Dear friends, please I would like to ask for your help with the following problem: 

I have a remember table generated by a recursive procedure

x:= proc(n)
option remember; 
....
end proc:

It helps compute x(1), x(2), x(3), x(4). 

After several additional steps I have a new x(2), say 

x(2):= 3; 

With this new x(2) I need to recompute x(3), x(4). I've tried 

forget( x, [ x(3), x(4) ], subfunctions = false ); 

x(3); 

x(4); 

However, I do not get the new values of x(3) and x(4) but the old ones. What could it be wrong? 

Many thanks for your help.  

Hello!

I have a matrix and all elements has two indexes. For example 3x3 case:

1,1 1,2 1,3

2,1 2,2 2,3

3,1 3,2 3,3

So if I want to travers this matrix in zig-zag way and fill it with increasing numbers I will get this matrix:

1 2 6

3 5 7

4 8 9

From 1 to 2,3 and 4,5,6 ...

We have 9 elemets in this order:

1 - (1,1); 2 - (1,2); 3 - (2,1); 4 - (3,1); 5 - (2,2); 6 - (1,3); 7 - (2,3); 8 - (3,2); 9 - (3,3).

The question is - do we have a way to convert two indexes in one digit like (3,1) -> 4 or (2,3) -> 7

Thank you!

Could you help me please if there is a way to convert to

I am not able to get the proper integration results

Question_integration_eqn18.mw
 

Download Question_integration_eqn18.mw

So, here again, I'm still having this problem with Maple 2020 on Machbook OS 10.13.6 (all updates have been performed): Maple 2020 does not start. I see an icon appearing in the dock but it then disappears soon without showing anything like splash something. I reinstalled and restarted the copmuter several times, reactivated the software several times (always successful), and still I'm having the problem. I installed java and then it worked for one time, but after that the same problem happens and I'm still having this issue.

I went through steps suggestged in the help and arrived at JAVA reisntallation. What else can I try? 

Please help me. Thanks.

Hiro

Suddently Maple 2020 (on Macbook) stops launching... I reinstalled it and restarted a couple of times. 

Can someone give me some clues about what is causing this problem.

I really need it right now... 

Thanks,

Hiro

doubt_3.mw

Hi, I am trying to do a simple think like

od2 := diff(x^3, x)+v+2 = 0

od3 := diff(v^2, v)+x+4 = 0

solve({(1),(2)},{x,v})

but with my code,  I am doing the exact same but getting the following error

Error, invalid input: solve expects its 1st argument, eqs, to be of type {`and`, `not`, `or`, algebraic, relation(algebraic), ({list, set})({`and`, `not`, `or`, algebraic, relation(algebraic)})}, but received {[1316.872428*(-0.1500000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+3.000000*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.2250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.2304687500e-6*t__2^3*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^3*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.3662109374e-8*t__2^4*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^4*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.5320312500e-4*t__2^2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^2*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-3.000000)*exp(-0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))*(int(.2*(.1*t+1)*i__m2(t), t = 0 .. t__2))/N^.98-11.76000000/(N^.98*((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2))+1185.185185*(-0.1953125000e-5*t__2^3*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^3*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.4898437500e-3*t__2^2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^2*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.7500000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+6.0000*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-6.0000)*exp(-0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))/(N^.98*((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2))+6.00*(-75.50000000*N^2.02+45.45000000*N^1.02+306.00*N^0.2e-1)/((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2)-1.200000000/((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2)-9.6*(-75.37500000*N^3.02+45.30000000*N^2.02+303.00*N^1.02)/((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2)] = 0, [-650*(0.3750000000e-2*t__2^2+0.7500000000e-1*t__2-0.4166666667e-1*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+3/2+(1/12)*t__2*(0.900e-1*t__2+.90))/((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2)^2+65843.62140*N^0.2e-1*(-0.6750000000e-3*t__2^2-0.1350000000e-1*t__2+0.7500000000e-2*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`-0.9000000000e-1-0.1500000000e-1*t__2*(0.900e-1*t__2+.90)+3.000000*(0.5625000000e-3*t__2^2+0.1125000000e-1*t__2-0.6250000000e-2*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+0.7500000000e-1+0.1250000000e-1*t__2*(0.900e-1*t__2+.90))*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.2250000000e-1*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.2250000000e-1*t__2*(0.900e-1*t__2+.90)*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.2250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)*(0.5625000000e-3*t__2^2+0.1125000000e-1*t__2-0.6250000000e-2*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+0.7500000000e-1+0.1250000000e-1*t__2*(0.900e-1*t__2+.90))*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.6914062500e-6*t__2^2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^3*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.6914062500e-6*t__2^3*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^2*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))*(0.900e-1*t__2+.90)+0.2304687500e-6*t__2^3*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^3*(0.5625000000e-3*t__2^2+0.1125000000e-1*t__2-0.6250000000e-2*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+0.7500000000e-1+0.1250000000e-1*t__2*(0.900e-1*t__2+.90))*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.1464843750e-7*t__2^3*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^4*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.1464843750e-7*t__2^4*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^3*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))*(0.900e-1*t__2+.90)-0.3662109374e-8*t__2^4*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^4*(0.5625000000e-3*t__2^2+0.1125000000e-1*t__2-0.6250000000e-2*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+0.7500000000e-1+0.1250000000e-1*t__2*(0.900e-1*t__2+.90))*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.1064062500e-3*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^2*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.1064062500e-3*t__2^2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))*(0.900e-1*t__2+.90)+0.5320312500e-4*t__2^2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^2*(0.5625000000e-3*t__2^2+0.1125000000e-1*t__2-0.6250000000e-2*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+0.7500000000e-1+0.1250000000e-1*t__2*(0.900e-1*t__2+.90))*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)))*exp(-0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))*(int(.2*(.1*t+1)*i__m2(t), t = 0 .. t__2))+65843.62140*N^0.2e-1*(-0.1500000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+3.000000*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.2250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.2304687500e-6*t__2^3*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^3*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.3662109374e-8*t__2^4*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^4*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.5320312500e-4*t__2^2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^2*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-3.000000)*(-0.5625000000e-3*t__2^2-0.1125000000e-1*t__2+0.6250000000e-2*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`-0.7500000000e-1-0.1250000000e-1*t__2*(0.900e-1*t__2+.90))*exp(-0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))*(int(.2*(.1*t+1)*i__m2(t), t = 0 .. t__2))+13168.72428*N^0.2e-1*(-0.1500000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+3.000000*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.2250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.2304687500e-6*t__2^3*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^3*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.3662109374e-8*t__2^4*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^4*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.5320312500e-4*t__2^2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^2*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-3.000000)*exp(-0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))*(.1*t__2+1)*i__m2(t__2)+588.0000000*N^0.2e-1*(0.3750000000e-2*t__2^2+0.7500000000e-1*t__2-0.4166666667e-1*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+3/2+(1/12)*t__2*(0.900e-1*t__2+.90))/((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2)^2+.60*(98765.43210*N^0.2e-1*(-0.5859375000e-5*t__2^2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^3*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.5859375000e-5*t__2^3*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^2*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))*(0.900e-1*t__2+.90)-0.1953125000e-5*t__2^3*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^3*(0.5625000000e-3*t__2^2+0.1125000000e-1*t__2-0.6250000000e-2*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+0.7500000000e-1+0.1250000000e-1*t__2*(0.900e-1*t__2+.90))*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.9796875000e-3*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^2*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.9796875000e-3*t__2^2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))*(0.900e-1*t__2+.90)+0.4898437500e-3*t__2^2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^2*(0.5625000000e-3*t__2^2+0.1125000000e-1*t__2-0.6250000000e-2*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+0.7500000000e-1+0.1250000000e-1*t__2*(0.900e-1*t__2+.90))*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.7500000000e-1*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.7500000000e-1*t__2*(0.900e-1*t__2+.90)*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.7500000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)*(0.5625000000e-3*t__2^2+0.1125000000e-1*t__2-0.6250000000e-2*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+0.7500000000e-1+0.1250000000e-1*t__2*(0.900e-1*t__2+.90))*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+6.0000*(0.5625000000e-3*t__2^2+0.1125000000e-1*t__2-0.6250000000e-2*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+0.7500000000e-1+0.1250000000e-1*t__2*(0.900e-1*t__2+.90))*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)))*exp(-0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+98765.43210*N^0.2e-1*(-0.1953125000e-5*t__2^3*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^3*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.4898437500e-3*t__2^2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^2*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.7500000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+6.0000*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-6.0000)*(-0.5625000000e-3*t__2^2-0.1125000000e-1*t__2+0.6250000000e-2*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`-0.7500000000e-1-0.1250000000e-1*t__2*(0.900e-1*t__2+.90))*exp(-0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+i__m2(t__2))/((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2)-.60*(98765.43210*N^0.2e-1*(-0.1953125000e-5*t__2^3*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^3*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.4898437500e-3*t__2^2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^2*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.7500000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+6.0000*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-6.0000)*exp(-0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+int(i__m2(t), t = 0 .. t__2))*(0.3750000000e-2*t__2^2+0.7500000000e-1*t__2-0.4166666667e-1*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+3/2+(1/12)*t__2*(0.900e-1*t__2+.90))/((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2)^2-(0.1500000000e-2*T^2+0.3000000000e-1*T)*(0.3750000000e-2*t__2^2+0.7500000000e-1*t__2-0.4166666667e-1*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+3/2+(1/12)*t__2*(0.900e-1*t__2+.90))/((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2)^2-6.00*(-25.00000000*N^3.02+22.50000000*N^2.02+300*N^1.02)*(0.3750000000e-2*t__2^2+0.7500000000e-1*t__2-0.4166666667e-1*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+3/2+(1/12)*t__2*(0.900e-1*t__2+.90))/((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2)^2-.1700000000*T*(0.3750000000e-2*t__2^2+0.7500000000e-1*t__2-0.4166666667e-1*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+3/2+(1/12)*t__2*(0.900e-1*t__2+.90))/((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2)^2-2.4*(.1000000000*T-.2000000000)*(0.3750000000e-2*t__2^2+0.7500000000e-1*t__2-0.4166666667e-1*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+3/2+(1/12)*t__2*(0.900e-1*t__2+.90))/((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2)^2-4*(0.1562500000e-3*T^2+0.1250000000e-1*T)*(0.3750000000e-2*t__2^2+0.7500000000e-1*t__2-0.4166666667e-1*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+3/2+(1/12)*t__2*(0.900e-1*t__2+.90))/((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2)^2-12.0*(0.2500000000e-1*T-.1000000000*N)*(0.3750000000e-2*t__2^2+0.7500000000e-1*t__2-0.4166666667e-1*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+3/2+(1/12)*t__2*(0.900e-1*t__2+.90))/((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2)^2+9.6*(-18.75000000*N^4.02+15.00000000*N^3.02+150*N^2.02)*(0.3750000000e-2*t__2^2+0.7500000000e-1*t__2-0.4166666667e-1*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+3/2+(1/12)*t__2*(0.900e-1*t__2+.90))/((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2)^2] = 0}

Please help

Thanks in advance 

Unfortunately,  Optimization:-Maximize command in following example returns a not precise result (I use Maple 2020).

restart:
s1:= Optimization:-Maximize((x-2*y)/(5*x^2-2*x*y+2*y^2), {2*x^2 - y^2 + x*y=1})

Maple is running the following results:

I read help of  Maximize, It seems to be using only numerical methods .

Can't Maple find a symbolic solution for extreme values under such constrained inequality or equality conditions?

Ps:

For the correct  symbolic  solution, we can try to  use Mathematica 12.

Maximize[{(x - 2*y)/(5*x^2 - 2*x*y + 2*y^2), 
  2*x^2 - y^2 + x*y == 1}, {x, y}]

  We can compare numerical sizes of Optimal solution between maple and mathematica. 

Digits:=20;
sqrt(2.)/4.

Another Problem:

If I accept numerical solutions of maple ,how do I estimate errors without knowing the exact solution ?

I am trying to compute the rank of the Commutator Matrix of a Lie algebra. That is, I wish to construct a matrix version of the multiplication table for a given matrix Lie algebra, and then compute the rank of this matrix.

Download CommutatorExample.mw
 

I have the above, but I run into two issues:

1. It doesn't have matrix format, so Rank is undefined (I have tried convert(T,matrix) to no avail),

2. I need to be able to remove the first and second rows and columns from T (because these rows/columns are occupied by the Lie algebra's basis elements, and separating lines, respectively).

I believe that if I can convert T into a matrix somehow, I can simply use SubMatrix to remove the things I don't want, and then Rank should work.

Any help would be greatly appreciated!

P.S. Thanks to dharr1338 for the suggestion of including the worksheet, I'm very new to Maple and MaplePrimes, so I appreciate the patience.

Hi, I am working on a bification diagram and was wondering if there is a way to plot the stable and unstable curves onto one figure.

I have two curves, if the eq1<eq2 I would like to indicate when this happens, with a dashed line.

When eq1>eq3 I would like to indicate this with a soild line.

implicitplot, x[m] vs x[u] with axis[2]=[mode=log] 

r:=0.927: K:=1.8182*10^8:d[v]:=0.0038:d[u]:=2: delta:=1: p[m]:=2.5: M:=10^4: p[e]:=0.4: d[e]:=0.1: d[t]:=5*10^(-9): omega:=2.042: b:=1000: h[e]:=1000:h[u]:=1:h[v]:=10^4:

eq1 := r*d[t]*h[e]*x[u]^3+(r*h[e]*(-K*d[t]+d[t]*h[v]+d[e])+r*p[e]*x[m])*x[u]^2+(r*h[e]*(-K*d[t]*h[v]-K*d[e]+d[e]*h[v])+K*p[e]*(d[u]-r)*x[m])*x[u]-r*K*h[e]*d[e]*h[v];

eq2 := (d[t]*x[u]+d[e])*(2*r*x[u]/K+d[u]*p[e]*x[m]*x[u]/((h[v]+x[u])*(d[t]*x[u]+d[e])*(h[e]+p[e]*x[m]*x[u]/((h[v]+x[u])*(d[t]*x[u]+d[e]))))-r)+d[u]*h[e]*x[u]*(p[e]*h[v]*x[m]/(h[v]+x[u])^2-d[t]*p[e]*x[m]*x[u]/((h[v]+x[u])*(d[t]*x[u]+d[e])))/(h[e]+p[e]*x[m]*x[u]/((h[v]+x[u])*(d[t]*x[u]+d[e])))^2

i have matrix M depend on x1 x2 x3 .... want limit of M. for sure can use loop like M[i,j]:=limit(M[i,j],[x1=0,x2=0,...]; i=1.. j=1..

want use map2 to do all at same time, try map2(limit,[x1=0,x2=0],M); gives error

Error, invalid input: limit expects its 1st argument, expr, to be of type Or(equation, algebraic), but received [x1 = 0, x2 = 0]

is possible to do using map or other thing not loop

@ianmccr posted here about making help for a package using makehelp. Here I show how to do this with the HelpTools package.

The attached worksheet shows how to create the help database for the Orbitals package available at the Applications Center or in the Maple Cloud. The help pages were created as worksheets - start using an existing help page as a model - use View/Open Page As Worksheet and then save from there. The topics and other information are entered by adding Attributes under File/Document Properties - for example for the realY help page these are:

Active=false means a regular help page; Active=true means an example worksheet.

There may be several aliases, for example the cartesion help page also describes the fullcartesian command and so Alias is: Orbitals[fullcartesian],cartesian,fullcartesian and Keyword is: Orbitals,cartesian,fullcartesian

Once a worksheet is created for each help page they are assembled into the help database with the attached file. More information is in the attached file

Orbitals_Make_help_database.mw

Hello,

I have tried to get a simple matlab example of a fourier transform code to work in Maple. This is just to understand a simple fourier transform and eventually try some more difficult 2D transforms.

restart:
with(LinearAlgebra):
with(RandomTools):
with(orthopoly):
with(plots):
with(ArrayTools):
with(DiscreteTransforms):
Digits:=15:

# 1D Fourier Transform

Fs := 1000;                       # Sampling frequency                    
T := 1/Fs;                        # Sampling period       
L := 1500;                        # Length of signal
t := Vector(L, i -> i-1)*T:       # Time vector

f := Fs*Vector(floor(L/2)+1, i-> i-1)/L:   # Frequency                 


S:= Vector(L, i -> 0.7*sin(2.0*Pi*50*t[i]) + sin(2.0*Pi*120*t[i])):    # Signal


Z1 := FourierTransform(Vector(L, j->S[j])):              # DFT 
Z2 := Vector(L, i-> sqrt(Re(Z1[i])**2 + Im(Z1[i])**2)):  # Amplitude
                

FP1 := pointplot({seq([f[n],Z2[n]],n=1..floor(L/2)+1)}, labels=["Frequency","Amplitude"], connect=true, color=green):

display(FP1, axes=boxed);

The right answer should be a plot with frequencies at 50Hz and 120Hz, with amplitudes at 0.7 and 1.0, respectively. However my amplitude axes is off somehow and I don't understand why. 

Hello!

Could you help me please to plot a fuction with domain and complex range (Maple 2020.1). For example:

f := (x, w) -> exp(w*x*I)

x,w are real numbers

Hello!

I've just want to use indexes in functions, like this (Maple 2020.1)

But I can't get the result of it:

f[1,1](2,2)

Maple show me not 4, but the same function.