Ahmed111

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These are questions asked by Ahmed111

how to find CharacteristicPolynomiall of matrix with vector entries? 

restart

with(LinearAlgebra)

with(ArrayTools)

M := Matrix([[-(I*2)*lambda+I*(lambda+m0), c], [-Transpose(c), I*a+I*(lambda+m0)]])

Matrix(%id = 36893490099698106484)

(1)

P := CharacteristicPolynomial(M, eta)

eta^2+(-I*a-(2*I)*m0)*eta+a*lambda-a*m0+c^2+lambda^2-m0^2

(2)

NULL

NULL

NULL

NULL

Download characpol.mw

Maple continuously shows 'Evaluating' and there is no output. How to fix it?

restart

with(LinearAlgebra)

assume(x::real); assume(t::real); assume(`α__1`::real); assume(`α__2`::real); assume(nu::real)

A2s := Matrix([[H__11*exp(I*v__11)/(`λ__1`-conjugate(`λ__1`))+H__13*exp(I*v__21)/(`λ__1`-conjugate(`λ__2`))+1, H__12*exp(-I*v__11)/(`λ__1`-conjugate(`λ__1`))+H__14*exp(-I*v__21)/(`λ__1`-conjugate(`λ__2`)), H__11*exp(I*v__12)/(`λ__2`-conjugate(`λ__1`))+H__13*exp(I*v__22)/(`λ__2`-conjugate(`λ__2`)), H__12*exp(-I*v__12)/(`λ__2`-conjugate(`λ__1`))+H__14*exp(-I*v__22)/(`λ__2`-conjugate(`λ__2`))], [H__12*exp(I*v__11)/(`λ__1`-conjugate(`λ__1`))+H__14*exp(I*v__21)/(`λ__1`-conjugate(`λ__2`)), 1+H__11*exp(-I*v__11)/(`λ__1`-conjugate(`λ__1`))+H__13*exp(-I*v__21)/(`λ__1`-conjugate(`λ__2`)), H__12*exp(I*v__12)/(`λ__2`-conjugate(`λ__1`))+H__14*exp(I*v__22)/(`λ__2`-conjugate(`λ__2`)), H__11*exp(-I*v__12)/(`λ__2`-conjugate(`λ__1`))+H__13*exp(-I*v__22)/(`λ__2`-conjugate(`λ__2`))], [H__13*exp(I*v__11)/(`λ__1`-conjugate(`λ__1`))+H__33*exp(I*v__21)/(`λ__1`-conjugate(`λ__2`)), H__14*exp(-I*v__11)/(`λ__1`-conjugate(`λ__1`))+H__34*exp(-I*v__21)/(`λ__1`-conjugate(`λ__2`)), 1+H__13*exp(I*v__12)/(`λ__2`-conjugate(`λ__1`))+H__33*exp(I*v__22)/(`λ__2`-conjugate(`λ__2`)), H__14*exp(-I*v__12)/(`λ__2`-conjugate(`λ__1`))+H__34*exp(-I*v__22)/(`λ__2`-conjugate(`λ__2`))], [H__14*exp(I*v__11)/(`λ__1`-conjugate(`λ__1`))+H__34*exp(I*v__21)/(`λ__1`-conjugate(`λ__2`)), H__13*exp(-I*v__11)/(`λ__1`-conjugate(`λ__1`))+H__33*exp(-I*v__21)/(`λ__1`-conjugate(`λ__2`)), H__14*exp(I*v__12)/(`λ__2`-conjugate(`λ__1`))+H__34*exp(I*v__22)/(`λ__2`-conjugate(`λ__2`)), H__13*exp(-I*v__12)/(`λ__2`-conjugate(`λ__1`))+H__33*exp(-I*v__22)/(`λ__2`-conjugate(`λ__2`))+1]])

Matrix(%id = 36893490803012390908)

(1)

vvalue := {v__11 = (conjugate(`λ__1`)-`#msub(mi("λ",fontstyle = "normal"),mn("1"))`)*x+(4*`α__1`*(conjugate(`λ__1`)^3-`λ__1`^3)+2*`α__2`*(conjugate(`λ__1`)^2-`λ__1`^2)-8*nu*(conjugate(`λ__1`)^4-`λ__1`^4))*t, v__12 = (conjugate(`λ__1`)-`#msub(mi("λ",fontstyle = "normal"),mn("2"))`)*x+(4*`α__1`*(conjugate(`λ__1`)^3-`λ__2`^3)+2*`α__2`*(conjugate(`λ__1`)^2-`λ__2`^2)-8*nu*(conjugate(`λ__1`)^4-`λ__2`^4))*t, v__21 = (conjugate(`λ__2`)-`#msub(mi("λ",fontstyle = "normal"),mn("1"))`)*x+(4*`α__1`*(conjugate(`λ__2`)^3-`λ__1`^3)+2*`α__2`*(conjugate(`λ__2`)^2-`λ__1`^2)-8*nu*(conjugate(`λ__2`)^4-`λ__1`^4))*t, v__22 = (conjugate(`λ__2`)-`#msub(mi("λ",fontstyle = "normal"),mn("2"))`)*x+(4*`α__1`*(conjugate(`λ__2`)^3-`λ__2`^3)+2*`α__2`*(conjugate(`λ__2`)^2-`λ__2`^2)-8*nu*(conjugate(`λ__2`)^4-`λ__2`^4))*t}

{v__11 = (conjugate(lambda__1)-`#msub(mi("λ",fontstyle = "normal"),mn("1"))`)*x+(4*alpha__1*(conjugate(lambda__1)^3-lambda__1^3)+2*alpha__2*(conjugate(lambda__1)^2-lambda__1^2)-8*nu*(conjugate(lambda__1)^4-lambda__1^4))*t, v__12 = (conjugate(lambda__1)-`#msub(mi("λ",fontstyle = "normal"),mn("2"))`)*x+(4*alpha__1*(conjugate(lambda__1)^3-lambda__2^3)+2*alpha__2*(conjugate(lambda__1)^2-lambda__2^2)-8*nu*(conjugate(lambda__1)^4-lambda__2^4))*t, v__21 = (conjugate(lambda__2)-`#msub(mi("λ",fontstyle = "normal"),mn("1"))`)*x+(4*alpha__1*(conjugate(lambda__2)^3-lambda__1^3)+2*alpha__2*(conjugate(lambda__2)^2-lambda__1^2)-8*nu*(conjugate(lambda__2)^4-lambda__1^4))*t, v__22 = (conjugate(lambda__2)-`#msub(mi("λ",fontstyle = "normal"),mn("2"))`)*x+(4*alpha__1*(conjugate(lambda__2)^3-lambda__2^3)+2*alpha__2*(conjugate(lambda__2)^2-lambda__2^2)-8*nu*(conjugate(lambda__2)^4-lambda__2^4))*t}

(2)

NULL

A2s2 := Determinant(A2s); dets22 := simplify(A2s2, size); length(%)

8949

(3)

dets22f := simplify(subs(vvalue, dets22))

NULL

Download sol1det.mw

please help, thank you!

restart

with(LinearAlgebra)

alias(u = u(x, t), ub = ub(x, t))

u, ub

(1)

``

z1 := (2*I)*u*(2*gamma*lambda^2+alpha*lambda-1/4)*(diff(ub, x))+(2*I)*ub*(-2*gamma*lambda^2+alpha*lambda-1/4)*(diff(u, x))+I*ub*gamma*(diff(u, x, x, x))+Typesetting[delayDotProduct](4*u*gamma, lambda*ub.u.ub, true)+Typesetting[delayDotProduct](4*ub*gamma, lambda*u.ub.u, true)+Typesetting[delayDotProduct]((3*I)*gamma, ub.u.ub.(diff(u, x)), true)+Typesetting[delayDotProduct]((3*I)*gamma, ub.u.(diff(ub, x)).u, true)+Typesetting[delayDotProduct]((3*I)*gamma, ub.(diff(u, x)).ub.u, true)+Typesetting[delayDotProduct]((3*I)*gamma, (diff(ub, x)).u.ub.u, true)+Typesetting[delayDotProduct](I*gamma, (diff(u, x)).(diff(ub, x, x)), true)-Typesetting[delayDotProduct](I*gamma, (diff(ub, x, x)).(diff(u, x)), true)+Typesetting[delayDotProduct](I*gamma, u.(diff(ub, x, x, x)), true)+Typesetting[delayDotProduct](I*gamma, ub.(diff(u, x, x, x)), true)-Typesetting[delayDotProduct]((2*I)*u*gamma, ub.(3*u.(diff(ub, x))-(4*I)*lambda^3), true)+Typesetting[delayDotProduct]((2*I)*ub*gamma, u.(3*ub.(diff(u, x))-(4*I)*lambda^3), true)+(1/2)*Typesetting[delayDotProduct](-4*gamma*lambda-2*alpha, u.(diff(ub, x, x)), true)+(1/2)*Typesetting[delayDotProduct](4*gamma*lambda+2*alpha, ub.(diff(u, x, x)), true)+(1/2)*Typesetting[delayDotProduct](-4*gamma*lambda-2*alpha, (diff(u, x)).(diff(ub, x)), true)+(1/2)*Typesetting[delayDotProduct](4*gamma*lambda+2*alpha, (diff(ub, x)).(diff(u, x)), true)+(1/2)*Typesetting[delayDotProduct](-(8*I)*gamma*lambda^2-(4*I)*alpha*lambda+I, (diff(ub, x)).u, true)+(1/2)*Typesetting[delayDotProduct](-(8*I)*gamma*lambda^2-(4*I)*alpha*lambda+I, ub.(diff(u, x)), true)-ub*(-2*gamma*lambda+alpha)*(diff(u, x, x))+u*(2*gamma*lambda+alpha)*(diff(ub, x, x))+Typesetting[delayDotProduct](2*u, u.ub.u, true)*alpha-Typesetting[delayDotProduct](2*ub, ub.u.ub, true)*alpha-I*u*gamma*(diff(ub, x, x, x)) = 0

(1/2)*(4*gamma*lambda+2*alpha)*((diff(ub, x)).(diff(u, x)))-ub*(-2*gamma*lambda+alpha)*(diff(diff(u, x), x))+u*(2*gamma*lambda+alpha)*(diff(diff(ub, x), x))+(3*I)*gamma*(`.`(ub, diff(u, x), ub, u))+(3*I)*gamma*(`.`(diff(ub, x), u, ub, u))+I*gamma*((diff(u, x)).(diff(diff(ub, x), x)))+I*gamma*(u.(diff(diff(diff(ub, x), x), x)))+(3*I)*gamma*(`.`(ub, u, ub, diff(u, x)))+(3*I)*gamma*(`.`(ub, u, diff(ub, x), u))+4*ub*gamma*(`.`(lambda*u, ub, u))+4*u*gamma*(`.`(lambda*ub, u, ub))+I*gamma*(ub.(diff(diff(diff(u, x), x), x)))+2*u*(`.`(u, ub, u))*alpha-2*ub*(`.`(ub, u, ub))*alpha-I*gamma*((diff(diff(ub, x), x)).(diff(u, x)))+(1/2)*(-4*gamma*lambda-2*alpha)*((diff(u, x)).(diff(ub, x)))+(1/2)*(4*gamma*lambda+2*alpha)*(ub.(diff(diff(u, x), x)))+(1/2)*(-4*gamma*lambda-2*alpha)*(u.(diff(diff(ub, x), x)))+(1/2)*(-(8*I)*gamma*lambda^2-(4*I)*alpha*lambda+I)*(ub.(diff(u, x)))+(2*I)*u*(2*gamma*lambda^2+alpha*lambda-1/4)*(diff(ub, x))+(2*I)*ub*(-2*gamma*lambda^2+alpha*lambda-1/4)*(diff(u, x))-I*u*gamma*(diff(diff(diff(ub, x), x), x))+(2*I)*ub*gamma*(u.(3*(ub.(diff(u, x)))-(4*I)*lambda^3))+I*ub*gamma*(diff(diff(diff(u, x), x), x))-(2*I)*u*gamma*(ub.(3*(u.(diff(ub, x)))-(4*I)*lambda^3))+(1/2)*(-(8*I)*gamma*lambda^2-(4*I)*alpha*lambda+I)*((diff(ub, x)).u) = 0

(2)

Parse:-ConvertTo1D, "first argument to _Inert_ASSIGN must be assignable"

Error, illegal use of an object as a name

"for m from 0 to 5 do  lambda^m:=coeff(lhs(z1),lambda,m)=0;  od;"

 

NULL

Download compare.mw

What kind of solution is it (see (3))? Why is there no solution when I put the initial condition v(0)=C1? Secondly, eq. (2) can be reduced to a first-order differential equation?

restart

interface(showassumed = 0)

declare(v(y))

(1)

q := v(y)*(diff(diff(diff(v(y), y), y), y))+(2*v(y)-(diff(v(y), y)))*(diff(diff(v(y), y), y))+(diff(v(y), y))*(v(y)^3+v(y)-(diff(v(y), y))) = 0

v(y)*(diff(diff(diff(v(y), y), y), y))+(2*v(y)-(diff(v(y), y)))*(diff(diff(v(y), y), y))+(diff(v(y), y))*(v(y)^3+v(y)-(diff(v(y), y))) = 0

(2)

dsolve(q)

v(y) = ODESolStruc(_a, [{(diff(diff(_b(_a), _a), _a))*_b(_a)^2+_b(_a)*((diff(_b(_a), _a))^2*_a+_a^3-(diff(_b(_a), _a))*_b(_a)+2*(diff(_b(_a), _a))*_a-_b(_a)+_a)/_a = 0}, {_a = v(y), _b(_a) = diff(v(y), y)}, {y = Int(1/_b(_a), _a)+_C1, v(y) = _a}])

(3)

NULL

dsolve({q, v(0) = C1})

v(y) = C1

(4)

NULL

Download CD_ode.mw

I try to find the value of the highest peak by using Optimization. But Maple returns an error with the comment "Error, (in Optimization:-NLPSolve) abs is not differentiable at non-real arguments". How to remove it?

plot.mw

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