Maple 15 Questions and Posts

These are Posts and Questions associated with the product, Maple 15

Dear users! I need the help in attached file. Please see and fix it. I am waiting your positive answer.

File_to_help.mw

 

Hi Dears,

Let us consider the following polyhedral cone which is defined by 8 inequalities (also, x,y,z ≥0): 

1. y-z ≥0

2. 3y-2z ≥0

3. 2y-2z ≥0

4. x-2y+z ≥0

5. x-y ≥0

6. 2x-y ≥0

7. x-z ≥0

8. x+y-z ≥0. 

How can we deduce that the inequalities 3 and 4 may be define this polyhedral cone and the others are redundant?

How can remove the redundant inequalities for defining this polyhedral cone?

Is there any Maple command or function that recive these 8 inequalities and return inequalities 3 and 4? In fact, inequalities 3 and 4 are facets of this polyhedral cone. 

 

Thank you in advanced. 

Sincerely yours

Hi, I do not understand how to solve errors in MAPLE on my project. My project is to solve Vehicle Routing Problem with Time Windows, and then the error is "Error, (in Optimization: -LPSolve) no feasible integer point found; use feasibilitytolerance option to adjust tolerance". I do not understand about feasibilitytolerance. Can anyone help me? Thankyou.
 

NULL

HASIL*MAPLE*UNTUK*KECAMATAN*COBLONGNULL

restart

with(Optimization);

[ImportMPS, Interactive, LPSolve, LSSolve, Maximize, Minimize, NLPSolve, QPSolve]

(1)

with(linalg);

[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp, QRdecomp, Wronskian, addcol, addrow, adj, adjoint, angle, augment, backsub, band, basis, bezout, blockmatrix, charmat, charpoly, cholesky, col, coldim, colspace, colspan, companion, concat, cond, copyinto, crossprod, curl, definite, delcols, delrows, det, diag, diverge, dotprod, eigenvals, eigenvalues, eigenvectors, eigenvects, entermatrix, equal, exponential, extend, ffgausselim, fibonacci, forwardsub, frobenius, gausselim, gaussjord, geneqns, genmatrix, grad, hadamard, hermite, hessian, hilbert, htranspose, ihermite, indexfunc, innerprod, intbasis, inverse, ismith, issimilar, iszero, jacobian, jordan, kernel, laplacian, leastsqrs, linsolve, matadd, matrix, minor, minpoly, mulcol, mulrow, multiply, norm, normalize, nullspace, orthog, permanent, pivot, potential, randmatrix, randvector, rank, ratform, row, rowdim, rowspace, rowspan, rref, scalarmul, singularvals, smith, stackmatrix, submatrix, subvector, sumbasis, swapcol, swaprow, sylvester, toeplitz, trace, transpose, vandermonde, vecpotent, vectdim, vector, wronskian]

(2)

with(ExcelTools);

[Export, Import, WorkbookData]

(3)

with(CodeTools);

[CPUTime, DecodeName, EncodeName, Profiling, RealTime, Test, Usage]

(4)

``

c := convert(Import("C:\\Users\\VaniaMR\\Documents\\SEMANGAT SKRIPSI\\skripsi\\Bab-bab\\data Bandung Utara.xlsx", 6, "B2:I9"), matrix)

array( 1 .. 8, 1 .. 8, [( 5, 8 ) = (2.9), ( 4, 1 ) = (2.5), ( 2, 2 ) = (0.), ( 8, 3 ) = (3.1), ( 2, 4 ) = (1.9), ( 7, 5 ) = (3.7), ( 6, 6 ) = (0.), ( 3, 7 ) = (3.9), ( 6, 8 ) = (2.7), ( 5, 1 ) = (.28), ( 7, 3 ) = (3.9), ( 1, 2 ) = (3.2), ( 3, 4 ) = (3.7), ( 8, 5 ) = (2.9), ( 5, 6 ) = (.26), ( 2, 7 ) = (1.8), ( 3, 8 ) = (3.1), ( 6, 1 ) = (.25), ( 8, 2 ) = (1.1), ( 2, 3 ) = (2.8), ( 4, 4 ) = (0.), ( 5, 5 ) = (0.), ( 8, 6 ) = (2.7), ( 1, 7 ) = (3.5), ( 4, 8 ) = (2.3), ( 7, 1 ) = (3.5), ( 7, 2 ) = (1.8), ( 1, 3 ) = (4.1), ( 5, 4 ) = (2.7), ( 6, 5 ) = (.26), ( 7, 6 ) = (3.4), ( 8, 7 ) = (1.6), ( 1, 8 ) = (3.3), ( 8, 1 ) = (3.3), ( 6, 2 ) = (2.9), ( 4, 3 ) = (3.7), ( 6, 4 ) = (2.7), ( 3, 5 ) = (4.0), ( 2, 6 ) = (2.9), ( 7, 7 ) = (0.), ( 2, 8 ) = (1.1), ( 5, 2 ) = (3.1), ( 2, 1 ) = (3.2), ( 3, 3 ) = (0.), ( 7, 4 ) = (1.3), ( 4, 5 ) = (2.7), ( 1, 6 ) = (.25), ( 6, 7 ) = (3.4), ( 7, 8 ) = (1.6), ( 4, 2 ) = (1.9), ( 6, 3 ) = (3.8), ( 8, 4 ) = (2.3), ( 1, 1 ) = (0.), ( 1, 5 ) = (.28), ( 4, 6 ) = (2.7), ( 5, 7 ) = (3.7), ( 8, 8 ) = (0.), ( 3, 1 ) = (4.1), ( 3, 2 ) = (2.8), ( 5, 3 ) = (4.0), ( 1, 4 ) = (2.5), ( 2, 5 ) = (3.1), ( 3, 6 ) = (3.8), ( 4, 7 ) = (1.3)  ] )

(5)

t := convert(Import("C:\\Users\\VaniaMR\\Documents\\SEMANGAT SKRIPSI\\skripsi\\Bab-bab\\data Bandung Utara1.xlsx", 7, "B2:I9"), matrix)

array( 1 .. 8, 1 .. 8, [( 5, 8 ) = (9.0), ( 4, 1 ) = (8.0), ( 2, 2 ) = (0.), ( 8, 3 ) = (8.0), ( 2, 4 ) = (6.0), ( 7, 5 ) = (10.0), ( 6, 6 ) = (0.), ( 3, 7 ) = (9.0), ( 6, 8 ) = (7.0), ( 5, 1 ) = (2.0), ( 7, 3 ) = (9.0), ( 1, 2 ) = (9.0), ( 3, 4 ) = (12.0), ( 8, 5 ) = (9.0), ( 5, 6 ) = (2.0), ( 2, 7 ) = (4.0), ( 3, 8 ) = (8.0), ( 6, 1 ) = (2.0), ( 8, 2 ) = (3.0), ( 2, 3 ) = (7.0), ( 4, 4 ) = (0.), ( 5, 5 ) = (0.), ( 8, 6 ) = (7.0), ( 1, 7 ) = (10.0), ( 4, 8 ) = (6.0), ( 7, 1 ) = (10.0), ( 7, 2 ) = (4.0), ( 1, 3 ) = (11.0), ( 5, 4 ) = (9.0), ( 6, 5 ) = (2.0), ( 7, 6 ) = (8.0), ( 8, 7 ) = (3.0), ( 1, 8 ) = (9.0), ( 8, 1 ) = (9.0), ( 6, 2 ) = (8.0), ( 4, 3 ) = (12.0), ( 6, 4 ) = (9.0), ( 3, 5 ) = (12.0), ( 2, 6 ) = (8.0), ( 7, 7 ) = (0.), ( 2, 8 ) = (3.0), ( 5, 2 ) = (10.0), ( 2, 1 ) = (9.0), ( 3, 3 ) = (0.), ( 7, 4 ) = (4.0), ( 4, 5 ) = (9.0), ( 1, 6 ) = (2.0), ( 6, 7 ) = (8.0), ( 7, 8 ) = (3.0), ( 4, 2 ) = (6.0), ( 6, 3 ) = (10.0), ( 8, 4 ) = (6.0), ( 1, 1 ) = (0.), ( 1, 5 ) = (2.0), ( 4, 6 ) = (9.0), ( 5, 7 ) = (10.0), ( 8, 8 ) = (0.), ( 3, 1 ) = (11.0), ( 3, 2 ) = (7.0), ( 5, 3 ) = (12.0), ( 1, 4 ) = (8.0), ( 2, 5 ) = (10.0), ( 3, 6 ) = (10.0), ( 4, 7 ) = (4.0)  ] )

(6)

a := `<,>`(0, 0, 0, 0, 0, 0, 0, 0)

a := Vector(8, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0, (8) = 0})

(7)

b := `<,>`(30, 30, 30, 30, 30, 30, 30, 30)

b := Vector(8, {(1) = 30, (2) = 30, (3) = 30, (4) = 30, (5) = 30, (6) = 30, (7) = 30, (8) = 30})

(8)

n := sqrt(numelems(c)):

{1, 2, 3, 4, 5, 6, 7, 8}

(9)

z := add(add(c[i, j]*x[i, j], j = N), i = N);

3.2*x[1, 2]+4.1*x[1, 3]+2.5*x[1, 4]+.28*x[1, 5]+.25*x[1, 6]+3.5*x[1, 7]+3.3*x[1, 8]+3.2*x[2, 1]+2.8*x[2, 3]+1.9*x[2, 4]+3.1*x[2, 5]+2.9*x[2, 6]+1.8*x[2, 7]+1.1*x[2, 8]+4.1*x[3, 1]+2.8*x[3, 2]+3.7*x[3, 4]+4.0*x[3, 5]+3.8*x[3, 6]+3.9*x[3, 7]+3.1*x[3, 8]+2.5*x[4, 1]+1.9*x[4, 2]+3.7*x[4, 3]+2.7*x[4, 5]+2.7*x[4, 6]+1.3*x[4, 7]+2.3*x[4, 8]+.28*x[5, 1]+3.1*x[5, 2]+4.0*x[5, 3]+2.7*x[5, 4]+.26*x[5, 6]+3.7*x[5, 7]+2.9*x[5, 8]+.25*x[6, 1]+2.9*x[6, 2]+3.8*x[6, 3]+2.7*x[6, 4]+.26*x[6, 5]+3.4*x[6, 7]+2.7*x[6, 8]+3.5*x[7, 1]+1.8*x[7, 2]+3.9*x[7, 3]+1.3*x[7, 4]+3.7*x[7, 5]+3.4*x[7, 6]+1.6*x[7, 8]+3.3*x[8, 1]+1.1*x[8, 2]+3.1*x[8, 3]+2.3*x[8, 4]+2.9*x[8, 5]+2.7*x[8, 6]+1.6*x[8, 7]

(10)

conx := seq(add(x[i, j], i = `minus`(N, {j})) = 1, j = N);

x[2, 1]+x[3, 1]+x[4, 1]+x[5, 1]+x[6, 1]+x[7, 1]+x[8, 1] = 1, x[1, 2]+x[3, 2]+x[4, 2]+x[5, 2]+x[6, 2]+x[7, 2]+x[8, 2] = 1, x[1, 3]+x[2, 3]+x[4, 3]+x[5, 3]+x[6, 3]+x[7, 3]+x[8, 3] = 1, x[1, 4]+x[2, 4]+x[3, 4]+x[5, 4]+x[6, 4]+x[7, 4]+x[8, 4] = 1, x[1, 5]+x[2, 5]+x[3, 5]+x[4, 5]+x[6, 5]+x[7, 5]+x[8, 5] = 1, x[1, 6]+x[2, 6]+x[3, 6]+x[4, 6]+x[5, 6]+x[7, 6]+x[8, 6] = 1, x[1, 7]+x[2, 7]+x[3, 7]+x[4, 7]+x[5, 7]+x[6, 7]+x[8, 7] = 1, x[1, 8]+x[2, 8]+x[3, 8]+x[4, 8]+x[5, 8]+x[6, 8]+x[7, 8] = 1

(11)

conV := seq(add(x[i, k], i = N)-add(x[k, j], j = N) = 0, k = N);

x[2, 1]+x[3, 1]+x[4, 1]+x[5, 1]+x[6, 1]+x[7, 1]+x[8, 1]-x[1, 2]-x[1, 3]-x[1, 4]-x[1, 5]-x[1, 6]-x[1, 7]-x[1, 8] = 0, x[1, 2]+x[3, 2]+x[4, 2]+x[5, 2]+x[6, 2]+x[7, 2]+x[8, 2]-x[2, 1]-x[2, 3]-x[2, 4]-x[2, 5]-x[2, 6]-x[2, 7]-x[2, 8] = 0, x[1, 3]+x[2, 3]+x[4, 3]+x[5, 3]+x[6, 3]+x[7, 3]+x[8, 3]-x[3, 1]-x[3, 2]-x[3, 4]-x[3, 5]-x[3, 6]-x[3, 7]-x[3, 8] = 0, x[1, 4]+x[2, 4]+x[3, 4]+x[5, 4]+x[6, 4]+x[7, 4]+x[8, 4]-x[4, 1]-x[4, 2]-x[4, 3]-x[4, 5]-x[4, 6]-x[4, 7]-x[4, 8] = 0, x[1, 5]+x[2, 5]+x[3, 5]+x[4, 5]+x[6, 5]+x[7, 5]+x[8, 5]-x[5, 1]-x[5, 2]-x[5, 3]-x[5, 4]-x[5, 6]-x[5, 7]-x[5, 8] = 0, x[1, 6]+x[2, 6]+x[3, 6]+x[4, 6]+x[5, 6]+x[7, 6]+x[8, 6]-x[6, 1]-x[6, 2]-x[6, 3]-x[6, 4]-x[6, 5]-x[6, 7]-x[6, 8] = 0, x[1, 7]+x[2, 7]+x[3, 7]+x[4, 7]+x[5, 7]+x[6, 7]+x[8, 7]-x[7, 1]-x[7, 2]-x[7, 3]-x[7, 4]-x[7, 5]-x[7, 6]-x[7, 8] = 0, x[1, 8]+x[2, 8]+x[3, 8]+x[4, 8]+x[5, 8]+x[6, 8]+x[7, 8]-x[8, 1]-x[8, 2]-x[8, 3]-x[8, 4]-x[8, 5]-x[8, 6]-x[8, 7] = 0

(12)

conz := add(x[i, 1], i = N) = 1;

x[1, 1]+x[2, 1]+x[3, 1]+x[4, 1]+x[5, 1]+x[6, 1]+x[7, 1]+x[8, 1] = 1

(13)

conD := add(x[1, j], j = N) = 1;

x[1, 1]+x[1, 2]+x[1, 3]+x[1, 4]+x[1, 5]+x[1, 6]+x[1, 7]+x[1, 8] = 1

(14)

conTW := seq(seq(y[i]-y[j]+max(b[i]+t[i, j]-a[j], 0)*x[i, j] <= b[i]-a[j], i = `minus`(N, {j})), j = N);

y[2]-y[1]+39.0*x[2, 1] <= 30, y[3]-y[1]+41.0*x[3, 1] <= 30, y[4]-y[1]+38.0*x[4, 1] <= 30, y[5]-y[1]+32.0*x[5, 1] <= 30, y[6]-y[1]+32.0*x[6, 1] <= 30, y[7]-y[1]+40.0*x[7, 1] <= 30, y[8]-y[1]+39.0*x[8, 1] <= 30, y[1]-y[2]+39.0*x[1, 2] <= 30, y[3]-y[2]+37.0*x[3, 2] <= 30, y[4]-y[2]+36.0*x[4, 2] <= 30, y[5]-y[2]+40.0*x[5, 2] <= 30, y[6]-y[2]+38.0*x[6, 2] <= 30, y[7]-y[2]+34.0*x[7, 2] <= 30, y[8]-y[2]+33.0*x[8, 2] <= 30, y[1]-y[3]+41.0*x[1, 3] <= 30, y[2]-y[3]+37.0*x[2, 3] <= 30, y[4]-y[3]+42.0*x[4, 3] <= 30, y[5]-y[3]+42.0*x[5, 3] <= 30, y[6]-y[3]+40.0*x[6, 3] <= 30, y[7]-y[3]+39.0*x[7, 3] <= 30, y[8]-y[3]+38.0*x[8, 3] <= 30, y[1]-y[4]+38.0*x[1, 4] <= 30, y[2]-y[4]+36.0*x[2, 4] <= 30, y[3]-y[4]+42.0*x[3, 4] <= 30, y[5]-y[4]+39.0*x[5, 4] <= 30, y[6]-y[4]+39.0*x[6, 4] <= 30, y[7]-y[4]+34.0*x[7, 4] <= 30, y[8]-y[4]+36.0*x[8, 4] <= 30, y[1]-y[5]+32.0*x[1, 5] <= 30, y[2]-y[5]+40.0*x[2, 5] <= 30, y[3]-y[5]+42.0*x[3, 5] <= 30, y[4]-y[5]+39.0*x[4, 5] <= 30, y[6]-y[5]+32.0*x[6, 5] <= 30, y[7]-y[5]+40.0*x[7, 5] <= 30, y[8]-y[5]+39.0*x[8, 5] <= 30, y[1]-y[6]+32.0*x[1, 6] <= 30, y[2]-y[6]+38.0*x[2, 6] <= 30, y[3]-y[6]+40.0*x[3, 6] <= 30, y[4]-y[6]+39.0*x[4, 6] <= 30, y[5]-y[6]+32.0*x[5, 6] <= 30, y[7]-y[6]+38.0*x[7, 6] <= 30, y[8]-y[6]+37.0*x[8, 6] <= 30, y[1]-y[7]+40.0*x[1, 7] <= 30, y[2]-y[7]+34.0*x[2, 7] <= 30, y[3]-y[7]+39.0*x[3, 7] <= 30, y[4]-y[7]+34.0*x[4, 7] <= 30, y[5]-y[7]+40.0*x[5, 7] <= 30, y[6]-y[7]+38.0*x[6, 7] <= 30, y[8]-y[7]+33.0*x[8, 7] <= 30, y[1]-y[8]+39.0*x[1, 8] <= 30, y[2]-y[8]+33.0*x[2, 8] <= 30, y[3]-y[8]+38.0*x[3, 8] <= 30, y[4]-y[8]+36.0*x[4, 8] <= 30, y[5]-y[8]+39.0*x[5, 8] <= 30, y[6]-y[8]+37.0*x[6, 8] <= 30, y[7]-y[8]+33.0*x[7, 8] <= 30

(15)

batasan1 := seq(a[i] <= y[i], i = N);

0 <= y[1], 0 <= y[2], 0 <= y[3], 0 <= y[4], 0 <= y[5], 0 <= y[6], 0 <= y[7], 0 <= y[8]

(16)

batasan2 := seq(y[i] <= b[i], i = N);

y[1] <= 30, y[2] <= 30, y[3] <= 30, y[4] <= 30, y[5] <= 30, y[6] <= 30, y[7] <= 30, y[8] <= 30

(17)

binaryvariables = {seq(seq(x[i, j], i = `minus`(N, {j})), j = N)};

binaryvariables = {x[1, 2], x[1, 3], x[1, 4], x[1, 5], x[1, 6], x[1, 7], x[1, 8], x[2, 1], x[2, 3], x[2, 4], x[2, 5], x[2, 6], x[2, 7], x[2, 8], x[3, 1], x[3, 2], x[3, 4], x[3, 5], x[3, 6], x[3, 7], x[3, 8], x[4, 1], x[4, 2], x[4, 3], x[4, 5], x[4, 6], x[4, 7], x[4, 8], x[5, 1], x[5, 2], x[5, 3], x[5, 4], x[5, 6], x[5, 7], x[5, 8], x[6, 1], x[6, 2], x[6, 3], x[6, 4], x[6, 5], x[6, 7], x[6, 8], x[7, 1], x[7, 2], x[7, 3], x[7, 4], x[7, 5], x[7, 6], x[7, 8], x[8, 1], x[8, 2], x[8, 3], x[8, 4], x[8, 5], x[8, 6], x[8, 7]}

(18)

conu := seq(seq(u[i]-u[j]+n*x[i, j] <= n-1, i = `minus`(N, {1, j})), j = `minus`(N, {1}));

u[3]-u[2]+8*x[3, 2] <= 7, u[4]-u[2]+8*x[4, 2] <= 7, u[5]-u[2]+8*x[5, 2] <= 7, u[6]-u[2]+8*x[6, 2] <= 7, u[7]-u[2]+8*x[7, 2] <= 7, u[8]-u[2]+8*x[8, 2] <= 7, u[2]-u[3]+8*x[2, 3] <= 7, u[4]-u[3]+8*x[4, 3] <= 7, u[5]-u[3]+8*x[5, 3] <= 7, u[6]-u[3]+8*x[6, 3] <= 7, u[7]-u[3]+8*x[7, 3] <= 7, u[8]-u[3]+8*x[8, 3] <= 7, u[2]-u[4]+8*x[2, 4] <= 7, u[3]-u[4]+8*x[3, 4] <= 7, u[5]-u[4]+8*x[5, 4] <= 7, u[6]-u[4]+8*x[6, 4] <= 7, u[7]-u[4]+8*x[7, 4] <= 7, u[8]-u[4]+8*x[8, 4] <= 7, u[2]-u[5]+8*x[2, 5] <= 7, u[3]-u[5]+8*x[3, 5] <= 7, u[4]-u[5]+8*x[4, 5] <= 7, u[6]-u[5]+8*x[6, 5] <= 7, u[7]-u[5]+8*x[7, 5] <= 7, u[8]-u[5]+8*x[8, 5] <= 7, u[2]-u[6]+8*x[2, 6] <= 7, u[3]-u[6]+8*x[3, 6] <= 7, u[4]-u[6]+8*x[4, 6] <= 7, u[5]-u[6]+8*x[5, 6] <= 7, u[7]-u[6]+8*x[7, 6] <= 7, u[8]-u[6]+8*x[8, 6] <= 7, u[2]-u[7]+8*x[2, 7] <= 7, u[3]-u[7]+8*x[3, 7] <= 7, u[4]-u[7]+8*x[4, 7] <= 7, u[5]-u[7]+8*x[5, 7] <= 7, u[6]-u[7]+8*x[6, 7] <= 7, u[8]-u[7]+8*x[8, 7] <= 7, u[2]-u[8]+8*x[2, 8] <= 7, u[3]-u[8]+8*x[3, 8] <= 7, u[4]-u[8]+8*x[4, 8] <= 7, u[5]-u[8]+8*x[5, 8] <= 7, u[6]-u[8]+8*x[6, 8] <= 7, u[7]-u[8]+8*x[7, 8] <= 7

(19)

Sol := Optimization[LPSolve](z, {conD, conTW, conV, conu, conx, conz, batasan1, batasan2}, binaryvariables = {seq(seq(x[i, j], i = `minus`(N, {j})), j = N)})

Error, (in Optimization:-LPSolve) no feasible integer point found; use feasibilitytolerance option to adjust tolerance

 

X := eval(Matrix(n, symbol = x), {Sol[2][], seq(x[i, i] = 0, i = 1 .. n)})

Error, invalid input: eval expects its 2nd argument, eqns, to be of type {integer, equation, set(equation)}, but received {Sol[2][], seq(x[i, i] = 0, i = 1 .. n)}

 

f := [1, 5, 6, 3, 2, 8, 7, 4, 1];

[1, 5, 6, 3, 2, 8, 7, 4, 1]

(20)

add(c[f[i], f[i+1]], i = 1 .. nops(f)-1);

13.64

(21)

``

 

``

NULL

``

``

NULL


 

Download dataayosemangat.mw

Hi all,

 

I am totally stuck in the question:

I can do it for seperate cases, but how to do it, with somekind of sequence

 

Integral for x= 0 to infinity of [2 sin(x/2)/x] ^ 2n 

this has to be equal to:

2n* pi (sum of [(-1)^j * (n-j)^(2n-1)] / [j! * (2n-j)!]

I showed it for j=0 and n=1

But how to do it for n =1,2,3 and 4

 

what package I need to add in order to use commands named "Drawmatrix, Translatemat and Transform" ? I add package named Lamp but it is not working. I have maple 15. Please try to respond as soon as possible because its urgent.

 

Thank you

Hello dear!

Hope everyone is fine. I am facing problem to fins the inverse transfrom in the attached file. Please find the attachment and fix the problem. Thanks in advance

Help.mw

Dears,

Let C a square in the n-diemnsional Euclidean space. Somebody know how to divide C into 2^{n} congruent subsquares? 

For instance, for n=2 and  say C:=[0,1]x[0,1], the unit closed square, we will obtain the 2^{2}=4 subsquares [0,1/4]x[0,1/4], [0,1/4]x[1/2], [1/2,1]x[0,1/4] and [1/2,1]x[1/2,1].  

Many thanks in advance for your comments!!

Dear all

Hope everything is fine with everything. I want to draw the graph of the u(x,0.5) and T(x,0.5) for different values of alpha like alpha =0.4,0.6,0.8 while keeping Gr, R and Pr are fixed. Please solve the following problem I shall be vary thankful to you. Thanks in advance

with the following BCs

Hello dearz.

Hope you will be fine with everything. I am facing in plotting the set of points like seq(u[i,20] $ i=1..25) in the attached file. Please see the problem and fix it. I shall be vary thankful. Waiting quick and positive response.

Help.mw 

I want to find an approximation for a 3-dim vector y(t)=(y1,y2,y3) at multiple times t, so as to get:

y(t1)=[b0,0,0](y1(t1))^0(y2(t1))^0(y3(t1))^0 + [b0,0,1](y1(t1))^0(y2(t1))^0(y3(t1))^1 + ... + [b3,0,0](y1(t1))^3(y2(t1))^0(y3(t1))^0

y(t2)=[b0,0,0](y1(t2))^0(y2(t2))^0(y3(t2))^0 + [b0,0,1](y1(t2))^0(y2(t2))^0(y3(t2))^1 + ... + [b3,0,0](y1(t2))^3(y2(t2))^0(y3(t2))^0

...

So I want 20 b coefficients with quaternary-base subscripts (I belive it is called) for multiple values of t.

I want to have enough approximations to solve for the the coefficients b and then perform a Least Squares method Calculation thereafter. 

Can anyone help me please?

Hello,

I hope my question is not to general. I have a polynomial of 8th order

expression:=a8(z) * x^8 + .... + a1(z) * x + a0(z) = 0

on which I am using solve/RootOf

sol:=[solve(expression,x)]

Now when I plot it against z the solution has a jump, why?

When deriving the polynomial I could as well have used another variable instead of x above, say y. These two are related by a function...Then when I write down the 8th order polynomial in y and use RootOf/solve, then no jump occurs.

Is there a way to handle this because left of the jump the solution is not correct while right of it, it is...

Hi!,

Assume that we hace a set points in the plane, put X:=[a1,a2,...,aN] where each ai is given by its coordinates [x,y]. The commnad "convexhull(X)" give us the points of the convex hull of X, but how I can find to "lower-right" of these points? Please, see the attached image. I need to findo the points A,C,E and F, marked with a solid circle.

Many thanks in advances for your comments.

 

 

with(PDEtools); declare(u(x, y, z, t), U(X, Y, Z, T)); interface(showassumed = 0); assume(a > 0, p > 0); W := diff_table(u(x, y, z, t)); E := 6*W[]*W[x]+W[t]+W[x, y, z] = 0; InvE := proc (PDE) local Eq1, Eq2, Eq3, Eq4, tr1, tr2, tr3, tr4, term1, term2, term3, term4, sys1; tr1 := {t = T/a^beta, x = X/a^alpha, y = Y/a^mu, z = Z/a^nu, u(x, y, z, t) = U(X, Y, Z, T)/a^zeta}; tr2 := eval(tr1, zeta = 1); Eq1 := combine(dchange(tr2, PDE, [X, Y, Z, T, U])); Eq2 := map(lhs, PDE = Eq1); term1 := select(has, select(has, select(has, rhs(Eq2), a), beta), a); term2 := expand(rhs(Eq2)/term1); term3 := select(has, select(has, term2, a), a); sys1 := {select(has, op(1, term3), a) = 1, select(has, op(2, term3), a) = 1}; tr3 := solve(sys1, {alpha, beta, mu, nu}); tr4 := subs(tr3, tr2); print(tr3, tr4); Eq3 := dchange(tr4, PDE, [X, Y, Z, T, U]); term4 := select(has, op(1, lhs(Eq3)), a); Eq4 := expand(Eq3/term4); PDE = simplify(Eq4) end proc; InvE(E)

how to find the contour of time series data? and how to find curvature function of this contour?

The representation of the tangent plane in the form of a square with a given length of the side at any point on the surface.

The equation of the tangent plane to the surface at a given point is obtained from the condition that the tangent plane is perpendicular to the normal vector. With the aid of any auxiliary point not lying on this normal to the surface, we define the direction on the tangent plane. From the given point in this direction, we lay off segments equal to half the length of the side of our square and with the help of these segments we construct the square itself, lying on the tangent plane with the center at a given point.

An examples of constructing tangent planes at points of the same intersection line for two surfaces.
Tangent_plane.mw

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