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salim-barzani 1555 Maple 2024
collect simplification latex
December 13 2024
2 10

I was rejected because the editor said my equation is too long. My question is: Is there a way to rewrite the equation in a more concise form? Additionally, is there a package in Maple that allows for automatic simplification or collection of terms without using specific commands? Any suggestions for addressing this issue would be appreciated.

> 

restart
> 

``
> 

eq3 := -6*lambda*beta[0]^2*alpha[1]^2*a[3]-2*lambda*beta[0]^2*a[5]*alpha[0]+6*mu*beta[0]*alpha[1]^2*a[2]+3*mu*beta[0]*a[5]*alpha[0]^2+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*alpha[0]^3*a[4]+(6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*alpha[0]^2*a[3]+(4*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^2*a[5]*alpha[0]-12*mu^2*alpha[1]^2*a[5]*alpha[0]+(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*alpha[0]*a[2]-(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*k^2*a[1]*alpha[1]^2+(1/2)*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*lambda*a[1]+(5*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^4*alpha[0]*a[4]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*lambda*a[5]*alpha[0]-k^2*a[1]*beta[0]^2+10*beta[0]^2*alpha[0]^3*a[4]+6*beta[0]^2*alpha[0]^2*a[3]+3*beta[0]^2*alpha[0]*a[2]-(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*w*alpha[1]^2-(1/4)*lambda*beta[0]^2*a[1]-9*mu^2*alpha[1]^2*a[1]*(1/4)+3*mu*a[1]*alpha[0]*beta[0]*(1/2)+(1/4)*(3*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^2*a[1]+(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2)*alpha[1]^4*a[3]-w*beta[0]^2-30*lambda*beta[0]^2*alpha[1]^2*alpha[0]*a[4]-20*mu*beta[0]*lambda*alpha[1]^4*a[4]-7*mu*beta[0]*lambda*a[5]*alpha[1]^2+24*mu*beta[0]*alpha[1]^2*alpha[0]*a[3]+60*mu*beta[0]*alpha[1]^2*alpha[0]^2*a[4] = 0

-k^2*a[1]*beta[0]^2+4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*lambda*a[5]*alpha[0]-30*lambda*beta[0]^2*alpha[1]^2*alpha[0]*a[4]-20*mu*beta[0]*lambda*alpha[1]^4*a[4]+60*mu*beta[0]*alpha[1]^2*alpha[0]^2*a[4]-7*mu*beta[0]*lambda*a[5]*alpha[1]^2+24*mu*beta[0]*alpha[1]^2*alpha[0]*a[3]-w*beta[0]^2-(9/4)*mu^2*alpha[1]^2*a[1]+6*beta[0]^2*alpha[0]^2*a[3]-(1/4)*lambda*beta[0]^2*a[1]+3*beta[0]^2*alpha[0]*a[2]+(3/4)*(-2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*lambda+4*mu^2)*alpha[1]^2*a[1]-(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*w*alpha[1]^2+10*beta[0]^2*alpha[0]^3*a[4]+(-2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*lambda+4*mu^2)*alpha[1]^4*a[3]+6*mu*beta[0]*alpha[1]^2*a[2]+3*mu*beta[0]*a[5]*alpha[0]^2+(3/2)*mu*a[1]*alpha[0]*beta[0]-6*lambda*beta[0]^2*alpha[1]^2*a[3]-2*lambda*beta[0]^2*a[5]*alpha[0]-12*mu^2*alpha[1]^2*a[5]*alpha[0]+3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*alpha[0]*a[2]-(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*k^2*a[1]*alpha[1]^2+(1/2)*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*lambda*a[1]+5*(-2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*lambda+4*mu^2)*alpha[1]^4*alpha[0]*a[4]+10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*alpha[0]^3*a[4]+6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*alpha[0]^2*a[3]+4*(-2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*lambda+4*mu^2)*alpha[1]^2*a[5]*alpha[0] = 0

 (1)
> 

numer(lhs(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*alpha[0]*a[2]+5*(-2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*lambda+4*mu^2)*alpha[1]^4*alpha[0]*a[4]+10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*alpha[0]^3*a[4]+6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*alpha[0]^2*a[3]+4*(-2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*lambda+4*mu^2)*alpha[1]^2*a[5]*alpha[0]-6*lambda*beta[0]^2*alpha[1]^2*a[3]-2*lambda*beta[0]^2*a[5]*alpha[0]+6*mu*beta[0]*alpha[1]^2*a[2]+3*mu*beta[0]*a[5]*alpha[0]^2+(3/2)*mu*a[1]*alpha[0]*beta[0]-12*mu^2*alpha[1]^2*a[5]*alpha[0]-(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*k^2*a[1]*alpha[1]^2+(1/2)*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*lambda*a[1]-w*beta[0]^2+4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*lambda*a[5]*alpha[0]-30*lambda*beta[0]^2*alpha[1]^2*alpha[0]*a[4]-20*mu*beta[0]*lambda*alpha[1]^4*a[4]-7*mu*beta[0]*lambda*a[5]*alpha[1]^2+24*mu*beta[0]*alpha[1]^2*alpha[0]*a[3]+60*mu*beta[0]*alpha[1]^2*alpha[0]^2*a[4]+(-2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*lambda+4*mu^2)*alpha[1]^4*a[3]+(3/4)*(-2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*lambda+4*mu^2)*alpha[1]^2*a[1]-k^2*a[1]*beta[0]^2+10*beta[0]^2*alpha[0]^3*a[4]+6*beta[0]^2*alpha[0]^2*a[3]+3*beta[0]^2*alpha[0]*a[2]-(9/4)*mu^2*alpha[1]^2*a[1]-(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*w*alpha[1]^2-(1/4)*lambda*beta[0]^2*a[1] = 0))*denom(rhs(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*alpha[0]*a[2]+5*(-2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*lambda+4*mu^2)*alpha[1]^4*alpha[0]*a[4]+10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*alpha[0]^3*a[4]+6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*alpha[0]^2*a[3]+4*(-2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*lambda+4*mu^2)*alpha[1]^2*a[5]*alpha[0]-6*lambda*beta[0]^2*alpha[1]^2*a[3]-2*lambda*beta[0]^2*a[5]*alpha[0]+6*mu*beta[0]*alpha[1]^2*a[2]+3*mu*beta[0]*a[5]*alpha[0]^2+(3/2)*mu*a[1]*alpha[0]*beta[0]-12*mu^2*alpha[1]^2*a[5]*alpha[0]-(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*k^2*a[1]*alpha[1]^2+(1/2)*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*lambda*a[1]-w*beta[0]^2+4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*lambda*a[5]*alpha[0]-30*lambda*beta[0]^2*alpha[1]^2*alpha[0]*a[4]-20*mu*beta[0]*lambda*alpha[1]^4*a[4]-7*mu*beta[0]*lambda*a[5]*alpha[1]^2+24*mu*beta[0]*alpha[1]^2*alpha[0]*a[3]+60*mu*beta[0]*alpha[1]^2*alpha[0]^2*a[4]+(-2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*lambda+4*mu^2)*alpha[1]^4*a[3]+(3/4)*(-2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*lambda+4*mu^2)*alpha[1]^2*a[1]-k^2*a[1]*beta[0]^2+10*beta[0]^2*alpha[0]^3*a[4]+6*beta[0]^2*alpha[0]^2*a[3]+3*beta[0]^2*alpha[0]*a[2]-(9/4)*mu^2*alpha[1]^2*a[1]-(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*w*alpha[1]^2-(1/4)*lambda*beta[0]^2*a[1] = 0)) = numer(rhs(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*alpha[0]*a[2]+5*(-2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*lambda+4*mu^2)*alpha[1]^4*alpha[0]*a[4]+10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*alpha[0]^3*a[4]+6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*alpha[0]^2*a[3]+4*(-2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*lambda+4*mu^2)*alpha[1]^2*a[5]*alpha[0]-6*lambda*beta[0]^2*alpha[1]^2*a[3]-2*lambda*beta[0]^2*a[5]*alpha[0]+6*mu*beta[0]*alpha[1]^2*a[2]+3*mu*beta[0]*a[5]*alpha[0]^2+(3/2)*mu*a[1]*alpha[0]*beta[0]-12*mu^2*alpha[1]^2*a[5]*alpha[0]-(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*k^2*a[1]*alpha[1]^2+(1/2)*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*lambda*a[1]-w*beta[0]^2+4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*lambda*a[5]*alpha[0]-30*lambda*beta[0]^2*alpha[1]^2*alpha[0]*a[4]-20*mu*beta[0]*lambda*alpha[1]^4*a[4]-7*mu*beta[0]*lambda*a[5]*alpha[1]^2+24*mu*beta[0]*alpha[1]^2*alpha[0]*a[3]+60*mu*beta[0]*alpha[1]^2*alpha[0]^2*a[4]+(-2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*lambda+4*mu^2)*alpha[1]^4*a[3]+(3/4)*(-2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*lambda+4*mu^2)*alpha[1]^2*a[1]-k^2*a[1]*beta[0]^2+10*beta[0]^2*alpha[0]^3*a[4]+6*beta[0]^2*alpha[0]^2*a[3]+3*beta[0]^2*alpha[0]*a[2]-(9/4)*mu^2*alpha[1]^2*a[1]-(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*w*alpha[1]^2-(1/4)*lambda*beta[0]^2*a[1] = 0))*denom(lhs(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*alpha[0]*a[2]+5*(-2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*lambda+4*mu^2)*alpha[1]^4*alpha[0]*a[4]+10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*alpha[0]^3*a[4]+6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*alpha[0]^2*a[3]+4*(-2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*lambda+4*mu^2)*alpha[1]^2*a[5]*alpha[0]-6*lambda*beta[0]^2*alpha[1]^2*a[3]-2*lambda*beta[0]^2*a[5]*alpha[0]+6*mu*beta[0]*alpha[1]^2*a[2]+3*mu*beta[0]*a[5]*alpha[0]^2+(3/2)*mu*a[1]*alpha[0]*beta[0]-12*mu^2*alpha[1]^2*a[5]*alpha[0]-(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*k^2*a[1]*alpha[1]^2+(1/2)*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*lambda*a[1]-w*beta[0]^2+4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*lambda*a[5]*alpha[0]-30*lambda*beta[0]^2*alpha[1]^2*alpha[0]*a[4]-20*mu*beta[0]*lambda*alpha[1]^4*a[4]-7*mu*beta[0]*lambda*a[5]*alpha[1]^2+24*mu*beta[0]*alpha[1]^2*alpha[0]*a[3]+60*mu*beta[0]*alpha[1]^2*alpha[0]^2*a[4]+(-2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*lambda+4*mu^2)*alpha[1]^4*a[3]+(3/4)*(-2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*lambda+4*mu^2)*alpha[1]^2*a[1]-k^2*a[1]*beta[0]^2+10*beta[0]^2*alpha[0]^3*a[4]+6*beta[0]^2*alpha[0]^2*a[3]+3*beta[0]^2*alpha[0]*a[2]-(9/4)*mu^2*alpha[1]^2*a[1]-(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*w*alpha[1]^2-(1/4)*lambda*beta[0]^2*a[1] = 0))

-40*lambda^3*B[1]^2*a[4]*alpha[0]*alpha[1]^4+40*lambda^3*B[2]^2*a[4]*alpha[0]*alpha[1]^4-8*lambda^3*B[1]^2*a[3]*alpha[1]^4+8*lambda^3*B[2]^2*a[3]*alpha[1]^4+40*lambda^2*B[1]^2*a[4]*alpha[0]^3*alpha[1]^2-40*lambda^2*B[2]^2*a[4]*alpha[0]^3*alpha[1]^2-4*k^2*lambda^2*B[1]^2*a[1]*alpha[1]^2+4*k^2*lambda^2*B[2]^2*a[1]*alpha[1]^2-16*lambda^3*B[1]^2*a[5]*alpha[0]*alpha[1]^2+16*lambda^3*B[2]^2*a[5]*alpha[0]*alpha[1]^2-80*lambda^2*mu*a[4]*alpha[1]^4*beta[0]+24*lambda^2*B[1]^2*a[3]*alpha[0]^2*alpha[1]^2-24*lambda^2*B[2]^2*a[3]*alpha[0]^2*alpha[1]^2+120*lambda*mu^2*a[4]*alpha[0]*alpha[1]^4-4*lambda^3*B[1]^2*a[1]*alpha[1]^2+4*lambda^3*B[2]^2*a[1]*alpha[1]^2+12*lambda^2*B[1]^2*a[2]*alpha[0]*alpha[1]^2-12*lambda^2*B[2]^2*a[2]*alpha[0]*alpha[1]^2-120*lambda^2*a[4]*alpha[0]*alpha[1]^2*beta[0]^2+24*lambda*mu^2*a[3]*alpha[1]^4+240*lambda*mu*a[4]*alpha[0]^2*alpha[1]^2*beta[0]-40*mu^2*a[4]*alpha[0]^3*alpha[1]^2+4*k^2*mu^2*a[1]*alpha[1]^2-28*lambda^2*mu*a[5]*alpha[1]^2*beta[0]-4*lambda^2*w*B[1]^2*alpha[1]^2+4*lambda^2*w*B[2]^2*alpha[1]^2-24*lambda^2*a[3]*alpha[1]^2*beta[0]^2+32*lambda*mu^2*a[5]*alpha[0]*alpha[1]^2+96*lambda*mu*a[3]*alpha[0]*alpha[1]^2*beta[0]+40*lambda*a[4]*alpha[0]^3*beta[0]^2-24*mu^2*a[3]*alpha[0]^2*alpha[1]^2-4*k^2*lambda*a[1]*beta[0]^2-8*lambda^2*a[5]*alpha[0]*beta[0]^2+7*lambda*mu^2*a[1]*alpha[1]^2+24*lambda*mu*a[2]*alpha[1]^2*beta[0]+12*lambda*mu*a[5]*alpha[0]^2*beta[0]+24*lambda*a[3]*alpha[0]^2*beta[0]^2-12*mu^2*a[2]*alpha[0]*alpha[1]^2-lambda^2*a[1]*beta[0]^2+6*lambda*mu*a[1]*alpha[0]*beta[0]+12*lambda*a[2]*alpha[0]*beta[0]^2+4*mu^2*w*alpha[1]^2-4*lambda*w*beta[0]^2 = 0

 (2)
> 

simplify(-40*lambda^3*B[1]^2*a[4]*alpha[0]*alpha[1]^4+40*lambda^3*B[2]^2*a[4]*alpha[0]*alpha[1]^4-8*lambda^3*B[1]^2*a[3]*alpha[1]^4+8*lambda^3*B[2]^2*a[3]*alpha[1]^4+40*lambda^2*B[1]^2*a[4]*alpha[0]^3*alpha[1]^2-40*lambda^2*B[2]^2*a[4]*alpha[0]^3*alpha[1]^2-4*k^2*lambda^2*B[1]^2*a[1]*alpha[1]^2+4*k^2*lambda^2*B[2]^2*a[1]*alpha[1]^2-16*lambda^3*B[1]^2*a[5]*alpha[0]*alpha[1]^2+16*lambda^3*B[2]^2*a[5]*alpha[0]*alpha[1]^2-80*lambda^2*mu*a[4]*alpha[1]^4*beta[0]+24*lambda^2*B[1]^2*a[3]*alpha[0]^2*alpha[1]^2-24*lambda^2*B[2]^2*a[3]*alpha[0]^2*alpha[1]^2+120*lambda*mu^2*a[4]*alpha[0]*alpha[1]^4-4*lambda^3*B[1]^2*a[1]*alpha[1]^2+4*lambda^3*B[2]^2*a[1]*alpha[1]^2+12*lambda^2*B[1]^2*a[2]*alpha[0]*alpha[1]^2-12*lambda^2*B[2]^2*a[2]*alpha[0]*alpha[1]^2-120*lambda^2*a[4]*alpha[0]*alpha[1]^2*beta[0]^2+24*lambda*mu^2*a[3]*alpha[1]^4+240*lambda*mu*a[4]*alpha[0]^2*alpha[1]^2*beta[0]-40*mu^2*a[4]*alpha[0]^3*alpha[1]^2+4*k^2*mu^2*a[1]*alpha[1]^2-28*lambda^2*mu*a[5]*alpha[1]^2*beta[0]-4*lambda^2*w*B[1]^2*alpha[1]^2+4*lambda^2*w*B[2]^2*alpha[1]^2-24*lambda^2*a[3]*alpha[1]^2*beta[0]^2+32*lambda*mu^2*a[5]*alpha[0]*alpha[1]^2+96*lambda*mu*a[3]*alpha[0]*alpha[1]^2*beta[0]+40*lambda*a[4]*alpha[0]^3*beta[0]^2-24*mu^2*a[3]*alpha[0]^2*alpha[1]^2-4*k^2*lambda*a[1]*beta[0]^2-8*lambda^2*a[5]*alpha[0]*beta[0]^2+7*lambda*mu^2*a[1]*alpha[1]^2+24*lambda*mu*a[2]*alpha[1]^2*beta[0]+12*lambda*mu*a[5]*alpha[0]^2*beta[0]+24*lambda*a[3]*alpha[0]^2*beta[0]^2-12*mu^2*a[2]*alpha[0]*alpha[1]^2-lambda^2*a[1]*beta[0]^2+6*lambda*mu*a[1]*alpha[0]*beta[0]+12*lambda*a[2]*alpha[0]*beta[0]^2+4*mu^2*w*alpha[1]^2-4*lambda*w*beta[0]^2 = 0, 'symbolic')

-40*(B[1]-B[2])*((a[4]*alpha[0]+(1/5)*a[3])*alpha[1]^2+(2/5)*a[5]*alpha[0]+(1/10)*a[1])*alpha[1]^2*(B[1]+B[2])*lambda^3+4*(-20*a[4]*beta[0]*alpha[1]^4*mu+(10*(B[1]^2-B[2]^2)*a[4]*alpha[0]^3+6*a[3]*(B[1]^2-B[2]^2)*alpha[0]^2+3*(B[1]^2*a[2]-B[2]^2*a[2]-10*a[4]*beta[0]^2)*alpha[0]-6*beta[0]^2*a[3]-7*a[5]*beta[0]*mu-(B[1]-B[2])*(B[1]+B[2])*(k^2*a[1]+w))*alpha[1]^2-2*(a[5]*alpha[0]+(1/8)*a[1])*beta[0]^2)*lambda^2+(120*(a[4]*alpha[0]+(1/5)*a[3])*mu^2*alpha[1]^4+(240*a[4]*beta[0]*alpha[0]^2*mu+32*(mu^2*a[5]+3*mu*a[3]*beta[0])*alpha[0]+24*beta[0]*mu*a[2]+7*mu^2*a[1])*alpha[1]^2-4*(-10*a[4]*beta[0]*alpha[0]^3+3*(-mu*a[5]-2*a[3]*beta[0])*alpha[0]^2+3*(-beta[0]*a[2]-(1/2)*mu*a[1])*alpha[0]+beta[0]*(k^2*a[1]+w))*beta[0])*lambda+4*alpha[1]^2*mu^2*(-10*a[4]*alpha[0]^3+k^2*a[1]-6*a[3]*alpha[0]^2-3*a[2]*alpha[0]+w) = 0

  

 

 

Error, (in collect) invalid input: collect uses a 2nd argument, x, which is missing

  
> 

Q1 := collect(%, {B__1, B__2})

-40*(B[1]-B[2])*((a[4]*alpha[0]+(1/5)*a[3])*alpha[1]^2+(2/5)*a[5]*alpha[0]+(1/10)*a[1])*alpha[1]^2*(B[1]+B[2])*lambda^3+4*(-20*a[4]*beta[0]*alpha[1]^4*mu+(10*(B[1]^2-B[2]^2)*a[4]*alpha[0]^3+6*a[3]*(B[1]^2-B[2]^2)*alpha[0]^2+3*(B[1]^2*a[2]-B[2]^2*a[2]-10*a[4]*beta[0]^2)*alpha[0]-6*beta[0]^2*a[3]-7*a[5]*beta[0]*mu-(B[1]-B[2])*(B[1]+B[2])*(k^2*a[1]+w))*alpha[1]^2-2*(a[5]*alpha[0]+(1/8)*a[1])*beta[0]^2)*lambda^2+(120*(a[4]*alpha[0]+(1/5)*a[3])*mu^2*alpha[1]^4+(240*a[4]*beta[0]*alpha[0]^2*mu+32*(mu^2*a[5]+3*mu*a[3]*beta[0])*alpha[0]+24*beta[0]*mu*a[2]+7*mu^2*a[1])*alpha[1]^2-4*(-10*a[4]*beta[0]*alpha[0]^3+3*(-mu*a[5]-2*a[3]*beta[0])*alpha[0]^2+3*(-beta[0]*a[2]-(1/2)*mu*a[1])*alpha[0]+beta[0]*(k^2*a[1]+w))*beta[0])*lambda+4*alpha[1]^2*mu^2*(-10*a[4]*alpha[0]^3+k^2*a[1]-6*a[3]*alpha[0]^2-3*a[2]*alpha[0]+w) = 0

 (3)
> 

latex(Q1)

-40 \left(B_{1}-B_{2}\right) \left(\left(a_{4} \alpha_{0}+\frac{a_{3}}{5}\right) \alpha_{1}^{2}+\frac{2 a_{5} \alpha_{0}}{5}+\frac{a_{1}}{10}\right) \alpha_{1}^{2} \left(B_{1}+B_{2}\right) \lambda^{3}+4 \left(-20 a_{4} \beta_{0} \alpha_{1}^{4} \mu +\left(10 \left(B_{1}^{2}-B_{2}^{2}\right) a_{4} \alpha_{0}^{3}+6 a_{3} \left(B_{1}^{2}-B_{2}^{2}\right) \alpha_{0}^{2}+3 \left(B_{1}^{2} a_{2}-B_{2}^{2} a_{2}-10 a_{4} \beta_{0}^{2}\right) \alpha_{0}-6 \beta_{0}^{2} a_{3}-7 a_{5} \beta_{0} \mu -\left(B_{1}-B_{2}\right) \left(B_{1}+B_{2}\right) \left(k^{2} a_{1}+w \right)\right) \alpha_{1}^{2}-2 \left(a_{5} \alpha_{0}+\frac{a_{1}}{8}\right) \beta_{0}^{2}\right) \lambda^{2}+\left(120 \left(a_{4} \alpha_{0}+\frac{a_{3}}{5}\right) \mu^{2} \alpha_{1}^{4}+\left(240 a_{4} \beta_{0} \alpha_{0}^{2} \mu +32 \left(\mu^{2} a_{5}+3 \mu  a_{3} \beta_{0}\right) \alpha_{0}+24 \beta_{0} \mu  a_{2}+7 \mu^{2} a_{1}\right) \alpha_{1}^{2}-4 \left(-10 a_{4} \beta_{0} \alpha_{0}^{3}+3 \left(-\mu  a_{5}-2 a_{3} \beta_{0}\right) \alpha_{0}^{2}+3 \left(-\beta_{0} a_{2}-\frac{\mu  a_{1}}{2}\right) \alpha_{0}+\beta_{0} \left(k^{2} a_{1}+w \right)\right) \beta_{0}\right) \lambda +4 \alpha_{1}^{2} \mu^{2} \left(-10 a_{4} \alpha_{0}^{3}+k^{2} a_{1}-6 a_{3} \alpha_{0}^{2}-3 a_{2} \alpha_{0}+w \right)
 = 0

  
 

NULL

Download coment.mw

Techniques for Simplifying Differential ...

salim-barzani 1555 Maple 2024
pde differential-equations
December 11 2024
0 0

I'm trying to transform a partial differential equation (PDE) into an ordinary differential equation (ODE) as demonstrated in the paper. However, I find some steps confusing and difficult to follow. The process often feels chaotic, and managing the complexity of the equations is overwhelming. Could you suggest an effective and systematic method to handle such transformations more easily?

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

NULL
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

declare(Omega(x, t)); declare(U(xi))

Omega(x, t)*`will now be displayed as`*Omega

  

U(xi)*`will now be displayed as`*U

 (2)
> 

tr := {t = tau, x = tau*c[0]+xi, Omega(x, t) = U(xi)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau))}

{t = tau, x = tau*c[0]+xi, Omega(x, t) = U(xi)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau))}

 (3)
> 

P1 := diff(Omega(x, t)^m, t)

Omega(x, t)^m*m*(diff(Omega(x, t), t))/Omega(x, t)

 (4)
> 

L1 := PDEtools:-dchange(tr, P1, [xi, tau, U])

(U(xi)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))^m*m*(-((diff(U(xi), xi))*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau))-I*U(xi)*k*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))*c[0]+I*U(xi)*(-k*c[0]+w+delta*(diff(W(tau), tau))-delta^2)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))/(U(xi)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))

 (5)
 
> 

pde1 := I*(diff(Omega(x, t)^m, t))+alpha*(diff(Omega(x, t)^m, `$`(x, 2)))+I*beta*(diff(abs(Omega(x, t))^(2*n)*Omega(x, t)^m, x))+m*sigma*Omega(x, t)^m*(diff(W(t), t)) = I*gamma*abs(Omega(x, t))^(2*n)*(diff(Omega(x, t)^m, x))+delta*abs(Omega(x, t))^(4*n)*Omega(x, t)^m

I*Omega(x, t)^m*m*(diff(Omega(x, t), t))/Omega(x, t)+alpha*(Omega(x, t)^m*m^2*(diff(Omega(x, t), x))^2/Omega(x, t)^2+Omega(x, t)^m*m*(diff(diff(Omega(x, t), x), x))/Omega(x, t)-Omega(x, t)^m*m*(diff(Omega(x, t), x))^2/Omega(x, t)^2)+I*beta*(2*abs(Omega(x, t))^(2*n)*n*(diff(Omega(x, t), x))*abs(1, Omega(x, t))*Omega(x, t)^m/abs(Omega(x, t))+abs(Omega(x, t))^(2*n)*Omega(x, t)^m*m*(diff(Omega(x, t), x))/Omega(x, t))+m*sigma*Omega(x, t)^m*(diff(W(t), t)) = I*gamma*abs(Omega(x, t))^(2*n)*Omega(x, t)^m*m*(diff(Omega(x, t), x))/Omega(x, t)+delta*abs(Omega(x, t))^(4*n)*Omega(x, t)^m

 (6)
> 

NULL
> 

L1 := PDEtools:-dchange(tr, pde1, [xi, tau, U])

I*(U(xi)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))^m*m*(-((diff(U(xi), xi))*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau))-I*U(xi)*k*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))*c[0]+I*U(xi)*(-k*c[0]+w+delta*(diff(W(tau), tau))-delta^2)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))/(U(xi)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))+alpha*((U(xi)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))^m*m^2*((diff(U(xi), xi))*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau))-I*U(xi)*k*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))^2/(U(xi)^2*(exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))^2)+(U(xi)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))^m*m*((diff(diff(U(xi), xi), xi))*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau))-(2*I)*(diff(U(xi), xi))*k*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau))-U(xi)*k^2*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))/(U(xi)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))-(U(xi)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))^m*m*((diff(U(xi), xi))*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau))-I*U(xi)*k*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))^2/(U(xi)^2*(exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))^2))+I*beta*(2*(abs(U(xi))*exp(-Im(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))^(2*n)*n*((diff(U(xi), xi))*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau))-I*U(xi)*k*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))*abs(1, U(xi)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))*(U(xi)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))^m/(abs(U(xi))*exp(-Im(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))+(abs(U(xi))*exp(-Im(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))^(2*n)*(U(xi)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))^m*m*((diff(U(xi), xi))*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau))-I*U(xi)*k*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))/(U(xi)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau))))+m*sigma*(U(xi)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))^m*(diff(W(tau), tau)) = I*gamma*(abs(U(xi))*exp(-Im(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))^(2*n)*(U(xi)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))^m*m*((diff(U(xi), xi))*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau))-I*U(xi)*k*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))/(U(xi)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))+delta*(abs(U(xi))*exp(-Im(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))^(4*n)*(U(xi)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau)))^m

 (7)
> 

``

``

 (8)

Download transform-pde-to-ode-hard_example.mw

How to Derive a System of Equations from...

salim-barzani 1555 Maple 2024
pde differential-equations pdetest
December 11 2024
1 1

Is there a way to determine how we can construct a system of equations from this complex PDE? Also, moderator, you mentioned I could create a new question using the branch option, but you deleted my previous question, which led me to delete my earlier post. don't delete this one.

Download PDE-Hard.mw

How this ODE will be zero-the result in ...

salim-barzani 1555 Maple 2024
ode homework differential-equations
December 11 2024
1 3

this equation will be solve by changing variable but when  i found the function and substitute the ODE is not zero where  is mistake?

> 

restart
> 

with(PDEtools); _local(gamma)

Warning, A new binding for the name `gamma` has been created. The global instance of this name is still accessible using the :- prefix, :-`gamma`.  See ?protect for details.

  
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

declare(phi(x, t)); declare(psi(x, t)); declare(U(xi))

phi(x, t)*`will now be displayed as`*phi

  

psi(x, t)*`will now be displayed as`*psi

  

U(xi)*`will now be displayed as`*U

 (2)
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

NULL
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (3)
> 

ode := (diff(diff(U(xi), xi), xi))*lambda^2+(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*lambda*k^3-6*(diff(diff(U(xi), xi), xi))*k^2*(diff(U(xi), xi))*lambda = 0

(diff(diff(U(xi), xi), xi))*lambda^2+(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*lambda*k^3-6*(diff(diff(U(xi), xi), xi))*k^2*(diff(U(xi), xi))*lambda = 0

 (4)
> 

W := diff(U(xi), xi) = T(xi)

diff(U(xi), xi) = T(xi)

 (5)
> 

ode1 := lambda^2*T(xi)+lambda*k^3*(diff(diff(T(xi), xi), xi))-3*k^2*lambda*T(xi)^2 = 0

lambda^2*T(xi)+lambda*k^3*(diff(diff(T(xi), xi), xi))-3*k^2*lambda*T(xi)^2 = 0

 (6)
> 

K := T(xi) = A[0]+A[1]*(exp(2*xi)-1)/(exp(2*xi)+1)+A[2]*(exp(2*xi)-1)^2/(exp(2*xi)+1)^2+B[1]*(exp(2*xi)+1)/(exp(2*xi)-1)+B[2]*(exp(2*xi)+1)/(exp(2*xi)-1)

T(xi) = A[0]+A[1]*(exp(2*xi)-1)/(exp(2*xi)+1)+A[2]*(exp(2*xi)-1)^2/(exp(2*xi)+1)^2+B[1]*(exp(2*xi)+1)/(exp(2*xi)-1)+B[2]*(exp(2*xi)+1)/(exp(2*xi)-1)

 (7)
> 

case1 := [k = (1/2)*A[2], lambda = -(1/2)*A[2]^3, A[0] = -A[2], A[1] = 0, A[2] = A[2], B[1] = -B[2], B[2] = B[2]]

[k = (1/2)*A[2], lambda = -(1/2)*A[2]^3, A[0] = -A[2], A[1] = 0, A[2] = A[2], B[1] = -B[2], B[2] = B[2]]

 (8)
> 

F1 := subs(case1, K)

T(xi) = -A[2]+A[2]*(exp(2*xi)-1)^2/(exp(2*xi)+1)^2

 (9)
> 

F2 := subs(case1, ode1)

(1/4)*A[2]^6*T(xi)-(1/16)*A[2]^6*(diff(diff(T(xi), xi), xi))+(3/8)*A[2]^5*T(xi)^2 = 0

 (10)
> 

odetest(F1, F2)

0

 (11)
> 

subs(F1, W)

diff(U(xi), xi) = -A[2]+A[2]*(exp(2*xi)-1)^2/(exp(2*xi)+1)^2

 (12)
> 

E := map(int, diff(U(xi), xi) = -A[2]+A[2]*(exp(2*xi)-1)^2/(exp(2*xi)+1)^2, xi)

U(xi) = A[2]*((1/2)*ln(exp(2*xi))+2/(exp(2*xi)+1))-A[2]*xi

 (13)
> 

odetest(E, ode)

32*A[2]*exp(8*xi)*lambda*k^3/(exp(2*xi)+1)^5-352*A[2]*exp(6*xi)*lambda*k^3/(exp(2*xi)+1)^5+192*A[2]^2*exp(6*xi)*lambda*k^2/(exp(2*xi)+1)^5+8*A[2]*exp(8*xi)*lambda^2/(exp(2*xi)+1)^5+352*A[2]*exp(4*xi)*lambda*k^3/(exp(2*xi)+1)^5-192*A[2]^2*exp(4*xi)*lambda*k^2/(exp(2*xi)+1)^5+8*A[2]*exp(6*xi)*lambda^2/(exp(2*xi)+1)^5-32*A[2]*exp(2*xi)*lambda*k^3/(exp(2*xi)+1)^5-8*A[2]*exp(4*xi)*lambda^2/(exp(2*xi)+1)^5-8*A[2]*exp(2*xi)*lambda^2/(exp(2*xi)+1)^5

 (14)
 

NULL

Download problem.mw

Apply Bilinear form for some PDE...

salim-barzani 1555 Maple 2024
pde differential-equations incomplete-question
December 03 2024
0 1

I try to get some Bilinear form for some PDE equation  and already i have algorithm by writing in lecture but i can't apply i don't what is mistake i did, and i didn't seen some of this lecture code in maple  like (myint(expr,var))
 i  do upload PIcture of algorithm and example which they get Bilinear form 

Bilinear.mw

thanks for any help

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