1.

entail logic ⊨ is equivalent to what logic which in terms of conj and disj and not 

for example ⊨A <-> B, there is nothing in left hand side, 

2.

does it mean that it should represent Entail(_, A<->B)  where _ is wildcard? 

I can get the function to iterate as a recursive function by just reevaluating the x := evalf(x-(f1*j-i*g1)/(h*k-i*j), 25); y := evalf(y-(h*g1-f1*j)/(h*k-i*j), 25) portion of the function below but im trying beneath it to assign it as newt2d so that i can iterate it as newtons method in two variables like (newt2d@@10) and I can't seem to figure out what im doing wrong. Thanks for any help you can provide!

f := proc (x, y) options operator, arrow; x+y-cos(x)+sin(y-1) end proc; f1 := f(x, y)

(x, y) -> x + y - cos(x) + sin(y - 1)
x + y - cos(x) + sin(y - 1)

> g := proc (x, y) options operator, arrow; x^4+y^4-2*x*y end proc; g1 := g(x, y);

(x, y) -> x + y - 2 x y
x + y - 2 x y

> dh := D[1](f); h := dh(x, y);

(x, y) -> 1 + sin(x)
1 + sin(x)

> di := D[2](f); i := di(x, y);

(x, y) -> 1 + cos(y - 1)
1 + cos(y - 1)

> dj := D[1](g); j := dj(x, y);

(x, y) -> 4 x - 2 y
4 x - 2 y

> dk := D[2](g); k := dk(x, y);

(x, y) -> 4 y - 2 x
4 y - 2 x

x := .3; y := .8

0.3
0.8

> x := evalf(x-(f1*j-i*g1)/(h*k-i*j), 25); y := evalf(y-(h*g1-f1*j)/(h*k-i*j), 25);

0.2924403963319692595180140
0.8321243516906678979858730

> newt2d(.3, .8);

0.2577789764, 0.8333916830

> (newt2d@@5)(.3, .8);

Error, (in @@) invalid arguments

Hi There,

Could you let me know how to tell Maple to use the ln simplification to give -ln(x)+ln(y) = ln(y/x).

I tried following command.

simplify(-ln(x)+ln(y), ln)

However, it is not able to give the required simplification.

Hi,
can you please help me solve that?
I want to write maple procedure that checks if a number is prime or not and I need to do it so that it doesn`t take forever to give an answer.
I wrote a procedure that works good with small numbers but when I put bigger numbers eg.9999971 it is taking far too long (5min) to get the answer, I tried to modify it and I think I find out something that could be modified to make it more efficient, like for example in the line:   for j from 2 to n-1 do     (I changed it to: ) for j from 2 to n-1  by n do    - it tooks 9.953 second to get the answer   (or I changed it to: ) for j from 2 to (n-1)/2  do   - it tooks 262.062 second I also tried many things and I always get an answer after long time excepte when I changed the line to for j from 2 to (n-1)/n  do   - it tooks 0 second but I didn't find any explanation why should I devide it by n as j from 2 to ((n-1)/n) = 1-(1/n) which is less than 2 as it make no sence....
But it still not efficient enough, because if for example I use the maple command isprime,then I got the result in less than 1 second.
In the program I used other procedure that I think will make it quicker which is a floor function procedure. please see bellow :  

> flr:=proc(a,b)

      local n:

      n:=0:

      while a>=b*(n+1) do

         n:=n+1:

     od:

       n;

   end:

> Isprime:=proc(n)        

         local j, p:      

         p:=true:               

         if n=2 then

            p:=true;       

        else

             for j from 2 to n-1 do 

                  if (n/j-flr(n,j))=0 then

                       p:=false:

                  fi:

              od:

         fi:

     p:

     end:

>zeit:=time():

Isprime(9999971); 

time()-zeit,`second`;

                                                                   true

                                                                    309.558, second

Please reply and thank you in advance

Maple crashed while saving and now there is nothing in my file. Lost a bunch of work, any way to fix it?

Thanks
EquationSheet357.mw

(x+y)(x²+y²⁾ = 5500

(x-y)(x²-y²⁾ = 352

Hi,

I wrote the following code which is properly run

restart:

# parametrs

MUR:=(1-phi)^2.5:
RhoUR:=(1-phi+phi*rho[p]/rho[f]):
RhoCPR:=(1-phi+phi*rhocp[p]/rhocp[f]):
BetaUR:=(phi*rho[p]*beta[p]+(1-phi)*rho[f]*beta[f])/(RhoUR*rho[f])/beta[f]:

dqu3:=diff(h(x),x$1)-RhoUR*BetaUR*T(x);
dqu2:=5*diff(T(x),x$2)+k[f]/k[nf]*Pr*RhoCPR*f(x)*diff(T(x),x$1);
dqu1:=5/(MUR)*diff(f(x),x$3)
+ 2*(diff(h(x),x$1)*x-h(x))
+RhoUR*(3*f(x)*diff(f(x),x$2)-diff(f(x),x$1)^2);
rho[f]:=998.2: cp[f]:=4182: k[f]:=0.597:   beta[f]:= 2.066/10000:
rho[p]:=3380: cp[p]:=773: k[p]:=36:   beta[p]:= 8.4/1000000:

k[nf]:=((k[p]+2*k[f])-2*phi*(k[f]-k[p]))/((k[p]+2*k[f])+phi*(k[f]-k[p])):
rhocp[nf]:=rho[p]*cp[p]*phi+rho[f]*cp[f]*(1-phi):
rhocp[p]:=rho[p]*cp[p]:
rhocp[f]:=rho[f]*cp[f]:

phi:=0.00:
binfinitive:=6: Pr:=7: lambda:=0:


with(plots):
pppe:=dsolve( {dqu1=0,dqu2=0,dqu3=0,T(0)=1,T(binfinitive)=0,f(0)=0,D(f)(0)=lambda,D(f)(binfinitive)=0,h(binfinitive)=0}, numeric );
-pppe(0);
print(odeplot(pppe,[x,diff(f(x),x)],0..binfinitive,color=black,numpoints=400));
print(odeplot(pppe,[[x,diff(f(x),x)]],0..binfinitive,color=black,numpoints=400));
print(odeplot(pppe,[[x,T(x)]],0..binfinitive,color=black,numpoints=400));

However, in some range of parameters, I must increase the value of binfinitive (for example binfinitive=50). however, my code is doesnt converge for higher values of 10 (at most). Can anyone change this algorithm in a way that it insensitive to the value of binfinitive?

Many thanks for your attention in advance

Amir

AOA... I want to convert system of equations into matirx form.

F[0] := u[0, n]-u[0, n-1]+u[1, n]-u[1, n-1]+u[2, n]-u[2, n-1]+u[3, n]-u[3, n-1]

F[1] := u[0, n]-u[0, n-1]-u[1, n]+u[1, n-1]+u[2, n]-u[2, n-1]-u[3, n]+u[3, n-1];

F[2] := u[0, n]/P-u[0, n-1]/P-.7071067810*u[1, n]/P+.7071067810*u[1, n-1]/P+.7071067810*u[3, n]/P-.7071067810*u[3, n-1]/P+0.4549512860e-1*exp(-1.*t)-.3431457508*u[2, n]+.3431457508*u[2, n-1]+1.556349186*u[3, n]-1.556349186*u[3, n-1] = 0;

F[3] := u[0, n]/P-u[0, n-1]/P-.7071067810*u[1, n]/P+.7071067810*u[1, n-1]/P+.7071067810*u[3, n]/P-.7071067810*u[3, n-1]/P+0.4549512860e-1*exp(-1.*t)-.3431457508*u[2, n]+.3431457508*u[2, n-1]+1.556349186*u[3, n]-1.556349186*u[3, n-1] = 0;

I want to export the above system of equation in to matrices of as

AU[n]+BU[n-1]-C = O;

where*U[n] = Typesetting[delayDotProduct](Vector(4, {(1) = u[0, n], (2) = u[1, n], (3) = u[2, n], (4) = u[3, n]}), a, true)*n*d*U[n-1] and Typesetting[delayDotProduct](Vector(4, {(1) = u[0, n], (2) = u[1, n], (3) = u[2, n], (4) = u[3, n]}), a, true)*n*d*U[n-1] = (Vector(4, {(1) = u[0, n-1], (2) = u[1, n-1], (3) = u[2, n-1], (4) = u[3, n-1]})), Help me plz;

Help_Constrct.mw

how to transform

Matrix([[1,0,0],[1,0,0],[0,0,0]])

to

Matrix([[0,0,0],[0,0,1],[0,0,1]])

so we have to Write a maple function with -> that takes an integer N and a boolean function

F: {(i,j) l 0<= i,j<= N} -> {true,false} 

and returns a list containing all [i,j] such that F(i,j). A procedure that does this
would be

proc(N,F) local i, j, RV;
RV:=NULL;
for i from 1 to N do for j from 1 to N do
if F(i,j) then RV:=RV,[i,j] ; end if ;
end do ; end do ;
return RV ;
end proc ;

The problem is to do this inline, i.e. you have to write
(i,j)-> ...

please help...

I am trying some data analysis on an Excel worksheet using Maple. I have the following procedure but I don't know how to make it work for a specific subset of cells (this is a psychological studiy, so I want to have all my scores for each subject, located on the rows, and variable, located on a subset of columns). Example: I want to get an array of all the average scores in a rectangle of cells which goes horizontallyfrom A to AB, and vertically from row 1 to 15. Hope you can help me out! Cheers!

MediaRighe := proc (M) local i, j, r, c, S, N; r := LinearAlgebra:-RowDimension(M); c := LinearAlgebra:-ColumnDimension(M); S := Array(1 .. r); for i to r do S[i] := 0; N := 0; for j to c do if M(i, j) <> "-" then S[j] := S[j]+M(i, j); N := N+1 end if end do; S[i] := S[i]/N end do; return S end proc

I also have this for the columns (same thing, basically):

MediaColonne := proc (M) local i, j, r, c, S, N; r := LinearAlgebra:-RowDimension(M); c := LinearAlgebra:-ColumnDimension(M); S := Array(1 .. c); for j to c do S[j] := 0; N := 0; for i to r do if M(i, j) <> "-" then S[j] := S[j]+M(i, j); N := N+1 end if end do; S[j] := S[j]/N end do; return S end proc

Thanks everybody!

I plot a curve with "plot" command, how to export the figure to .emf format file?

Please advise as to the proper coding entries needed in the triple integration palette  to transform from the Cartesian placeholders x;y;z to spherical coordinates rho; theta; phi so that the triple integration palette can be used in spherical coordinmates. Dr. Lopez alreadyb has a standalone template which does this but I would like to set a palette option for spherical  calculations.

Thanx

This is one of these silly ones that crop up every-so-often (and yes, beta, gamma are just the relativistic v/c and energy):

gamma=1/sqrt(1-beta^2);
solve(%,beta);

comes up with ±I*sqrt(-gamma^2+1)/gamma.

While this is not wrong it is nothing I want to throw at any student trying hard enough as it is to keep his/her head above water. What I want is beta=sqrt(1-1/gamma^2) and I am having a devil of a time getting Maple to do this. even doing it "by hand" the I comes in the moment I take the sqrt. "assuming" does not help (and when I try ...assuming beta::positive, gamma > 1 I get an error claiming these to be inconsistent).

What gives?

Mac Dude

Hi. 

I have this expresssion:

I know the result is:

But it takes 13 minutes for maple to get to that solution, and i do not need the part with the I, complex number.

Is there any way to make maple evaluate this expression without computeing the complex number? A setting in generel, or some function to put the expression into?

Thanks in advance!

Emil Kristensen