MaplePrimes Questions

Hi,

Sorry to ask such a stupid question but I can't find out where my error is. Probably it's so huge it blinds me!

The double loop and the matrix product F^+ . F should give the same result, no? (it seems that F^+ . F has its rows reordered ?)


 

restart:

N   := 3:
P   := 2:
niv := [seq(Z[i], i=1..N)];
f   := Matrix(N^P, P, (i,j) -> `if`(j=P, niv[(i mod 3)+1], niv[iquo(i-1,3)+1]));

niv := [Z[1], Z[2], Z[3]]

 

f := Matrix(9, 2, {(1, 1) = Z[1], (1, 2) = Z[2], (2, 1) = Z[1], (2, 2) = Z[3], (3, 1) = Z[1], (3, 2) = Z[1], (4, 1) = Z[2], (4, 2) = Z[2], (5, 1) = Z[2], (5, 2) = Z[3], (6, 1) = Z[2], (6, 2) = Z[1], (7, 1) = Z[3], (7, 2) = Z[2], (8, 1) = Z[3], (8, 2) = Z[3], (9, 1) = Z[3], (9, 2) = Z[1]})

(1)

ds := subs(niv =~ [$0..N-1], f);

ds := Matrix(9, 2, {(1, 1) = 0, (1, 2) = 1, (2, 1) = 0, (2, 2) = 2, (3, 1) = 0, (3, 2) = 0, (4, 1) = 1, (4, 2) = 1, (5, 1) = 1, (5, 2) = 2, (6, 1) = 1, (6, 2) = 0, (7, 1) = 2, (7, 2) = 1, (8, 1) = 2, (8, 2) = 2, (9, 1) = 2, (9, 2) = 0})

(2)

vs := [ seq(V__||i, i=1..P)]:
es := unapply( sort( [ seq( mul(vs ^~ [entries(ds[i,..], nolist)]), i=1..N^P) ] ), vs);
 

proc (V__1, V__2) options operator, arrow; [1, V__1, V__2, V__1^2, V__2^2, V__1*V__2, V__1*V__2^2, V__1^2*V__2, V__1^2*V__2^2] end proc

(3)

ff := convert([ seq(es(entries(ffd[i,..], nolist)), i=1..N^P) ], Matrix);


UnityRoots := [solve(z^3=1, z)]:
F := simplify(subs(niv =~ UnityRoots, ff)) /~ sqrt(N^P):

ff := Matrix(9, 9, {(1, 1) = 1, (1, 2) = Z[1], (1, 3) = Z[2], (1, 4) = Z[1]^2, (1, 5) = Z[2]^2, (1, 6) = Z[1]*Z[2], (1, 7) = Z[1]*Z[2]^2, (1, 8) = Z[1]^2*Z[2], (1, 9) = Z[1]^2*Z[2]^2, (2, 1) = 1, (2, 2) = Z[1], (2, 3) = Z[3], (2, 4) = Z[1]^2, (2, 5) = Z[3]^2, (2, 6) = Z[1]*Z[3], (2, 7) = Z[1]*Z[3]^2, (2, 8) = Z[1]^2*Z[3], (2, 9) = Z[1]^2*Z[3]^2, (3, 1) = 1, (3, 2) = Z[1], (3, 3) = Z[1], (3, 4) = Z[1]^2, (3, 5) = Z[1]^2, (3, 6) = Z[1]^2, (3, 7) = Z[1]^3, (3, 8) = Z[1]^3, (3, 9) = Z[1]^4, (4, 1) = 1, (4, 2) = Z[2], (4, 3) = Z[2], (4, 4) = Z[2]^2, (4, 5) = Z[2]^2, (4, 6) = Z[2]^2, (4, 7) = Z[2]^3, (4, 8) = Z[2]^3, (4, 9) = Z[2]^4, (5, 1) = 1, (5, 2) = Z[2], (5, 3) = Z[3], (5, 4) = Z[2]^2, (5, 5) = Z[3]^2, (5, 6) = Z[2]*Z[3], (5, 7) = Z[2]*Z[3]^2, (5, 8) = Z[2]^2*Z[3], (5, 9) = Z[2]^2*Z[3]^2, (6, 1) = 1, (6, 2) = Z[2], (6, 3) = Z[1], (6, 4) = Z[2]^2, (6, 5) = Z[1]^2, (6, 6) = Z[1]*Z[2], (6, 7) = Z[1]^2*Z[2], (6, 8) = Z[1]*Z[2]^2, (6, 9) = Z[1]^2*Z[2]^2, (7, 1) = 1, (7, 2) = Z[3], (7, 3) = Z[2], (7, 4) = Z[3]^2, (7, 5) = Z[2]^2, (7, 6) = Z[2]*Z[3], (7, 7) = Z[2]^2*Z[3], (7, 8) = Z[2]*Z[3]^2, (7, 9) = Z[2]^2*Z[3]^2, (8, 1) = 1, (8, 2) = Z[3], (8, 3) = Z[3], (8, 4) = Z[3]^2, (8, 5) = Z[3]^2, (8, 6) = Z[3]^2, (8, 7) = Z[3]^3, (8, 8) = Z[3]^3, (8, 9) = Z[3]^4, (9, 1) = 1, (9, 2) = Z[3], (9, 3) = Z[1], (9, 4) = Z[3]^2, (9, 5) = Z[1]^2, (9, 6) = Z[1]*Z[3], (9, 7) = Z[1]^2*Z[3], (9, 8) = Z[1]*Z[3]^2, (9, 9) = Z[1]^2*Z[3]^2})

(4)

Scalar products of pairs of comumn vectors

F must be an orthogonal array

for i1 from 1 to N^P do
  for i2 from 1 to N^P do
    printf("%a ", simplify(add(F[..,i1] . F[.., i2])))
  end do:
  printf("\n"):
end do:
printf("\n");

1 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0
0 0 0 0 1 0 0 0 0
0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 1
 

 

or more simply:

simplify(F^+ . F)

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

(5)

 


 

Download Too_Blind_To_Find_My_Mistake.mw

I have several plots where I use display(a,b,c). Maple displays them with display(actual plot of a, actual plot of b, ...).
I've tried adding insequence but nothing and also tried passing them as sets or lists. In earlier versions I could use display(plots) and it would display all the plots on one plot together but now maple always separates them. I'd rather have the old behavior.

How do I get them to plot on the same plot and is there any way to set it as a global ooption?

what is the wrong in this operations for isentropic process ( isentropic-process) 

 

Restart: with(RealDomain) : interface(dispalyprecision=4) : ; Isentropical := proc(N,v) local K,PTR,KM1,KP1,GO, M,MS,C,PPT,TTT,RRT,AAS,eq,o ; K : = G() : KM1 : = k - 1 : KP1 : = K + 1 : GO := 1 : If N=1 then M := v Elif N=2 then PPT := v : M := sqrt ( 2 * (PPT^(-KM/K) -1 ) : Elif N=3 then MS := v : M := sqrt ( 1 / (KP1/ (2*MS^2) –KM1/2 ) : Elif N=4 then C := v : M := sqrt ( 2 / (KM1* (1 /(C^2) -1 )) ) : Elif N=5 then TTT := v : M := sqrt ( 2 * (1/TTT-1 ) / KM1 : Elif N=6 then RRT := v : M := sqrt ( 2 * (1/RRT^KM1 -1 ) / KM1 : Elif N=7 then AAS := v : eq :=AAS- (2*(1+KM1*M^2/2)/ KP1) ^ (KP1/ (2*KM1)) /M : M := fsolve(eq,M,0..1) : GO :=2 : Elif N=8 then AAS := v : eq :=AAS- (2*(1+KM1*M^2/2)/ KP1) ^ (KP1/ (2*KM1)) /M : M := fsolve(eq,M,1..infinity) : GO :=2 : Fi:fi GO<>2 then ASS := (2 *(1+ KM1*M^2/2/KP1) ^ (KP1/ (2*KM1)) /M fi: PTR := (1+ KM1*M^2/2/KP1) : PPT := PTR^(-K/KM1) : TTT:=PTR^ (-1) : RRT:+PTR^(-1/KM1) : If N <> 3 then MS := sqrt ( KP1 / ( 2 / ( M^2)+KM1) ) If N <> 3 then C := sqrt( 1 / (2 / (KM1*M^2) + 1 ) ) O := evalf([m,1./PPT,MS,C,1./TTT,1./RRT,AAS]) end : irp := proc (N, v) local f; f:=Isentropic1(N,v) : printf(cat(`% 9.4f `$7, ` \ n`) , f[ii$ii=1..7]) end : G := ( ) -> 1.4 : For mi form .1 to .5 do irp(1.mi) od : > > > Eq := table( [ (M2) = M2 , (MS2) = (K+1) /2 (2 / ( M2)+ (K-1) ) (C2) = 1 / (2 / (K-1)*M2+1 ) (PP0) = (1+(K-1)*M2/2)^(-K/(K-1) ) (RR0) = (1+(K-1)*M2/2)^(-1/(K-1) ) (TT0) = (1+(K-1)*M2/2)^(-1) (AAS) = (2 *(1 +(K-1)*M2/2 ) / (K+1) )^( (k-1) /(2*(k-1)))/ squt(M2) ]) : if vL=M then M2v := solve ( M2 -Eq[M2 ] , M2 ) : M2v := eval(M2v ,M2 = VR^2 ) : elif vL=MS then M2v := solve( M2 -Eq[MS2 ] , M2 ) : M2v := eval(M2v ,MS2 = VR^2 ) : elif vL=C then M2v := solve( M2 -Eq[C2 ] , M2 ) : M2v := eval(M2v ,C2 = VR^2 ) : elif vL=PP0 then M2v := solve( M2 -Eq[PP0] , M2 ) : M2v := eval(M2v ,PP0 = VR ) : elif vL=RR0 then M2v := solve( M2 -Eq[RR0] , M2 ) : M2v := eval(M2v ,RR0 = VR ) : elif vL=TT0 then M2v := solve( M2 -Eq[TT0] , M2 ) : M2v := eval(M2v ,TT0 = VR ) : elif vL=AASsub then M2v := fsolve( M2 -Eq[AAS] , M2 ) : M2 :=0..1 : elif vL=AASup then M2v := fsolve( M2 -Eq[AAS] , M2 ) : M2 :=1..infinity : fi: Eqsva1 := eva1(Eq, M2 = M2v) : Eqava1 [M] := sqrt(EqsVa1[M2] ) : Eqsva1[MS] := sqrt(EqsVa1[MS2] ) : Eqava1 [C] := sqrt(EqsVa1[C2] ) : 1var := [M, MS, C, PP0, RR0, TT0, AAS] : [seq(1var[i]=EqsVA1[1var[i] ] , I=1…nope(1var))] end: Egs :=[M=0.5, MS=0.53452, C=0.2182, P0P=0.84302, RR0=0.88517, TT0=0.95238, AASsub=1.33985, AASsup=0.95238] : For i from 1 to nops(Egs) do print(I,Isentropic2(Egs[i])) od : (process)

I have functions with sin(x) and  cos(x) terms with x values are degrees.

How to calculate sin(30 degree)?

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Hi,

Idea for trigonometric animation like this? Thanks

Please I need help with my proc.

 

> RK2skritt:=proc(FR::procedure,xo,yo,vxo,vyo,h) local x, y, vx, vy, r, kx1, kx2, kx3, kx4, ky1, ky2, ky3, ky4, l x1, l x2, l x3, l x4, ly1, ly2, ly3, ly4, tmp; r:=sqrt(xo*xo+yo*yo); tmp:=-(h*FR(r))/(r); lx1:=h*vxo; ly1:=h*vyo; kx1:=tmp*xo; ky1:=tmp*yo; lx2:=h*(vxo+0.5*kx1); ly2:=h*(vyo+0.5 ky1); r:=sqrt((xo+0.5*lx1)^(2)+(yo+0.5*ly1)^(2)); tmp:=-(h*FR(r))/(r); kx2:=tmp*(xo+0.5*lx1); ky2:=tmp*(yo+0.5*ly1); lx3:=h*(vxo+0.5*kx2); ly3:=h*(vyo+0.5*ky2); r:=sqrt((xo+0.5*lx2)^(2)+(yo+0.5*ly2)^(2)); tmp:=-(h*FR(r))/(r); kx3:=tmp*(xo+0.5*lx2); ky3:=tmp*(yo+0.5*ly2); lx4:=h*(vxo+kx3); ly4:=h*(vyo+ky3); r:=sqrt((xo+lx3)^(2)+(yo+ly3)^(2)); tmp:=-(h*FR(r))/(r); kx4:=tmp*(xo+lx3); ky4:=tmp(yo+ly3); x:=xo+(lx1+2*lx2+2*lx3+lx4)/(6); y:=yo+(ly1+2*ly2+2*ly3+ly4)/(6); vx:=vxo+(kx1+2*kx2+2*kx3+kx4)/(6); vy:=vyo+(ky1+2*ky2+2*ky3+ky4)/(6); [x,y,vx,vy]; end proc: Error, invalid local declaration Please someone help me!!!!!!!!

in maple after fitting an equation (A + B.x) in the experimental data, how to assign to parameters A and B the adjusted values will be assigned in the equation?

 

Thanks

I have a surface described by the equation.

f := (x, y) -> 3*(1 - x)^2*exp(-x^2 - (y + 1)^2) - (2*x - 10*x^3 - 10*y^5)*exp(-x^2 - y^2) - 1/3*exp(-(x + 1)^2 - y^2)

with(plots):
plot3d(f(x,y),x=-3..3,y=-3..3,orientation=[-40,60,0])

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I expect the output for the following code to be a Matrix containing 720 and a Matrix containing 21. What I get is a Matrix containing x^6 and one containing 21, which shows an unexpected difference between the parameter evaluation rule for Matrix products and that for Matrix sums. Is there a good reason for this, or is it a bug? Do any other binary operators between rtables also show this weirdness? 

proc(n::nonnegint) 
local x, q, v:= <<x>>, s:= <<0>>, p:= <<1>>; 
   for x to n do p:= p.v; s:= s+v od; 
   p, s 
end proc(6);

 

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proc() local x, v:= <x>; x:= 1; rtable_eval(v) end proc();

My actual goal is to have a Matrix with a parameter inside a procedure and to create different instantiations of the Matrix in a loop by changing the parameter. 

What is the problem with the initialconsiditions that caused this error?

"Error, (in dsolve/numeric/DAE/initial) missing initial conditions for the following: {Integer}"

Thanks.

Hi

I use Maple 2016.

The following command calculates semicircle perimeter, but it returns infinity.

`assuming`([int(sqrt(1+(diff(sqrt(R^2-(x-R)^2), x))^2), x = 0 .. 2*R)], [R > 0])

I am running a for loop which for some loop index may give error message but it is fine for me to go with next loop indexes. but maple stop after the error message. How can I make maple to run even after the error message. Thank you

Can I do something like it?

Hi, 

I am trying to solve 1 equation with goniometric functions so I know the range (0..2*Pi), but it just doesnt solve it (though it solved similar ones before).

fsolve(3.*10^6 = sqrt((-4.2*10^14*(-1.*10^7*u*cos(u) + 3.84*10^8)/((-1.*10^7*u*cos(u) + 3.84*10^8)^2 + 1.*10^14*u^2*sin(u)^2)^(3/2) + 4.2*10^21*u*cos(u)/((-1.*10^7*u*cos(u) + 3.84*10^8)^2 + 1.*10^14*u^2*sin(u)^2)^(3/2))^2 + 7.056*10^43*u^2*sin(u)^2/((-1.*10^7*u*cos(u) + 3.84*10^8)^2 + 1.*10^14*u^2*sin(u)^2)^3), u, u = 0 .. 2*Pi)

Is there some way to get the solution?

Thank you in advance

 

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