Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

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eithne

fn1 and gn1 are the 2x2 matrices. For example
 

fn1:=Matrix(2,2,[seq(f[i],i=1..4)])
gn1:=Matrix(2,2,[seq(g[i],i=1..4)])


eq1:=evalm(Matrix(2,2, [1, 1, 0, 3])&*fn1+gn1)=Matrix(2,2,[0]);

eq2:=evalm(fn1+gn1)=Matrix(2,2, [0]);

how can we find fn1 and gn1 matrices?

Consider the following code:

LM := [
   Matrix([[1,2],[3,4]]),
   Matrix([[5,6],[7,8]])
];
A := Matrix([[0,1],[1,0]]);
map(x -> A . x,LM);
A .~ LM;

where LM is a list of two matrices (just a test example), and A is some (test)matrix that I want to multiply onto each of these two matrices from the left, say. The map-construction works, as expected, but the elementwise operation .~ produces an error. Why?

Greetings

How can I get LPSolve to output the unique subsets of {3,1,1,2,2,1} which sum to 5 (no recycling of set values)

partition.mw

(the code is a Yury/Love hybrid).

I have several maple worksheets (from the web) that have discussion blocks mixed within executable blocks.

All the executable blocks are delineated with a single '[' at the left while the discussion blocks do not.

How do I do this?

Tom Dean

I wish to apply several i-j constraints to an optimization problem that involves minimizing a function x[i,j]. 

Does anyone know of a simple way to exclude values for i and j? For instance, how do we specify the conditions, i not equal to j, i is not equal to 1, etc.?

Thanks in advance!

 

 

Hi all, i wan to write getCoeff() function get coefficient general.

Example

f := a^2*b^2*c^2 + 2*a^2*b^2 + 2*a^2*c^2 + 2*b^2*c^2 + a^2 - 6*a*b - 6*a*c + b^2 - 6*b*c + c^2 + 8

getCoeff(f,a^2*b^2*c^2) return 1.

getCoeff(f,a^2*b^2) return 2.

getCoeff(f,a*b) return -6.

getCoeff(f,a^2) return 1, ...

and how to get coefficients freedom ?

Thank you very much.

can anyone run my code?
please do it and send it for me.
thanks.

restart;
with(plottools): with(LinearAlgebra): with(plots):
ode := `assuming`([diff(Y(X), `$`(X, 2))+2*alpha*(diff(Y(X), X))+beta^2*Y(X) = 0], [alpha >= 0, beta >= 0, alpha+beta > 0]):
F := unapply(solve(subs({X = x, Y(X) = y, diff(Y(X), X) = yp, diff(Y(X), `$`(X, 2)) = yz}, ode), yz), x, y, yp):
Fp := unapply(solve(subs({X = x, Y(X) = y, diff(Y(X), X) = yp, diff(Y(X), `$`(X, 2)) = yz, diff(Y(X), `$`(X, 3)) = yt}, diff(ode, X)), yt), x, y, yp, yz):
Ni := seq(i, i = 0 .. 9), 15, 20:
for i in Ni do
print(ni);
st := time[real]();
f[0, ni] := F(x[0], y[0, ni], yp[0, ni]);
fp[0, ni] := Fp(x[0], y[0, ni], yp[0, ni], f[0, ni]);
f[1, ni] := F(x[1], y[1, ni], yp[1, ni]);
fp[1, ni] := Fp(x[1], y[1, ni], yp[1, ni], f[1, ni]);
y[2, 0] := y[0, ni]+2*h*yp[0, ni]+(6/5)*f[0, ni]*h^2+(4/15)*fp[0, ni]*h^3+(4/5)*f[1, ni]*h^2+(4/15)*fp[1, ni]*h^3;
yp[2, 0] := yp[0, ni]+2*f[0, ni]*h+(2/3)*fp[0, ni]*h^2+(4/3)*fp[1, ni]*h^2;
for j to ni do
f[2, j-1] := F(x[2], y[2, j-1], yp[2, j-1]);
fp[2, j-1] := Fp(x[2], y[2, j-1], yp[2, j-1], f[2, j-1]);
y[2, j] := y[1, ni]+h*yp[1, ni]+(7/20)*f[1, ni]*h^2+(1/20)*fp[1, ni]*h^3+(3/20)*f[2, j-1]*h^2-(1/30)*fp[2, j-1]*h^3;
yp[2, j] := yp[1, ni]+(1/2)*f[1, ni]*h+(1/12)*fp[1, ni]*h^2+(1/2)*f[2, j-1]*h-(1/12)*fp[2, j-1]*h^2;
end do:
Ms := Matrix(4, 4); Ms[1, 3] := 1; Ms[2, 4] := 1;
y[2, ni] := collect(algsubs(h*alpha = H1, expand(algsubs(h*beta = H2, expand(y[2, ni])))), {y[0, ni], y[1, ni], yp[0, ni], yp[1, ni]});
Ms[3, 1] := coeff(y[2, ni], y[0, ni]);
Ms[3, 2] := coeff(y[2, ni], yp[0, ni])/h;
Ms[3, 3] := coeff(y[2, ni], y[1, ni]);
Ms[3, 4] := coeff(y[2, ni], yp[1, ni])/h;
hyp[2, ni] := collect(algsubs(h*alpha = H1, expand(algsubs(h*beta = H2, expand(h*yp[2, ni])))), {y[0, ni], y[1, ni], yp[0, ni], yp[1, ni]});
Ms[4, 1] := coeff(hyp[2, ni], y[0, ni]);
Ms[4, 2] := coeff(hyp[2, ni], yp[0, ni])/h;
Ms[4, 3] := coeff(hyp[2, ni], y[1, ni]);
Ms[4, 4] := coeff(hyp[2, ni], yp[1, ni])/h;
sol := Eigenvalues(Ms);
print(time[real]()-st);
st := time[real]();
SR[ni, 1] := implicitplot(max(seq(abs(sol[ii]), ii = 1 .. numelems(sol))) <= 1, H1 = 0 .. 3, H2 = 0 .. 3, filledregions, gridrefine = 3, axes = Boxed, view = [-2 .. 3, -3 .. 3], labels = [H[1], H[2]], labeldirections = ["horizontal", "vertical"]);
SR[ni, 2] := implicitplot(max(seq(abs(sol[ii]), ii = 1 .. numelems(sol))) <= 1, H1 = -2 .. 3, H2 = -2 .. 3, gridrefine = 3, axes = Boxed, view = [-2 .. 3, -3 .. 3], labels = [H[1], H[2]], labeldirections = ["horizontal", "vertical"]);
print(time[real]()-st);
end do;
for i in Ni do
i;
display({SR[i, 1], SR[i, 2], line([-1, 0], [3, 0], color = red, linestyle = dash), line([0, -3], [0, 3], color = red, linestyle = dash)});
end do;
display({seq(SR[i, 2], i = 0 .. Ni)});

This is my code

restart; L := [];
for a from -10 to 10 do
for b from -10 to 10 do
for c from -10 to 10 do
k := (-a*b*c+a*b*z+a*c*y+b*c*x)/igcd(a*b, b*c, c*a, a*b*c); if a*b*c <> 0 then L := [op(L), [[a, 0, 0], [0, b, 0], [0, 0, c]], k*signum(lcoeff(k)) = 0] end if end do end do end do; nops(L); L

I think my code was error, because  a from -10 to 10. 

[Delta][4*4]*{b}[4*1]={0}

Which {b} is an eigenvector

When I try the example from Maple Help for LPSolve (I use Windows)

with(Optimization);
LPSolve(-4*x-5*y, {0 <= x, 0 <= y, x+2*y <= 6, 5*x+4*y <= 20});

I do not get the same solution like in the example: [-19., [x = 2.66666666666667, y = 1.66666666666667]]
Instead I get

Warning, problem appears to be unbounded
            [0., [x = HFloat(0.0), y = HFloat(0.0)]]


My Professor uses the same version, but with Linux and do not have such problems. Why my installation does not solve the standart Help example?

Thank you

Hi

Let D={ Z=x+I*y,    -Pi*(n+1/2) <= x, y <= Pi*(n+1/2)}  

z belong the boundary of the previous square.

I would like to compute the modul of this function  f (z) =  coth(z) using the usual function  cos(x) cos(y), sinh(x) or cosh(y)  and show that | f(z)|  is less than one

Many thanks for any help

 

 

Hello, im a total begineer with maple and i need help defining a matrix, i need to get this into a matrix

 anyone knows how could i put this in a matriz of n x 1?   (the one thats only a column)

any help would be greatly appreciated

 

Thanks in advance!

Hello I was trying to manipulate maple to write a procedure checking a matrix , say A with n rows and n columns. That matrix A given any row/column the sum of the entries for every row and column are equal. For example matrix [(-1,2)(2,-1)], every row and column in this matrix sums to 1. The entries in the matrix can be any real number.

Put x=f1(t1,t2,t3), y=f2(t1,t2,t3), z=f3(t1,t2,t3).  

The question is that: How to plot all points of form [x,y,z] with t1 in [a1,b1], t2 in [a2,b2], t3 in [a3,b3].

Thank you.

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