Maple Questions and Posts

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Please I need Correction on this code particularly if I can make do without the declaration of vector in the third subroutine . The idea is to get maximum error. The code has 3 subroutine. The problem I think is in the third subroutine (Display of results).

Thank you in anticipation of positive response.

# First Declaration of the problem

restart:
Digits:=30:
interface(rtablesize=infinity):

f1:=proc(n)
    y2[n]:
end proc:
f2:=proc(n)
    -y1[n]+0.001*cos(t[n]):
end proc:
f3:=proc(n)
    y4[n]:
end proc:
f4:=proc(n)
    -y3[n]+0.001*sin(t[n]):
end proc:
F1:=proc(n)
    f2(n):
end proc:
F2:=proc(n)
    -(f1(n))-0.001*sin(t[n]):
end proc:
F3:=proc(n)
    f4(n):
end proc:
F4:=proc(n)
    -f3(n)+0.001*cos(t[n]):
end proc:


# Declaration of the Numerical methods

e1:=y1[n+2] = (7/23)*y1[n]+(16/23)*y1[n+1]+(12/23)*f1(n+2)*h+(16/23)*f1(n+1)*h-(2/23)*F1(n+2)*h^2+(2/23)*h*f1(n)+((24/3703)*y1[n]-(24/3703)*y1[n+1]+(48/18515)*f1(n+2)*h+(8/55545)*f1(n+1)*h-(116/55545)*F1(n+2)*h^2+(208/55545)*h*f1(n))*u^2+((901/2980915)*y1[n]-(901/2980915)*y1[n+1]+(7109/89427450)*f1(n+2)*h+(923/14904575)*f1(n+1)*h-(6241/89427450)*F1(n+2)*h^2+(14383/89427450)*h*f1(n))*u^4+((1979723/158376013950)*y1[n]-(1979723/158376013950)*y1[n+1]+(6364571/2375640209250)*f1(n+2)*h+(728327/215967291750)*f1(n+1)*h-(11785633/4751280418500)*F1(n+2)*h^2+(5106559/791880069750)*h*f1(n))*u^6+((6488435581/13259239887894000)*y1[n]-(6488435581/13259239887894000)*y1[n+1]+(8693517709/91794737685420000)*f1(n+2)*h+(260601208141/1789997384865690000)*f1(n+1)*h-(323357994149/3579994769731380000)*F1(n+2)*h^2+(891627999937/3579994769731380000)*h*f1(n))*u^8+((25090513463/1343541160668420000)*y1[n]-(25090513463/1343541160668420000)*y1[n+1]+(190450718149/55421072877572325000)*f1(n+2)*h+(47563947061/8210529315195900000)*f1(n+1)*h-(1475729910283/443368583020578600000)*F1(n+2)*h^2+(261738159769/27710536438786162500)*h*f1(n))*u^10+((244426606265778733/347060946154014557665200000)*y1[n]-(244426606265778733/347060946154014557665200000)*y1[n+1]+(1316372988977975777/10411828384620436729956000000)*f1(n+2)*h+(105391490263288387/473264926573656214998000000)*f1(n+1)*h-(1284959669761615073/10411828384620436729956000000)*F1(n+2)*h^2+(72506125749079249/204153497737655622156000000)*h*f1(n))*u^12:

e2:=h^2*F1(n+1) = (60/23)*y1[n]-(60/23)*y1[n+1]+(25/46)*f1(n+2)*h+(32/23)*f1(n+1)*h-(4/23)*F1(n+2)*h^2+(31/46)*h*f1(n)+((209/3703)*y1[n]-(209/3703)*y1[n+1]+(1313/222180)*f1(n+2)*h+(1304/55545)*f1(n+1)*h-(131/18515)*F1(n+2)*h^2+(6011/222180)*h*f1(n))*u^2+((77491/35770980)*y1[n]-(77491/35770980)*y1[n+1]+(574843/2146258800)*f1(n+2)*h+(113536/134141175)*f1(n+1)*h-(53461/178854900)*F1(n+2)*h^2+(2258041/2146258800)*h*f1(n))*u^4+((151508243/1900512167400)*y1[n]-(151508243/1900512167400)*y1[n+1]+(1290306599/114030730044000)*f1(n+2)*h+(18919693/647901875250)*f1(n+1)*h-(113769323/9502560837000)*F1(n+2)*h^2+(4470322013/114030730044000)*h*f1(n))*u^6+((42120775181/14464625332248000)*y1[n]-(42120775181/14464625332248000)*y1[n+1]+(332746636891/734357901483360000)*f1(n+2)*h+(302396120633/298332897477615000)*f1(n+1)*h-(369019384141/795554393273640000)*F1(n+2)*h^2+(13797329479621/9546652719283680000)*h*f1(n))*u^8+((18953368786273/177347433208231440000)*y1[n]-(18953368786273/177347433208231440000)*y1[n+1]+(2430202319484337/138330997902420523200000)*f1(n+2)*h+(310803544671199/8645687368901282700000)*f1(n+1)*h-(203453960588449/11527583158535043600000)*F1(n+2)*h^2+(7380568619069419/138330997902420523200000)*h*f1(n))*u^10+((16436168060905785763/4164731353848174691982400000)*y1[n]-(16436168060905785763/4164731353848174691982400000)*y1[n+1]+(167160345356705269819/249883881230890481518944000000)*f1(n+2)*h+(461636091223370027/354948694930242161248500000)*f1(n+1)*h-(13852288092290788813/20823656769240873459912000000)*F1(n+2)*h^2+(29059878239787610409/14699051837111204795232000000)*h*f1(n))*u^12:


e3:=y2[n+2] = (7/23)*y2[n]+(16/23)*y2[n+1]+(12/23)*f2(n+2)*h+(16/23)*f2(n+1)*h-(2/23)*F2(n+2)*h^2+(2/23)*h*f2(n)+((24/3703)*y2[n]-(24/3703)*y2[n+1]+(48/18515)*f2(n+2)*h+(8/55545)*f2(n+1)*h-(116/55545)*F2(n+2)*h^2+(208/55545)*h*f2(n))*u^2+((901/2980915)*y2[n]-(901/2980915)*y2[n+1]+(7109/89427450)*f2(n+2)*h+(923/14904575)*f2(n+1)*h-(6241/89427450)*F2(n+2)*h^2+(14383/89427450)*h*f2(n))*u^4+((1979723/158376013950)*y2[n]-(1979723/158376013950)*y2[n+1]+(6364571/2375640209250)*f2(n+2)*h+(728327/215967291750)*f2(n+1)*h-(11785633/4751280418500)*F2(n+2)*h^2+(5106559/791880069750)*h*f2(n))*u^6+((6488435581/13259239887894000)*y2[n]-(6488435581/13259239887894000)*y2[n+1]+(8693517709/91794737685420000)*f2(n+2)*h+(260601208141/1789997384865690000)*f2(n+1)*h-(323357994149/3579994769731380000)*F2(n+2)*h^2+(891627999937/3579994769731380000)*h*f2(n))*u^8+((25090513463/1343541160668420000)*y2[n]-(25090513463/1343541160668420000)*y2[n+1]+(190450718149/55421072877572325000)*f2(n+2)*h+(47563947061/8210529315195900000)*f2(n+1)*h-(1475729910283/443368583020578600000)*F2(n+2)*h^2+(261738159769/27710536438786162500)*h*f2(n))*u^10+((244426606265778733/347060946154014557665200000)*y2[n]-(244426606265778733/347060946154014557665200000)*y2[n+1]+(1316372988977975777/10411828384620436729956000000)*f2(n+2)*h+(105391490263288387/473264926573656214998000000)*f2(n+1)*h-(1284959669761615073/10411828384620436729956000000)*F2(n+2)*h^2+(72506125749079249/204153497737655622156000000)*h*f2(n))*u^12:

e4:=h^2*F2(n+1) = (60/23)*y2[n]-(60/23)*y2[n+1]+(25/46)*f2(n+2)*h+(32/23)*f2(n+1)*h-(4/23)*F2(n+2)*h^2+(31/46)*h*f2(n)+((209/3703)*y2[n]-(209/3703)*y2[n+1]+(1313/222180)*f2(n+2)*h+(1304/55545)*f2(n+1)*h-(131/18515)*F2(n+2)*h^2+(6011/222180)*h*f2(n))*u^2+((77491/35770980)*y2[n]-(77491/35770980)*y2[n+1]+(574843/2146258800)*f2(n+2)*h+(113536/134141175)*f2(n+1)*h-(53461/178854900)*F2(n+2)*h^2+(2258041/2146258800)*h*f2(n))*u^4+((151508243/1900512167400)*y2[n]-(151508243/1900512167400)*y2[n+1]+(1290306599/114030730044000)*f2(n+2)*h+(18919693/647901875250)*f2(n+1)*h-(113769323/9502560837000)*F2(n+2)*h^2+(4470322013/114030730044000)*h*f2(n))*u^6+((42120775181/14464625332248000)*y2[n]-(42120775181/14464625332248000)*y2[n+1]+(332746636891/734357901483360000)*f2(n+2)*h+(302396120633/298332897477615000)*f2(n+1)*h-(369019384141/795554393273640000)*F2(n+2)*h^2+(13797329479621/9546652719283680000)*h*f2(n))*u^8+((18953368786273/177347433208231440000)*y2[n]-(18953368786273/177347433208231440000)*y2[n+1]+(2430202319484337/138330997902420523200000)*f2(n+2)*h+(310803544671199/8645687368901282700000)*f2(n+1)*h-(203453960588449/11527583158535043600000)*F2(n+2)*h^2+(7380568619069419/138330997902420523200000)*h*f2(n))*u^10+((16436168060905785763/4164731353848174691982400000)*y2[n]-(16436168060905785763/4164731353848174691982400000)*y2[n+1]+(167160345356705269819/249883881230890481518944000000)*f2(n+2)*h+(461636091223370027/354948694930242161248500000)*f2(n+1)*h-(13852288092290788813/20823656769240873459912000000)*F2(n+2)*h^2+(29059878239787610409/14699051837111204795232000000)*h*f2(n))*u^12:

e5:=y3[n+2] = (7/23)*y3[n]+(16/23)*y3[n+1]+(12/23)*f3(n+2)*h+(16/23)*f3(n+1)*h-(2/23)*F3(n+2)*h^2+(2/23)*h*f3(n)+((24/3703)*y3[n]-(24/3703)*y3[n+1]+(48/18515)*f3(n+2)*h+(8/55545)*f3(n+1)*h-(116/55545)*F3(n+2)*h^2+(208/55545)*h*f3(n))*u^2+((901/2980915)*y3[n]-(901/2980915)*y3[n+1]+(7109/89427450)*f3(n+2)*h+(923/14904575)*f3(n+1)*h-(6241/89427450)*F3(n+2)*h^2+(14383/89427450)*h*f3(n))*u^4+((1979723/158376013950)*y3[n]-(1979723/158376013950)*y3[n+1]+(6364571/2375640209250)*f3(n+2)*h+(728327/215967291750)*f3(n+1)*h-(11785633/4751280418500)*F3(n+2)*h^2+(5106559/791880069750)*h*f3(n))*u^6+((6488435581/13259239887894000)*y3[n]-(6488435581/13259239887894000)*y3[n+1]+(8693517709/91794737685420000)*f3(n+2)*h+(260601208141/1789997384865690000)*f3(n+1)*h-(323357994149/3579994769731380000)*F3(n+2)*h^2+(891627999937/3579994769731380000)*h*f3(n))*u^8+((25090513463/1343541160668420000)*y3[n]-(25090513463/1343541160668420000)*y3[n+1]+(190450718149/55421072877572325000)*f3(n+2)*h+(47563947061/8210529315195900000)*f3(n+1)*h-(1475729910283/443368583020578600000)*F3(n+2)*h^2+(261738159769/27710536438786162500)*h*f3(n))*u^10+((244426606265778733/347060946154014557665200000)*y3[n]-(244426606265778733/347060946154014557665200000)*y3[n+1]+(1316372988977975777/10411828384620436729956000000)*f3(n+2)*h+(105391490263288387/473264926573656214998000000)*f3(n+1)*h-(1284959669761615073/10411828384620436729956000000)*F3(n+2)*h^2+(72506125749079249/204153497737655622156000000)*h*f3(n))*u^12:
e6:=h^2*F3(n+1) = (60/23)*y3[n]-(60/23)*y3[n+1]+(25/46)*f3(n+2)*h+(32/23)*f3(n+1)*h-(4/23)*F3(n+2)*h^2+(31/46)*h*f3(n)+((209/3703)*y3[n]-(209/3703)*y3[n+1]+(1313/222180)*f3(n+2)*h+(1304/55545)*f3(n+1)*h-(131/18515)*F3(n+2)*h^2+(6011/222180)*h*f3(n))*u^2+((77491/35770980)*y3[n]-(77491/35770980)*y3[n+1]+(574843/2146258800)*f3(n+2)*h+(113536/134141175)*f3(n+1)*h-(53461/178854900)*F3(n+2)*h^2+(2258041/2146258800)*h*f3(n))*u^4+((151508243/1900512167400)*y3[n]-(151508243/1900512167400)*y3[n+1]+(1290306599/114030730044000)*f3(n+2)*h+(18919693/647901875250)*f3(n+1)*h-(113769323/9502560837000)*F3(n+2)*h^2+(4470322013/114030730044000)*h*f3(n))*u^6+((42120775181/14464625332248000)*y3[n]-(42120775181/14464625332248000)*y3[n+1]+(332746636891/734357901483360000)*f3(n+2)*h+(302396120633/298332897477615000)*f3(n+1)*h-(369019384141/795554393273640000)*F3(n+2)*h^2+(13797329479621/9546652719283680000)*h*f3(n))*u^8+((18953368786273/177347433208231440000)*y3[n]-(18953368786273/177347433208231440000)*y3[n+1]+(2430202319484337/138330997902420523200000)*f3(n+2)*h+(310803544671199/8645687368901282700000)*f3(n+1)*h-(203453960588449/11527583158535043600000)*F3(n+2)*h^2+(7380568619069419/138330997902420523200000)*h*f3(n))*u^10+((16436168060905785763/4164731353848174691982400000)*y3[n]-(16436168060905785763/4164731353848174691982400000)*y3[n+1]+(167160345356705269819/249883881230890481518944000000)*f3(n+2)*h+(461636091223370027/354948694930242161248500000)*f3(n+1)*h-(13852288092290788813/20823656769240873459912000000)*F3(n+2)*h^2+(29059878239787610409/14699051837111204795232000000)*h*f3(n))*u^12:

e7:=y4[n+2] = (7/23)*y4[n]+(16/23)*y4[n+1]+(12/23)*f4(n+2)*h+(16/23)*f4(n+1)*h-(2/23)*F4(n+2)*h^2+(2/23)*h*f4(n)+((24/3703)*y4[n]-(24/3703)*y4[n+1]+(48/18515)*f4(n+2)*h+(8/55545)*f4(n+1)*h-(116/55545)*F4(n+2)*h^2+(208/55545)*h*f4(n))*u^2+((901/2980915)*y4[n]-(901/2980915)*y4[n+1]+(7109/89427450)*f4(n+2)*h+(923/14904575)*f4(n+1)*h-(6241/89427450)*F4(n+2)*h^2+(14383/89427450)*h*f4(n))*u^4+((1979723/158376013950)*y4[n]-(1979723/158376013950)*y4[n+1]+(6364571/2375640209250)*f4(n+2)*h+(728327/215967291750)*f4(n+1)*h-(11785633/4751280418500)*F4(n+2)*h^2+(5106559/791880069750)*h*f4(n))*u^6+((6488435581/13259239887894000)*y4[n]-(6488435581/13259239887894000)*y4[n+1]+(8693517709/91794737685420000)*f4(n+2)*h+(260601208141/1789997384865690000)*f4(n+1)*h-(323357994149/3579994769731380000)*F4(n+2)*h^2+(891627999937/3579994769731380000)*h*f4(n))*u^8+((25090513463/1343541160668420000)*y4[n]-(25090513463/1343541160668420000)*y4[n+1]+(190450718149/55421072877572325000)*f4(n+2)*h+(47563947061/8210529315195900000)*f4(n+1)*h-(1475729910283/443368583020578600000)*F4(n+2)*h^2+(261738159769/27710536438786162500)*h*f4(n))*u^10+((244426606265778733/347060946154014557665200000)*y4[n]-(244426606265778733/347060946154014557665200000)*y4[n+1]+(1316372988977975777/10411828384620436729956000000)*f4(n+2)*h+(105391490263288387/473264926573656214998000000)*f4(n+1)*h-(1284959669761615073/10411828384620436729956000000)*F4(n+2)*h^2+(72506125749079249/204153497737655622156000000)*h*f4(n))*u^12:

e8:=h^2*F4(n+1) = (60/23)*y4[n]-(60/23)*y4[n+1]+(25/46)*f4(n+2)*h+(32/23)*f4(n+1)*h-(4/23)*F4(n+2)*h^2+(31/46)*h*f4(n)+((209/3703)*y4[n]-(209/3703)*y4[n+1]+(1313/222180)*f4(n+2)*h+(1304/55545)*f4(n+1)*h-(131/18515)*F4(n+2)*h^2+(6011/222180)*h*f4(n))*u^2+((77491/35770980)*y4[n]-(77491/35770980)*y4[n+1]+(574843/2146258800)*f4(n+2)*h+(113536/134141175)*f4(n+1)*h-(53461/178854900)*F4(n+2)*h^2+(2258041/2146258800)*h*f4(n))*u^4+((151508243/1900512167400)*y4[n]-(151508243/1900512167400)*y4[n+1]+(1290306599/114030730044000)*f4(n+2)*h+(18919693/647901875250)*f4(n+1)*h-(113769323/9502560837000)*F4(n+2)*h^2+(4470322013/114030730044000)*h*f4(n))*u^6+((42120775181/14464625332248000)*y4[n]-(42120775181/14464625332248000)*y4[n+1]+(332746636891/734357901483360000)*f4(n+2)*h+(302396120633/298332897477615000)*f4(n+1)*h-(369019384141/795554393273640000)*F4(n+2)*h^2+(13797329479621/9546652719283680000)*h*f4(n))*u^8+((18953368786273/177347433208231440000)*y4[n]-(18953368786273/177347433208231440000)*y4[n+1]+(2430202319484337/138330997902420523200000)*f4(n+2)*h+(310803544671199/8645687368901282700000)*f4(n+1)*h-(203453960588449/11527583158535043600000)*F4(n+2)*h^2+(7380568619069419/138330997902420523200000)*h*f4(n))*u^10+((16436168060905785763/4164731353848174691982400000)*y4[n]-(16436168060905785763/4164731353848174691982400000)*y4[n+1]+(167160345356705269819/249883881230890481518944000000)*f4(n+2)*h+(461636091223370027/354948694930242161248500000)*f4(n+1)*h-(13852288092290788813/20823656769240873459912000000)*F4(n+2)*h^2+(29059878239787610409/14699051837111204795232000000)*h*f4(n))*u^12:

# Display of the solutions


h:=evalf(Pi/6):

omega:=1.0:
u:=omega*h:
N:=solve(h*p = 12*Pi/6, p):
n:=0:

exy1:= [seq](eval(cos(i)+0.0005*i*sin(i)), i=h..N,h):
exy2:= [seq](eval(-0.9995*sin(i)+0.0005), i=h..N,h):
exy3:= [seq](eval(sin(i)-0.0005*i*cos(i)), i=h..N,h):
exy4:= [seq](eval(0.9995*sin(i)+0.0005*i*sin(i)), i=h..N,h):

iny1:=1:
iny2:=0:
iny3:=0:
iny4:=0.9995:

err1 := Vector(N):
err2 := Vector(N):
c:=1:
inx:=0:
vars := y1[n+1],y1[n+2],y2[n+1],y2[n+2],y3[n+1],y3[n+2],y4[n+1],y4[n+2]:
for j from 0 to 2 do
    x[j]:=inx+j*h:
end do:
printf("%4s%9s%9s%9s%9s%9s%9s%10s%10s%9s%9s%9s%10s\n",
    "h","numy1","numy2","numy3","numy4",
    "exy1","exy2","exy3","exy4",
    "erry1","erry2","erry3","erry4");
    
st := time():
for k from 1 to N/2 do
    param1:=y1[n]=iny1,y2[n]=iny2,y3[n]=iny3,y4[n]=iny4:
    param2:=t[n]=x[0],t[n+1]=x[1],t[n+2]=x[2]:
    
    res:=eval(<vars>, fsolve(eval({e||(1..8)},[param1,param2]),{vars})):
    
    for i from 1 to 2 do
        printf("%5.2f%9.3f%9.3f%9.3f%9.3f %8.5f%10.5f%10.5f%10.5f %8.2g%9.3g%9.3g%8.3g\n",
        h*c,res[i],res[i+2],res[i+4],res[i+6],
        exy1[c],exy2[c],exy3[c],exy4[c],
        abs(res[i]-exy1[c]),abs(res[i+2]-exy2[c]),abs(res[i+4]-exy3[c]),abs(res[i+6]-exy4[c])):

        err1[c] := abs(evalf(res[i]-exy1)):
        err2[c] := abs(evalf(res[i+4]-exy3)):
        c:=c+1:
    end do:
    iny1:=res[2]:
    iny2:=res[4]:
    iny3:=res[6]:
    iny4:=res[8]:
    inx:=x[2]:
    for j from 0 to 2 do
        x[j]:=inx+j*h:
    end do:
end do:
v:=time() - st;
printf("Maximum error is %.13g", max(err1));
printf("Maximum error is %.13g", max(err2));

 

i got some trouble when i tried to build large matrix. in my case, notification error out of bound appear when looping stop at 9 from 24 repeatation. 

and this is my looping command:

the result of the script was:

now i feel so desperate so finish my final project because the error, please help me

Hello,
I try to visualize this formula in a 3D graphic.
However, I get again and again this error message displayed and unfortunately knows no more solution.
I am a total beginner with Maple, I hope here can help me.

plot3d(100*(0,15+0,035*x)+100*(0,15+0,035*9), 100*(35*9))+0,05*(100-(100*(0,15+0,035*x)))*(0,15+9*y), x = 2 .. 9, y = 0, 1 .. 0, 45, axes = boxed);

Error, (in plot3d) unexpected options: [5*(100+(0, -1500, -3500*x))*(0, 15+9*y), x = 2 .. 9, y = 0, 1 .. 0, 45]

 

Hi everyone

I am stuck in my code. I have a multivariate polynomial and I am trying to define an order on the variables such that I can write my polynomials in a desired normal form. I tried with the Groebner package but that's quite different from what I want.

I want to define the order on the variables as u[i]=v[i] and u[i]<u[i+1].

Lets say my polynomial is f then,

input f= u[1]^2+u[2]+v[3]

output f = v[3]+u[2]+u[1]^2.

If there is a clash between u and v then, either of them can come first, for example,

input f= u[1]^2+u[2]+v[3]+u[3]^2

 output f=v[3]+u[3]^2+u[2]+u[1]^2 or f=u[3]^2+v[3]+u[2]+u[1]^2

I hope my question is clear. Thank you for helping me out. Your time is much appreciated :)

Dear all,

I have the following problem: Maple does not simplify the denominator in the following example:

which gives

16*a^8*B/((dz*L*sqrt(s)*sqrt(s+c)*sqrt(L^2*s*(s+c)*dz^2+4*a^2)+L^2*s*(s+c)*dz^2+2*a^2)^2*(-dz*L*sqrt(s)*sqrt(s+c)*sqrt(L^2*s*(s+c)*dz^2+4*a^2)+L^2*s*(s+c)*dz^2+2*a^2)^2)

However, the result should be B. If only the denomiator is expanded it works: 

gives

16*a^8

which equals the nominator except for the B...

How can I use simplify in order to yield the desired result? 

Thanks a lot!

 

 

 

Hello maple users. 

I am learning to use this incredible software, but I am not getting to obtain all binary 4x4 matrices of rank 3 and 4?

Anyone knows how to do that ?

Thanks
My best regards!

Gustavo

Hello

Dear I want to solve the system of ODEs in attached file for different values of m1 i.e., 3,4,5 how I will use the value of m1 in dsolve. I am waiting your positive response thanks in advance.

Help.mw

 

Hi, My Error is this:

DEtools; DEplot(MODEL, VARS, DOMAIN, RANGE, [IC1, IC2], stepsize = .1, arrows = THIN, linecolor = COLORS);
%;
Error, (in DEtools/DEplot) invalid range for independent variablehow can i remove error?

Hi,

Why pdsolve is not correctly solving the following

where I get    

but it is correctly solving the next one

where I get ???

 

I see that it is due to the fact that the variable x is multiplied by a constant, but why is not maple able to manage that?

 

Thanks for your help,

Javier

 

 

 

 

 

 

Hi Mapleprimes,

I wrote some quick maple code -

for a from 1 to 10 do
if isprime(a)=false then print(ifactor(a)) else print('1',a) end do;
end do

I want to use the factors command to reproduce oeis.org/A027750/

Can anyone help me with this?

Regards,

Matt

 

Good day!

As part of an exercise I've calculated the length of a hypotrochoid numerically. To check my result I repeated the calculation in Maple, but received a different result. When double checking using WolframAlpha I got the same result as with my numerics. Maybe someone of you can tell me where I made a mistake.

Thanks in advance.
Sören


Link to WolframAlpha calculation: http://www.wolframalpha.com/input/?i=x%28t%29+%3D+%281-0.6%29+cos%28t%29+%2B+0.8+cos+%28+%281-0.6%29%2F0.6+*+t%29,+y%28t%29+%3D+%281-0.6%29+sin%28t%29+-+0.8+sin+%28+%281-0.6%29%2F0.6+*+t%29+from+t%3D0+to+6*pi

restart; with(VectorCalculus)

R := 1;

1

 

.6

 

.8

(1)

x := proc (t) options operator, arrow; (R-r)*cos(t)+d*cos((R-r)*t/r) end proc:

y := proc (t) options operator, arrow; (R-r)*sin(t)-d*sin((R-r)*t/r) end proc:

plot([x(t), y(t), t = 0 .. VectorCalculus:-`*`(6, Pi)]);

 

ArcLength(`<,>`(x(t), y(t)), t = 0 .. VectorCalculus:-`*`(6, Pi))

12.67823876+0.*I

(2)

diff(x(t), t);

-.4*sin(t)-.5333333334*sin(.6666666668*t)

(3)

diff(y(t), t)

.4*cos(t)-.5333333334*cos(.6666666668*t)

(4)

sqrt(VectorCalculus:-`+`((-.4*sin(t)-.5333333334*sin(.6666666668*t))^2, (.4*cos(t)-.5333333334*cos(.6666666668*t))^2))

((-.4*sin(t)-.5333333334*sin(.6666666668*t))^2+(.4*cos(t)-.5333333334*cos(.6666666668*t))^2)^(1/2)

(5)

simplify(((-.4*sin(t)-.5333333334*sin(.6666666668*t))^2+(.4*cos(t)-.5333333334*cos(.6666666668*t))^2)^(1/2))

(.4444444445+.4266666668*sin(t)*sin(.6666666668*t)-.4266666668*cos(t)*cos(.6666666668*t))^(1/2)

(6)

int(((-.4*sin(t)-.5333333334*sin(.6666666668*t))^2+(.4*cos(t)-.5333333334*cos(.6666666668*t))^2)^(1/2), t = 0 .. VectorCalculus:-`*`(6, Pi))

12.67823876+0.*I

(7)

int(((-.4*sin(t)-.5333333334*sin(.6666666668*t))^2+(.4*cos(t)-.5333333334*cos(.6666666668*t))^2)^(1/2), t)

-1.120000000*((0.2133333334e20*cos(.8333333334*t)^2-0.2177777778e20)*(cos(.8333333334*t)^2-1.))^(1/2)*(-1.*cos(.8333333334*t)^2+1.)^(1/2)*EllipticE(cos(.8333333334*t), .9897433186)/((0.2133333334e20*cos(.8333333334*t)^4-0.4311111112e20*cos(.8333333334*t)^2+0.2177777778e20)^(1/2)*sin(.8333333334*t))

(8)

evalf(VectorCalculus:-`+`(limit(-1.120000000*((0.2133333334e20*cos(.8333333334*t)^2-0.2177777778e20)*(cos(.8333333334*t)^2-1.))^(1/2)*(-1.*cos(.8333333334*t)^2+1.)^(1/2)*EllipticE(cos(.8333333334*t), .9897433186)/((0.2133333334e20*cos(.8333333334*t)^4-0.4311111112e20*cos(.8333333334*t)^2+0.2177777778e20)^(1/2)*sin(.8333333334*t)), t = VectorCalculus:-`*`(6, Pi)), VectorCalculus:-`-`(limit(-1.120000000*((0.2133333334e20*cos(.8333333334*t)^2-0.2177777778e20)*(cos(.8333333334*t)^2-1.))^(1/2)*(-1.*cos(.8333333334*t)^2+1.)^(1/2)*EllipticE(cos(.8333333334*t), .9897433186)/((0.2133333334e20*cos(.8333333334*t)^4-0.4311111112e20*cos(.8333333334*t)^2+0.2177777778e20)^(1/2)*sin(.8333333334*t)), t = 0))))

Float(undefined)

(9)

simplify(diff(-1.120000000*((0.2133333334e20*cos(.8333333334*t)^2-0.2177777778e20)*(cos(.8333333334*t)^2-1.))^(1/2)*(-1.*cos(.8333333334*t)^2+1.)^(1/2)*EllipticE(cos(.8333333334*t), .9897433186)/((0.2133333334e20*cos(.8333333334*t)^4-0.4311111112e20*cos(.8333333334*t)^2+0.2177777778e20)^(1/2)*sin(.8333333334*t)), t))

.9333333334*(1.-.9795918367*cos(.8333333334*t)^2)^(1/2)

(10)

``

Download hypotrochoid.mw

I have a complex function for both the electric and magnetic fields for 2 laser pluses colliding they are only 2 dimensions z,t;

E(z,t) := -I*a*exp(-(z-Z+t)^2/sigma^2)*sin(omega*(z-Z+t))+a*exp(-(z+Z-t)^2/sigma^2)*sin(omega*(z+Z-t))

B(z,t) := -a*exp(-(z-Z+t)^2/sigma^2)*sin(omega*(z-Z+t))+I*a*exp(-(z+Z-t)^2/sigma^2)*sin(omega*(z+Z-t))

Where a,omegasigma are real constants and Z is the initial offset for the pluses,

I would like to plot them together with there real and imaginary parts on two axes and then extended along the z direction, if possible I would like to animate them. To hopefully get a moving plot like this except it's a laser pluse not a continuous wave,

Hey guys,

I have the following occurence:

ii_inf:=x^(2-s)*(x^(-s)*GAMMA(3-s)*GAMMA(2-2*s)/(GAMMA(2-s)*GAMMA(3-2*s))+x^(s-2)*GAMMA(3-s)*GAMMA(2*s-2)/GAMMA(s))/(2-s)+(1/2)*(2*s*x-x+1)*(x+1)/(((x+1)^s)^2*(2*s^2-3*s+1))+x^(1-s)*(x^(-s)*GAMMA(2-s)*GAMMA(-2*s+1)/(GAMMA(1-s)*GAMMA(2-2*s))+x^(-1+s)*GAMMA(2-s)*GAMMA(2*s-1)/GAMMA(s))/(1-s)+(x+1)/((2*s-1)*((x+1)^s)^2)+x/((-1+s)*x^s)-(x+1)/((-1+s)*(x+1)^s);

ii_inf=simplify(ii_inf);

asympt(ii_inf,x,3);

Multiseries:-asympt(ii_inf,x,1);
gives different results...the last one however seems to be the correct one...

What is happening here?

 

I want to solve the problem described below. I tried using two methods as shown below, each method has been runing for days without solving it. I will really appreciate your help.

 
Thanks for your help.

 

Det1 := (1/256)*(Aiso*(c+t)^2*(a^2+b^2)*(mu-1)*Pi^2-4*a^2*b^2*c*Gc)*(16*Aiso^2*Do^2*(c+t)^4*(a^2+b^2)^6*Pi^12+10*(a^2+b^2)^5*((c+t)^2*Aiso+4*Do)*Gc*(c+t)^2*c*a^2*Do*b^2*Aiso*Pi^10+(a^2+b^2)^4*((c+t)^2*Aiso+4*Do)^2*Gc^2*c^2*a^4*b^4*Pi^8-(1024/81)*a^6*Aiso^2*b^6*Tcr^2*(c+t)^4*(a^2+b^2)^2*Pi^4-(2560/81)*a^8*Aiso*b^8*c*Gc*Tcr^2*(c+t)^2*(a^2+b^2)*Pi^2-(1024/81)*a^10*b^10*c^2*Gc^2*Tcr^2)*(Aiso*(c+t)^2*(a^2+4*b^2)*(mu-1)*Pi^2-4*a^2*b^2*c*Gc)*(Aiso*(c+t)^2*(a^2+b^2)*(mu-1)*Pi^2-a^2*b^2*c*Gc)*(16*(c+t)^4*(a^2+(1/4)*b^2)^3*Do^2*(a^2+4*b^2)^3*Aiso^2*Pi^12+(10*(a^2+b^2))*((c+t)^2*Aiso+4*Do)*Gc*(c+t)^2*(a^2+(1/4)*b^2)^2*c*a^2*Do*(a^2+4*b^2)^2*b^2*Aiso*Pi^10+((c+t)^2*Aiso+4*Do)^2*Gc^2*(a^2+(1/4)*b^2)^2*c^2*a^4*(a^2+4*b^2)^2*b^4*Pi^8-(1024/81)*(c+t)^4*(a^2+(1/4)*b^2)*Tcr^2*a^6*(a^2+4*b^2)*b^6*Aiso^2*Pi^4-(2560/81)*a^8*Aiso*b^8*c*Gc*Tcr^2*(c+t)^2*(a^2+b^2)*Pi^2-(1024/81)*a^10*b^10*c^2*Gc^2*Tcr^2)*((mu-1)*(c+t)^2*(a^2+(1/4)*b^2)*Aiso*Pi^2-a^2*b^2*c*Gc)/(b^20*a^20*(c+t)^16) = 0;

 

# method 1;
EQN := RootOf(Det1, Tcr);

EQN_2 := allvalues(EQN);

# method 2;

EQN := solve(Det1, Tcr);

mar.mw
hi..how i can dsolve these differential equations? omega is unknown and fir solving i add an extra boundary condition, but the error "unable to store %1 when datatype=%2" is appear!!!

how i can remove this error?

thanks

dsys3 := {-6*(diff(f5(x), x, x))+2*f3(x)-(22/3)*f5(x)*omega^2-(2/3)*f4(x)*omega^2+(1/3)*(diff(f1(x), x))*omega^2-(2/3)*(diff(f2(x), x))*omega^2-(14/5)*(diff(f2(x), x, x, x, x, x))+(56/5)*(diff(f5(x), x, x, x, x)), (13/1800)*(diff(f3(x), x, x, x, x, x, x, x, x))+(154/5625)*(diff(f3(x), x, x, x, x, x, x))-(475051/67500)*(diff(f3(x), x, x, x, x))-(2491/4500)*(diff(f1(x), x, x, x, x, x))+(1648/1125)*(diff(f2(x), x, x, x, x, x))-(427/375)*(diff(f1(x), x, x, x))+(24/125)*(diff(f2(x), x, x, x))-(953/375)*(diff(f3(x), x, x))+(28/25)*(diff(f4(x), x, x, x, x)), -6*(diff(f4(x), x, x))-2*f3(x)-(22/3)*f4(x)*omega^2-(2/3)*f5(x)*omega^2+(2/3)*(diff(f1(x), x))*omega^2-(1/3)*(diff(f2(x), x))*omega^2-(44/625)*(diff(f3(x), x, x, x, x, x, x))-(422/75)*(diff(f1(x), x, x, x, x, x))-(28/75)*(diff(f2(x), x, x, x, x, x))+(72/5)*(diff(f4(x), x, x, x, x))+(8/25)*(diff(f3(x), x, x, x, x))-(8/3)*(diff(f2(x), x, x, x))+(8/3)*(diff(f1(x), x, x, x)), (583/30)*(diff(f2(x), x, x, x, x))-2*(diff(f3(x), x))+4*f2(x)-4*f1(x)-(22/3)*f2(x)*omega^2+(2/3)*(diff(f5(x), x))*omega^2-(1/6)*(diff(f1(x), x, x))*omega^2+(1/3)*(diff(f4(x), x))*omega^2+(1/3)*(diff(f2(x), x, x))*omega^2-(2/3)*f1(x)*omega^2+(929/150)*(diff(f1(x), x, x, x, x))+(517/900)*(diff(f3(x), x, x, x, x, x))-(133/75)*(diff(f1(x), x, x, x, x, x, x))-(152/75)*(diff(f2(x), x, x, x, x, x, x))-(9/25)*(diff(f3(x), x, x, x))+(724/45)*(diff(f1(x), x, x))-(724/45)*(diff(f2(x), x, x))-(16/3)*(diff(f4(x), x, x, x))-(14/225)*(diff(f3(x), x, x, x, x, x, x, x)), -(22/3)*f1(x)*omega^2-(2/3)*f2(x)*omega^2-(1/6)*(diff(f2(x), x, x))*omega^2-(1/3)*(diff(f5(x), x))*omega^2-(2/3)*(diff(f4(x), x))*omega^2+(1/3)*(diff(f1(x), x, x))*omega^2-(224/25)*(diff(f1(x), x, x, x, x, x, x))-(12/5)*(diff(f3(x), x, x))-(733/300)*(diff(f3(x), x, x, x))-(1/3)*(diff(f3(x), x, x, x, x))-4*(diff(f2(x), x, x, x))+(24/25)*(diff(f2(x), x, x, x, x))-(133/75)*(diff(f2(x), x, x, x, x, x, x))+(689/900)*(diff(f3(x), x, x, x, x, x))-(6743/31500)*(diff(f3(x), x, x, x, x, x, x, x))+(16/3)*(diff(f4(x), x, x, x))+4*f1(x)-(1036/75)*(diff(f1(x), x, x))-4*(diff(f1(x), x, x, x))+(337/50)*(diff(f1(x), x, x, x, x))-4*f2(x)+(724/45)*(diff(f2(x), x, x))-2*(diff(f3(x), x)), -(14/5)*((D@@3)(f2))(0)+(56/5)*((D@@2)(f5))(0) = 0, -(14/5)*((D@@3)(f2))(1)+(56/5)*((D@@2)(f5))(1) = 0, -(44/625)*((D@@4)(f3))(0)-(8/5)*((D@@3)(f1))(0)-(28/75)*((D@@3)(f2))(0)+(72/5)*((D@@2)(f4))(0)+(8/25)*((D@@2)(f3))(0)-(8/3)*(D(f2))(0)+(8/3)*(D(f1))(0) = 0, (13/1800)*((D@@4)(f3))(0)-(97/4500)*((D@@2)(f3))(0)+(1/9)*(D(f1))(0)-(1/9)*(D(f2))(0)-(31/150)*((D@@2)(f4))(0)+(49/225)*((D@@3)(f1))(0)+(14/225)*((D@@3)(f2))(0) = 0, -(44/625)*((D@@4)(f3))(1)-(8/5)*((D@@3)(f1))(1)-(28/75)*((D@@3)(f2))(1)+(72/5)*((D@@2)(f4))(1)+(8/25)*((D@@2)(f3))(1)-(8/3)*(D(f2))(1)+(8/3)*(D(f1))(1) = 0, (13/1800)*((D@@4)(f3))(1)-(97/4500)*((D@@2)(f3))(1)+(1/9)*(D(f1))(1)-(1/9)*(D(f2))(1)-(31/150)*((D@@2)(f4))(1)+(49/225)*((D@@3)(f1))(1)+(14/225)*((D@@3)(f2))(1) = 0, (109/10)*((D@@2)(f1))(0)+(263/300)*((D@@3)(f3))(0)-(922/75)*((D@@4)(f1))(0)-(133/75)*((D@@4)(f2))(0)+(32/15)*((D@@2)(f2))(0)-(167/75)*(D(f3))(0)+(862/75)*((D@@3)(f4))(0)-(6743/31500)*((D@@5)(f3))(0) = 0, (109/10)*((D@@2)(f1))(1)+(263/300)*((D@@3)(f3))(1)-(922/75)*((D@@4)(f1))(1)-(133/75)*((D@@4)(f2))(1)+(32/15)*((D@@2)(f2))(1)-(167/75)*(D(f3))(1)+(862/75)*((D@@3)(f4))(1)-(6743/31500)*((D@@5)(f3))(1) = 0, -(13/1800)*((D@@5)(f3))(0)-(6/125)*((D@@3)(f3))(0)+(16697/4500)*(D(f3))(0)-(143/300)*((D@@2)(f1))(0)-(373/225)*((D@@2)(f2))(0)+(31/150)*((D@@3)(f4))(0)-(49/225)*((D@@4)(f1))(0)-(14/225)*((D@@4)(f2))(0) = 0, -(13/1800)*((D@@5)(f3))(1)-(6/125)*((D@@3)(f3))(1)+(16697/4500)*(D(f3))(1)-(143/300)*((D@@2)(f1))(1)-(373/225)*((D@@2)(f2))(1)+(31/150)*((D@@3)(f4))(1)-(49/225)*((D@@4)(f1))(1)-(14/225)*((D@@4)(f2))(1) = 0, (189/10)*((D@@2)(f2))(0)+(23/10)*((D@@2)(f1))(0)+(139/300)*((D@@3)(f3))(0)-(133/75)*((D@@4)(f1))(0)-(112/75)*((D@@4)(f2))(0)+(13/75)*(D(f3))(0)+(28/15)*((D@@3)(f4))(0)+(14/5)*((D@@3)(f5))(0)-(14/225)*((D@@5)(f3))(0) = 0, (189/10)*((D@@2)(f2))(1)+(23/10)*((D@@2)(f1))(1)+(139/300)*((D@@3)(f3))(1)-(133/75)*((D@@4)(f1))(1)-(112/75)*((D@@4)(f2))(1)+(13/75)*(D(f3))(1)+(28/15)*((D@@3)(f4))(1)+(14/5)*((D@@3)(f5))(1)-(14/225)*((D@@5)(f3))(1) = 0, -(13/1800)*((D@@8)(f3))(0)-(154/5625)*((D@@6)(f3))(0)+(475051/67500)*((D@@4)(f3))(0)+(2491/4500)*((D@@5)(f1))(0)-(1648/1125)*((D@@5)(f2))(0)+(427/375)*((D@@3)(f1))(0)-(24/125)*((D@@3)(f2))(0)+(953/375)*((D@@2)(f3))(0)-(28/25)*((D@@4)(f4))(0) = 0, -(13/1800)*((D@@8)(f3))(1)-(154/5625)*((D@@6)(f3))(1)+(475051/67500)*((D@@4)(f3))(1)+(2491/4500)*((D@@5)(f1))(1)-(1648/1125)*((D@@5)(f2))(1)+(427/375)*((D@@3)(f1))(1)-(24/125)*((D@@3)(f2))(1)+(953/375)*((D@@2)(f3))(1)-(28/25)*((D@@4)(f4))(1) = 0, (13/1800)*((D@@6)(f3))(0)+(154/5625)*((D@@4)(f3))(0)-(111533/33750)*((D@@2)(f3))(0)-(2491/4500)*((D@@3)(f1))(0)+(1648/1125)*((D@@3)(f2))(0)-(212/375)*(D(f1))(0)+(212/375)*(D(f2))(0)+(152/125)*((D@@2)(f4))(0)-(31/150)*((D@@4)(f4))(0)+(49/225)*((D@@5)(f1))(0)+(14/225)*((D@@5)(f2))(0) = 0, (13/1800)*((D@@6)(f3))(1)+(154/5625)*((D@@4)(f3))(1)-(111533/33750)*((D@@2)(f3))(1)-(2491/4500)*((D@@3)(f1))(1)+(1648/1125)*((D@@3)(f2))(1)-(212/375)*(D(f1))(1)+(212/375)*(D(f2))(1)+(152/125)*((D@@2)(f4))(1)-(31/150)*((D@@4)(f4))(1)+(49/225)*((D@@5)(f1))(1)+(14/225)*((D@@5)(f2))(1) = 0, f1(0) = 0, f1(1) = 0, f2(0) = 0, f2(1) = 0, f4(0) = 0, f4(1) = 0, f5(0) = 0, f5(1) = 0, ((D@@2)(f1))(0) = 0, ((D@@2)(f1))(1) = 0, ((D@@2)(f2))(0) = 0, ((D@@2)(f2))(1) = 0}:

dsys4 := subs(omega^2 = omega2, dsys3):

Typesetting:-mrow(Typesetting:-mo("for", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("bb", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("in", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("extra_bcs", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("do", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(":", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("try", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(":", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("print", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("bb", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(":", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("res", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("bb", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo("&coloneq;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("dsolve", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("dsys4", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("union", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("bb", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo("=", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn(".00000000001", font_style_name = "2D Input", mathvariant = "normal")), font_style_name = "2D Input", mathvariant = "normal", open = "{", close = "}"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("numeric", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("output", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo("=", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("listprocedure", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("initmesh", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("3024", font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("abserr", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo("=", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("1e&minus;5", font_style_name = "2D Input", mathvariant = "normal")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(";", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("catch", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(":", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("print", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("lasterror", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(":", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("end", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("try", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(":", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("end", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("do", bold = "true", font_style_name = "2D Input", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(":", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("indx", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("&coloneq;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("indices", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("res", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("nolist", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(";", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mi("nops", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("indx", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal", open = "[", close = "]")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(":", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mi("res", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("indx", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("1", font_style_name = "2D Input", mathvariant = "normal")), font_style_name = "2D Input", mathvariant = "normal", open = "[", close = "]")), font_style_name = "2D Input", mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(":", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("Sol", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo("&coloneq;", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("seq", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("subs", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("res", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("indx", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("i", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal", open = "[", close = "]")), font_style_name = "2D Input", mathvariant = "normal", open = "[", close = "]"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0", font_style_name = "2D Input", mathvariant = "normal")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("omega2", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0", font_style_name = "2D Input", mathvariant = "normal")), font_style_name = "2D Input", mathvariant = "normal")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(",", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("i", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mo("=", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("1", font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo("..", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.0em"), Typesetting:-mi("nops", italic = "true", font_style_name = "2D Input", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("indx", italic = "true", font_style_name = "2D Input", mathvariant = "italic")), font_style_name = "2D Input", mathvariant = "normal", open = "[", close = "]")), font_style_name = "2D Input", mathvariant = "normal")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(";", font_style_name = "2D Input", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"))

Error, invalid input: subs received res[indx[1]](0), which is not valid for its 1st argument

 

``

``


 

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