Advanced Search

acer

32333 Reputation

29 Badges

19 years, 320 days
Ontario, Canada

Social Networks and Content at Maplesoft.com

Contact acer

MaplePrimes Activity


These are answers submitted by acer

dynamically saved...

acer 32333
July 25 2020
1 3

As I'm sure you're aware, there are several ways to manually store a Matrix between sessions, by issuing a command. Eg. storing to .mla, text file, or workbook.

But you seem to be asking about the Matrix being automatically and dynamically stored/saved so that its saved version matches its running values -- with no command needed prior to closing/restart apart from normal closing of the Worksheet/Document.

The answer is that this is one of the purposes why the DataTable was invented. It provides this functionality that otherwise did not conveniently and robustly exist.

(The "State" embedded-component provides a similar mechanism, but it is really just a kind of hidden DataTable -- and is designed more for programmatically constructed embedded-component assemblies.)

eval(...,1)...

acer 32333
July 23 2020
2 0

As I showed you in your earlier question, you can utilize eval(...,1) to useful effect. In particular, you can compare it against the result from a full eval call.

> 

restart;
> 

ode1 := :-parse("diff(y(x),x$2)=0"):
> 

lprint(eval(ode1,1));

diff(y(x),x $ 2) = 0

> 

evalb(eval(ode1)=eval(ode1,1));

false

> 

f := proc()
  local ode1;
  ode1 := :-parse("diff(y(x),x$2)=0");
  evalb(eval(ode1)=eval(ode1,1));
end proc:
f();

false

> 

ode1 := eval(:-parse("diff(y(x),x$2)=0")):
> 

lprint(eval(ode1,1));

diff(diff(y(x),x),x) = 0

> 

evalb(eval(ode1)=eval(ode1,1));

true

> 

f := proc()
  local ode1;
  ode1 := eval(:-parse("diff(y(x),x$2)=0"));
  evalb(eval(ode1)=eval(ode1,1));
end proc:
f();

true

> 

restart;
> 

ode1 := 'sin(2.1)':
> 

lprint(eval(ode1,1));

sin(2.1)

> 

evalb(eval(ode1)=eval(ode1,1));

false

> 

f := proc()
  local ode1;
  ode1 := 'sin(2.1)';
  evalb(eval(ode1)=eval(ode1,1));
end proc:
f();

false

> 

ode1 := sin(2.1):
> 

lprint(eval(ode1,1));

.8632093666

> 

evalb(eval(ode1)=eval(ode1,1));

true

> 

f := proc()
  local ode1;
  ode1 := eval(sin(2.1));
  evalb(eval(ode1)=eval(ode1,1));
end proc:
f();

true

> 

 

Download eval_1.mw

evaluation...

acer 32333
July 23 2020
3 2

If you call the parse command with no options then it does not evaluate its result. And inside your procedure the local ode gets only 1-level evaluation.

You can wrap parse with a call to eval, or you can supply the option statement.

> 

restart;
foo:=proc()
  local ode,func;  
  local x,y; #adding this did not  help

  ode  :=  :-parse("diff(y(x),x$2)=0", statement);
  func :=  :-parse("y(x)");

  try
     dsolve(ode), DEtools:-odeadvisor(ode,func);
  catch:
     error lastexception;
  end try;

end proc:

foo();

y(x) = _C1*x+_C2, [[_2nd_order, _quadrature]]

> 

restart;
foo:=proc()
  local ode,func;  
  local x,y; #adding this did not  help

  ode  :=  eval(:-parse("diff(y(x),x$2)=0"));
  func :=  :-parse("y(x)");

  try
     dsolve(ode), DEtools:-odeadvisor(ode,func);
  catch:
     error lastexception;
  end try;

end proc:

foo();

y(x) = _C1*x+_C2, [[_2nd_order, _quadrature]]

> 

 

Download parse_example.mw

indexing...

acer 32333
July 23 2020
1 0

If that is assigned to the name M then try accessing the entry by indexing, eg.   M[1,1]

Upload and attach your worksheet, if you want to help us to help you.

something...

acer 32333
July 23 2020
1 6

I got this:

restart;
Digits:=16:
P:=...your long expression... :
newP:=eval(P,[k=0.1,beta=0.2]):
plot(newP,lambda=0.4..0.85);

fsolve(newP,lambda=0.4..0.85,maxsols=4);

   0.4632186949799427, 0.5169368305419582, 0.7781636733300423, 0.8094962147692479

help_rf_ac.mw

eval...

acer 32333
July 22 2020
1 1

Are you saying the your fsolve call already works, and produces results like, say, this:

   SOL1 := fsolve({ODE11, ODE12}, {N, t__2});
                 SOL1 := {N=3, t__2=5.6666}

In that case you can do the following to access the values:

   eval(N, SOL1);
                               3
   eval(t__2,SOL1);
                          5.6666

And you can use those wherever you need the values, or you can assign each to temporary variables, etc.

If your situation is different then please explain in more detail what you need.

syntax...

acer 32333
July 21 2020
1 1
> 

restart;
> 

x:=proc(j)
> 

option remember;

> 

x(j-1) + 1;

> 

end proc:

> 

 

> 

x(1):=2;

2

> 

x(2), x(3), x(4);

3, 4, 5

> 

x(2):=7;

7

> 

forget(x, 3); forget(x, 4);
> 

x(3), x(4);

8, 9

> 

x(2):=13

13

> 

map[2](forget, x, [3,4]):
> 

x(3), x(4);

14, 15

> 

x(2):=10

10

> 

forget~(x, [3,4]):
> 

x(3), x(4);

11, 12

> 

 

Download EXAMPLES_ac.mw

something...

acer 32333
July 21 2020
3 4

If I understand you, here is one way to contruct it. (I expect that there are slicker ways.)

> 

restart;
> 

F:=(N::posint)->ArrayTools:-FlipDimension(Matrix(N,N,
  [seq([seq(j+i*(i-1)/2,
    j=`if`(i::odd,1..i,i..1),(-1)^(i+1))],i=1..N),
   seq([seq(N^2+1-(j+i*(i-1)/2),
    j=`if`(i::even,1..i,i..1),(-1)^(i))],i=N-1..1,-1)],
  scan=band[N-1,N-1]),1):
> 

F(2);

Matrix(2, 2, {(1, 1) = 1, (1, 2) = 2, (2, 1) = 3, (2, 2) = 4})

> 

F(3);

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

> 

F(4);

Matrix(4, 4, {(1, 1) = 1, (1, 2) = 2, (1, 3) = 6, (1, 4) = 7, (2, 1) = 3, (2, 2) = 5, (2, 3) = 8, (2, 4) = 13, (3, 1) = 4, (3, 2) = 9, (3, 3) = 12, (3, 4) = 14, (4, 1) = 10, (4, 2) = 11, (4, 3) = 15, (4, 4) = 16})

> 

F(5);

Matrix(5, 5, {(1, 1) = 1, (1, 2) = 2, (1, 3) = 6, (1, 4) = 7, (1, 5) = 15, (2, 1) = 3, (2, 2) = 5, (2, 3) = 8, (2, 4) = 14, (2, 5) = 16, (3, 1) = 4, (3, 2) = 9, (3, 3) = 13, (3, 4) = 17, (3, 5) = 22, (4, 1) = 10, (4, 2) = 12, (4, 3) = 18, (4, 4) = 21, (4, 5) = 23, (5, 1) = 11, (5, 2) = 19, (5, 3) = 20, (5, 4) = 24, (5, 5) = 25})

> 

F(6);

Matrix(6, 6, {(1, 1) = 1, (1, 2) = 2, (1, 3) = 6, (1, 4) = 7, (1, 5) = 15, (1, 6) = 16, (2, 1) = 3, (2, 2) = 5, (2, 3) = 8, (2, 4) = 14, (2, 5) = 17, (2, 6) = 26, (3, 1) = 4, (3, 2) = 9, (3, 3) = 13, (3, 4) = 18, (3, 5) = 25, (3, 6) = 27, (4, 1) = 10, (4, 2) = 12, (4, 3) = 19, (4, 4) = 24, (4, 5) = 28, (4, 6) = 33, (5, 1) = 11, (5, 2) = 20, (5, 3) = 23, (5, 4) = 29, (5, 5) = 32, (5, 6) = 34, (6, 1) = 21, (6, 2) = 22, (6, 3) = 30, (6, 4) = 31, (6, 5) = 35, (6, 6) = 36})

> 

 

Download mattrav.mw

maximize...

acer 32333
July 20 2020
2 1

Here is one way to treat your example symbolically (exactly).

> 

restart;
> 

obj:=(x-2*y)/(5*x^2-2*x*y+2*y^2);

(x-2*y)/(5*x^2-2*x*y+2*y^2)

> 

cond:=isolate(2*x^2-y^2+x*y=1,x);

x = -(1/4)*y-(1/4)*(9*y^2+8)^(1/2)

> 

sol:=simplify([maximize(eval(obj,cond),location)]);

[(1/4)*2^(1/2), {[{y = -(1/6)*2^(1/2)*(3+3^(1/2))}, (1/4)*2^(1/2)]}]

> 

pt:=[simplify(eval(cond,sol[2,1,1])), sol[2,1,1,1]];

[x = -(1/3)*6^(1/2), y = -(1/6)*2^(1/2)*(3+3^(1/2))]

> 

simplify(eval(obj,pt));

(1/4)*2^(1/2)

> 

 

Download maximize_exact.mw

like this...

acer 32333
July 20 2020
1 4

Is this the kind of thing that you had in mind?

The grey region denotes eq1<eq2, and the red curve denotes eq1=0 and the blue curve denotes eq2=0.

So their linestyle depends on whether the portion lie within the grey region, or not.

You may wish to adjust, as I used strict inequalities (which are also subject to roundoff). So results may vary if where the curves lie right along the border of the grey region. (But it may be "OK", with the curve dashed along the edge of the grey region which is also dashed -- ie. the strict inequality may not hold there.)

I did not both to figure out what value of working precision (Digits) would be fastest while accurate, and so on.

> 

restart;
> 

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:
> 

Digits:=40:
> 

TL:=plottools:-transform(
     proc(a,b)
      Digits:=40:
      `if`(evalf(eval(eq1<eq2,[x[m]=a,x[u]=b])),[a,b],[undefined,undefined])
     end proc):
TU:=plottools:-transform(
     proc(a,b)
      Digits:=40:
      `if`(evalf(eval(eq1>=eq2,[x[m]=a,x[u]=b])),[a,b],[undefined,undefined])
     end proc):
> 

PR:=plots:-inequal(eq1<eq2, x[m]=-1e3..1e3, x[u]=-3e8..3e8, color=gray):
> 

P1:=plots:-implicitplot(eq1=0, x[m]=-1e3..1e3, x[u]=-3e8..3e8, color=red, thickness=3,
                        grid=[51,51], gridrefine=0, crossingrefine=0):
P2:=plots:-implicitplot(eq2=0, x[m]=-1e3..1e3, x[u]=-3e8..3e8, color=blue, thickness=3,
                        grid=[151,151], gridrefine=0, crossingrefine=0):
> 

PC:=plots:-display(
  plots:-display(TL(P1),overrideoption,linestyle=dash),
  plots:-display(TU(P1)),
  plots:-display(TL(P2),overrideoption,linestyle=dash),
  plots:-display(TU(P2))
);

> 

plots:-display(PC,PR,view=[-1e3..1e3, -3e8..3e8]);

> 

 


 

Download eq1eq2.mw

UseUnit and Units:-Simple...

acer 32333
July 20 2020
1 5

Here's an explanation of what's going wrong. 

The MQ procedure (in source local Studienblatt_1_8) calls UseUnit several time, every time it is called. For example, it calls UseUnit('m') each time it is used. This gets into trouble when a call to a command such as Units:-Simple:-`*` produces a result with a new local name m upon each invocation. (I am going to submit a bug report with the details.)

Your GeneralStartup source attachment calls with(Units), which has the effect of rebinding UseUnit so that its calls in the read source will resolve to Units:-UseUnit. It also has the effect of loading the Units:-Simple package, so that calls to `*` in the parsed (read) MQ source resolve to Units:-Simple:-`*`, etc.

I expect that you want the Units:-Simple effects of combining units. (I suggest utilizing uses Units:-Simple in the procedures like MQ rather than the utilizing with, but the problem would occur either way.)

The easiest and probably best fix would be to only call UseUnit with the same input name once per restart. I'll leave it to you to decide where you'd like to place it, say at the top-level in your Studienblatt_1_8 source, say.

An alternative but crude workaround might be for computation routines (such as your seqMQ, say) to execute combine(...,units) or simplify. I am not sure that would always suffice easily.

> 

restart;
> 

lg := Units:-Unit('m');

Units:-Unit(m)

> 

[indets(lg,name), map(addressof,indets(lg,name))];

[{m}, {18446884599300013950}]

> 

F:=proc(len)
  local fuzz;
  Units:-UseUnit('m');
  fuzz := Units:-Simple:-`*`(3, len);
  [indets(fuzz,name), map(addressof,indets(fuzz,name))];
end proc:
> 

 

> 

F(lg);

[{m}, {18446884599192877630}]

> 

F(lg);

[{m}, {18446884599192866750}]

> 

F(lg);

[{m}, {18446884599192847646}]

> 

restart;
> 

lg := Units:-Unit('m');

Units:-Unit(m)

> 

[indets(lg,name), map(addressof,indets(lg,name))];

[{m}, {18446884599300013950}]

> 

tot := 0:
for i from 1 to 3 do
  Units:-UseUnit('m');
  fuzz := Units:-Simple:-`*`(3, lg);
  [indets(fuzz,name), map(addressof,indets(fuzz,name))];
  tot := tot + fuzz;
end do;

false

3*Units:-Unit(m)

[{m}, {18446884599192874270}]

3*Units:-Unit(m)

true

3*Units:-Unit(m)

[{m}, {18446884599192165854}]

3*Units:-Unit(m)+3*Units:-Unit(m)

true

3*Units:-Unit(m)

[{m}, {18446884599191917950}]

3*Units:-Unit(m)+3*Units:-Unit(m)+3*Units:-Unit(m)

> 

simplify(tot);

9*Units:-Unit(m)

> 

combine(tot, units);

9*Units:-Unit(m)

> 

 

Download UseUnit_Simple_oddness.mw

(I'm still looking at revising the procedures to utilize uses instead of relying on the top-level with calls, and to use a parant module locals instead of the declared globals in the procedures.)

Here is the simple move of the three calls to UseUnit outside of the MQ procedure -- now at the top level, inside the Studientblatt_1_8 source.
Koyaanisqatsi_acc.zip

various...

acer 32333
July 19 2020
2 3

There are other things you could do with this.

Since the height simplifies to just 1 for your example, and 2D densityplot might be another reasonable choice.

(I don't know whether this is your actual problem, or just a toy example to illustrate. If you have a more complicated example then it might be useful to show it.)

> 

restart;
> 

f := (x, w) -> exp(w*x*I);

proc (x, w) options operator, arrow; exp(I*w*x) end proc

> 

evalc(f(x,w));

cos(w*x)+I*sin(w*x)

> 

evalc(abs(f(x,w)));

1

> 

evalc(argument(f(x,w)));

arctan(sin(w*x), cos(w*x))

> 

plot3d(evalc(abs(f(x,w))), x=-2*Pi..2*Pi, w=-2*Pi..2*Pi,
       style=surface,
       color=evalc(argument(f(x,w))));

> 

plots:-densityplot(evalc(argument(f(x,w))),
                   x=-2*Pi..2*Pi, w=-2*Pi..2*Pi,
                   colorstyle=HUE, style=surface, grid=[301,301]);

> 

 

Download plot_cmplx.mw

no orientation...

acer 32333
July 18 2020
2 0

A 1-dimensional Array has no orientation. It is not a row Array. It pretty-prints in a row for convenience, as do lists and a few other structures.

If you want to make it pretty-print vertically then you could cast it to a Vector[column]., or you could extract it with 2 dimensions as,  b[1 .. 2, 1 .. 1].

try...catch...

acer 32333
July 18 2020
3 0

You could utilize some variant on the following:

try
  a:=ModularSquareRoot(10,11);
  b:=b+1;
catch "":
  c:=c+1;
end try;

A (deprecated), older mechanism is something like this:

a:=traperror(ModularSquareRoot(10,11));
if a<>lasterror then b:=b+1 else c:=c+1 end if;

something...

acer 32333
July 17 2020
1 3

Here is one way to plot your data.

I am presuming that you know whether your numerical method (which produces the data) makes sense and is accurate in some sense that is acceptable to you.

(I don't know why portions of your worksheet don't inline well on this forum. It looks better in the actual GUI. I used Maple 18 to match the version in which your attachment was last saved.)

> 

restart
> 

lambda := 3.64*10^10

0.3640000000e11

> 

mu := 5.46*10^10

0.5460000000e11

> 

rho := 2330

2330

> 

tau := 5*10^(-5)

1/20000

> 

T[0] := 800

800

> 

d[n] := -9*10^(-31)

-9/10000000000000000000000000000000

> 

d[e] := 2.5*10^(-3)

0.2500000000e-2

> 

E[g] := 1.11

1.11

> 

C[e] := 695

695

> 

alpha[T] := 4.14*10^(-6)

0.4140000000e-5

> 

delta := (3*lambda+2*mu)*alpha[T];

904176.0000

> 

r := 2

2

> 

omega[0] := -.3

-.3

> 

NULL
> 

epsilon[0] := 8.85*10^(-12)

0.8850000000e-11

> 

k := 800

800

> 

C[T] := sqrt((2*mu+lambda)/rho)

7905.015521

> 

mu[0] := (4*3.17)*10^(-7)

0.1268000000e-5

> 

t[1] := k/(rho*C[e]*C[T]^2)

0.7905763302e-11

> 

q[2] := k*t[1]/(d[e]*rho*tau*C[e])

0.3124518178e-7

> 

q[1] := k/(d[e]*rho*C[e])

.1976101522

> 

a := .5

.5

> 

mu := 5.46*10^10

0.5460000000e11

> 

NULL
> 

q[3] := a/C[T]^2

0.8001373626e-8

> 

epsilon[1] := delta^2*T[0]*t[1]/(k*rho)

0.2773919393e-2

> 

epsilon[2] := alpha[T]*E[g]*t[1]/(d[n]*rho*tau*C[e])

-0.4985559321e12

> 

kappa := 386

386

> 

epsilon[3] := d[n]*k*kappa*t[1]/(alpha[T]*rho*C[e]*d[e])

-0.1310939149e-33

> 

``
> 

``
> 

delta[n] := (3*lambda+2*mu)*d[n]

-0.1965600000e-18

> 

H0 := 10^5

100000

> 

R[H] := 1+epsilon[0]*((4*3.17)*10^(-7))^2*H0^2/rho

1.

> 

alpha[0] := 1+(4*3.17)*10^(-7)*H0^2

12681.00000

> 

nu := 2

2

> 

for y from 0 to 300 do x := 0+0.1e-1*y; t := .8; s := 4.7/t; A[1] := -(-s^4*R[H]-s^3*R[H]*q[3]-s^3*alpha[0]*q[1]-s^2*alpha[0]*q[1]*q[3]+s^2*epsilon[2]*q[1]*q[3]-s^3*alpha[0]+s^3*epsilon[2]-s^2*alpha[0]*q[2]-s*alpha[0]*q[2]*q[3]+s*epsilon[2]*epsilon[3]*q[3]+s*epsilon[2]*q[2]*q[3]+alpha[0]*epsilon[1]*epsilon[3]*q[3])/(s^2*alpha[0]+s*alpha[0]*q[3]-s*epsilon[2]*q[3]); A[2] := (s^5*R[H]*q[1]+s^4*R[H]*q[1]*q[3]+s^5*R[H]+s^4*R[H]*q[2]+s^4*alpha[0]*q[1]-s^4*epsilon[2]*q[1]+s^3*R[H]*q[2]*q[3]-s^2*R[H]*epsilon[1]*epsilon[3]*q[3]+s^3*alpha[0]*q[2]-s^3*epsilon[2]*epsilon[3]-s^3*epsilon[2]*q[2]-s^2*alpha[0]*epsilon[1]*epsilon[3])/(s^2*alpha[0]+s*alpha[0]*q[3]-s*epsilon[2]*q[3]); A[3] := (-s^6*R[H]*q[1]-s^5*R[H]*q[2]+s^4*R[H]*epsilon[1]*epsilon[3])/(-s^2*alpha[0]-s*alpha[0]*q[3]+s*epsilon[2]*q[3]); M[1] := (1/6)*sqrt(6)*sqrt((8*A[1]^3-36*A[1]*A[2]+108*A[3]+12*sqrt(12*A[1]^3*A[3]-3*A[1]^2*A[2]^2-54*A[1]*A[2]*A[3]+12*A[2]^3+81*A[3]^2))^(1/3)*((8*A[1]^3-36*A[1]*A[2]+108*A[3]+12*sqrt(12*A[1]^3*A[3]-3*A[1]^2*A[2]^2-54*A[1]*A[2]*A[3]+12*A[2]^3+81*A[3]^2))^(2/3)+2*A[1]*(8*A[1]^3-36*A[1]*A[2]+108*A[3]+12*sqrt(12*A[1]^3*A[3]-3*A[1]^2*A[2]^2-54*A[1]*A[2]*A[3]+12*A[2]^3+81*A[3]^2))^(1/3)+4*A[1]^2-12*A[2]))/(8*A[1]^3-36*A[1]*A[2]+108*A[3]+12*sqrt(12*A[1]^3*A[3]-3*A[1]^2*A[2]^2-54*A[1]*A[2]*A[3]+12*A[2]^3+81*A[3]^2))^(1/3); M[2] := (1/6)*sqrt(3)*sqrt((8*A[1]^3-36*A[1]*A[2]+108*A[3]+12*sqrt(12*A[1]^3*A[3]-3*A[1]^2*A[2]^2-54*A[1]*A[2]*A[3]+12*A[2]^3+81*A[3]^2))^(1/3)*(I*sqrt(3)*(8*A[1]^3-36*A[1]*A[2]+108*A[3]+12*sqrt(12*A[1]^3*A[3]-3*A[1]^2*A[2]^2-54*A[1]*A[2]*A[3]+12*A[2]^3+81*A[3]^2))^(2/3)-(4*I)*sqrt(3)*A[1]^2+(12*I)*sqrt(3)*A[2]-(8*A[1]^3-36*A[1]*A[2]+108*A[3]+12*sqrt(12*A[1]^3*A[3]-3*A[1]^2*A[2]^2-54*A[1]*A[2]*A[3]+12*A[2]^3+81*A[3]^2))^(2/3)+4*A[1]*(8*A[1]^3-36*A[1]*A[2]+108*A[3]+12*sqrt(12*A[1]^3*A[3]-3*A[1]^2*A[2]^2-54*A[1]*A[2]*A[3]+12*A[2]^3+81*A[3]^2))^(1/3)-4*A[1]^2+12*A[2]))/(8*A[1]^3-36*A[1]*A[2]+108*A[3]+12*sqrt(12*A[1]^3*A[3]-3*A[1]^2*A[2]^2-54*A[1]*A[2]*A[3]+12*A[2]^3+81*A[3]^2))^(1/3); M[3] := (1/6)*sqrt(-3*(8*A[1]^3-36*A[1]*A[2]+108*A[3]+12*sqrt(12*A[1]^3*A[3]-3*A[1]^2*A[2]^2-54*A[1]*A[2]*A[3]+12*A[2]^3+81*A[3]^2))^(1/3)*(I*sqrt(3)*(8*A[1]^3-36*A[1]*A[2]+108*A[3]+12*sqrt(12*A[1]^3*A[3]-3*A[1]^2*A[2]^2-54*A[1]*A[2]*A[3]+12*A[2]^3+81*A[3]^2))^(2/3)-(4*I)*sqrt(3)*A[1]^2+(12*I)*sqrt(3)*A[2]+(8*A[1]^3-36*A[1]*A[2]+108*A[3]+12*sqrt(12*A[1]^3*A[3]-3*A[1]^2*A[2]^2-54*A[1]*A[2]*A[3]+12*A[2]^3+81*A[3]^2))^(2/3)-4*A[1]*(8*A[1]^3-36*A[1]*A[2]+108*A[3]+12*sqrt(12*A[1]^3*A[3]-3*A[1]^2*A[2]^2-54*A[1]*A[2]*A[3]+12*A[2]^3+81*A[3]^2))^(1/3)+4*A[1]^2-12*A[2]))/(8*A[1]^3-36*A[1]*A[2]+108*A[3]+12*sqrt(12*A[1]^3*A[3]-3*A[1]^2*A[2]^2-54*A[1]*A[2]*A[3]+12*A[2]^3+81*A[3]^2))^(1/3); m[1, 1] := -(M[1]^2*q[3]-s^2)/s^2; m[1, 2] := -(M[2]^2*q[3]-s^2)/s^2; m[1, 3] := -(M[3]^2*q[3]-s^2)/s^2; m[2, 1] := epsilon[3]*(M[1]^2*q[3]-s^2)/(s^2*(-s*q[1]+M[1]^2-q[2])); m[2, 2] := epsilon[3]*(M[2]^2*q[3]-s^2)/(s^2*(-s*q[1]+M[2]^2-q[2])); m[2, 3] := epsilon[3]*(M[3]^2*q[3]-s^2)/(s^2*(-s*q[1]+M[3]^2-q[2])); m[3, 1] := (-M[1]*(M[1]^2*q[3]-s^2)*(-s*q[1]+M[1]^2-epsilon[3]-q[2])/(s^2*(-s*q[1]+M[1]^2-q[2])*(-s^2*R[H]+M[1]^2*alpha[0]))-epsilon[3]*(M[1]^2*q[3]-s^2)/(s^2*(-s*q[1]+M[1]^2-q[2]))+(M[1]^2*q[3]-s^2)/s^2)/mu; m[3, 2] := (-M[2]*(M[2]^2*q[3]-s^2)*(-s*q[1]+M[2]^2-epsilon[3]-q[2])/(s^2*(-s*q[1]+M[2]^2-q[2])*(-s^2*R[H]+M[2]^2*alpha[0]))-epsilon[3]*(M[2]^2*q[3]-s^2)/(s^2*(-s*q[1]+M[2]^2-q[2]))+(M[2]^2*q[3]-s^2)/s^2)/mu; m[3, 3] := (-M[3]*(M[3]^2*q[3]-s^2)*(-s*q[1]+M[3]^2-epsilon[3]-q[2])/(s^2*(-s*q[1]+M[3]^2-q[2])*(-s^2*R[H]+M[3]^2*alpha[0]))-epsilon[3]*(M[3]^2*q[3]-s^2)/(s^2*(-s*q[1]+M[3]^2-q[2]))+(M[3]^2*q[3]-s^2)/s^2)/mu; V[1] := (m[2, 2]*m[3, 3]-m[2, 3]*m[3, 2])*T[0]/((m[1, 1]*m[2, 2]*m[3, 3]-m[1, 1]*m[2, 3]*m[3, 2]-m[1, 2]*m[2, 1]*m[3, 3]+m[1, 2]*m[2, 3]*m[3, 1]+m[1, 3]*m[2, 1]*m[3, 2]-m[1, 3]*m[2, 2]*m[3, 1])*r)-(m[1, 2]*m[3, 3]-m[1, 3]*m[3, 2])*nu/((m[1, 1]*m[2, 2]*m[3, 3]-m[1, 1]*m[2, 3]*m[3, 2]-m[1, 2]*m[2, 1]*m[3, 3]+m[1, 2]*m[2, 3]*m[3, 1]+m[1, 3]*m[2, 1]*m[3, 2]-m[1, 3]*m[2, 2]*m[3, 1])*r*d[e]); V[2] := -(m[2, 1]*m[3, 3]-m[2, 3]*m[3, 1])*T[0]/((m[1, 1]*m[2, 2]*m[3, 3]-m[1, 1]*m[2, 3]*m[3, 2]-m[1, 2]*m[2, 1]*m[3, 3]+m[1, 2]*m[2, 3]*m[3, 1]+m[1, 3]*m[2, 1]*m[3, 2]-m[1, 3]*m[2, 2]*m[3, 1])*r)+(m[1, 1]*m[3, 3]-m[1, 3]*m[3, 1])*nu/((m[1, 1]*m[2, 2]*m[3, 3]-m[1, 1]*m[2, 3]*m[3, 2]-m[1, 2]*m[2, 1]*m[3, 3]+m[1, 2]*m[2, 3]*m[3, 1]+m[1, 3]*m[2, 1]*m[3, 2]-m[1, 3]*m[2, 2]*m[3, 1])*r*d[e]); V[3] := (m[2, 1]*m[3, 2]-m[2, 2]*m[3, 1])*T[0]/((m[1, 1]*m[2, 2]*m[3, 3]-m[1, 1]*m[2, 3]*m[3, 2]-m[1, 2]*m[2, 1]*m[3, 3]+m[1, 2]*m[2, 3]*m[3, 1]+m[1, 3]*m[2, 1]*m[3, 2]-m[1, 3]*m[2, 2]*m[3, 1])*r)-(m[1, 1]*m[3, 2]-m[1, 2]*m[3, 1])*nu/((m[1, 1]*m[2, 2]*m[3, 3]-m[1, 1]*m[2, 3]*m[3, 2]-m[1, 2]*m[2, 1]*m[3, 3]+m[1, 2]*m[2, 3]*m[3, 1]+m[1, 3]*m[2, 1]*m[3, 2]-m[1, 3]*m[2, 2]*m[3, 1])*r*d[e]); F[k] := sum(exp(-M[i]*x)*V[i], i = 1 .. 3); s := (4.7+I*m*Pi)/(.8); G[k] := sum((sum(exp(-M[i]*x)*V[i], i = 1 .. 3))(-1)^(4.7/t), m = 1 .. 1000); B[k] := exp(4.7)*Re((1/2)*F[k]+G[k])/t; X[y] := x; Bk[y] := B[k]/10^213 end do:
> 

plot(`<|>`(`<,>`(convert(X, list)), `<,>`(convert(Bk, list))));

> 

 

``

Download x_phi_ac.mw

First 115 116 117 118 119 120 121 Last Page 117 of 336