Maple Questions and Posts

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An n*n matrix A is called an MDS matrix over an arbitrary field if all determinant of square sub-matrices of A are non-zero over the field. It is not difficult to prove that the number of all square sub-matrices of A is binomial(2*n, n)-1. The code that I use to check whether A is an MDS matrix is in the following form 

 u := 1;
 for k to n do
 P := choose(n, k);
   for i to nops(P) do
    for j to nops(P) do
         F := A(P[i], P[j]);
         r := Determinant(F);
        if r = 0 then

           u := 0; k:=n+1;

            i := nops(P)+1; j := nops(P)+1;

        end if;

    end do;

      end do; 
   if u = 1 then

      print(A is an MDS Matrix) 

   end if; 
  end do:

When I run the mentioned code for n=16, it takes long time since we need to check binomial(32, 16)-1=601080389 cases to verify that A is an MDS matrix or not. 

My Question: Is there a modified procedure which can be used to check that an n*n matrix is  whether an MDS matrix for n>=16. 


 

i'm doing an optimaztion for my final project. when i execute the coding, it says: 

Warning, initial point [m1 = .900000000000000, m2 = .900000000000000, m3 = .900000000000000, sigma1 = .900000000000000, sigma2 = .900000000000000, sigma3 = .900000000000000] does not satisfy the inequality constraints; trying to find a feasible initial point
Error, (in DirectSearch:-Search) cannot find feasible initial point; last infeasible trial point is [m1 = HFloat(0.9), m2 = HFloat(1.9), m3 = HFloat(1.9), sigma1 = HFloat(1.9), sigma2 = HFloat(0.9), sigma3 = HFloat(0.9)].

here my full coding:


restart;
with(linalg);
with(Optimization);
with(DirectSearch);
[BoundedObjective, CompromiseProgramming, DataFit, 

  ExponentialWeightedSum, GlobalOptima, GlobalSearch, Minimax, 

  ModifiedTchebycheff, Search, SolveEquations, WeightedProduct, 

  WeightedSum]
q := Array(0 .. .111, [0.586e-2, 0.67475e-3, 0.52476e-3, 0.419785e-3, 0.354814e-3, 0.324859e-3, 0.319948e-3, 0.31e-3, 0.295013e-3, 0.28e-3, 0.259974e-3, 0.25496e-3, 0.26e-3, 0.270027e-3, 0.280026e-3, 0.284987e-3, 0.274934e-3, 0.279893e-3, 0.294824e-3, 0.324765e-3, 0.374672e-3, 0.439555e-3, 0.509439e-3, 0.56934e-3, 0.60923e-3, 0.634201e-3, 0.634233e-3, 0.624319e-3, 0.61442e-3, 0.624491e-3, 0.6495e-3, 0.684465e-3, 0.714452e-3, 0.729463e-3, 0.749451e-3, 0.789387e-3, 0.864347e-3, 0.964331e-3, 0.1064261e-2, 0.119413e-2, 0.1333876e-2, 0.150354e-2, 0.1683293e-2, 0.1883023e-2, 0.2102591e-2, 0.2356929e-2, 0.2656062e-2, 0.3004981e-2, 0.3403637e-2, 0.3841874e-2, 0.4349482e-2, 0.4931339e-2, 0.5587622e-2, 0.6293742e-2, 0.7044467e-2, 0.780967e-2, 0.8563865e-2, 0.9291539e-2, 0.9987678e-2, 0.10677379e-1, 0.1139506e-1, 0.12195833e-1, 0.13108819e-1, 0.14262384e-1, 0.15557439e-1, 0.17002799e-1, 0.18574592e-1, 0.20263971e-1, 0.22103523e-1, 0.24043337e-1, 0.26165465e-1, 0.28548531e-1, 0.31489568e-1, 0.3458584e-1, 0.37891201e-1, 0.41511365e-1, 0.45444649e-1, 0.49867283e-1, 0.54877269e-1, 0.60478547e-1, 0.66532745e-1, 0.7397857e-1, 0.81900977e-1, 0.90034141e-1, 0.98921462e-1, .108746024, .11839162, .130752255, .14368791, .157201822, .169770195, .177233464, .188823516, .204733363, .224639756, .249617627, .273409998, .298674064, .304378882, .319592743, .342821691, .367512872, .395257421, .426270115, .460795318, .498484563, .537417055, .577542345, .618093683, .660441764, .703856817, 1]);
variables = [m1, m2, m3, sigma1, sigma2, sigma3];
        variables = [m1, m2, m3, sigma1, sigma2, sigma3]
psi1 := 0.11480601e-1; psi2 := 0.8890123e-2; psi3 := .979629276;
                          0.011480601
                          0.008890123
                          0.979629276
s1(x):=exp(-(x/(m1))^((m1/(sigma1)))):  s1(x+1):=exp(-((x+1)/(m1))^((m1/(sigma1)))):  s2(x):=1-exp(-(x/(m2))^((-m2/(sigma2)))):  s2(x+1):=1-exp(-((x+1)/(m2))^((-m2/(sigma2)))):  s3(x):=exp(exp(-m3/(sigma3))-exp((x-m3)/(sigma3))): s3(x+1):=exp(exp(-m3/(sigma3))-exp((x+1-m3)/(sigma3)))  :  s(x):=(psi1*s1(x)+psi2*s2(x)+psi3*s3(x)): s(x+1):=(psi1*s1(x+1)+psi2*s2(x+1)+psi3*s3(x+1)):   qtopi(x):=1-((s(x+1))/(s(x))):
fungsikerugian := add((1-qtopi(x)/q[x])^2, x = 0 .. .110);
for x from 0 to 111 do c1[x] := 0 <= s1(x+1); c2[x] := 1 >= s1(x+1); c3[x] := 0 <= s2(x+1); c4[x] := 1 >= s2(x+1); c5[x] := 0 <= s3(x+1); c6[x] := 1 >= s3(x+1); c7[x] := 0 <= s1(x); c8[x] := 1 >= s1(x); c9[x] := 0 <= s2(x); c10[x] := 1 >= s2(x); c11[x] := 0 <= s3(x); c12[x] := 1 >= s3(x); c13[x] := 0 <= s(x); c14[x] := 1 >= s(x); c15[x] := 0 <= s(x+1); c16[x] := 1 >= s(x+1); c17[x] := 0 <= qtopi(x); c18[x] := 1 >= qtopi(x) end do;

constr := {m2 > sigma2, m3 > sigma3, seq(c1[x], x = 0 .. .110), seq(c10[x], x = 0 .. .111), seq(c11[x], x = 0 .. .111), seq(c12[x], x = 0 .. .111), seq(c13[x], x = 0 .. .111), seq(c14[x], x = 0 .. .111), seq(c15[x], x = 0 .. .110), seq(c16[x], x = 0 .. .110), seq(c17[x], x = 0 .. .110), seq(c18[x], x = 0 .. .110), seq(c2[x], x = 0 .. .110), seq(c3[x], x = 0 .. .110), seq(c4[x], x = 0 .. .110), seq(c5[x], x = 0 .. .110), seq(c6[x], x = 0 .. .110), seq(c7[x], x = 0 .. .111), seq(c8[x], x = 0 .. .111), seq(c9[x], x = 0 .. .111), m1 < sigma1, 0 <= m1 and m1 < 17, 17 <= m2 and m2 < 33, 33 <= m3 and m3 < 111};
solusi := DirectSearch:-Search(fungsikerugian, constr, assume = positive, evaluationlimit = 5555);
Warning, initial point [m1 = .900000000000000, m2 = .900000000000000, m3 = .900000000000000, sigma1 = .900000000000000, sigma2 = .900000000000000, sigma3 = .900000000000000] does not satisfy the inequality constraints; trying to find a feasible initial point
Error, (in DirectSearch:-Search) cannot find feasible initial point; last infeasible trial point is [m1 = HFloat(0.9), m2 = HFloat(1.9), m3 = HFloat(1.9), sigma1 = HFloat(1.9), sigma2 = HFloat(0.9), sigma3 = HFloat(0.9)]

thanks before

The command

taylor( (2 * pi * n) ^ (1/(2n), n = 2)

return   1+((1/2)*ln(2*Pi)+(1/2)*ln(n))/n+O(1/n^2)

I think, this is incorrect, in my oppinion must be:

1+((1/2)*ln(2*Pi)+(1/2)*ln(n))/n+O(ln(n)^2/n^2)

Is this error in maple?

 

A common question to our tech support team is about completing the square for a univariate polynomial of even degree, and how to do that in Maple. We’ve put together a solution that we think you’ll find useful. If you have any alternative methods or improvements to our code, let us know!

restart;

# Procedure to complete the square for a univariate
# polynomial of even degree.

CompleteSquare := proc( f :: depends( 'And'( polynom, 'satisfies'( g -> ( type( degree(g,x), even ) ) ) ) ), x :: name )

       local a, g, k, n, phi, P, Q, r, S, T, u:

       # Degree and parameters of polynomial.
       n := degree( f, x ):
       P := indets( f, name ) minus { x }:

       # General polynomial of square plus constant.
       g := add( a[k] * x^k, k=0..n/2 )^2 + r:

       # Solve for unknowns in g.
       Q := indets( g, name ) minus P:

       S := map( expand, { solve( identity( expand( f - g ) = 0, x ), Q ) } ):

       if numelems( S ) = 0 then
              return NULL:
       end if:

       # Evaluate g at the solution, and re-write square term
       # so that the polynomial within the square is monic.

       phi := u -> lcoeff(op(1,u),x)^2 * (expand(op(1,u)/lcoeff(op(1,u),x)))^2:  
       T := map( evalindets, map( u -> eval(g,u), S ), `^`(anything,identical(2)), phi ):

       return `if`( numelems(T) = 1, T[], T ):

end proc:


# Examples.

CompleteSquare( x^2 + 3 * x + 2, x );
CompleteSquare( a * x^2 + b * x + c, x );
CompleteSquare( 4 * x^8 + 8 * x^6 + 4 * x^4 - 246, x );

m, n := 4, 10;
r := rand(-10..10):
for i from 1 to n do
       CompleteSquare( r() * ( x^(m/2) + randpoly( x, degree=m-1, coeffs=r ) )^2 + r(), x );
end do;

# Compare quadratic examples with Student:-Precalculus:-CompleteSquare()
# (which is restricted to quadratic expressions).

Student:-Precalculus:-CompleteSquare( x^2 + 3 * x + 2 );
Student:-Precalculus:-CompleteSquare( a * x^2 + b * x + c );

For a higher-order example:

f := 5*x^4 - 70*x^3 + 365*x^2 - 840*x + 721;
g := CompleteSquare( f, x ); # 5 * ( x^2 - 7 * x + 12 )^2 + 1
h := evalindets( f, `*`, factor ); 4 * (x-3)^2 * (x-4)^2 + 1
p1 := plot( f, x=0..5, y=-5..5, color=blue ):
p2 := plots:-pointplot( [ [3,1], [4,1] ], symbol=solidcircle, symbolsize=20, color=red ):
plots:-display( p1, p2 );

tells us that the minimum value of the expression is 1, and it occurs at x=3 and x=4.

Assume that a[1],a[2],..a[k] are positive integer numbers. Let n be a positive integer number. 

Suppose that igcd(a[1],a[2],..a[k])=1. 

My question: Is there a command in Maple such that the output of the this command be true provided that there are "non-negative integer numbers" x[1],x[2],..x[k] which satisfy the following condition:

a1*x1+a2*x2+...+ak*xk=n

Thanks in advance

How to let sqrt(5*x+5+y) become sqrt(5*(x+1)+y) automatically?

Dear all,

Following the comments I am editing this post:

I have a function F of variables (r1,r2,theta1,theta2,r,theta,a). r1, r2,theta1,theta2 are function of r,  theta and a. I want to take derivative of F with respect to a. r and theta are independent of a . I expressed everything in terms of 'a' as a function of 'a' at first. Then I use diff(F, a). I see there is an error in the final expression G .There is a restriction that theta1 should lie between -Pi to Pi and theta2 between 0 to 2*Pi. I speculate this is the source of error. Work sheet is attached. Reason: value of G: integration in 0 to pi/4 gives some  value but for 0 to pi it evaluates to zero and so is the case with 0 to 2*Pi. As "G "physically represents energy it must be a positive value.
 


restart;

theta1 := unapply(arctan(r*sin(theta)/(r*cos(theta)-a)), a);

proc (a) options operator, arrow; arctan(r*sin(theta)/(r*cos(theta)-a)) end proc

(1)

 

## theta1 -->[-Pi,Pi] and theta2-->[0,2*Pi]

NULL

theta2 := unapply(arctan(r*sin(theta)/(r*cos(theta)+a)), a);

proc (a) options operator, arrow; arctan(r*sin(theta)/(r*cos(theta)+a)) end proc

(2)

``

r1:=unapply(sqrt((r*cos(theta)-a)^2+r^2*(sin(theta))^2),a);r2:=unapply(sqrt((r*cos(theta)+a)^2+r^2*(sin(theta))^2),a);

proc (a) options operator, arrow; ((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2) end proc

 

proc (a) options operator, arrow; ((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2) end proc

(3)

sigma12:=0;sigma22:=sigma;

0

 

sigma

(4)

plot(arctan(tan(x)), x = (1/2)*Pi .. Pi)

 

## I have to use a constraint that

assume(theta1(a) < Pi, theta1(a) > -Pi, theta2(a) > 0, theta2(a) < 2*Pi, a>0,r>0)

u1:=(1+nu)*sigma22*sqrt(r1(a)*r2(a))*(4*(1-2*nu)*cos((theta1(a)+(theta2(a)))/2)-4*r*(1-nu)*cos(theta)/sqrt(r1(a)*r2(a))-2*r^2/(r1(a)*r2(a))*(cos((theta1(a)+(theta2(a)))/2)-cos(2*theta-theta1(a)/2-(theta2(a))/2)))/(4*E)+(1+nu)*sigma12*sqrt(r1(a)*r2(a))*(2*(1-2*nu)*sin((theta1(a)+(theta2(a)))/2)-2*r*(1-nu)*sin(theta)/sqrt(r1(a)*r2(a))+1*r^2/(r1(a)*r2(a))*sin(theta)*cos(theta-theta1(a)/2-(theta2(a))/2))/(E);

 

(1/4)*(1+nu)*sigma*(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2))^(1/2)*(4*(1-2*nu)*cos((1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))+(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))-4*r*(1-nu)*cos(theta)/(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2))^(1/2)-2*r^2*(cos((1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))+(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))-cos(2*theta-(1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))-(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a))))/(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2)))/E

(5)

NULL

u2:=(1+nu)*sigma*sqrt(r1(a)*r2(a))*(8*(1-nu)*sin((theta1(a)+(theta2(a)))/2)-4*r*(nu)*sin(theta)/sqrt(r1(a)*r2(a))-2*r^2/(r1(a)*r2(a))*(sin((theta1(a)+(theta2(a)))/2)+sin(2*theta-theta1(a)/2-(theta2(a))/2)))/(4*E)+(1+nu)*sigma12*sqrt(r1(a)*r2(a))*((1-2*nu)*cos((theta1(a)+theta2(a))/2)+2*r*(1-nu)*cos(theta)/sqrt(r1(a)*r2(a))-1*r^2/(r1(a)*r2(a))*sin(theta)*sin(theta-theta1(a)/2-theta2(a)/2))/(E);

 

(1/4)*(1+nu)*sigma*(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2))^(1/2)*(8*(1-nu)*sin((1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))+(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))-4*r*nu*sin(theta)/(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2))^(1/2)-2*r^2*(sin((1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))+(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))+sin(2*theta-(1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))-(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a))))/(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2)))/E

(6)

 

## get u_r and u_theta as u[1] and u[2]

u[1] := u1*cos(theta)+u2*sin(theta);

(1/4)*(1+nu)*sigma*(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2))^(1/2)*(4*(1-2*nu)*cos((1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))+(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))-4*r*(1-nu)*cos(theta)/(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2))^(1/2)-2*r^2*(cos((1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))+(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))-cos(2*theta-(1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))-(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a))))/(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2)))*cos(theta)/E+(1/4)*(1+nu)*sigma*(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2))^(1/2)*(8*(1-nu)*sin((1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))+(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))-4*r*nu*sin(theta)/(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2))^(1/2)-2*r^2*(sin((1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))+(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))+sin(2*theta-(1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))-(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a))))/(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2)))*sin(theta)/E

(7)

u[2] := -sin(theta)*u1+cos(theta)*u2;

-(1/4)*sin(theta)*(1+nu)*sigma*(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2))^(1/2)*(4*(1-2*nu)*cos((1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))+(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))-4*r*(1-nu)*cos(theta)/(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2))^(1/2)-2*r^2*(cos((1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))+(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))-cos(2*theta-(1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))-(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a))))/(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2)))/E+(1/4)*cos(theta)*(1+nu)*sigma*(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2))^(1/2)*(8*(1-nu)*sin((1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))+(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))-4*r*nu*sin(theta)/(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2))^(1/2)-2*r^2*(sin((1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))+(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))+sin(2*theta-(1/2)*arctan(r*sin(theta)/(r*cos(theta)-a))-(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a))))/(((r*cos(theta)-a)^2+r^2*sin(theta)^2)^(1/2)*((r*cos(theta)+a)^2+r^2*sin(theta)^2)^(1/2)))/E

(8)

Diff_ur := simplify(diff(u[1], a));

(1/2)*sigma*(1+nu)*a*(-(-2*cos(theta)*a*r+a^2+r^2)^(1/2)*(2*cos(theta)*a*r+a^2+r^2)^(1/2)*r^2*cos(theta)*(a-r)*(a+r)*cos(2*theta+(1/2)*arctan(r*sin(theta)/(-r*cos(theta)+a))-(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))+(-2*cos(theta)*a*r+a^2+r^2)^(1/2)*(2*cos(theta)*a*r+a^2+r^2)^(1/2)*r^2*sin(theta)*(a^2+r^2)*sin(2*theta+(1/2)*arctan(r*sin(theta)/(-r*cos(theta)+a))-(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))+((a^2*r^2-r^4)*(2*cos(theta)*a*r+a^2+r^2)^(1/2)*(-2*cos(theta)*a*r+a^2+r^2)^(1/2)-4*(-2*cos(theta)*a*r+a^2+r^2)*(2*cos(theta)*a*r+a^2+r^2)*(-4*r^2*(nu-3/4)*cos(theta)^2+(3*nu-5/2)*r^2+a^2*(nu-1/2)))*cos(theta)*cos((1/2)*arctan(r*sin(theta)/(-r*cos(theta)+a))-(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))-sin(theta)*((2*cos(theta)*a*r+a^2+r^2)^(1/2)*r^2*(a^2+r^2)*(-2*cos(theta)*a*r+a^2+r^2)^(1/2)-4*(-2*cos(theta)*a*r+a^2+r^2)*(2*cos(theta)*a*r+a^2+r^2)*(-4*r^2*(nu-3/4)*cos(theta)^2+(a^2+r^2)*(nu-1)))*sin((1/2)*arctan(r*sin(theta)/(-r*cos(theta)+a))-(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a))))/((-2*cos(theta)*a*r+a^2+r^2)^(3/2)*(2*cos(theta)*a*r+a^2+r^2)^(3/2)*((-2*cos(theta)*a*r+a^2+r^2)^(1/2)*(2*cos(theta)*a*r+a^2+r^2)^(1/2))^(1/2)*E)

(9)

``

 

Diff_ut := simplify(diff(u[2], a));

-(1/2)*sigma*(1+nu)*a*(-(-2*cos(theta)*a*r+a^2+r^2)^(1/2)*(2*cos(theta)*a*r+a^2+r^2)^(1/2)*r^2*sin(theta)*(a^2+r^2)*cos(2*theta+(1/2)*arctan(r*sin(theta)/(-r*cos(theta)+a))-(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))-(-2*cos(theta)*a*r+a^2+r^2)^(1/2)*(2*cos(theta)*a*r+a^2+r^2)^(1/2)*r^2*cos(theta)*(a-r)*(a+r)*sin(2*theta+(1/2)*arctan(r*sin(theta)/(-r*cos(theta)+a))-(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))+sin(theta)*((2*cos(theta)*a*r+a^2+r^2)^(1/2)*r^2*(a^2+r^2)*(-2*cos(theta)*a*r+a^2+r^2)^(1/2)-4*(-2*cos(theta)*a*r+a^2+r^2)*(-4*r^2*(nu-3/4)*cos(theta)^2+(a^2+r^2)*(nu-1/2))*(2*cos(theta)*a*r+a^2+r^2))*cos((1/2)*arctan(r*sin(theta)/(-r*cos(theta)+a))-(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))+((a^2*r^2-r^4)*(2*cos(theta)*a*r+a^2+r^2)^(1/2)*(-2*cos(theta)*a*r+a^2+r^2)^(1/2)-4*(-2*cos(theta)*a*r+a^2+r^2)*(-4*r^2*(nu-3/4)*cos(theta)^2+(3*nu-2)*r^2+a^2*(nu-1))*(2*cos(theta)*a*r+a^2+r^2))*sin((1/2)*arctan(r*sin(theta)/(-r*cos(theta)+a))-(1/2)*arctan(r*sin(theta)/(r*cos(theta)+a)))*cos(theta))/((-2*cos(theta)*a*r+a^2+r^2)^(3/2)*(2*cos(theta)*a*r+a^2+r^2)^(3/2)*((-2*cos(theta)*a*r+a^2+r^2)^(1/2)*(2*cos(theta)*a*r+a^2+r^2)^(1/2))^(1/2)*E)

(10)

``

# find the limiting case

Att := limit(Diff_ut*r*sin(2*theta), r = infinity);

(2*a*sigma*cos(theta)^3*sin(theta)^2*nu+2*a*sigma*cos(theta)*sin(theta)^4*nu+2*a*sigma*cos(theta)^3*sin(theta)^2+2*a*sigma*cos(theta)*sin(theta)^4-8*a*sigma*cos(theta)*sin(theta)^2*nu^2-6*a*sigma*cos(theta)*sin(theta)^2*nu+2*a*sigma*cos(theta)*sin(theta)^2)/(((cos(theta)^2+sin(theta)^2)/cos(theta)^2)^(1/2)*E)

(11)

Arr := limit(Diff_ur*r*(1-cos(2*theta)), r = infinity);

(-16*a*sigma*cos(theta)^6*nu^2-16*a*sigma*cos(theta)^4*sin(theta)^2*nu^2-6*a*sigma*cos(theta)^6*nu-6*a*sigma*cos(theta)^4*nu*sin(theta)^2+10*a*sigma*cos(theta)^6+10*a*sigma*sin(theta)^2*cos(theta)^4+28*a*sigma*cos(theta)^4*nu^2+20*a*sigma*cos(theta)^2*sin(theta)^2*nu^2+10*a*sigma*cos(theta)^4*nu+4*a*sigma*cos(theta)^2*sin(theta)^2*nu-18*a*sigma*cos(theta)^4-16*a*sigma*sin(theta)^2*cos(theta)^2-12*a*sigma*cos(theta)^2*nu^2-4*a*sigma*sin(theta)^2*nu^2-4*a*sigma*cos(theta)^2*nu+2*a*sigma*sin(theta)^2*nu+8*a*sigma*cos(theta)^2+6*a*sigma*sin(theta)^2)/(cos(theta)*((cos(theta)^2+sin(theta)^2)/cos(theta)^2)^(1/2)*E)

(12)

G := (1/8)*(int(Arr+Att, theta = 0 .. Pi/2))*sigma*4;

-(1/8)*Pi*a*sigma^2*(4*nu^2-nu-5)/E

(13)

simplify(G)

-(1/8)*Pi*a*sigma^2*(4*nu^2-nu-5)/E

(14)

 


Download Derivative_implicit_maplePrime.mw

 

Thanks,

Hi,

 

Is there any way to add arrows to the parametrics plot to show the direction they are going? Thanks. 

Hi,

How would I tell maple to solve for the variable t? The answer should be 4. 

[t-2,(t-2)^2]

[(3t/2)-4,(3t/2)-2]

I need to set them equal to eachother and then solve for t. 

 

Thanks!

Suppose that n is a positive integer number and [k1,k2,...,kn] is a list of non-negative integer numbers. 

My Question: How to create the procedure proc([k1,k2,...,kn]) such that the output of this procedure is in the following form:

For i1 from 0 to k1 do

for i2 from 0 to k2 do

......................

for in from 0 to kn do

i1+i2+...+in

end do; end do;...end do;

This application describes the motion of a pendulum attached to a moving pivot, all in 2D.

https://www.maplesoft.com/applications/view.aspx?SID=4888

 
How can this situation be generalized to a pendulum attached to a pivot which moves along a 3D spacecurve?

The Joint Mathematics Meetings are taking place next week (January 16 – 19) in Baltimore, Maryland, U.S.A. This will be the 102nd annual winter meeting of the Mathematical Association of America (MAA) and the 125th annual meeting of the American Mathematical Society (AMS).

Maplesoft will be exhibiting at booth #501 as well as in the networking area. Please stop by to chat with me and other members of the Maplesoft team, as well as to pick up some free Maplesoft swag or win some prizes.

This year we will be hosting a hands-on workshop on Maple: A Natural Way to Work with Math

This special event will take place on Thursday, January 17 at 6:00 -8:00 P.M. in the Holiday Ballroom 4 at the Hilton Baltimore.

 

There are also several other interesting Maple related talks:

MYMathApps Tutorials

MAA General Contributed Paper Session on Mathematics and Technology 

Wednesday January 16, 2019, 1:00 p.m.-1:55 p.m.

Room 323, BCC
Matthew Weihing*, Texas A&M University 
Philip B Yasskin, Texas A&M University 

 

The Logic Behind the Turing Bombe's Role in Breaking Enigma. 

MAA General Contributed Paper Session on Mathematics and Technology 

Wednesday January 16, 2019, 1:00 p.m.-1:55 p.m.
Room 323, BCC
Neil Sigmon*, Radford University 
Rick Klima, Appalachian State University 

 

On a software accessible database of faithful representations of Lie algebras. 

MAA General Contributed Paper Session on Algebra, I 

Wednesday January 16, 2019, 2:15 p.m.-6:25 p.m.
Room 348, BCC
Cailin Foster*, Dixie State University 
 

Discussion of Various Technical Strategies Used in College Math Teaching. 

MAA Contributed Paper Session on Open Educational Resources: Combining Technological Tools and Innovative Practices to Improve Student Learning, IV 

Friday January 18, 2019, 8:00 a.m.-10:55 a.m.
Room 303, BCC
Lina Wu*, Borough of Manhattan Community College-The City University of New York 
 

An Enticing Simulation in Ordinary Differential Equations that predict tangible results. 

MAA Contributed Paper Session on The Teaching and Learning of Undergraduate Ordinary Differential Equations 

Friday January 18, 2019, 1:00 p.m.-4:55 p.m.
Room 324, BCC
Satyanand Singh*, New York City College of Technology of CUNY 
 

An Effort to Assess the Impact a Modeling First Approach has in a Traditional Differential Equations Class. 

AMS Special Session on Using Modeling to Motivate the Study of Differential Equations, I 
Saturday January 19, 2019, 8:00 a.m.-11:50 a.m.

Room 336, BCC
Rosemary C Farley*, Manhattan College 
Patrice G Tiffany, Manhattan College 

 

If you are attending the Joint Math meetings this week and plan on presenting anything on Maple, please feel free to let me know and I'll update this list accordingly.


See you in Baltimore!

Daniel

Maple Product Manager

Hello,

I will explain my problem on a simple function and some data.

mg:=78.54*7.85*1e-9*1000*9.81;l:=10000;l0:=12000;h:=0;H := 28.399;
eta:=mg*l/(2*H);
zeta:=arcsinh(mg*h/(2*H*sinh(eta)))-eta;
z:=H/mg*(cosh(mg/H*x+zeta)-cosh(zeta));
plot(z,x=0..l);

Above is a definition of an initial plot. Now I would like to draw a new plot in which every x coordinate is shifted horizontally by a function:

deltax:=H*arcsinh(x)-x;

As you see I can't use translate or scale so I've tried to use a transform function but I can't do it the right way.

I would be grateful for any ideas.

 

Greetings,

Iza

Hi!

I have a rather long Maple code and want it to be executed multiple times with a parameter changed each time.

Surely this can be done with the loop structure, but it seems the whole loop structure must be contained into one single execution group, which makes it to be a little inconvenient, since the code is too long.

 

So is there any alternative way to realize this utility?

 

Best regard and thanks!

I have a function defined which maps x to a polynomial.

The coefficients are highly precise floating point numbers, which is necessary since it needs to be accurate, however when I try to print the function it looks like a massive mess.

I tried to use print(evalf[4](f)); in an attempt to simplify it however this evaluation seems to have no effect on how it is displayed.

As I said, I can't use evalf when defining the function since it needs high precision.

Is there a way to do this without creating a clone of the function with the coefficients evaluated, just to print it on screen?
 

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