Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

During running my ws I faced with memory error as below, where as my system have enough memory (120GB)

Warning, Run: unable to set assignto result due to error:  Maple was unable to allocate enough memory to complete this computation.  Please see ?alloc

Maple's help suggests :Software limits are imposed by the -T command-line argument, the datalimit argument to kernelopts and system imposed user limits (for example shell limits).
  But I could not understand how to increase software limit.

 

how to fix that?

find the fourier cosine and sine transform. Use your identites and integrals to eliminate all exponents.

piecewise function is {cosh(t) for 0 less or equal to t, t is less than 1,

                                   0 for 1is less than or equal to t.}

alpha+{6*RK[1]*alpha+2+(96/5)*R^2*K^2*alpha^2-(1/6)*R*alpha+64*R^3*K^3*alpha^3}*beta+{(24/5)*RK+44*R^2*K^2*alpha^3}*beta^2=0

i am currently using Maple 18, i have a problem on inserting 12 row by 12 column matrix and above is seem to be impossible. please can help or direct me on how to insert 12 row by 12 column matrix in maple. because my maple 18 seem to stop in 10 row by 10 column matrix.  thanks

Hi everybody.....

I want to obtain the roots of below equation, How? 

eq:=1+cos(beta)*cosh(beta)+.5720823799*beta*(cos(beta)*sinh(beta)-cosh(beta)*sin(beta))-0.1285578382e-1*beta^2*sin(beta)*sinh(beta)-0.9629800618e-4*beta^3*(cos(beta)*sinh(beta)+cosh(beta)*sin(beta))+0.1377259814e-4*beta^4*(1-cos(beta)*cosh(beta)) = 0

Tnx...

Dear users,

I have an issue with finding real part of a complex variable function. In calculating the real part I see two arguments and the plot is not smooth. How to get real part correct. The worksheet is attached.
 

``

 

 

##Toya complex variable method

``

restart;

stress_c:=-(1+1/nu_c)*k*p2*zeta_c/2;

-(1/2)*(1+1/nu_c)*k*p2*zeta_c

(1.1)

p2:=(c0_c-d_1c/k)*(z-a*(cos(alpha)+2*lambda*sin(alpha)))+(1-k)/k*a*(N_infty-T_infty)*exp(2*I*phi_c+2*lambda*(alpha-Pi))*((a*(cos(alpha)-2*lambda*sin(alpha)))/z-a^2/z^2)

(c0_c-d_1c/k)*(z-a*(cos(alpha)+2*lambda*sin(alpha)))+(1-k)*a*(N_infty-T_infty)*exp((2*I)*phi_c+2*lambda*(alpha-Pi))*(a*(cos(alpha)-2*lambda*sin(alpha))/z-a^2/z^2)/k

(1.2)

``

z := exp(I*theta)

exp(I*theta)

(1.3)

``

k := beta_c/(1+nu_c)

beta_c/(1+nu_c)

(1.4)

nu_c := (kappa2*mu+mu2)/(kappa*mu2+mu)

(kappa2*mu+mu2)/(kappa*mu2+mu)

(1.5)

d_1c := (N_infty+T_infty)*(1/2)

(1/2)*N_infty+(1/2)*T_infty

(1.6)

lambda := -evalf(ln(nu_c)/(2*Pi))

-.1591549430*ln((kappa2*mu+mu2)/(kappa*mu2+mu))

(1.7)

``

beta_c := mu*(1+kappa2)/(kappa*mu2+mu)

mu*(1+kappa2)/(kappa*mu2+mu)

(1.8)

zeta_c := ((z-a*exp(I*alpha))/(z-a*exp(-I*alpha)))^(I*lambda)/((z-a*exp(I*alpha))^.5*(z-a*exp(-I*alpha))^.5)

((exp(I*theta)-a*exp(I*alpha))/(exp(I*theta)-a*exp(-I*alpha)))^(-(.1591549430*I)*ln((kappa2*mu+mu2)/(kappa*mu2+mu)))/((exp(I*theta)-a*exp(I*alpha))^.5*(exp(I*theta)-a*exp(-I*alpha))^.5)

(1.9)

``

c0_c := G_c+I*H_c

G_c+I*H_c

(1.10)

G_c:=(0.5*(T_infty+N_infty)*(1-(cos(alpha)+2*lambda*sin(alpha))*exp(2*lambda*(evalf(Pi)-alpha)))-0.5*(1-k)*(1+4*lambda^2)*(N_infty-T_infty)*(sin(alpha))^2*cos(2*phi_c))/(2-k-k*(cos(alpha)+2*lambda*sin(alpha))*exp(evalf(2*lambda*(Pi-alpha))));

(.5*(N_infty+T_infty)*(1-(cos(alpha)-.3183098860*ln((kappa2*mu+mu2)/(kappa*mu2+mu))*sin(alpha))*exp(-.3183098860*ln((kappa2*mu+mu2)/(kappa*mu2+mu))*(3.141592654-alpha)))-.5*(1-mu*(1+kappa2)/((kappa*mu2+mu)*(1+(kappa2*mu+mu2)/(kappa*mu2+mu))))*(.1013211835*ln((kappa2*mu+mu2)/(kappa*mu2+mu))^2+1)*(N_infty-T_infty)*sin(alpha)^2*cos(2*phi_c))/(2-mu*(1+kappa2)/((kappa*mu2+mu)*(1+(kappa2*mu+mu2)/(kappa*mu2+mu)))-mu*(1+kappa2)*(cos(alpha)-.3183098860*ln((kappa2*mu+mu2)/(kappa*mu2+mu))*sin(alpha))*exp(-.3183098860*ln((kappa2*mu+mu2)/(kappa*mu2+mu))*(3.141592654-1.*alpha))/((kappa*mu2+mu)*(1+(kappa2*mu+mu2)/(kappa*mu2+mu))))

(1.11)

H_c:=0.5*(1-k)*(1+4*lambda^2)*(-T_infty+N_infty)*(sin(alpha))^2*sin(2*phi_c)/(k*(1+(cos(alpha)+2*lambda*sin(alpha))*exp(2*lambda*(evalf(Pi)-alpha))));

.5*(1-mu*(1+kappa2)/((kappa*mu2+mu)*(1+(kappa2*mu+mu2)/(kappa*mu2+mu))))*(.1013211835*ln((kappa2*mu+mu2)/(kappa*mu2+mu))^2+1)*(N_infty-T_infty)*sin(alpha)^2*sin(2*phi_c)*(kappa*mu2+mu)*(1+(kappa2*mu+mu2)/(kappa*mu2+mu))/(mu*(1+kappa2)*(1+(cos(alpha)-.3183098860*ln((kappa2*mu+mu2)/(kappa*mu2+mu))*sin(alpha))*exp(-.3183098860*ln((kappa2*mu+mu2)/(kappa*mu2+mu))*(3.141592654-alpha))))

(1.12)

##Input

alpha:=evalf(Pi/6)

.5235987758

(1.13)

phi_c:=alpha;

.5235987758

(1.14)

N_infty:=0;

0

(1.15)

T_infty:=1;

1

(1.16)

a:=1;nu2:=22/100;kappa2:=3-4*nu2;nu:=35/100;kappa:=3-4*nu;mu:=239/100;mu2:=442/10;

1

 

11/50

 

53/25

 

7/20

 

8/5

 

239/100

 

221/5

(1.17)

``

stress_c

-(9321/123167)*(((.5586916801-.5*(.8660254037-.1591549431*ln(123167/182775))*exp(-.8333333329*ln(123167/182775))+0.5946710490e-2*ln(123167/182775)^2)/(22817/11767-(717/11767)*(.8660254037-.1591549431*ln(123167/182775))*exp(-.8333333329*ln(123167/182775)))-(1.668336947*I)*(.1013211835*ln(123167/182775)^2+1)/(1+(.8660254037-.1591549431*ln(123167/182775))*exp(-.8333333329*ln(123167/182775)))-11767/1434)*(exp(I*theta)-.8660254037+.1591549431*ln(123167/182775))-(11050/717)*exp(1.047197552*I+.8333333328*ln(123167/182775))*((.8660254037+.1591549431*ln(123167/182775))/exp(I*theta)-1/(exp(I*theta))^2))*((exp(I*theta)+(-.8660254037-.5000000002*I))/(exp(I*theta)+(-.8660254037+.5000000002*I)))^(-(.1591549430*I)*ln(123167/182775))/((exp(I*theta)+(-.8660254037-.5000000002*I))^.5*(exp(I*theta)+(-.8660254037+.5000000002*I))^.5)

(1.18)

assume((1/6)*Pi < theta, theta < 2*Pi-(1/6)*Pi)

simplify(evalc(Re(stress_c)))

-0.8815855810e-10*((((1.000000000*cos(theta)^7+(0.5294827753e-2+.5671599115*sin(theta))*cos(theta)^6-4.533186669*cos(theta)^5+(-11.80630620+4.886343937*sin(theta))*cos(theta)^4+3.402782742*cos(theta)^3+(9213180122.+0.9866808100e-1*sin(theta))*cos(theta)^2+(-0.1055437876e11+0.1595769608e11*sin(theta))*cos(theta)-5794103792.*sin(theta)+1760041721.)*cos(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037))+(-.5600908440*cos(theta)^7+(0.6523625301e-2+1.134319823*sin(theta))*cos(theta)^6+4.644568297*cos(theta)^5+(-0.2905669688e-1+10.20004207*sin(theta))*cos(theta)^4-0.1774243515e-1*cos(theta)^3+(0.1595769609e11-9.082306669*sin(theta))*cos(theta)^2+(-7023191163.-9213180109.*sin(theta))*cos(theta)-3154310102.*sin(theta)-7408031461.)*sin(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037)))*cos(.5*arctan(sin(theta)-.5000000002, cos(theta)-.8660254037))+(-.5600908440*cos(theta)^7+(1.134319823*sin(theta)+0.4756356038e-2)*cos(theta)^6+4.644568284*cos(theta)^5+(11.37920491*sin(theta)-0.2640575516e-1)*cos(theta)^4-0.1774243890e-1*cos(theta)^3+(-11.39571957*sin(theta)+0.1595769607e11)*cos(theta)^2+(-9213180108.*sin(theta)-7023191160.)*cos(theta)-7408031458.-3154310086.*sin(theta))*sin(.5*arctan(sin(theta)-.5000000002, cos(theta)-.8660254037))*cos(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037))+(-1.000000000*cos(theta)^7+(-.5671599115*sin(theta)-0.5294826902e-2)*cos(theta)^6+4.531921682*cos(theta)^5+(-4.886343941*sin(theta)+11.76153292)*cos(theta)^4-3.358186195*cos(theta)^3+(-0.9866807692e-1*sin(theta)-9213180122.)*cos(theta)^2+(-0.1595769609e11*sin(theta)+0.1055437877e11)*cos(theta)-1760041726.+5794103798.*sin(theta))*sin(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037))*sin(.5*arctan(sin(theta)-.5000000002, cos(theta)-.8660254037)))*cos(0.314104002e-1*ln(1492820323.-1292820323.*cos(theta)+746410161.*sin(theta))-0.314104002e-1*ln(-1292820322.*cos(theta)-746410161.4*sin(theta)+1492820322.))+(((-.5600908440*cos(theta)^7+(1.134319823*sin(theta)+0.4756356038e-2)*cos(theta)^6+4.626658979*cos(theta)^5+(-0.2905667760e-1+10.24488508*sin(theta))*cos(theta)^4-.1341529536*cos(theta)^3+(0.1595769608e11-9.127079936*sin(theta))*cos(theta)^2+(-7023191161.-9213180109.*sin(theta))*cos(theta)-3154310089.*sin(theta)-7408031435.)*cos(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037))+(-1.134319823*cos(theta)^7-.5671599115*sin(theta)*cos(theta)^6+4.531921682*cos(theta)^5+(11.80860365-4.107288978*sin(theta))*cos(theta)^4-3.402959469*cos(theta)^3+(-9213180123.+0.1774243833e-1*sin(theta))*cos(theta)^2+(0.1055437876e11-0.1595769608e11*sin(theta))*cos(theta)+5794103807.*sin(theta)-1760041748.)*sin(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037)))*cos(.5*arctan(sin(theta)-.5000000002, cos(theta)-.8660254037))+(-1.000000000*cos(theta)^7-.5671599115*sin(theta)*cos(theta)^6+4.537223485*cos(theta)^5+(-4.886343950*sin(theta)+11.80860366)*cos(theta)^4-3.358186195*cos(theta)^3+(-0.9866807250e-1*sin(theta)-9213180123.)*cos(theta)^2+(0.1055437876e11-0.1595769608e11*sin(theta))*cos(theta)-1760041739.+5794103821.*sin(theta))*sin(.5*arctan(sin(theta)-.5000000002, cos(theta)-.8660254037))*cos(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037))+(.5600908440*cos(theta)^7+(-1.134319823*sin(theta)-0.4756356038e-2)*cos(theta)^6-4.644554360*cos(theta)^5+(-10.21771474*sin(theta)+0.2905668928e-1)*cos(theta)^4+0.1774243685e-1*cos(theta)^3+(9.082306650*sin(theta)-0.1595769608e11)*cos(theta)^2+(9213180109.*sin(theta)+7023191165.)*cos(theta)+7408031453.+3154310085.*sin(theta))*sin(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037))*sin(.5*arctan(sin(theta)-.5000000002, cos(theta)-.8660254037)))*sin(0.314104002e-1*ln(1492820323.-1292820323.*cos(theta)+746410161.*sin(theta))-0.314104002e-1*ln(-1292820322.*cos(theta)-746410161.4*sin(theta)+1492820322.)))/((-sin(theta)+2.-1.732050807*cos(theta))^(1/4)*(sin(theta)+2.-1.732050807*cos(theta))^(1/4))

(1.19)

plot(%, theta = (1/6)*Pi .. 2*Pi-(1/6)*Pi)

 


 

Download Toya_complexPlot2.mw

Hi all, how to get name file  in directory?

Example. I have  and I want call then return

["equals", "function", "polynomial", "viete"]

or

["equals.txt", "function.txt", "polynomial.txt", "viete.txt"]

Thank you very much.

Dear authors,
How to solve this ode problem.

Download link ode.mw

In this problem the boundary condition is

Note: F=g in our problem.

eta approaches N.

Thank you.

 

I am trying to put a number of related 2-d plots into a 3-d frame so I can see them stacked up in the third dimension (which follows a parameter) and rotate things around.

The way I once did this successfully was to create the 2-d plots and then use plottools:-transform to move the individual plots in the third dimension, like so:

plt:=plot(something);

tr:=plottools:-transform((x,y) -> [x,2,y]); # the "2" gets changed for the other plots (not shown here).

plots:-display(tr(plt));

The only effect I can get is that the GUI gets confused and I have to close and reload the sheet to get it back again. I have a (complicated) sheet where this actually works, but I am not able to make it work even in the small example I am posting below.

Any hint of where I am going off trail is appreciated. Incidentally, this problem is what led to the corrupted sheet I had maybe a week ago.

Thanks,

Mac Dude.

display3d.mw

 

I unprotect the GAMMA, but still receives error:

Error, attempting to assign to `GAMMA` which is protected.  Try declaring `local GAMMA`; see ?protect for details.


 

NULL

restart

II := 2

2

(1)

JJ := 2

2

(2)

N := 2:

unprotect(GAMMA):

q := max(II+1, JJ+1):

M := 5:

seq(seq(seq(assign(GAMMA[i, j, r], a*`#mover(mi("&Gamma;",fontstyle = "normal"),mo("&uminus0;"))`[i, j, r]), i = 0 .. q), j = 0 .. q), r = 1 .. N):

a := .2:

RrProc := proc (i, m) local K, j, Q; if i <= m then 0 else K := 1; Q := Matrix(i, 1); for j by 2 to i do Q(j) := 2*i-K; K := 4+K end do; Q := FlipDimension(Q, 1); Q(m+1) end if end proc:
``

`#mover(mi("&Gamma;",fontstyle = "normal"),mo("&uminus0;"))` := Array(0 .. II, 0 .. JJ, 1 .. 6, 1 .. M):

f1 := RandomArray(II+1, JJ+1):

for m to M do `&Gamma;m`[1, m] := f1; `&Gamma;m`[2, m] := f2; `&Gamma;m`[3, m] := f3; `&Gamma;m`[4, m] := f4; `&Gamma;m`[5, m] := f5; `&Gamma;m`[6, m] := f6 end do:

unprotect(`#mover(mi("&Gamma;",fontstyle = "normal"),mo("&uminus0;"))`):

for m to M do `#mover(mi("&Gamma;",fontstyle = "normal"),mo("&uminus0;"))`[0 .. II, 0 .. JJ, 1, m] := ArrayTools:-Alias(`&Gamma;m`[1, m], [0 .. II, 0 .. JJ]); `#mover(mi("&Gamma;",fontstyle = "normal"),mo("&uminus0;"))`[0 .. II, 0 .. JJ, 2, m] := ArrayTools:-Alias(`&Gamma;m`[2, m], [0 .. II, 0 .. JJ]); `#mover(mi("&Gamma;",fontstyle = "normal"),mo("&uminus0;"))`[0 .. II, 0 .. JJ, 3, m] := ArrayTools:-Alias(`&Gamma;m`[3, m], [0 .. II, 0 .. JJ]); `#mover(mi("&Gamma;",fontstyle = "normal"),mo("&uminus0;"))`[0 .. II, 0 .. JJ, 4, m] := ArrayTools:-Alias(`&Gamma;m`[4, m], [0 .. II, 0 .. JJ]); `#mover(mi("&Gamma;",fontstyle = "normal"),mo("&uminus0;"))`[0 .. II, 0 .. JJ, 5, m] := ArrayTools:-Alias(`&Gamma;m`[5, m], [0 .. II, 0 .. JJ]); `#mover(mi("&Gamma;",fontstyle = "normal"),mo("&uminus0;"))`[0 .. II, 0 .. JJ, 6, m] := ArrayTools:-Alias(`&Gamma;m`[6, m], [0 .. II, 0 .. JJ]) end do:

UP := proc (s, GAMMA, N, M, a, b, II, JJ) local k; i, j, r, p, m, q, n, l; if s = 1 then add(add(add(add(add(add((2/3)*Rr[i, m]*Rr[k, m]*b*add(GAMMA[i, j, q, p]*GAMMA[k, j, q, r]*tau[p](t)*tau[r](t), q = 1 .. N)/((2*m+1)*(2*j+1)*a), i = 0 .. II), k = 0 .. II), m = 0 .. II), j = 0 .. JJ), p = 1 .. M), r = 1 .. M) elif s = 2 then add(add(add(add(add(add((1/2)*Rr[i, m]*Rr[k, m]*b*add(GAMMA[i, j, q, p]*GAMMA[k, j, q, r]*tau[p](t)*tau[r](t), q = 1 .. N)/((2*m+1)*(2*j+1)*a), i = 0 .. II), k = 0 .. II), m = 0 .. II), j = 0 .. JJ), p = 1 .. M), r = 1 .. M) end if end proc:

Grid:-Seq(UP(s, GAMMA, N, M, a, b, II, JJ), s = 1 .. 2)

Error, attempting to assign to `GAMMA` which is protected.  Try declaring `local GAMMA`; see ?protect for details.

 

Error, attempting to assign to `GAMMA` which is protected.  Try declaring `local GAMMA`; see ?protect for details.

 

Error, attempting to assign to `GAMMA` which is protected.  Try declaring `local GAMMA`; see ?protect for details.

 

Error, attempting to assign to `GAMMA` which is protected.  Try declaring `local GAMMA`; see ?protect for details.

 

UP(1, GAMMA, N, M, a, b, II, JJ), UP(2, GAMMA, N, M, a, b, II, JJ)

(3)

NULL


 

Download soal.mw

 

What is the problem?

 

Hi, I'm investigating an equation of motion, and I'm attempting to plot t against different values of thetabn. I have acquired a list of my data points (in the real domain) of the form [thetabn1, t1], [thetabn2, t2] ... etc. But I am struggling to figure out how to plot it. Using dataplot gives me a graph but it is incorrect. I would like a scatterplot, ideally once I have refined my range of thetabn I would like to be able to join it up with a line to create a nice looking plot. Also any improvements to my method would be appreciated. v[i], thetavn and omegac are set variables and s[n] is my function which I am setting equal to zero, and solving for t.

 

with(RealDomain);
v[i] := 145000;
thetavn := (1/6)*Pi;
omegac := .1;
s[n] := v[i]*cos(thetavn)*(cos(2*thetabn)*tan(thetabn)+sin(2*thetabn)*sin(omegac*t)/omegac);
for thetabn from evalf((1/100)*Pi) by evalf((1/100)*Pi) to evalf(Pi) do assign('result', [op(result), [thetabn, solve(v[i]*cos(thetavn)*(cos(2*thetabn)*tan(thetabn)+sin(2*thetabn)*sin(omegac*t)/omegac) = 0, t)]]) end do;
dataplot(result);

 

Hello, I need to figure out what theta is through this matrix:

https://imgur.com/RldbcJD

Should I use a solve command for this?

hello everyone,

I am trying to optimize expressions symbolically. I need to find out the maximum value possible for an variable, so that the expressoin still have a valid solution.

For Example:

expr:=a-b/b-a^3;  # a=(0,10), b=(0,10)

In this eypression b=a^3 is the only case where undefined solution is possible, for a given interval of variables

This looks fine for simple expression. But in reality there are complex equations to solve with more than 2 varibles.

1) first thing is to find out all values of a variable resulting in undeifined output(or infinite)
2) assign a symbolic value(variable < or > some value) to the variable so that the undefined result can be eliminated.

 I need to optimize the given expression so that it does not have any undefined cases when solving. I understood that when optimizing, there always be a condition on variables(in this case variable max is the condition, maximum value the variable can take). output of an expression is always a real value

OptimizedExpr:=a-b[max]/b[max]-a^3 --> b[max]>a^3 or b[max]<a^3

(it is easy to to say b[max] is not equal to a^3 , also a^3 is the limiting value. In some case it is more resonable to just ignore other part of limiting value. Hence, I would like to optimize using greaterthan or lessthan of limiting value).

I would be very glad to know how I can find Optimized expressions. I tried using the solve function but observed that expressions are equalled to zero and solving. which is completely opposite to what I was looking. I really do not know is there any way to find out undefined cases in expressions and on what varibale at what values.

I tried to explain the situation at my best and I welcome for any suggested edits or furthur information required.

 

Thank you

how I can determied  this integral in figure below or compute area in figure which adressed in the following website?

https://en.m.wikipedia.org/wiki/Spherical_cap

Hello everyone !

 when I use  the command   ''G1:=NonIsomorphicGraphs(5, output = graphs, outputform = adjacency)''  , I want to compute the   rank of   adjacent  matrices of 

every graph in  G1,. I try to do , but maple  retutn false:

Rank(G1);
Error, invalid input: too many and/or wrong type of arguments passed to LinearAlgebra:-Rank; first unused argument is Matrix(5, 5, {(1, 1) = 0, (1, 2) = 1, (1, 3) = 1, (1, 4) = 1, (1, 5) = 1, (2, 2) = 0, (2, 3) = 1, (2, 4) = 1, (2, 5) = 1, (3, 3) = 0, (3, 4) = 1, (3, 5) = 1, (4, 4) = 0, (4, 5) = 1, (5, 5) = 0}, datatype = integer[1], storage = triangular[upper], shape = [symmetric])

  How to achieve it , I do not konw to  invoke these adjacent matrices . Would someboby 

give me a hand. 

Thanks very much!


 

 

 

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