Maple 2016 Questions and Posts

These are Posts and Questions associated with the product, Maple 2016

In my worksheet today my intention was to compare the least squares linear regression for three datasets as indicated, but when I right click on the output as seen in the bottom line to select the plot type, all options state there to be independant variables K[0] and K[1], where as the output displays only the variable K as I intended, which part of my code is creating this confusion for maple?

 

 

 

Worksheet Specific Investigation Content

 

S[0] := proc (N, K) options operator, arrow; map(simplify, {seq(seq(seq(piecewise((a^`ϕ`(b))^(1/(c+1))-floor((a^`ϕ`(b))^(1/(c+1))) = 0, [a, b, c], NULL), a = 1 .. N), b = 1 .. N), c = 1 .. K)}, 'radical') end proc

T := proc (N, K) options operator, arrow; {seq(seq(seq([a, b, c], a = 1 .. N), b = 1 .. N), c = 1 .. K)} end proc:

S[1] := proc (N, K) options operator, arrow; `minus`(T(N, K), S[0](N, K)) end proc:

CardRatio := proc (N, K) options operator, arrow; nops(S[0](N, K))/nops(S[1](N, K)) end proc:

{CurveFitting[LeastSquares]([seq([k, CardRatio(2, k)], k = 1 .. 10)], K), CurveFitting[LeastSquares]([seq([k, CardRatio(3, k)], k = 1 .. 10)], K), CurveFitting[LeastSquares]([seq([k, CardRatio(4, k)], k = 1 .. 10)], K)}

{1, 44268857/45401356-(532409481/9988298320)*K, 24308311919/13309971675-(135902619982/773879781675)*K}

(1.1)

``

 

 

 

 

Download ask_maple.mw

 

 

Hi,

I am writing the following code and MAPLE is giving me operator error. Please help (file: doubt_6.mw)

d2:=100000000

for m in set_m do
    for n in set_n do
        SOL1 := fsolve({ODE11, ODE12}, {N, t__2});
        N1:=eval(N,SOL1);
        t_2_1 :=eval(t__2,SOL1);
        T_1:= eval(T, [lambda = 3, a = 300, b = .15, c = .25, A__m = 300, A__d = 150, A__r = 50,C__m = 4, P__m = 8, P__d = 10, 
        P__r = 12, theta__m = .15, theta__d = .12, theta__r = 0.5e-1, h__m = .2, h__d = .3, h__r = .5, i__m = .1, i__d = .1, 
        i__r = .1, i__om = .1, i__OD = .15, i__c = .3, i__e = .2, M = 2, alpha = 0.2e-1, t__2 = t_2_1]):
        t_31:= T_1 /m ;
        t_41:= T_1 /(m*n) ;
        if (N1<=t_41 and 2>=t_31) then
            d1:= eval(TCS__1, [lambda = 3, a = 300, b = .15, c = .25, A__m = 300, A__d = 150, A__r = 50, C__m = 4, P__m = 8, 
            P__d = 10, P__r = 12, theta__m = .15, theta__d = .12, theta__r = 0.5e-1, h__m = .2, h__d = .3, h__r = .5, i__m = .1, 
            i__d = .1, i__r = .1, i__om = .1, i__OD = .15, i__c = .3, i__e = .2, M = 2, alpha = 0.2e-1, t__2=t_2_1, N=N1]):
            if (d1<= d2) then
                d2:= d1;
                print("Value is updated",d2,N1,t_2_1,"for",m,n)
            end if
        end if    
        print(N1,t_2_1,t_31,t_41,d1,m,n)
    end do
end do

 

Thanks in advance

 

[[p__jb = (Typesetting[delayDotProduct](c__a . ((rho*(-1+alpha)*t__a-alpha*t__b)/(t__b*t__a)), t__b, true)*t__a+((c__b+`p__-jb`)*alpha-c__b-t__b-`p__-jb`)*t__a-alpha*t__b*(c__b+`p__-jb`))/((2*alpha-2)*t__a-2*alpha*t__b)]]

hi

I'm working on my thesis,to solve a particular problem,I created a 84*84 matrix in Matlab.

I want to calculate the determinat of that matrix in maple,so from tools>assistance>import date added this matrix in maple.

every thing seems to be ok but when i want to caculate the determinant this error apears :

 Error, (in LinearAlgebra:-Determinant) matrix must be square

does anybody know what is the problem here?

Also sorry for my weak English 

and it's worth mentioning that I'm a beginner in maple programming 

thank you

 

 

doubt5.mw

Hi I want to run the following algorithm in code edit region:

for m in set_m do
    for n in set_n do
      solve for N solving ODE11 and ODE12 simultaneously
      solve for t_2 solving ODE11 and ODE12 simultaneouly
      find t__3 and t__4
      if (N<=t_4 and M>=t_3) then
        d1= TCS__1 using n,m,t__2 and N
          if (d1< d2)
            d2=d1
            print(d2,m,n,N,t_2)
    end do
end do
 

But I am struck for to how to extract N and t__2 from SOL1 in code edit region

SOL1 := fsolve({ODE11, ODE12}, {N, t__2});

Thanks in advance

doubt4.mw

Hi, As shown in the figure(red color). I am not able to understand why Exp(0) is not showing as 1. As evaluating rules of maple says that it evaluates everything till it gets unassigned variables.

Do I am doing something wrong? There is a link to the file. 

Thanks in advance

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 

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

Hi, am trying to differentiate the following eq w.r.t t2 and N. But in t2 I am getting zero and in wrt N, an Error (non-algebraic expressions cannot be differentiated). But according to the article, I am following expression should come.

I am differentiating following

TCS := proc (N, T, m, n) options operator, arrow; piecewise(M <= t__3 and N <= t__4, TCS__1, M <= t__3 and t__4 < N, TCS__2, t__3 <= M and N <= t__4, TCS__3, `t__3 ` <= M and t__4 < N, TCS__4) end proc

ode5 := diff(proc (N, T, m, n) options operator, arrow; piecewise(M <= t__3 and N <= t__4, TCS__1, M <= t__3 and t__4 < N, TCS__2, t__3 <= M and N <= t__4, TCS__3, `t__3 ` <= M and t__4 < N, TCS__4) end proc, t__2) = 0

ode6 := diff(proc (N, T, m, n) options operator, arrow; piecewise(M <= t__3 and N <= t__4, TCS__1, M <= t__3 and t__4 < N, TCS__2, t__3 <= M and N <= t__4, TCS__3, `t__3 ` <= M and t__4 < N, TCS__4) end proc, N) = 0

Error, non-algebraic expressions cannot be differentiated
 

following are the pre-requisite to use above (also in the attachment doubt_2.mw)

i__m1(t) = ((-c*t^2*theta__m^2+b*t*theta__m^2+2*c*t*theta__m-b*theta__m+theta__m^2-2*c)*exp(theta__m*t)*a*N^alpha*(lambda-1)/theta__m^3-(-b*theta__m+theta__m^2-2*c)*a*N^alpha*(lambda-1)/theta__m^3)*exp(-theta__m*t)

i__m2(t) = (-(-c*t^2*theta__m^2+b*t*theta__m^2+2*c*t*theta__m-b*theta__m+theta__m^2-2*c)*exp(theta__m*t)*a*N^alpha/theta__m^3+(-c*t__2^2*theta__m^2+b*t__2*theta__m^2+2*c*t__2*theta__m-b*theta__m+theta__m^2-2*c)*exp(theta__m*t__2)*a*N^alpha/theta__m^3)*exp(-theta__m*t)

TC__m := A__m/(t__1+t__2)+(int(h__m*(i__m*t+1)*i__m1(t), t = 0 .. t__1))*(int(h__m*(i__m*t+1)*i__m2(t), t = 0 .. t__2))+P__m*I__om*m*(-(1/3)*a*c*N^alpha*M^3+(1/2)*a*b*N^alpha*M^2+a*N^alpha*M)/(t__1+t__2)+C__m*theta__m*(int(i__m1(t), t = 0 .. t__1)+int(i__m2(t), t = 0 .. t__2))/(t__1+t__2)

i__d(t) = (-(-c*t^2*theta__d^2+b*t*theta__d^2+2*c*t*theta__d-b*theta__d+theta__d^2-2*c)*a*N^alpha*exp(theta__d*t)/theta__d^3+(-c*t__3^2*theta__d^2+b*t__3*theta__d^2+2*c*t__3*theta__d-b*theta__d+theta__d^2-2*c)*a*N^alpha*exp(theta__d*t__3)/theta__d^3)*exp(-theta__d*t)

TC__d1 := A__d*m/(t__1+t__2)+m*(int(h__d*(i__d*t+1)*i__d(t), t = 0 .. t__3))/(t__1+t__2)+P__d*I__OD*m*n*(-(1/3)*a*c*N^alpha*N^3+(1/2)*a*b*N^alpha*N^2+a*N^alpha*N)/(t__1+t__2)+P__m*theta__m*m*(int(i__d(t), t = 0 .. t__3))/(t__1+t__2)+P__m*I__c*m*(int(i__d(t), t = M .. t__3))/(t__1+t__2)-P__d*I__e*m*(-(1/3)*a*c*N^alpha*M^3+(1/2)*a*b*N^alpha*M^2+a*N^alpha*M)/(t__1+t__2)

TC__d2 := A__d*m/(t__1+t__2)+m*(int(h__d*(i__d*t+1)*i__d(t), t = 0 .. t__3))/(t__1+t__2)+P__d*I__OD*m*n*(-(1/3)*a*c*N^alpha*N^3+(1/2)*a*b*N^alpha*N^2+a*N^alpha*N)/(t__1+t__2)+P__m*theta__m*m*(int(i__d(t), t = 0 .. t__3))/(t__1+t__2)-P__d*I__e*m*(-(1/4)*a*c*N^alpha*t__3^4+(1/3)*a*b*N^alpha*t__3^3+(1/2)*a*N^alpha*t__3^2+M-t__3-(1/3)*a*c*N^alpha*t__3^3+(1/2)*a*b*N^alpha*t__3^2+a*N^alpha*t__3)/(t__1+t__2)

i__r(t) = (-(-c*t^2*theta__r^2+b*t*theta__r^2+2*c*t*theta__r-b*theta__r+theta__r^2-2*c)*a*N^alpha*exp(theta__r*t)/theta__r^3+(-c*t__4^2*theta__r^2+b*t__4*theta__r^2+2*c*t__4*theta__r-b*theta__r+theta__r^2-2*c)*a*N^alpha*exp(theta__r*t__4)/theta__r^3)*exp(-theta__r*t)

TC__r1 := A__r*m*n/(t__1+t__2)+m*n*(int(h__r*(i__r*t+1)*i__r(t), t = 0 .. t__4))/(t__1+t__2)+P__d*theta__r*m*n*(int(i__r(t), t = 0 .. t__4))/(t__1+t__2)+P__d*I__c*m*n*(int(i__r(t), t = N .. t__4))/(t__1+t__2)-P__r*I__e*m*n*(-(1/4)*a*c*N^alpha*N^4+(1/3)*a*b*N^alpha*N^3+(1/2)*a*N^alpha*N^2)/(t__1+t__2)

TC__r2 := A__r*m*n/(t__1+t__2)+m*n*(int(h__r*(i__r*t+1)*i__r(t), t = 0 .. t__4))/(t__1+t__2)+P__d*theta__r*m*n*(int(i__r(t), t = 0 .. t__4))/(t__1+t__2)-P__r*I__e*m*n*(-(1/4)*a*c*N^alpha*t__4^4+(1/3)*a*b*N^alpha*t__4^3+(1/2)*a*N^alpha*t__4^2+N-t__4-(1/3)*a*c*N^alpha*t__4^3+(1/2)*a*b*N^alpha*t__4^2+a*N^alpha*t__4)/(t__1+t__2)

TCS__1 := TC__m+TC__d1+TC__r1

TCS__2 := TC__m+TC__d1+TC__r2

TCS__3 := TC__m+TC__d2+TC__r1

TCS__4 := TC__m+TC__d2+TC__r2

 

Thanks in advance.


doubt_1.mw

Hi, I am trying to solve two simultaneous equations (for t1) they are as follows-

eq 1

i__m2(0) = (-(-b*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`+`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^2-2*c)*exp(0)*a*N^alpha/`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^3+(-c*t__2^2*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^2+b*t__2*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^2+2*c*t__2*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`-b*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`+`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^2-2*c)*exp(`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`*t__2)*a*N^alpha/`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^3)*exp(0)

eq 2

i__m1(t__1) = ((-c*t__1^2*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^2+b*t__1*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^2+2*c*t__1*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`-b*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`+`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^2-2*c)*exp(`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`*t__1)*a*N^alpha*(lambda-1)/`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^3-(-b*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`+`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^2-2*c)*a*N^alpha*(lambda-1)/`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^3)*exp(-`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`*t__1)

rhs(i__m2(0) = (-(-b*theta__m+theta__m^2-2*c)*exp(0)*a*N^alpha/theta__m^3+(-c*t__2^2*theta__m^2+b*t__2*theta__m^2+2*c*t__2*theta__m-b*theta__m+theta__m^2-2*c)*exp(theta__m*t__2)*a*N^alpha/theta__m^3)*exp(0)) = rhs(i__m1(t__1) = ((-c*t__1^2*theta__m^2+b*t__1*theta__m^2+2*c*t__1*theta__m-b*theta__m+theta__m^2-2*c)*exp(theta__m*t__1)*a*N^alpha*(lambda-1)/theta__m^3-(-b*theta__m+theta__m^2-2*c)*a*N^alpha*(lambda-1)/theta__m^3)*exp(-theta__m*t__1))

solve({-(-b*theta__m+theta__m^2-2*c)*a*N^alpha/theta__m^3+(-c*t__2^2*theta__m^2+b*t__2*theta__m^2+2*c*t__2*theta__m-b*theta__m+theta__m^2-2*c)*exp(theta__m*t__2)*a*N^alpha/theta__m^3 = ((-c*t__1^2*theta__m^2+b*t__1*theta__m^2+2*c*t__1*theta__m-b*theta__m+theta__m^2-2*c)*exp(theta__m*t__1)*a*N^alpha*(lambda-1)/theta__m^3-(-b*theta__m+theta__m^2-2*c)*a*N^alpha*(lambda-1)/theta__m^3)*exp(-theta__m*t__1)}, [t__1]);
Warning, solutions may have been lost
 

Can someone, please help. Thanks in advance.

Dear All.

I hope we are all staying safe.

Please I want to solve Sine Gordon Equation using a numerical method I constructed (non-classical), I need to compare the result of the method with the exact solution to generate the errors. However, since the exact solution has two variables, x, and t, I really don't know how to accommodate the two in my coding.

Can someone be of help in this regard?

Thank you and kind regards

 


Download Discretization_of_Sine_Gordon_Equation.mw

Download Sine_Gordon_Implementation_Trial.mw

 

I am a little confused by why this error occurs in the second line and not the first, as well as the weird details specified in it. I don't know if the commands that are being called are inbuilt or not, but it is a safe bet that they will be. thankyou.


 

MAX := max({[seq(seq(n-(n^k-floor(n^(1/k))^(k-1)*igcd(floor(ithprime(n)^k/n^k), floor(n^(1/k))))^(1/k), n = 2 .. 100), k = 2 .. 100)][]}):

seq(seq(piecewise(radnormal(n-(n^k-floor(n^(1/k))^(k-1)*igcd(floor(ithprime(n)^k/n^k), floor(n^(1/k))))^(1/k)) = MAX, [n, k], NULL), n = 2 .. 100), k = 2 .. 100)

Error, (in radnormal/rational/nthpower) cannot determine if this expression is true or false: iroot(646162507019111437893207695980096110233782566593779/(_c27_37*_c25_38), [_c25_38, 1]) < 0

 

``


 

Download ASKMAPLE000.mw

Please, l need assistance on maplesoft activation code 

 

This is my code:

 

NEUZMinus:= proc(Unten, Oben, f,G,Liste,n)::real;
  #Unten:= Untere Intervallgrenze; Oben:= Obere Intervallgrenze; f:= zu integrierende Funktion;
  #G:= Gewicht; n:= Hinzuzufügende Knoten;
  local i;
  with(LinearAlgebra);     
  with(ListTools);
  Basenwechsel:=proc(Dividend, m);
 
  print(Anfang,Dividend,p[m]);
  Koeffizient:=quo(Dividend, p[m],x);

  Rest:=rem(Dividend, p[m],x);
 
  if m=0 then
    Basenwechsel:=[Koeffizient];
  else

    Basenwechsel:=[Koeffizient,op(Basenwechsel(Rest,m-1))];
   
  end if;
 
  end proc;
p[-1]:=0;
p[0]:=1;
for i from 1 to (numelems(Liste)+n)*2 do
  p[i]:=(x^i-add(int(x^i*p[j]*diff(G,x),x=Unten..Oben)*p[j]/int(p[j]^2*diff(G,x),x=Unten..Oben),j=0..i-1));
  print(p[i]);
c[i-1]:=coeff(p[i],x,i)/coeff(p[i-1],x,i-1);
d[i-1]:=(coeff(p[i],x,(i-1))-coeff(p[i-1],x,(i-2)))/coeff(p[i-1],x,(i-1));
if i <> 1 then
  e[i-1]:=coeff(p[i]-(c[i-1]*x+d[i-1])*p[i-1],x,i-2)/coeff(p[i-2],x,i-2);
else
  e[i-1]:=0;
end if;
end do;
print(Liste[1],numelems(Liste));
Hn:=mul(x-Liste[i],i=1..numelems(Liste));
print(Hn);
 Koeffizienten:=Reverse(Basenwechsel(Hn,n)); #!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
print(Koeffizienten,HIER);


print(c,d,e);
a[0][0]:=1;
a[1][0]:=x;
a[1][1]:=-e[1]*c[0]/c[1]+(d[0]-d[1]*c[0]/c[1])*x+c[0]/c[1]*x^2;
for s from 2 to numelems(Liste)+n do
  a[s][0]:=x^s;
  a[s][1]:=-e[s]*c[0]/c[s]*x^(s-1)+(d[0]-d[s]*c[0]/c[s])*x^s+c[0]/c[s]*x^(s+1);
    print (coeff(a[s][1],x,s),as1s);
end do;
for s from 2 to numelems(Liste)+n do
  for j from 2 to s do
    
      print(c[j-1]*sum(coeff(a[s][j-1],x,k-1)/c[k-1]*x^k,k=abs(s-j)+2..s+j));  print(sum((d[j-1]-c[j-1]*d[k]/c[k])*coeff(a[s][j-1],x,k)*x^k,k=abs(s-j)+1..s+j-1));  print(c[j-1]*sum(e[k+1]*coeff(a[s][j-1],x,k+1)/c[k+1]*x^k,k=abs(s-j)..s+j-2));print(e[j-1]*sum(coeff(a[s][j-2],x,k)*x^k,k=s-j+2..s+j-2));

     a[s][j]:=c[j-1]*sum(coeff(a[s][j-1],x,k-1)/c[k-1]*x^k,k=abs(s-j)+2..s+j)+sum((d[j-1]-c[j-1]*d[k]/c[k])*coeff(a[s][j-1],x,k)*x^k,k=abs(s-j)+1..s+j-1)-c[j-1]*sum(e[k+1]*coeff(a[s][j-1],x,k+1)/c[k+1]*x^k,k=abs(s-j)..s+j-2)+e[j-1]*sum(coeff(a[s][j-2],x,k)*x^k,k=abs(s-j)+2..s+j-2);

      
   
    
  end do;
end do;
for s from 0 to numelems(Liste)-1 do
  for j from 0 to s do
    print(a[s][j], Polynom[s][j]);
  end do;
end do;
M:=Matrix(n,n);
V:=Vector(n);
 
  for s from 0 to n-1 do
    for j from 0 to s do
      M(s+1,j+1):=sum(coeff(a[s][j],x,k)*Koeffizienten[k+1],k=0..n);
      if s<>j then
        M(j+1,s+1):=M(s+1,j+1);
      end if;
      print(M,1);
    end do;
    print(testb1);print(coeff(a[n][s],x,2));print(Koeffizienten[3]);print(testb2);
    V(s+1):=-sum(coeff(a[n][s],x,k)*Koeffizienten[k+1],k=0..n);
    
    print(M,V);
  end do;
print(M,V);
K:=LinearSolve(M,V);
K(n+1):=1;
print(K);

print(test2,coeff(a[max(3,2)][min(1,2)],x,2));
print(Koeffizienten[3]);
for l from 0 to n do
  for m from 0 to numelems(Liste)do
    print(Koeffizienten[m+1]*coeff(a[7][l],x,m),a[7][l],m,Koeff,Koeffizienten[m+1])
  end do;
end do;
for l from 0 to n do
  print(K(l+1)*add(Koeffizienten[m+1]*coeff(a[max(k,l)][min(k,l)],x,m),m=0..numelems(Liste)));
end do;
    nNeu:=add(p[k]*add(K(l+1)*add(Koeffizienten[m+1]*coeff(a[max(k,l)][min(k,l)],x,m),m=0..numelems(Liste)),l=0..n),k=numelems(Liste)..numelems(Liste)+n);
fsolve(nNeu);
Em:=add(p[i]*K[i+1],i=0..n);
Hnm:=Hn*Em;
KnotenHnm:=fsolve(Hnm);
print(Hn,alt,Em,neu,Hnm);
print(Testergebnis,nNeu);
print(fsolve(Hnm),fsolve(nNeu));
KoeffizientenHnm:=Reverse(Basenwechsel(Hnm,n+numelems(Liste)));  #!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
print(KoeffizientenHnm);
h0:=int(diff(G,x),x=Unten..Oben);
b[n+numelems(Liste)+2]:=0;
b[n+numelems(Liste)+1]:=0;
  for i from 1 to n+numelems(Liste) do
    for j from n+numelems(Liste) by -1 to 1 do
      print(test21);
      b[j]:=KoeffizientenHnm[j]+(d[j]+KnotenHnm[i]*c[j])*b[j+1]+e[j+1]*b[j+2];
  print(test22);
    end do;
    print(test23);
    gxi:=quo(Hnm,x-KnotenHnm[i],x);
   print(test24);
    Gewichte[i]:=c[1]*b[2]*h0/gxi(i);
   
    Delta[i]:=c[1]*b[2];
  end do;
print(KnotenHnm);
print(Gewichte);
sum(Knoten[k]*Gewichte[k],k=1..n+numelems(Liste));
end proc

With the first use of the subprocedure Basenwechsel, everything works fine. With the input

NEUZMinus(-1,1,x,x,[-sqrt(3/5),0,sqrt(3/5)],4)

I get the result [0,0,0,1,0] correctly.

The following time I use it, the polynomial is different, and m is 7 in that case, so the list should have 8 entries, it just returns the same [0,0,0,1,0] again, however. Changing the polynomial in the first application to say 5*Hn results in [0,0,0,5,0] in both cases again. The procedure seems to have saved the old values and never overwrites them. How can I fix this? I have highlighted the use of the procedure with exclamation marks.

 

Thank you in advance!

P.S.: The lengthy result is this:

NEUZMinus(-1,1,x,x,[-sqrt(3/5),0,sqrt(3/5)],4)

                               x
                              2   1
                             x  - -
                                  3
                             3   3  
                            x  - - x
                                 5  
                          4   3    6  2
                         x  + -- - - x
                              35   7   
                        5   5      10  3
                       x  + -- x - -- x
                            21     9    
                     6    5    5   2   15  4
                    x  - --- + -- x  - -- x
                         231   11      11   
                   7   35      105  3   21  5
                  x  - --- x + --- x  - -- x
                       429     143      13   
                8    7     28   2   14  4   28  6
               x  + ---- - --- x  + -- x  - -- x
                    1287   143      13      15   
              9    63      84   3   126  5   36  7
             x  + ---- x - --- x  + --- x  - -- x
                  2431     221      85       17   
         10    63     315   2   210  4   630  6   45  8
        x   - ----- + ---- x  - --- x  + --- x  - -- x
              46189   4199      323      323      19   
         11    33      55   3   330  5   330  7   55  9
        x   - ---- x + --- x  - --- x  + --- x  - -- x
              4199     323      323      133      21   
    12    33     198   2   2475  4   660  6   495  8   66  10
   x   + ----- - ---- x  + ---- x  - --- x  + --- x  - -- x  
         96577   7429      7429      437      161      23    
 13    429       2574   3   1287  5   1716  7   429  9   78  11
x   + ------ x - ----- x  + ---- x  - ---- x  + --- x  - -- x  
      185725     37145      2185      805       115      25    
     14     143      1001   2   1001  4   1001  6   1001  8
    x   - ------- + ------ x  - ---- x  + ---- x  - ---- x
          1671525   111435      6555      1035      345    

         1001  10   91  12
       + ---- x   - -- x  
         225        27    
                           1   (1/2)   
                         - - 15     , 3
                           5           
               /    1   (1/2)\   /    1   (1/2)\
               |x + - 15     | x |x - - 15     |
               \    5        /   \    5        /
           /    1   (1/2)\   /    1   (1/2)\   4   3    6  2
   Anfang, |x + - 15     | x |x - - 15     |, x  + -- - - x
           \    5        /   \    5        /       35   7   
                            3   3     3   3  
                   Anfang, x  - - x, x  - - x
                                5         5  
                                   2   1
                       Anfang, 0, x  - -
                                       3
                          Anfang, 0, x
                          Anfang, 0, 1
                     [0, 0, 0, 1, 0], HIER #!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
                            c, d, e
                            0, as1s
                            0, as1s
                            0, as1s
                            0, as1s
                            0, as1s
                            0, as1s
                           4   2    4
                           -- x  + x
                           15        
                               0
                            4    9   2
                          - -- - -- x
                            45   35   
                               1  2
                             - - x
                               3   
                           9   3    5
                           -- x  + x
                           35        
                               0
                          12      16  3
                        - --- x - -- x
                          175     63   
                               1  3
                             - - x
                               3   
                      12   2   8   4    6
                      --- x  + -- x  + x
                      175      45        
                               0
                        4     8   2   25  4
                     - --- - --- x  - -- x
                       175   175      99   
                          12   2   4   4
                        - --- x  - -- x
                          175      15   
                           16  4    6
                           -- x  + x
                           63        
                               0
                          16   2   25  4
                        - --- x  - -- x
                          245      99   
                               1  4
                             - - x
                               3   
                      16   3   40   5    7
                      --- x  + --- x  + x
                      245      231        
                               0
                     64       640   3   36   5
                  - ---- x - ----- x  - --- x
                    3675     14553      143   
                          64   3   4   5
                        - --- x  - -- x
                          945      15   
                  64   2   16   4   72   6    8
                 ---- x  + --- x  + --- x  + x
                 3675      385      455        
                               0
                64      144   2    40   4   49   6
             - ----- - ----- x  - ---- x  - --- x
               11025   13475      1001      195   
                     24   4   9   6   144   2
                   - --- x  - -- x  - ---- x
                     539      35      8575   
                           25  5    7
                           -- x  + x
                           99        
                               0
                         400   3   36   5
                       - ---- x  - --- x
                         6237      143   
                               1  5
                             - - x
                               3   
                     400   4   20   6    8
                     ---- x  + --- x  + x
                     6237      117        
                               0
                    80   2    500   4   49   6
                 - ---- x  - ----- x  - --- x
                   4851      11583      195   
                          20   4   4   6
                        - --- x  - -- x
                          297      15   
                  80   3    40   5   7   7    9
                 ---- x  + ---- x  + -- x  + x
                 4851      1001      45        
                               0
                64        640   3   28   5   64   7
             - ----- x - ----- x  - --- x  - --- x
               14553     63063      715      255   
                     4   5   9   7    80   3
                   - -- x  - -- x  - ---- x
                     91      35      4851   
           64    2    640   4   16   6   160   8    10
          ----- x  + ----- x  + --- x  + ---- x  + x  
          14553      63063      455      1071         
                               0
           64      128   2    80   4   224   6   81   8
        - ----- - ----- x  - ---- x  - ---- x  - --- x
          43659   49049      9009      5967      323   
               640   4   16   6   16  8    1280   2
            - ----- x  - --- x  - -- x  - ------ x
              63063      405      63      305613   
                          36   6    8
                          --- x  + x
                          143        
                               0
                         100   4   49   6
                       - ---- x  - --- x
                         1573      195   
                               1  6
                             - - x
                               3   
                     100   5   28   7    9
                     ---- x  + --- x  + x
                     1573      165        
                               0
                   1600   3   336   5   64   7
                 - ----- x  - ---- x  - --- x
                   99099      7865      255   
                          48   5   4   7
                        - --- x  - -- x
                          715      15   
                1600   4   28   6   144  8    10
                ----- x  + --- x  + --- x  + x  
                99099      715      935         
                               0
              320   2    140   4   2352   6   81   8
           - ----- x  - ----- x  - ----- x  - --- x
             77077      14157      60775      323   
                    12   6   9   8    180   4
                  - --- x  - -- x  - ----- x
                    275      35      11011   
           320   3    320   5   32   7   216   9    11
          ----- x  + ----- x  + --- x  + ---- x  + x  
          77077      33033      935      1463         
                               0
       256        5120    3    1152   5    4608   7   100  9
    - ------ x - ------- x  - ------ x  - ------ x  - --- x
      231231     2081079      133705      124355      399   
               64   5   256   7   16  9    25600   3
            - ---- x  - ---- x  - -- x  - ------- x
              6435      6545      63      6243237   
   256    2    320    4    1280   6    800   8   100  10    12
  ------ x  + ------ x  + ------ x  + ----- x  + --- x   + x  
  231231      127413      153153      24871      693          
                               0
   256      64    2    32000    4    1120   6    900   8   121  10
- ------ - ----- x  - -------- x  - ------ x  - ----- x  - --- x  
  693693   99099      15162147      138567      24871      483    
       8000    4    160   6    600   8   25  10    8000    2
    - ------- x  - ----- x  - ----- x  - -- x   - ------- x
      3270267      18513      16093      99       7630623   
                          49   7    9
                          --- x  + x
                          195        
                               0
                         588   5   64   7
                       - ---- x  - --- x
                         9295      255   
                               1  7
                             - - x
                               3   
                     588   6   112  8    10
                     ---- x  + --- x  + x  
                     9295      663         
                               0
                   980   4    5488   6   81   8
                - ----- x  - ------ x  - --- x
                  61347      129285      323   
                         196   6   4   8
                       - ---- x  - -- x
                         2925      15   
               980   5   2352   7   189   9    11
              ----- x  + ----- x  + ---- x  + x  
              61347      60775      1235         
                               0
            2240   3    84672   5    4032   7   100  9
         - ------ x  - ------- x  - ------ x  - --- x
           552123      8690825      104975      399   
                     48   7   9   9    756   5
                  - ---- x  - -- x  - ----- x
                    1105      35      46475   
         2240   4    896   6    7776   8   40   10    12
        ------ x  + ----- x  + ------ x  + --- x   + x  
        552123      94809      230945      273          
                               0
      64    2    22400   4    127008   6   1080   8   121  10
   - ----- x  - ------- x  - -------- x  - ----- x  - --- x  
     61347      9386091      15011425      29393      483    
              1792   6    48   8   16  10    2240   4
           - ------ x  - ---- x  - -- x   - ------ x
             182325      1235      63       552123   
  64    3    22400   5    1120   7    600   9   385   11    13
 ----- x  + ------- x  + ------ x  + ----- x  + ---- x   + x  
 61347      9386091      138567      19019      2691          
                               0
    256        51200    3    13440   5    2560   7    5500   9
 - ------ x - -------- x  - ------- x  - ------ x  - ------ x
   920205     84474819      6605027      323323      153387   

      144  11
    - --- x  
      575    
      22400   5    4320   7   1000   9   25  11    56000    3
   - ------- x  - ------ x  - ----- x  - -- x   - -------- x
     9386091      508079      27027      99       54660177   
  256    2     7168    4    13440   6    80000    8   100   10
 ------ x  + -------- x  + ------- x  + -------- x  + ---- x  
 920205      11471889      6605027      10669659      3289    

      504   12    14
    + ---- x   + x  
      3575          
                               0
    256       3072    2    112000    4    112000   6    8100    8
- ------- - -------- x  - --------- x  - -------- x  - ------- x
  2760615   19119815      217965891      59445243      1062347   

     264   10   169  12
   - ---- x   - --- x  
     7475       675    
     89600    4    13440   6    21600   8   140   10   36   12
 - --------- x  - ------- x  - ------- x  - ---- x   - --- x  
   149134557      6605027      2719717      3887       143    

        768    2
    - ------- x
      2924207   
                        1, Polynom[0][0]
                        x, Polynom[1][0]
                     1    2               
                     - + x , Polynom[1][1]
                     3                    
                        2               
                       x , Polynom[2][0]
                    4       3               
                    -- x + x , Polynom[2][1]
                    15                      
                 4   2    4   4                
                 -- x  + x  + --, Polynom[2][2]
                 21           45               
             Matrix(%id = 18446745693991291350), 1
                             testb1
                               0
                               0
                             testb2
          Matrix(%id = 18446745693991291350),

            Vector[column](%id = 18446745693991291470)
             Matrix(%id = 18446745693991291350), 1
             Matrix(%id = 18446745693991291350), 1
                             testb1
                               0
                               0
                             testb2
          Matrix(%id = 18446745693991291350),

            Vector[column](%id = 18446745693991291470)
             Matrix(%id = 18446745693991291350), 1
             Matrix(%id = 18446745693991291350), 1
             Matrix(%id = 18446745693991291350), 1
                             testb1
                              16
                              ---
                              245
                               0
                             testb2
          Matrix(%id = 18446745693991291350),

            Vector[column](%id = 18446745693991291470)
             Matrix(%id = 18446745693991291350), 1
             Matrix(%id = 18446745693991291350), 1
             Matrix(%id = 18446745693991291350), 1
             Matrix(%id = 18446745693991291350), 1
                             testb1
                               0
                               0
                             testb2
          Matrix(%id = 18446745693991291350),

            Vector[column](%id = 18446745693991291470)
          Matrix(%id = 18446745693991291350),

            Vector[column](%id = 18446745693991291470)
           Vector[column](%id = 18446745693991291830)
                                  9
                           test2, --
                                  35
                               0
                           7             
                       0, x , 0, Koeff, 0
                           7             
                       0, x , 1, Koeff, 0
                           7             
                       0, x , 2, Koeff, 0
                           7             
                       0, x , 3, Koeff, 1
                     49   6    8             
                  0, --- x  + x , 0, Koeff, 0
                     195                     
                     49   6    8             
                  0, --- x  + x , 1, Koeff, 0
                     195                     
                     49   6    8             
                  0, --- x  + x , 2, Koeff, 0
                     195                     
                     49   6    8             
                  0, --- x  + x , 3, Koeff, 1
                     195                     
                112  7    9   588   5             
             0, --- x  + x  + ---- x , 0, Koeff, 0
                663           9295                
                112  7    9   588   5             
             0, --- x  + x  + ---- x , 1, Koeff, 0
                663           9295                
                112  7    9   588   5             
             0, --- x  + x  + ---- x , 2, Koeff, 0
                663           9295                
                112  7    9   588   5             
             0, --- x  + x  + ---- x , 3, Koeff, 1
                663           9295                
         2352   6   189   8    10    980   4             
      0, ----- x  + ---- x  + x   + ----- x , 0, Koeff, 0
         60775      1235            61347                
         2352   6   189   8    10    980   4             
      0, ----- x  + ---- x  + x   + ----- x , 1, Koeff, 0
         60775      1235            61347                
         2352   6   189   8    10    980   4             
      0, ----- x  + ---- x  + x   + ----- x , 2, Koeff, 0
         60775      1235            61347                
         2352   6   189   8    10    980   4             
      0, ----- x  + ---- x  + x   + ----- x , 3, Koeff, 1
         60775      1235            61347                
    896   5    7776   7   40   9    11    2240   3             
0, ----- x  + ------ x  + --- x  + x   + ------ x , 0, Koeff, 0
   94809      230945      273            552123                
    896   5    7776   7   40   9    11    2240   3             
0, ----- x  + ------ x  + --- x  + x   + ------ x , 1, Koeff, 0
   94809      230945      273            552123                
    896   5    7776   7   40   9    11    2240   3             
0, ----- x  + ------ x  + --- x  + x   + ------ x , 2, Koeff, 0
   94809      230945      273            552123                
   2240    896   5    7776   7   40   9    11    2240   3     
  ------, ----- x  + ------ x  + --- x  + x   + ------ x , 3,
  552123  94809      230945      273            552123        

    Koeff, 1
                               0
                               0
                               0
                               0
                               0
/    1   (1/2)\   /    1   (1/2)\       155   10  2    4       
|x + - 15     | x |x - - 15     |, alt, --- - -- x  + x , neu,
\    5        /   \    5        /       891   9                

  /    1   (1/2)\   /    1   (1/2)\ /155   10  2    4\
  |x + - 15     | x |x - - 15     | |--- - -- x  + x |
  \    5        /   \    5        / \891   9         /
 Testergebnis,

      2459840   5    80254400        188027200   3    2240   7
   - --------- x  - ----------- x + ----------- x  + ------ x
     193795173      44766684963     19185722127      552123   
-0.9604912687, -0.7745966692, -0.4342437493, 0., 0.4342437493,

  0.7745966692, 0.9604912687, -1.435338337, -0.8946894490,

  -0.5176357564, 0., 0.5176357564, 0.8946894490, 1.435338337
                        [0, 0, 0, 1, 0] #!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
                             test21
Error, (in NEUZMinus) invalid subscript selector

 

Doing a routine simplification but got an error...Dont know where the mistake comes from.

 

simplification_error.mw

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