-7)*`ε`^13*sin(phi)^4+0.1581129253e-2*`ε`^7*sin(phi)^12+0.4208368033e-4*`ε`^11*sin(phi)^8+0.3826060948e-3*`ε`^9*sin(phi)^10+0.1532571718e-4*`ε`^11*sin(phi)^4+0.3372542624e-3*`ε`^9*sin(phi)^6+0.2880126182e-2*`ε`^7*sin(phi)^8+0.1656590034e-1*`ε`^3+0.1040621728e-1*`ε`^3*sin(phi)^12+0.2554034969e-2*`ε`*sin(phi)^14+0.2088928633e-5*`ε`^13*sin(phi)^6+0.6571147876e-1*`ε`*sin(phi)^6+0.6607466275e-2*`ε`*sin(phi)^12+0.8630154850e-1*`ε`+0.5804636993e-2*`ε`^5*sin(phi)^12+.1236996683*`ε`*sin(phi)^2+0.4171366139e-1*`ε`^3*sin(phi)^2+.1043183122*`ε`*sin(phi)^4+0.6676607029e-2*`ε`^5*sin(phi)^2+0.5385063897e-1*`ε`^3*sin(phi)^4+0.2601749508e-2*`ε`^7*sin(phi)^6+0.1286203486e-1*`ε`^5*sin(phi)^8+0.2001289770e-1*`ε`^3*sin(phi)^10+0.1838833200e-3*`ε`^9*sin(phi)^4+0.4355347758e-5*`ε`^11*sin(phi)^2+0.2479253172e-2*`ε`^7*sin(phi)^10+0.4786708231e-2*`ε`^3*sin(phi)^14+0.9108566220e-3*`ε`*sin(phi)^16+0.1723669271e-2*`ε`^7*sin(phi)^4+0.1427600691e-1*`ε`^5*sin(phi)^6+0.3374798727e-1*`ε`^3*sin(phi)^8+0.1581065081e-1*`ε`*sin(phi)^10+0.3228139272e-4*`ε`^11*sin(phi)^6+0.4334036365e-3*`ε`^9*sin(phi)^8+0.7318738454e-3*`ε`^7*sin(phi)^2+0.1201354005e-1*`ε`^5*sin(phi)^4+0.4804203645e-1*`ε`^3*sin(phi)^6+0.3437740782e-1*`ε`*sin(phi)^8+0.9442452638e-2*`ε`^5*sin(phi)^10+0.6256613610e-4*`ε`^9*sin(phi)^2+0.2767536266e-3*`ε`*sin(phi)^18, 0.2700449376e-1*sin(phi)^9*cos(phi)+.2284407905*sin(phi)*cos(phi)+0.2880126182e-2*`ε`^8*sin(phi)^7*cos(phi)+0.3121865183e-1*`ε`^4*sin(phi)^11*cos(phi)+0.1787824478e-1*`ε`^2*sin(phi)^13*cos(phi)+0.3467229094e-3*`ε`^10*sin(phi)^7*cos(phi)+1.323651599*10^(-9)*`ε`^16*sin(phi)*cos(phi)+0.3964479764e-1*`ε`^2*sin(phi)^11*cos(phi)+0.1573742107e-1*`ε`^6*sin(phi)^9*cos(phi)+0.5108572394e-5*`ε`^12*sin(phi)^3*cos(phi)+0.2023525575e-3*`ε`^10*sin(phi)^5*cos(phi)+0.1427600691e-1*`ε`^6*sin(phi)^5*cos(phi)+0.7355332797e-4*`ε`^10*sin(phi)^3*cos(phi)+0.6749597453e-1*`ε`^4*sin(phi)^7*cos(phi)+0.1951312131e-2*`ε`^8*sin(phi)^5*cos(phi)+0.1714937981e-1*`ε`^6*sin(phi)^7*cos(phi)+0.1288705036e-2*sin(phi)^15*cos(phi)+0.5385063897e-1*`ε`^4*sin(phi)^3*cos(phi)+2.810827088*10^(-7)*`ε`^14*sin(phi)^3*cos(phi)+0.2490782640e-2*`ε`^2*sin(phi)^17*cos(phi)+0.7232718893e-2*`ε`^4*sin(phi)^15*cos(phi)+0.3826060948e-3*`ε`^10*sin(phi)^9*cos(phi)+0.2371693880e-2*`ε`^8*sin(phi)^11*cos(phi)+0.4122181016e-3*sin(phi)^17*cos(phi)+0.1143691282e-3*sin(phi)^19*cos(phi)+0.6534056175e-2*`ε`^6*sin(phi)^13*cos(phi)+0.2225535677e-2*`ε`^6*sin(phi)*cos(phi)+0.8618346358e-3*`ε`^8*sin(phi)^3*cos(phi)+0.5003224422e-1*`ε`^4*sin(phi)^9*cos(phi)+.1971344362*`ε`^2*sin(phi)^5*cos(phi)+.2086366243*`ε`^2*sin(phi)^3*cos(phi)+0.8009026697e-2*`ε`^6*sin(phi)^3*cos(phi)+0.7905325406e-1*`ε`^2*sin(phi)^9*cos(phi)+.1375096313*`ε`^2*sin(phi)^7*cos(phi)+0.1251322722e-4*`ε`^10*sin(phi)*cos(phi)+0.7206305470e-1*`ε`^4*sin(phi)^5*cos(phi)+0.2085683069e-1*`ε`^4*sin(phi)*cos(phi)+.1236996683*`ε`^2*sin(phi)*cos(phi)+0.1829684614e-3*`ε`^8*sin(phi)*cos(phi)+0.1614069636e-4*`ε`^12*sin(phi)^5*cos(phi)+0.1160927399e-1*`ε`^6*sin(phi)^11*cos(phi)+0.3099066464e-2*`ε`^8*sin(phi)^9*cos(phi)+0.2805578688e-4*`ε`^12*sin(phi)^7*cos(phi)+0.1675347881e-1*`ε`^4*sin(phi)^13*cos(phi)+0.7286852972e-2*`ε`^2*sin(phi)^15*cos(phi)+7.258912934*10^(-7)*`ε`^12*sin(phi)*cos(phi)+3.499010359*10^(-8)*`ε`^14*sin(phi)*cos(phi)+3.426292272*10^(-11)*`ε`^18*sin(phi)*cos(phi)+1.083181744*10^(-8)*`ε`^16*sin(phi)^3*cos(phi)+8.952551282*10^(-7)*`ε`^14*sin(phi)^5*cos(phi)+0.1047101424e-1*sin(phi)^11*cos(phi)+0.3782211768e-2*sin(phi)^13*cos(phi)+.2125921316*sin(phi)^3*cos(phi)+.1294353588*sin(phi)^5*cos(phi)+0.6332296548e-1*sin(phi)^7*cos(phi)}, {phi, `ε`}, {phi = 0.1e-1 .. 1.57, `ε` = 0.1e-1 .. 10})

fsolve({0.2800309790e-2*`ε`^5*sin(phi)^14+0.1808179723e-2*`ε`^3*sin(phi)^16+0.1800064143e-2*`ε`^5+0.9975458560e-5*`ε`^9+0.2715095888e-7*`ε`^13+0.4363704318e-12*`ε`^19+0.5719268841e-6*`ε`^11+0.1472851728e-3*`ε`^7+0.1058921279e-7*`ε`^15*sin(phi)^2+0.9837894806e-6*`ε`^13*sin(phi)^4+0.3083663044e-9*`ε`^17*sin(phi)^2+0.2449307251e-6*`ε`^13*sin(phi)^2+0.4332726974e-7*`ε`^15*sin(phi)^4+0.1010054487e-8*`ε`^15+0.1581129253e-2*`ε`^7*sin(phi)^12+0.4208368033e-4*`ε`^11*sin(phi)^8+0.3826060948e-3*`ε`^9*sin(phi)^10+0.1532571718e-4*`ε`^11*sin(phi)^4+0.3372542624e-3*`ε`^9*sin(phi)^6+0.2880126182e-2*`ε`^7*sin(phi)^8+0.1656590034e-1*`ε`^3+0.1040621728e-1*`ε`^3*sin(phi)^12+0.2554034969e-2*`ε`*sin(phi)^14+0.2088928633e-5*`ε`^13*sin(phi)^6+0.6571147876e-1*`ε`*sin(phi)^6+0.6607466275e-2*`ε`*sin(phi)^12+0.8630154850e-1*`ε`+0.5804636993e-2*`ε`^5*sin(phi)^12+.1236996683*`ε`*sin(phi)^2+0.4171366139e-1*`ε`^3*sin(phi)^2+.1043183122*`ε`*sin(phi)^4+0.6676607029e-2*`ε`^5*sin(phi)^2+0.5385063897e-1*`ε`^3*sin(phi)^4+0.2601749508e-2*`ε`^7*sin(phi)^6+0.1286203486e-1*`ε`^5*sin(phi)^8+0.2001289770e-1*`ε`^3*sin(phi)^10+0.1838833200e-3*`ε`^9*sin(phi)^4+0.4355347758e-5*`ε`^11*sin(phi)^2+0.2479253172e-2*`ε`^7*sin(phi)^10+0.4786708231e-2*`ε`^3*sin(phi)^14+0.9108566220e-3*`ε`*sin(phi)^16+0.1723669271e-2*`ε`^7*sin(phi)^4+0.1427600691e-1*`ε`^5*sin(phi)^6+0.3374798727e-1*`ε`^3*sin(phi)^8+0.1581065081e-1*`ε`*sin(phi)^10+0.3228139272e-4*`ε`^11*sin(phi)^6+0.4334036365e-3*`ε`^9*sin(phi)^8+0.7318738454e-3*`ε`^7*sin(phi)^2+0.1201354005e-1*`ε`^5*sin(phi)^4+0.4804203645e-1*`ε`^3*sin(phi)^6+0.3437740782e-1*`ε`*sin(phi)^8+0.9442452638e-2*`ε`^5*sin(phi)^10+0.6256613610e-4*`ε`^9*sin(phi)^2+0.2695613387e-10*`ε`^17+0.2767536266e-3*`ε`*sin(phi)^18, 0.1083181744e-7*`ε`^16*sin(phi)^3*cos(phi)+0.1323651599e-8*`ε`^16*sin(phi)*cos(phi)+0.2810827088e-6*`ε`^14*sin(phi)^3*cos(phi)+0.3426292272e-10*`ε`^18*sin(phi)*cos(phi)+0.2700449376e-1*sin(phi)^9*cos(phi)+.2284407905*sin(phi)*cos(phi)+0.2880126182e-2*`ε`^8*sin(phi)^7*cos(phi)+0.3121865183e-1*`ε`^4*sin(phi)^11*cos(phi)+0.1787824478e-1*`ε`^2*sin(phi)^13*cos(phi)+0.3467229094e-3*`ε`^10*sin(phi)^7*cos(phi)+0.3499010359e-7*`ε`^14*sin(phi)*cos(phi)+0.7258912934e-6*`ε`^12*sin(phi)*cos(phi)+0.3964479764e-1*`ε`^2*sin(phi)^11*cos(phi)+0.1573742107e-1*`ε`^6*sin(phi)^9*cos(phi)+0.5108572394e-5*`ε`^12*sin(phi)^3*cos(phi)+0.2023525575e-3*`ε`^10*sin(phi)^5*cos(phi)+0.1427600691e-1*`ε`^6*sin(phi)^5*cos(phi)+0.7355332797e-4*`ε`^10*sin(phi)^3*cos(phi)+0.6749597453e-1*`ε`^4*sin(phi)^7*cos(phi)+0.1951312131e-2*`ε`^8*sin(phi)^5*cos(phi)+0.1714937981e-1*`ε`^6*sin(phi)^7*cos(phi)+0.1288705036e-2*sin(phi)^15*cos(phi)+0.5385063897e-1*`ε`^4*sin(phi)^3*cos(phi)+0.2490782640e-2*`ε`^2*sin(phi)^17*cos(phi)+0.7232718893e-2*`ε`^4*sin(phi)^15*cos(phi)+0.8952551282e-6*`ε`^14*sin(phi)^5*cos(phi)+0.3826060948e-3*`ε`^10*sin(phi)^9*cos(phi)+0.2371693880e-2*`ε`^8*sin(phi)^11*cos(phi)+0.4122181016e-3*sin(phi)^17*cos(phi)+0.1143691282e-3*sin(phi)^19*cos(phi)+0.6534056175e-2*`ε`^6*sin(phi)^13*cos(phi)+0.2225535677e-2*`ε`^6*sin(phi)*cos(phi)+0.8618346358e-3*`ε`^8*sin(phi)^3*cos(phi)+0.5003224422e-1*`ε`^4*sin(phi)^9*cos(phi)+.1971344362*`ε`^2*sin(phi)^5*cos(phi)+.2086366243*`ε`^2*sin(phi)^3*cos(phi)+0.8009026697e-2*`ε`^6*sin(phi)^3*cos(phi)+0.7905325406e-1*`ε`^2*sin(phi)^9*cos(phi)+.1375096313*`ε`^2*sin(phi)^7*cos(phi)+0.1251322722e-4*`ε`^10*sin(phi)*cos(phi)+0.7206305470e-1*`ε`^4*sin(phi)^5*cos(phi)+0.2085683069e-1*`ε`^4*sin(phi)*cos(phi)+.1236996683*`ε`^2*sin(phi)*cos(phi)+0.1829684614e-3*`ε`^8*sin(phi)*cos(phi)+0.1614069636e-4*`ε`^12*sin(phi)^5*cos(phi)+0.1160927399e-1*`ε`^6*sin(phi)^11*cos(phi)+0.3099066464e-2*`ε`^8*sin(phi)^9*cos(phi)+0.2805578688e-4*`ε`^12*sin(phi)^7*cos(phi)+0.1675347881e-1*`ε`^4*sin(phi)^13*cos(phi)+0.7286852972e-2*`ε`^2*sin(phi)^15*cos(phi)+0.1047101424e-1*sin(phi)^11*cos(phi)+0.3782211768e-2*sin(phi)^13*cos(phi)+.2125921316*sin(phi)^3*cos(phi)+.1294353588*sin(phi)^5*cos(phi)+0.6332296548e-1*sin(phi)^7*cos(phi)}, {phi, `ε`}, {phi = 0.1e-1 .. 1.57, `ε` = 0.1e-1 .. 10})

(1)

``


 

Download equation_solve(1).mw

 

@one man 

I have a function let me say f(\epsilon,\phi) I need to find minima of that function. So what I am doing is 

1)x=diff(f(\epsilon,\phi),\epsilon)

2)y=diff(f(\epsilon,\phi),\phi)

Now I am solving this fucntion to get \epsilon and \phi such that f(\epsilon,\phi) gives me minima. Condition \epsilon,\phi value should be greater than 0. 

I think my code is in agreement with what I have explained above. Please point out if there is any mistake and how to do that.

 

 

@one man 

I need to have \epsilon value greater than zero. How to give  that command. Basically I have a multivariable function for which i am finding the minima. I found the derivative of that function w.r.t \epsilon and \phi then solving those equation to get \epsilon and \phi such that it gives the minima.

 

@acer 

It works fine. Thanks a lot. Could you please give an idea of finding minima for multivariable function.

@Markiyan Hirnyk 

How can I get root of multivariable function. I mean the global minimum. I am getting the error 'Error, Usage is not a command in the CodeTools package' while using your first line of your above code.

@acer 

How can I do that.

 

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