Dear friends:

I am facing two problems

1. one is to get solution of the below system of ODE for L=100 (highlited as red) and

2. the other is I want the graph in the form of solid line not poit, asterisk etc.

restart; epsilon := .1; Pr := 1; beta := .1; Sc := 1; S := 1; L := 20;
for i from -L while i <= L do;
a[i] := 1.0*i/L;
end do;
for i2 from -L while i2 <= L do;

fw := a[i2]; 

Eq1[i2] := eval(diff(F(eta), eta, eta, eta)+F(eta)*(diff(F(eta), eta, eta))-(diff(F(eta), eta))^2+S*(epsilon-(diff(F(eta), eta)))+epsilon^2);
Eq2[i2] := eval((diff(G(eta), eta, eta))/Pr-G(eta)*(diff(F(eta), eta))+F(eta)*(diff(G(eta), eta))); 
Eq3[i2] := eval(diff(H(eta), eta, eta)+Sc*(F(eta)*(diff(H(eta), eta))-beta*H(eta)));
IC[i2] := F(0) = a[i2], (D(F))(0) = 1, (D(F))(L) = epsilon, G(0) = 1, G(L) = 0, H(0) = 1, H(L) = 0;
dsys1[i2] := {Eq1[i2], Eq2[i2], Eq3[i2], IC[i2]};
dsol1[i2] := dsolve(dsys1[i2], numeric, output = listprocedure, range = 0 .. L);
dsol1x[i2] := subs(dsol1[i2], diff(F(eta), eta, eta));
dsol1y[i2] := subs(dsol1[i2], G(eta));
dsol1z[i2] := subs(dsol1[i2], H(eta)) end do;

for j from -L while j <= L do; 
g[j] := eval(-dsol1x[j](0)) end do;
with(plots); 

g6 := pointplot({seq([n/L, g[n]], n = -L .. L)}, symbol = asterisk, symbolsize = 15, color = red);
display(g6);

Please see the problem and correct as soon as possible. I am waiting your positive respone.

Muhammad Usman

School of Mathematical Sciences 
Peking University, Beijing, China

How to pdeplot Curl(A(x,y,z))=0 in maple

it has A1(x,y,z) , A2(x,y,z) and A3(x,y,z)

How can I produce the same output with something like alphadeg := alpharad * 180/Pi?

T := proc (p, q, R) alpharad = evalf[5](arccos((1/2)*(p^2+R^2-q^2)/(p*R))), alphadeg = 180*evalf[5](arccos((1/2)*(p^2+R^2-q^2)/(p*R)))/Pi end proc;
T(3, 4, 3.75);
           alpharad = 1.2515, alphadeg = 71.70566805

When I try alphadeg = alpharad * 180/Pi I get
Error, illegal use of an object as a name
 

Thanks! Les    AB59_20170205_Post.mw

Is there a method to relate groebner bases with monomials ideals

How to plot magnetic field of maxwell equations like vector field

I am debugging a Maple program (and I cannot contact its author). Allegedly, the program ran under some old version of Maple, but it does not run under my Maple 2015 or Maple 9. I am trying to make it run under Maple 2015. I found a place where the program does not do what it is expected to do, but don't know how to make it do what I want:-)

I inserted a DEBUG statement at some place in the program, and the debugger window opens when the program comes to that statement. I execute  the following statement in the debugger:  traperror(Groebner:-NormalForm(g,AA,matermorder)); if I get some benign result, such as 0, I push "continue" in the debugger, and the program runs until it gets to the DEBUG statement again. I repeat these two operations several times until the traperror statement gives the following: polynomials must be members of the algebra" (my comment: only one quotation mark).

So I would like to amend the program to process the exception differently from how it is done now, but I don't know how to get access to the result of the traperror statement. For example, when I am trying to execute the following operators in the debugger: adebug:= traperror(Groebner:-NormalForm(g,AA,matermorder));adebug; , I only get the following diagnostics: Warning, extra characters at end of parsed string  So I don't understand what adebug contains and how I can introduce some logic based on the contents of adebug to handle the exception differently.

I suspect I am missing something simple due to my lack of experience with Maple. I tried to put the result of traperror into a parse statement, but did not get any satisfactory results.

Thank you 

I have to calculate a sort of trend line, but I don't know how it works with maple.
I tried with Excel.

Do you think the method is right? How can I replicate it on maple?

Thanks in advance

Dear friends! I am facing problem to solve the below system of ODEs numerically please find the mistake and correct it.

alpha := -1; R := 2; m := 2; Pr := 7; Le := 1.25; Nt := .2; Nb := .2; g := .5; K1 := .1; Q := .5

Eq1 := eta^3*(diff(F(eta), eta, eta, eta, eta))+alpha*(eta^4*(diff(F(eta), eta, eta, eta))+eta^3*(diff(F(eta), eta, eta))-eta^2*F(eta))-2*eta^2*(diff(F(eta), eta, eta, eta))+3*eta*(diff(F(eta), eta, eta))-3*(diff(F(eta), eta))+eta*R*(diff(F(eta), eta))^2-3*eta*R*F(eta)*(diff(F(eta), eta, eta))+3*R*F(eta)*(diff(F(eta), eta))+3*eta^2*R*F(eta)*(diff(F(eta), eta, eta, eta))-eta^2*(diff(F(eta), eta))*(diff(F(eta), eta, eta))-M^2*(eta^3*(diff(F(eta), eta, eta))-eta^2*(diff(F(eta), eta))); Eq2 := eta*(diff(G(eta), eta, eta))+alpha*Pr*eta^2*(diff(G(eta), eta))+R*Pr*F(eta)*(diff(G(eta), eta))+Nb*eta*(diff(G(eta), eta))*(diff(H(eta), eta))+Nt*eta*(diff(G(eta), eta))^2+diff(G(eta), eta)+Q*Pr*eta*G(eta) = 0; Eq3 := eta*(diff(H(eta), eta, eta))+alpha*Le*Pr*eta^2*(diff(H(eta), eta))+R*Le*Pr*F(eta)*(diff(H(eta), eta))+Nt*eta*(diff(G(eta), eta, eta))/Nb+Nt*(diff(G(eta), eta))/Nb+diff(H(eta), eta)-g*Le*Pr*eta*H(eta)-Le*Pr*K1*eta = 0;

IC1 := F(0) = 0, F(1) = 1, (D(F))(0) = 0, (D(F))(1) = 0, (D(G))(0) = 0, G(1) = 1, (D(H))(0) = 0, H(1) = lambda; dsys1 := {Eq1, Eq2, Eq3, IC1}; dsol1 := dsolve(dsys1, numeric, continuation = lambda, range = 0 .. 1);

dsol1x := subs(dsol1, F(eta));

dsol1y := subs(dsol1, G(eta)); dsol1z := subs(dsol1, H(eta));
 

With my best regards and sincerely.

Muhammad Usman

School of Mathematical Sciences 
Peking University, Beijing, China

Hi everybody, 

The sequence 
    writeto(MyFile)
    showstat(Myproc)
keeps printing the result on the screen

How is it possible to redirected the output of showstat(Myproc) into a file ?

Thanks in advance

how to convert a nested for loop to iterative version with stack

#my testing for wildcard to one
#after testing, it loop a very long time and not stop
ppp := [[0,0,0,x],[0,0,1,0],[0,1,0,0],[1,0,0,0]]:
check1 := [seq(0,ii=1..nops(ppp))];
ttt1 := [[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]]:
mmmeaght1 := [seq(0,ii=1..nops(ppp[1]))]:
bbb1 := [seq(0,ii=1..nops(ppp[1]))]:
emap := [(xx) -> if [xx < 0 assuming x > 0] then 0 else 1 end if, (xx) -> evalf(1/(1+exp(xx)))]:
#trace(perceptronrule1);
MM(ppp, ttt1, mmmeaght1, bbb1, check1, emap);
 

when test wildcard variable for input, would like to assume x > 0 then

i try assuming x > 0 , got error

I want to calculate the intersection between three circles.
I know that in this case i can calculate intersection of only the first and second equation, but I need this for a interactive component.

The command "intersection"[GEOMETRY] work only with 2 circles.

I did this but it doesn't work.

Thanks.

I used the command line betwen two poin, and i saw the graphic.

The line passes for my two point, but i I would like it started in the first point and finished in the second.

Thanks.

when test most simple case one to one, and many to one these two reasonable cases, it run a very long time without exit the program.

when i test with the example in book Neural Network Design, it can output correctly but only for book example.

restart:
with(ExcelTools):
with(ListTools):
with(plots):
with(LinearAlgebra):
zipplus := proc(mm, pp)
return zip((x,y) -> x+y, mm, pp)
end proc:
zipminus := proc(mm, pp)
return zip((x,y) -> x-y, mm, pp)
end proc:
zipstar := proc(mm, pp)
return zip((x,y) -> x*y, mm, pp)
end proc:

metara := proc(pp,meaght,bb,mapp,deep)
if deep > 0 then
 pp2 := metara([seq(pp[i], i = 1 .. nops(pp))],meaght,bb,mapp,deep-1):
 mp := zip((x,y) -> x*y,pp2,meaght):
 mpsam := sum(mp[m],m=1..nops(pp2)):
 mpb := [seq(0, i = 1 .. nops(pp2))]:
 for ii from 1 to nops(bb) do
  mpb[ii] := evalf(mpsam + bb[ii]);
 od:
 pa := [seq(0, i = 1 .. nops(pp2))]:
 for ii from 1 to nops(bb) do
  pa[ii] := evalf(mapp[deep](mpb[ii])):
 od:
 return pa:
else
 return pp:
end if:
end proc:

perceptronrule1 := proc(p, t1, meaght1, b1, checksum, mapp)
 meaght3 := meaght1:
 b3 := b1:
 checksum2 := checksum;
 print(p[1]):
 while sum(checksum2[jj], jj=1..nops(p)) <> nops(p) do
  #print("sum(checksum2[jj], jj=1..nops(p))");
  #print(sum(checksum2[jj], jj=1..nops(p)));
  for ii from 1 to nops(p) do
   #print("metara(p[ii],meaght3,b3,mapp,1)");
   #print("p[ii]");
   #print(p[ii]);
   #print("b3");
   #print(b3);
   #print("meaght3");
   #print(meaght3);
   #print(metara(p[ii],meaght3,b3,mapp,1));
   #print("t1[ii]");
   #print(t1[ii]);
   e := zipminus(t1[ii], metara(p[ii],meaght3,b3,mapp,1));
   #print("e");
   #print(e);
   meaght2 := meaght3 + zipstar(e,p[ii]);
   #print("meaght2");
   #print(meaght2);
   #print("meaght3");
   #print(meaght3);
   #print("b3");
   #print(b3);
   b2 := b3 + e;
   #print("b2");
   #print(b2);
   #print("b3");
   #print(b3);
   #print("checksum2");
   #print(checksum2);
   diff1 := zipminus(meaght2, meaght3):
   diff2 := zipminus(b2, b3):
   if sum(diff1[m],m=1..nops(diff1)) = 0 and sum(diff2[m],m=1..nops(diff2)) = 0 then
    checksum2[ii] := 1:
   else
    checksum2[ii] := 0:
    b3 := b2:
    meaght3 := meaght2:
   end if:
  od:
 od:
 return [meaght3, b3, checksum];
end proc:

#Example from book
ppp := [[2,2],[1,-2],[-2,2],[-1,1]]:
check1 := [seq(0,ii=1..nops(ppp))];
ttt1 := [[0,0],[1,1],[0,0],[1,1]]:
mmmeaght1 := [seq(0,ii=1..nops(ppp[1]))]:
bbb1 := [seq(0,ii=1..nops(ppp[1]))]:
emap := [(x) -> if x < 0 then 0 else 1 end if, (x) -> evalf(1/(1+exp(x)))]:
#trace(perceptronrule1);
perceptronrule1(ppp,ttt1,mmmeaght1,bbb1,check1,emap);

#my testing for one to one
#after testing, it loop a very long time and not stop
ppp := [[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]]:
check1 := [seq(0,ii=1..nops(ppp))];
ttt1 := [[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]]:
mmmeaght1 := [0,0,0,0]:
bbb1 := [0,0,0,0]:
emap := [(x) -> if x < 0 then 0 else 1 end if, (x) -> evalf(1/(1+exp(x)))]:
#trace(perceptronrule1);
perceptronrule1(ppp,ttt1,mmmeaght1,bbb1,check1,emap);

#my testing for many to one
#after testing, it loop a very long time and not stop
ppp := [[1,1,0,0],[0,1,1,0],[0,1,0,1]]:
check1 := [seq(0,ii=1..nops(ppp))];
ttt1 := [[1,0,0,0],[0,1,0,0],[0,0,0,1]]:
mmmeaght1 := [0,0,0,0]:
bbb1 := [0,0,0,0]:
emap := [(x) -> if x < 0 then 0 else 1 end if, (x) -> evalf(1/(1+exp(x)))]:
#trace(perceptronrule1);
perceptronrule1(ppp,ttt1,mmmeaght1,bbb1,check1,emap);

#my testing for one to many
#after testing, it loop a very long time and not stop
ppp := [[1,0,0,0],[0,1,0,0],[0,0,0,1]]:
check1 := [seq(0,ii=1..nops(ppp))];
ttt1 := [[1,1,0,0],[0,1,1,0],[0,1,0,1]]:
mmmeaght1 := [0,0,0,0]:
bbb1 := [0,0,0,0]:
emap := [(x) -> if x < 0 then 0 else 1 end if, (x) -> evalf(1/(1+exp(x)))]:
#trace(perceptronrule1);
perceptronrule1(ppp,ttt1,mmmeaght1,bbb1,check1,emap);

Hello,

i need to represent a circle using the command [geometry] circle because i have a problem and i have to calculate an 

intersection between two circles whit command intersection() which is ruled by Package geometry.

For example, with the first circle  i did like the help page says

 But it's Error:

centre of circle(3300;2200)

radius=110

I don't understand the eror. Can you help me?

Thanks in advance.