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mz6687

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2 years, 242 days
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These are questions asked by mz6687

Why is Maple not calculating 'sqrt' ?...

mz6687 40 Maple 2022
sqrt
September 03 2023
1 0

Why is Maple not calculating 'sqrt' and continuously showing 'Evaluating'?


 

> 

restart
> 

with(LinearAlgebra); with(PDEtools); with(DifferentialGeometry)
> 

with(plots)
> 

with(Physics)
> 

q := (31.00000000*exp(-4.976*t+2.*x)*exp((-2.488+.8336000001*I)*t+(1.+.2*I)*x)-3.000000000*exp(-4.976*t+2.*x)*exp((2.488+.8336000001*I)*t+(-1.+.2*I)*x)+(94.0*I)*exp(I*(.8336*t+.2000*x))*exp(-4.976*t+2.*x))/((11.50000000*I)*exp(-2.488*t+x)+132.44*exp(-4.976*t+2.*x)-(104.5000000*I)*exp(-7.464*t+3.*x)-5.25*exp(-9.952*t+4.*x)+.25)

(31.00000000*exp(-4.976*t+2.*x)*exp((-2.488+.8336000001*I)*t+(1.+.2*I)*x)-3.000000000*exp(-4.976*t+2.*x)*exp((2.488+.8336000001*I)*t+(-1.+.2*I)*x)+(94.0*I)*exp(I*(.8336*t+.2000*x))*exp(-4.976*t+2.*x))/((11.50000000*I)*exp(-2.488*t+x)+132.44*exp(-4.976*t+2.*x)-(104.5000000*I)*exp(-7.464*t+3.*x)-5.25*exp(-9.952*t+4.*x)+.25)

 (1)
> 

assume(x::real); assume(t::real)
> 

q1 := simplify(subs({I = -I}, q))

(-(94.*I)*exp(-I*(.8336*t+.2000*x))+31.*exp((-2.488-.8336000001*I)*t+(1.-.2*I)*x)-3.*exp((2.488-.8336000001*I)*t+(-1.-.2*I)*x))*exp(-4.976*t+2.*x)/(-(11.50000000*I)*exp(-2.488*t+x)+132.44*exp(-4.976*t+2.*x)+(104.5000000*I)*exp(-7.464*t+3.*x)-5.25*exp(-9.952*t+4.*x)+.25)

 (2)
> 

q2 := simplify(sqrt(q*q1))
> 

NULL

NULL


 

Download q_sqrt.mw

Error, invalid if statement termination...

mz6687 40 Maple 2022
optimization syntax if-then
February 06 2023
2 5

Why there is an error? Is any part missing in the if statement?

> 

restart
> 

rel := w+(1/2)*sqrt(960*c^6*gamma^2*k^2-336*c^4*gamma^2*k^4+64*c^2*gamma^2*k^6-4*gamma^2*k^8+576*alpha*c^6*gamma*k-288*alpha*c^4*gamma*k^3-16*alpha*c^2*gamma*k^5+8*alpha*gamma*k^7-144*alpha^2*c^4*k^2-48*alpha^2*c^2*k^4-4*alpha^2*k^6+128*c^4*gamma*k^2-40*c^2*gamma*k^4+4*gamma*k^6+48*alpha*c^4*k-16*alpha*c^2*k^3-4*alpha*k^5+4*c^2*k^2-k^4)

w+(1/2)*(960*c^6*gamma^2*k^2-336*c^4*gamma^2*k^4+64*c^2*gamma^2*k^6-4*gamma^2*k^8+576*alpha*c^6*gamma*k-288*alpha*c^4*gamma*k^3-16*alpha*c^2*gamma*k^5+8*alpha*gamma*k^7-144*alpha^2*c^4*k^2-48*alpha^2*c^2*k^4-4*alpha^2*k^6+128*c^4*gamma*k^2-40*c^2*gamma*k^4+4*gamma*k^6+48*alpha*c^4*k-16*alpha*c^2*k^3-4*alpha*k^5+4*c^2*k^2-k^4)^(1/2)

 (1)
> 

crit_points := solve(diff(rel, k) = 0, k); rel_at_crit := subs(k = crit_points, rel)
> 

"#` determine the maxima and minima by checking the sign of the second derivative at the critical points` for i from 1 to nops(crit_points) do if (eval(diff(diff(rel, k), k), k = crit_points[i]) > 0) then print("Minimum at k = ", crit_points[i], " with value ", rel_at_crit[i]); else if (eval(diff(diff(rel, k), k), k = crit_points[i]) < 0) then print("Maximum at k = ", crit_points[i], " with value ", rel_at_crit[i]); else print("Saddle point at k = ", crit_points[i], " with value ", rel_at_crit[i]); end if; end do; "

Error, invalid if statement termination

"#` determine the maxima and minima by checking the sign of the second derivative at the critical points` for i from 1 to nops(crit_points) do if (eval(diff(diff(rel, k), k), k = crit_points[i]) > 0) then print("Minimum at k = ", crit_points[i], " with value ", rel_at_crit[i]); else if (eval(diff(diff(rel, k), k), k = crit_points[i]) < 0) then print("Maximum at k = ", crit_points[i], " with value ", rel_at_crit[i]); else print("Saddle point at k = ", crit_points[i], " with value ", rel_at_crit[i]); end if; end do; "

  

NULL

Download maxnmin.mw

How do I find maximum value of k?...

mz6687 40 Maple 2022
optimization solve differentiation
January 11 2023
1 3

How do I find the maximum value of k by putting dw/dk = 0? Also, how to find the range of k for which w is real? 

> 

restart
> 

w = -(1/2)*sqrt(960*c^6*gamma^2*k^2-336*c^4*gamma^2*k^4+64*c^2*gamma^2*k^6-4*gamma^2*k^8+576*alpha*c^6*gamma*k-288*alpha*c^4*gamma*k^3-16*alpha*c^2*gamma*k^5+8*alpha*gamma*k^7-144*alpha^2*c^4*k^2-48*alpha^2*c^2*k^4-4*alpha^2*k^6+128*c^4*gamma*k^2-40*c^2*gamma*k^4+4*gamma*k^6+48*alpha*c^4*k-16*alpha*c^2*k^3-4*alpha*k^5+4*c^2*k^2-k^4)

w = -(1/2)*(960*c^6*gamma^2*k^2-336*c^4*gamma^2*k^4+64*c^2*gamma^2*k^6-4*gamma^2*k^8+576*alpha*c^6*gamma*k-288*alpha*c^4*gamma*k^3-16*alpha*c^2*gamma*k^5+8*alpha*gamma*k^7-144*alpha^2*c^4*k^2-48*alpha^2*c^2*k^4-4*alpha^2*k^6+128*c^4*gamma*k^2-40*c^2*gamma*k^4+4*gamma*k^6+48*alpha*c^4*k-16*alpha*c^2*k^3-4*alpha*k^5+4*c^2*k^2-k^4)^(1/2)

 (1)
> 

diff(w = -(1/2)*(960*c^6*gamma^2*k^2-336*c^4*gamma^2*k^4+64*c^2*gamma^2*k^6-4*gamma^2*k^8+576*alpha*c^6*gamma*k-288*alpha*c^4*gamma*k^3-16*alpha*c^2*gamma*k^5+8*alpha*gamma*k^7-144*alpha^2*c^4*k^2-48*alpha^2*c^2*k^4-4*alpha^2*k^6+128*c^4*gamma*k^2-40*c^2*gamma*k^4+4*gamma*k^6+48*alpha*c^4*k-16*alpha*c^2*k^3-4*alpha*k^5+4*c^2*k^2-k^4)^(1/2), k)

0 = -(1/4)*(1920*c^6*gamma^2*k-1344*c^4*gamma^2*k^3+384*c^2*gamma^2*k^5-32*gamma^2*k^7+576*alpha*c^6*gamma-864*alpha*c^4*gamma*k^2-80*alpha*c^2*gamma*k^4+56*alpha*gamma*k^6-288*alpha^2*c^4*k-192*alpha^2*c^2*k^3-24*alpha^2*k^5+256*c^4*gamma*k-160*c^2*gamma*k^3+24*gamma*k^5+48*alpha*c^4-48*alpha*c^2*k^2-20*alpha*k^4+8*c^2*k-4*k^3)/(960*c^6*gamma^2*k^2-336*c^4*gamma^2*k^4+64*c^2*gamma^2*k^6-4*gamma^2*k^8+576*alpha*c^6*gamma*k-288*alpha*c^4*gamma*k^3-16*alpha*c^2*gamma*k^5+8*alpha*gamma*k^7-144*alpha^2*c^4*k^2-48*alpha^2*c^2*k^4-4*alpha^2*k^6+128*c^4*gamma*k^2-40*c^2*gamma*k^4+4*gamma*k^6+48*alpha*c^4*k-16*alpha*c^2*k^3-4*alpha*k^5+4*c^2*k^2-k^4)^(1/2)

 (2)
> 

NULL

NULL

Download drelation.mw

possible transformations...

mz6687 40 Maple 2022
pde differential-equations invariant
December 14 2022
0 0

How can we unveil all the possible transformations that reduce the number of independent variables of a given pde? I tried it by using "InvarientSolutions" which gives eight possible transformations. But under those transformations, I got only two different odes. Is there any other method/command from which we can get other possible odes of a given pde?

 

pde_ode.mw

How can we put a z-axis label on the top...

mz6687 40 Maple
label axes plotting
November 30 2022
1 2

How can we put a z-axis label on the top as in the attached picture?

sine_fun.mw

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