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what is pronlem why i can't get solution?...

Asked by: salim-barzani 1550
syntax 2dmath
December 23 2024
0  10

i already use this method for a lot of equation but this time something not normal hapening what is problem?

``

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

with(Physics)
> 

with(SolveTools)
> 

``
> 

eq0 := -4*alpha*k^2*m^2*n^2*A[0]^2+4*beta*k*m*n^2*A[0]^3-4*gamma*k*m*n^2*A[0]^3+4*delta^2*m*n^2*A[0]^2-4*n^2*sigma*A[0]^4-4*m*n^2*w*A[0]^2 = 0
> 

eq1 := -8*alpha*k^2*m^2*n^2*A[0]*A[1]+12*beta*k*m*n^2*A[0]^2*A[1]-12*gamma*k*m*n^2*A[0]^2*A[1]+8*delta^2*m*n^2*A[0]*A[1]-16*n^2*sigma*A[0]^3*A[1]+2*a*alpha*m*n*A[0]*A[1]-8*m*n^2*w*A[0]*A[1] = 0
> 

eq2 := -4*alpha*k^2*m^2*n^2*A[1]^2+12*beta*k*m*n^2*A[0]*A[1]^2-12*gamma*k*m*n^2*A[0]*A[1]^2+4*delta^2*m*n^2*A[1]^2-24*n^2*sigma*A[0]^2*A[1]^2+a*alpha*m^2*A[1]^2+3*alpha*b*m*n*A[0]*A[1]-4*m*n^2*w*A[1]^2 = 0
> 

eq3 := 4*beta*k*m*n^2*A[1]^3-4*gamma*k*m*n^2*A[1]^3-16*n^2*sigma*A[0]*A[1]^3+alpha*b*m^2*A[1]^2+alpha*b*m*n*A[1]^2+4*alpha*c*m*n*A[0]*A[1] = 0
> 

eq4 := -4*n^2*sigma*A[1]^4+alpha*c*m^2*A[1]^2+2*alpha*c*m*n*A[1]^2 = 0
> 

C := solve({eq0, eq1, eq2, eq3, eq4}, {a, b, c, `__ `*A[0]})

Warning, solving for expressions other than names or functions is not recommended.

  

(1)
 

NULL

Download problem.mw

Determine if a point lies on a 3D line...

Asked by: Ronan 1336
geometry 3d
December 21 2024
0  5

It is not that this a terribly difficult to work out, but I feel I am probably missing something. I need to check if a 3D point lies on a 3D line. What is a good approach here. I started of with the idea all alpha's are equal. but there are exceptions. See P3 and P4

restart

NULL

l := `<,>`(3+2*alpha, 1+6*alpha, 4-5*alpha)

Vector[column](%id = 36893489809910741940)

 (1)

NULL

P := [9, 19, -11]

[9, 19, -11]

 (2)

seq(solve({l[i] = P[i]}, alpha), i = 1 .. 3)

{alpha = 3}, {alpha = 3}, {alpha = 3}

 (3)

l1 := `<,>`(3+2*alpha, 1+0*alpha, 4-5*alpha)

Vector[column](%id = 36893489809910721460)

 (4)

P1 := [9, 1, -11]

[9, 1, -11]

 (5)

seq(solve({l1[i] = P1[i]}, alpha), i = 1 .. 3)

{alpha = 3}, {alpha = alpha}, {alpha = 3}

 (6)

l2 := `<,>`(3+2*alpha, 1+0*alpha, 4-0*alpha)

Vector[column](%id = 36893489809910705556)

 (7)

P2 := [9, 1, 4]

[9, 1, 4]

 (8)

seq(solve({l2[i] = P2[i]}, alpha), i = 1 .. 3)

{alpha = 3}, {alpha = alpha}, {alpha = alpha}

 (9)

l3 := `<,>`(3+2*alpha, 0+0*alpha, 4-0*alpha)

Vector[column](%id = 36893489809963852012)

 (10)

P3 := [9, 0, 4]

[9, 0, 4]

 (11)

seq(solve({l3[i] = P3[i]}, alpha), i = 1 .. 3)

{alpha = 3}, {alpha = alpha}

 (12)

P4 := [9, 0, -2]

[9, 0, -2]

 (13)

seq(solve({l3[i] = P4[i]}, alpha), i = 1 .. 3)

{alpha = 3}, {alpha = alpha}

 (14)

 

Download 2024-12-21_Q_3D_point_lies_on_3D_line.mw

How to factor complex numbers?...

Asked by: paulmcquad 105
complex imaginary homework
December 21 2024
0  2

NULLComplex Numbers

 

Key Skills 11-48

NULLc11 := 2-3*i+(6+8*i)"(=)"8+5*i

c12 := 4+5*i-8+2*i"(=)"-4+7*i

c13 := -3+2*i-4+4*i"(=)"-7+6*i

c14 := 3-4*i+(3+4*i) = 6NULL

c15 := 2-5*i-8-6*i"(=)"-6-11*i

c16 := -8+4*i-2+2*i"(=)"-10+6*i

c17 := 3*(2-6*i)"(=)"6-18*i

c18 := -4*(2+8*i)"(=)"-8-32*i

NULLc19 := 2*i(2-3*i) = 2*i(2-3*i)NULL

c20 := 3*i*(-3+4*i) = 3*i*(-3+4*i)

c21 := (3-4*i)*(2+i) = (3-4*i)*(2+i)NULL

c22 := (5+3*i)*(2-i) = (5+3*i)*(2-i)

``

``

Download 1.3-Complex_Numbers_bad.mw

I'm trying to get my problems in standard form  a + bi . Questions 19 - 22 are wrong.

Instructions for symbolic calculation requested...

Asked by: Alfred_F 305
linear-algebra symbolic
December 21 2024
0  4

As a Maple beginner, I am now interested in symbolic calculations in Maple. As before, I set a problem from a subject area that interests me in order to learn from professional answers.

Determine all regular square (n;n) matrices (determinant not equal to zero) that are commutable with every regular (n;n) matrix with respect to matrix multiplication.

(I know the solution from long ago.)

How is the simplification achieved...

Asked by: Ronan 1336
radical simplification
December 20 2024
0  2

2024-12-20_Q_simplification_Question.mw
Solve the general cubic. Apply values and simplify. 

Could someone show how Maple simplifies to the value of X=3? I tried doing it manually and I could not figure it out. 

Also is there a Help assistant to see the setps?

> 

restart
> 

 

> 

 

> 

X^3+a*X=b

X^3+X*a = b

 (1)
> 

 

> 

 

> 

sol:=solve(X^3+a*X=b,[X])

[[X = (1/6)*(108*b+12*(12*a^3+81*b^2)^(1/2))^(1/3)-2*a/(108*b+12*(12*a^3+81*b^2)^(1/2))^(1/3)], [X = -(1/12)*(108*b+12*(12*a^3+81*b^2)^(1/2))^(1/3)+a/(108*b+12*(12*a^3+81*b^2)^(1/2))^(1/3)+((1/2)*I)*3^(1/2)*((1/6)*(108*b+12*(12*a^3+81*b^2)^(1/2))^(1/3)+2*a/(108*b+12*(12*a^3+81*b^2)^(1/2))^(1/3))], [X = -(1/12)*(108*b+12*(12*a^3+81*b^2)^(1/2))^(1/3)+a/(108*b+12*(12*a^3+81*b^2)^(1/2))^(1/3)-((1/2)*I)*3^(1/2)*((1/6)*(108*b+12*(12*a^3+81*b^2)^(1/2))^(1/3)+2*a/(108*b+12*(12*a^3+81*b^2)^(1/2))^(1/3))]]

 (2)
> 

vals:=[a=6,b=45]

[a = 6, b = 45]

 (3)
> 

Nans:=(map(eval,sol,vals))

[[X = (1/6)*(4860+12*166617^(1/2))^(1/3)-12/(4860+12*166617^(1/2))^(1/3)], [X = -(1/12)*(4860+12*166617^(1/2))^(1/3)+6/(4860+12*166617^(1/2))^(1/3)+((1/2)*I)*3^(1/2)*((1/6)*(4860+12*166617^(1/2))^(1/3)+12/(4860+12*166617^(1/2))^(1/3))], [X = -(1/12)*(4860+12*166617^(1/2))^(1/3)+6/(4860+12*166617^(1/2))^(1/3)-((1/2)*I)*3^(1/2)*((1/6)*(4860+12*166617^(1/2))^(1/3)+12/(4860+12*166617^(1/2))^(1/3))]]

 (4)
> 

simplify(Nans)

[[X = 3], [X = (1/4)*(I*3^(1/2)*(180+44*17^(1/2))^(2/3)+(8*I)*3^(1/2)-(180+44*17^(1/2))^(2/3)+8)/(180+44*17^(1/2))^(1/3)], [X = -3/2-((1/2)*I)*51^(1/2)]]

 (5)
 

 

Download 2024-12-20_Q_simplification_Question.mw

curve sought of triangle points...

Asked by: Alfred_F 305
geometry
December 20 2024
1  2

In a plane, equilateral triangles D(i) with side lengths a(i)= 2*i−1, i = 1; 2; 3; ... are arranged along a straight line g in such a way that the "right" corner point of triangle D(k) coincides with the "left" corner point of triangle D(k+1) and that the third corner points all lie in the same half-plane generated by g. Determine the curve/function on which the third corner points lie!

simultaneous animation of center of a circle movin...

Asked by: P M Dearing 15
December 19 2024
1  1

Given the center x1 of a circle in R^2 with radius d12, and a point p2 on the circle, so that d12=||p2-x1||, denote the points on the line segment from x1 to p2 as x1(t) = x1+t*v12, with t=0..d12, and v12 =( p2-x1)/d12.  I want to animate the points x1(t) moving along the line segment from x1 to p2 and the corresponding circles of decreasing radius, with center x(t) and radius d12-t, so that p2 remains on the circle.

I can animate the points along the line segment from x1 to p2 using ‘style=point, symbol=solidcircle’.

I would like to use plottools-circle, to plot the circles. I have also tried the following type commands for the circles of decreasing radius.

Plot([x1(1)+t*v12(1)+(d12-t)*cos(theta)*v12(1)+ (d12-t)*sin(theta)*u12(1), x1(2)+ +t*v12(2)+(d12-t)*d12*cos(theta)*v12(2)+(d12-t)*sin(theta)*u12(2), theta=0..2*PI]

where u12 is a unit vector orthogonal to v12.

I have not been able to combine the two plots into an animation. Thank you

Can I trust the diffrent engines of PolynomialSyst...

Asked by: Saalehorizontale 55
polynomial solvetools
December 18 2024
0  6

Hey Guys, 

I have to solve multiple system of equations under some restrictions given as inequalities. Sometimes solve is not able to find the result in houres so I tryd to break the problem in half. So in the first step I just want to solve my 8 polynomial equations with 8 variables and in a second step I want so take the solutions, bring them together with the set of inequalities and solve it again. Since also some sets of equations are to hard for the simple solve command I got the advice from people of this plattform to try PolynomialSystem with the diffrent engines. However I have the feeling they make misstakes and now Im not sure If I can trust my results. 

Attached you can find a file with an example. In the beginning I solve equations and restrictions together and there is a solutions. Then I tryd to solve only the equations with PolynomialSystem and the the four known engines and the eniges traditional and backsolve dont find the solution which as we saw before exist. When a soultions holds under restrictions it should always appear if I omit the restirctions. When I use the enige triade and groebner then the right solution is there. 
However in some other cases it feels the other way round.
So to me it looks like no matter which engine I take, I can never 100% trust my results. Did I something wrong? Whats the reason for those mistakes? Furthermore backsolve gives me 7 solutions, but solutions 2 and 7 are the same. I also recognized, that there is a diffrence between putting in the variable vars as a list or a set. What happens, if I dont specify which engine should be used?

I am happy about any advice. Thank you in advance.

Regards

Felix

> 

restart; equations := {-y*(m-p) = 0, ((-x-y+1)*k+x)*n+s*y-t = 0, (k-x-y)*t-k*p+y = 0, (-m+n+y)*x+m-1 = 0, -(x+y-1)*(p-t)*k+(-x-y+1)*t+x*p = 0, y^2+(-m-1)*y+1+x*(p-1) = 0, (-x-y+1)*t+(-m+1)*x+y*n+m-1 = 0, -k*n+s*x = 0}; restrictions := {0 < k, 0 < m, 0 < s, 0 < x, 0 < y, 0 < n+(t-1)*p, 0 < (m*y-1)*n+(1-p)*(m*x-m+1), 0 < (m*x-m-t+1)*p+m*y*(t-n), 1 < x+y, k < 1, m < 1, s < t, t < 1}; vars := indets(equations); evalf(solve(`union`(equations, restrictions), vars)); Sol_w := SolveTools:-PolynomialSystem(equations, vars); Sol_traditional := SolveTools:-PolynomialSystem(equations, vars, engine = traditional); nops([Sol_traditional]); Sol_backsolve := SolveTools:-PolynomialSystem(equations, vars, engine = backsolve); nops([Sol_backsolve]); Sol_triade_1 := SolveTools:-PolynomialSystem(equations, vars, engine = triade); nops([Sol_triade_1]); Sol_groebner := SolveTools:-PolynomialSystem(equations, vars, engine = groebner); nops([Sol_groebner])

{-y*(m-p) = 0, ((-x-y+1)*k+x)*n+s*y-t = 0, (k-x-y)*t-k*p+y = 0, (-m+n+y)*x+m-1 = 0, -(x+y-1)*(p-t)*k+(-x-y+1)*t+x*p = 0, y^2+(-m-1)*y+1+x*(p-1) = 0, (-x-y+1)*t+(-m+1)*x+y*n+m-1 = 0, -k*n+s*x = 0}

  

{k, m, n, p, s, t, x, y}

  

{k = 0.536796024e-1, m = .241141717, n = .54019322, p = .241141717, s = 0.35770767e-1, t = .4477103163, x = .8106439941, y = .6370663217}

  

{k = 1, m = m, n = 1, p = 0, s = 1, t = 1, x = 1, y = 0}, {k = 1, m = 1, n = 0, p = 1, s = t, t = t, x = 0, y = 1}, {k = k, m = 1, n = 0, p = 1, s = 1, t = 1, x = 0, y = 1}, {k = 1, m = 1, n = 0, p = 1, s = 0, t = 0, x = x, y = 1}, {k = 1/3, m = -1, n = 3, p = -1, s = 2, t = 2, x = 1/2, y = 0}, {k = 1/3, m = -1, n = 2, p = -1, s = 2/3, t = 2, x = 1, y = -1}, {k = -(1/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4+(2/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3+(16/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+(1/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)-7/9, m = (4/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-(20/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3-(17/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+21*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)-28/3, n = (11/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-(53/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3-(55/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+(152/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)-61/3, p = (4/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-(20/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3-(17/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+21*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)-28/3, s = -(8/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4+(40/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3+(35/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2-(127/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)+58/9, t = (1/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-(4/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3-(8/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+(7/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)+1/3, x = (1/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-(4/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3-(8/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+(4/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)+4/3, y = RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)}

  

{k = 1, m = m, n = 1, p = 0, s = 1, t = 1, x = 1, y = 0}, {k = 1/3, m = -1, n = 3, p = -1, s = 2, t = 2, x = 1/2, y = 0}, {k = k, m = 1, n = 0, p = 1, s = 1, t = 1, x = 0, y = 1}, {k = 1, m = 1, n = 0, p = 1, s = s, t = s, x = 0, y = 1}, {k = 1/3, m = -1, n = 2, p = -1, s = 2/3, t = 2, x = 1, y = -1}, {k = 1, m = 1, n = 0, p = 1, s = 0, t = 0, x = x, y = 1}

  

6

  

{k = 1, m = m, n = 1, p = 0, s = 1, t = 1, x = 1, y = 0}, {k = 1/3, m = -1, n = 3, p = -1, s = 2, t = 2, x = 1/2, y = 0}, {k = k, m = 1, n = 0, p = 1, s = 1, t = 1, x = 0, y = 1}, {k = 1, m = 1, n = 0, p = 1, s = s, t = s, x = 0, y = 1}, {k = 1/3, m = -1, n = 2, p = -1, s = 2/3, t = 2, x = 1, y = -1}, {k = 1, m = 1, n = 0, p = 1, s = 0, t = 0, x = x, y = 1}, {k = 1/3, m = -1, n = 3, p = -1, s = 2, t = 2, x = 1/2, y = 0}

  

7

  

{k = 1, m = 1, n = 0, p = 1, s = 0, t = 0, x = x, y = 1}, {k = 1, m = m, n = 1, p = 0, s = 1, t = 1, x = 1, y = 0}, {k = k, m = 1, n = 0, p = 1, s = 1, t = 1, x = 0, y = 1}, {k = 1, m = 1, n = 0, p = 1, s = t, t = t, x = 0, y = 1}, {k = -(1/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4+(2/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3+(16/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+(1/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)-7/9, m = (4/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-(20/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3-(17/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+21*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)-28/3, n = (11/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-(53/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3-(55/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+(152/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)-61/3, p = (4/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-(20/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3-(17/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+21*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)-28/3, s = -(8/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4+(40/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3+(35/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2-(127/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)+58/9, t = (1/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-(4/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3-(8/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+(7/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)+1/3, x = (1/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-(4/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3-(8/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+(4/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)+4/3, y = RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)}, {k = 1/3, m = -1, n = 2, p = -1, s = 2/3, t = 2, x = 1, y = -1}, {k = 1/3, m = -1, n = 3, p = -1, s = 2, t = 2, x = 1/2, y = 0}

  

7

  

{k = 1, m = m, n = 1, p = 0, s = 1, t = 1, x = 1, y = 0}, {k = 1, m = 1, n = 0, p = 1, s = t, t = t, x = 0, y = 1}, {k = k, m = 1, n = 0, p = 1, s = 1, t = 1, x = 0, y = 1}, {k = 1, m = 1, n = 0, p = 1, s = 0, t = 0, x = x, y = 1}, {k = 1/3, m = -1, n = 3, p = -1, s = 2, t = 2, x = 1/2, y = 0}, {k = 1/3, m = -1, n = 2, p = -1, s = 2/3, t = 2, x = 1, y = -1}, {k = -(1/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4+(2/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3+(16/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+(1/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)-7/9, m = (4/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-(20/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3-(17/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+21*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)-28/3, n = (11/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-(53/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3-(55/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+(152/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)-61/3, p = (4/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-(20/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3-(17/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+21*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)-28/3, s = -(8/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4+(40/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3+(35/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2-(127/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)+58/9, t = (1/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-(4/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3-(8/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+(7/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)+1/3, x = (1/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-(4/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3-(8/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2+(4/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)+4/3, y = RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)}

  

7

 (1)
> 

evalf(allvalues({k = -(1/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4+2*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3*(1/9)+16*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2*(1/9)+(1/9)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)-7/9, m = 4*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4*(1/3)-20*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3*(1/3)-17*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2*(1/3)+21*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)-28/3, n = 11*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4*(1/3)-53*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3*(1/3)-55*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2*(1/3)+152*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)*(1/3)-61/3, p = 4*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4*(1/3)-20*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3*(1/3)-17*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2*(1/3)+21*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)-28/3, s = -8*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4*(1/9)+40*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3*(1/9)+35*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2*(1/9)-127*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)*(1/9)+58/9, t = (1/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-4*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3*(1/3)-8*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2*(1/3)+7*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)*(1/3)+1/3, x = (1/3)*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^4-4*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^3*(1/3)-8*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)^2*(1/3)+4*RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)*(1/3)+4/3, y = RootOf(_Z^5-4*_Z^4-9*_Z^3+10*_Z^2+6*_Z-5)}))

{k = 0.536796024e-1, m = .241141717, n = .54019322, p = .241141717, s = 0.35770767e-1, t = .4477103163, x = .8106439941, y = .6370663217}, {k = .7943583912, m = 1.011543377, n = .16794280, p = 1.011543377, s = -.463558437, t = -.4040771797, x = -.287788440, y = .8837112597}, {k = -5.038767243, m = 3.694058367, n = 0.9373027e-1, p = 3.694058367, s = .299187114, t = 2.728412223, x = -1.578565716, y = 5.306977937}, {k = .2033642547, m = -26.40026363, n = -63.64948932, p = -26.40026363, s = 17.99511944, t = -2.562622110, x = -.719307867, y = -.8433142428}, {k = 2.542920564, m = -.546480183, n = 1.84762297, p = -.546480183, s = 1.244592174, t = .7905767063, x = 3.775017982, y = -1.984441276}

 (2)
 

NULL

Can_I_trust_the_diffrent_eniges_of_Polynomial_Systems.mw

How to solve for Algebraic linear equations like t...

Asked by: paulmcquad 105
December 17 2024
0  1

l45 := (x + 7)(x - 1) = (1 + x)^2;
                             "(->)"

Error, (in solve) cannot solve for an unknown function with other operations in its arguments

How remove error when changing delta parameter in ...

Asked by: salim-barzani 1550
finance spam numeric
December 17 2024
0  20

This is my first time working with plotting data from a matrix. However, with the help of a friends on MaplePrimes, I learned how to plot the data in both Maple and MATLAB. Despite this, I am having trouble with visualization. When I change the delta value, my function experiences vibrations or noise, which is clearly visible in the plot. But when I change delta, I encounter errors with my matrix data. How can I fix this problem? and there is any way for get better visualization by Explore ? also How show this vibration or noise in 2D?

> 

restart;
> 

randomize():
> 

local gamma;

gamma

 (1)
> 

currentdir(kernelopts(':-homedir'))
> 

NULL
> 

T3 := (B[1]*(tanh(2*n^2*(delta^2-w)*k*t/((k*n-1)*(k*n+1))+x)-1))^(1/(2*n))*exp(I*(-k*x+w*t+delta*W(t)-delta^2*t))

(B[1]*(tanh(2*n^2*(delta^2-w)*k*t/((k*n-1)*(k*n+1))+x)-1))^((1/2)/n)*exp(I*(-k*x+w*t+delta*W(t)-delta^2*t))

 (2)
> 

NULL
> 

params := {B[1]=1,n=2,delta=1,w=1,k=3 };

{delta = 1, k = 3, n = 2, w = 1, B[1] = 1}

 (3)
> 

NULL

insert numerical values

> 

solnum :=subs(params, T3);

(tanh(x)-1)^(1/4)*exp(I*(-3*x+W(t)))

 (4)
> 

CodeGeneration['Matlab']('(tanh(x)-1)^(1/4)*exp(I*(-3*x+W(t)))')

Warning, the function names {W} are not recognized in the target language

  

cg = ((tanh(x) - 0.1e1) ^ (0.1e1 / 0.4e1)) * exp(i * (-0.3e1 * x + W(t)));

  
> 

N := 100:

use Finance in:
  Wiener := WienerProcess():
  P := PathPlot(Wiener(t), t = 0..10, timesteps = N, replications = 1):
end use:
> 

W__points := plottools:-getdata(P)[1, -1]:
t_grid := convert(W__points[..,1], list):
x_grid := [seq(-2..2, 4/N)]:
> 

T, X := map(mul, [selectremove(has, [op(expand(solnum))], t)])[]:

ST := unapply(eval(T, W(t)=w), w)~(W__points[.., 2]):
SX := evalf(unapply(X, x)~(x_grid)):

STX := Matrix(N$2, (it, ix) -> ST[it]*SX[ix]);

_rtable[36893490640185799852]

 (5)
> 

opts := axis[1]=[tickmarks=[seq(k=nprintf("%1.1f", t_grid[k]), k=1..N, 40)]],
        axis[2]=[tickmarks=[seq(k=nprintf("%1.1f", x_grid[k]), k=1..N, 40)]],
        style=surface:

DocumentTools:-Tabulate(
  [
    plots:-matrixplot(Re~(STX), opts),
    plots:-matrixplot(Im~(STX), opts),
plots:-matrixplot(abs~(STX), opts)
  ]
  , width=60
)

"Tabulate"

 (6)
> 

MatlabFile := cat(currentdir(), "/ST2.txt"); ExportMatrix(MatlabFile, STX, target = MATLAB, format = rectangular, mode = ascii, format = entries)

421796

 (7)

NULL

Download data-analysis.mw

Area of octagon sought...

Asked by: Alfred_F 305
geometry
December 17 2024
3  4

A parallelogram is given in the Cartesian coordinate system. If the corner points of the parallelogram are connected to the midpoints of adjacent sides using lines, then the eight connecting lines form an octagon.
It must be proven that its area is one sixth of the parallelogram's area.

clarification on current status of odetest in Mapl...

Asked by: nm 11353
ode implicit differential-equations
December 16 2024
2  1

These two issues probably came up before, but I can't find where and when searching Maple primes.

So I thought to summarize the issues I see with odetest in one post, in the hope to get clarification on current status on these from the powers who know.

The first issue

The order in which odetest returns the answer. When odetest is called to check the ode and IC, as in 

the_status := odetest(sol,[ode,IC])

One would expect the_status to be a list, where the first entry tells if sol verifies the ode, and the second entry tells if sol verifies IC.

i.e. the order is the same as in the input. right? Since ode is first and IC is second in the input list.

But Maple sometimes mixes the order. See example 1 below. This makes it impossible to determine if the solution verifies the ode or IC,  when one of the entries in the_status is zero and the other is not, since order can be reversed sometimes.

Second issue:

When the solution is implicit, Maple gives invalid odetest result on the IC, unless one rewrites the solution using (lhs-rhs)(sol)=0.

i.e. move everything to the left side of the equation with RHS zero. This happens sometimes and when the solution is implicit.

I have thought this was fixed in current Maple, but it is not.  I remember this came up before, but can't find when and where.

Example 2 below shows an example.

Will these two issues hopefully be fixed in Maple 2025? Sometimes one forgets to rewrite the solution using (lhs-rhs)(sol)=0 and this results in false negative. 

Please see worksheet below. ps. I hope forum manager does not delete this question.

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.2, Windows 10, October 29 2024 Build ID 1872373`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1838 and is the same as the version installed in this computer, created 2024, December 2, 10:11 hours Pacific Time.`

> 

libname;

"C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib", "C:\Program Files\Maple 2024\lib"

> 

restart;
> 

 

Example 1: order of status from odetest is not same as order of input

 
> 

ode:=1+x*y(x)*(1+y(x)^2*x)*diff(y(x),x) = 0:
IC:=y(1) = 0:
sol:=x = 1/(3*exp(y(x)^2/2) - y(x)^2 - 2);

x = 1/(3*exp((1/2)*y(x)^2)-y(x)^2-2)

> 

#we see that odetest verifies the ode
odetest(sol,ode)

0

> 

#but when adding IC, 0 is now in second entry, instead of first

> 

odetest(sol,[ode,IC])

[(y(x)^4-y(x)^2*y(-1/(y(x)^2-3*exp((1/2)*y(x)^2)+2))*(D(y))(-1/(y(x)^2-3*exp((1/2)*y(x)^2)+2))+y(-1/(y(x)^2-3*exp((1/2)*y(x)^2)+2))^3*(D(y))(-1/(y(x)^2-3*exp((1/2)*y(x)^2)+2))-6*y(x)^2*exp((1/2)*y(x)^2)+3*exp((1/2)*y(x)^2)*y(-1/(y(x)^2-3*exp((1/2)*y(x)^2)+2))*(D(y))(-1/(y(x)^2-3*exp((1/2)*y(x)^2)+2))+4*y(x)^2-2*y(-1/(y(x)^2-3*exp((1/2)*y(x)^2)+2))*(D(y))(-1/(y(x)^2-3*exp((1/2)*y(x)^2)+2))+9*exp(y(x)^2)-12*exp((1/2)*y(x)^2)+4)/(y(x)^2-3*exp((1/2)*y(x)^2)+2)^2, 0]

> 

#SHOULD NOT zero above be in first slot in the list instead of second slot??

> 

 

> 

 

Example 2. We must write the solution using (lhs-rhs)(sol)=0

 
> 

restart;

> 

ode:=1+x*y(x)*(1+y(x)^2*x)*diff(y(x),x) = 0:
IC:=y(1) = 0:
sol:=x = 1/(3*exp(y(x)^2/2) - y(x)^2 - 2);

x = 1/(3*exp((1/2)*y(x)^2)-y(x)^2-2)

> 

odetest((lhs-rhs)(sol)=0,[ode,IC])

[0, 0]

> 

#we see that now it verified both IC and sol

> 

 

> 

 

> 

 

 

Download issues_with_odetest_dec_16_2024.mw

Transform data in maple to Matlab or make analysis...

Asked by: salim-barzani 1550
matlab excel export
December 16 2024
1  8

I have a matrix for data analysis that I want to plot. Ideally, I would like to use Maple, but I’m struggling to create a well-designed plot suitable for submission to journals. Because of this, I’m considering transferring the data to Excel or constructing a 3D graph using MATLAB.

My question is: how can I transfer this data to Excel? The data is currently saved as a Notepad file, but I’m unsure how to convert it into an Excel format. I will upload a figure to show the data structure.

also in last runig program give me error which is (Error, (in ExportMatrix) permission denied

Thank you in advance for any help!

> 

restart;
> 

randomize():
> 

local gamma;

gamma

 (1)
 
> 

T3 := (B[1]*(tanh(2*n^2*(delta^2-w)*k*t/((k*n-1)*(k*n+1))+x)-1))^(1/(2*n))*exp(I*(-k*x+w*t+delta*W(t)-delta^2*t))

(B[1]*(tanh(2*n^2*(delta^2-w)*k*t/((k*n-1)*(k*n+1))+x)-1))^((1/2)/n)*exp(I*(-k*x+w*t+delta*W(t)-delta^2*t))

 (2)
> 

``
> 

params := {B[1]=1,n=2,delta=1,w=1,k=3 };

{delta = 1, k = 3, n = 2, w = 1, B[1] = 1}

 (3)
> 

``

insert numerical values

> 

solnum :=subs(params, T3);

(tanh(x)-1)^(1/4)*exp(I*(-3*x+W(t)))

 (4)
> 

CodeGeneration['Matlab']('(tanh(x)-1)^(1/4)*exp(I*(-3*x+W(t)))')

Warning, the function names {W} are not recognized in the target language

  

cg = ((tanh(x) - 0.1e1) ^ (0.1e1 / 0.4e1)) * exp(i * (-0.3e1 * x + W(t)));

  
> 

N := 100:

use Finance in:
  Wiener := WienerProcess():
  P := PathPlot(Wiener(t), t = 0..10, timesteps = N, replications = 1):
end use:
> 

W__points := plottools:-getdata(P)[1, -1]:
t_grid := convert(W__points[..,1], list):
x_grid := [seq(-2..2, 4/N)]:
> 

T, X := map(mul, [selectremove(has, [op(expand(solnum))], t)])[]:

ST := unapply(eval(T, W(t)=w), w)~(W__points[.., 2]):
SX := evalf(unapply(X, x)~(x_grid)):

STX := Matrix(N$2, (it, ix) -> ST[it]*SX[ix]);

_rtable[36893489786521178348]

 (5)
> 

opts := axis[1]=[tickmarks=[seq(k=nprintf("%1.1f", t_grid[k]), k=1..N, 40)]],
        axis[2]=[tickmarks=[seq(k=nprintf("%1.1f", x_grid[k]), k=1..N, 40)]],
        style=surface:

DocumentTools:-Tabulate(
  [
    plots:-matrixplot(Re~(STX), opts),
    plots:-matrixplot(Im~(STX), opts),
plots:-matrixplot(abs~(STX), opts)
  ]
  , width=60
)

"Tabulate"

 (6)
> 

MatlabFile := cat(currentdir(), "/ST2.txt"); ExportMatrix(MatlabFile, STX, target = MATLAB, format = rectangular, mode = ascii, format = entries)

Error, (in ExportMatrix) permission denied

  
 

 

Download data-analysis.mw

Christmas greeting is the solution...

Asked by: Alfred_F 305
geometry
December 15 2024
1  1

A gardener wants to spread 25 roses over an area so that there are 5 roses in each of 15 straight rows. The roses should be arranged rotationally symmetrically so that more than 3/4 of them are less than half as far from the center of symmetry as the outermost ones and that the center of symmetry itself remains unplanted. How is such an arrangement possible?

How to do change of variable in ode using z=g(x) ...

Asked by: nm 11353
ode differential-equations pdetools
December 14 2024
3  1

What is the correct syntax to do this change of variable from the text book:

The problem is that using PDEtools:-dchange, it wants the transformation to have form { old = new}, i.e. x=...  so I can not write  z=g(x) in the transformation. 

For example

ode:= diff(y(x),x$2)+diff(y(x),x)+y(x)=sin(x);
PDEtools:-dchange({z= g(x)},ode,known={x},unknown={z});

Error, (in dchange/info) missing a list with the new variables
And if I first solve for x so that I can write the transformation with x on left side, it still does not work

ode:= diff(y(x),x$2)+diff(y(x),x)+y(x)=sin(x);
PDEtools:-dchange({x=RootOf(g(_Z) - z)},ode,known={x},unknown={z});

Where RootOf(g(_Z) - z) was result of solve(z=g(x),x);

I am sure this can be done in Maple, I just do not know the right syntax to use with dchange.

Maple 2024.2

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