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A basic question mostly I am not able find the ans...

Asked by: vs140580 490
do-loop pause
April 21 2023
0  1

Inside a big running for loop 

If a particular condition is satisfied I want loop to pause until i again press the enter key again 

As if the condition is satisfied I want to note down the output results printed on screen when that condition is satisfied.

previously C I used to use like getch() for it to wait

Kind help please.

I dont want  breakpoint it will simply call the debugger so only.

idk what this line should do...

Asked by: adr279 10
rtfm statistics fit
April 21 2023
2  3

H:= Fit(a*B+b*sinh(c*B), Bdata, Hdata, B)

can someone help me ? i have never used maple13 and i have to describe a code but i cant understand what this line does. can someone help me, please?! 
thank u in advance. 

How do I calculus the K constant in Einstein's equ...

Asked by: michaelvio 35
tensor physics
April 21 2023
1  0

How can I solve Einstein’s equation and calculus of the value of the K constant in Einstein's equation and the value of the tensor stress energy that fits in this equation?

   

 

QTBend.docxSqBend.mw

Double collect function ...

Asked by: ControlLaw 40
collect incomplete-question
April 21 2023
1  4

Hello,
I m wondering if/how (i) can use the collect function twice:  collect(a, x, form, func ):  
collect(a, x, form, collect(x)), but it seems I can't use a func with opt. 
Can someone help please? 

Merci 

Working symbolically with general/unknown matrices...

Asked by: Diasaur 20
linear-algebra abstract incomplete-question
April 21 2023
4  10

Hello Y'all,

I've been on this problem for a few days now and can't seem to find a solution and hope you fine people here can help me.

Is there a way to symbolically work with matrices? In detail I'm trying to calculate blocks in a block matrix equation symbolically/analytically. The first problem I had was that of course matrices dont commutate, which is solvable by just using the LinearAlgebra package and typing in

A.B instead of A*B

For now the big problem that remains is that of course in addition to that the inversion of a matrix A is not just 1/A (or \frac{1}{A} in LaTeX) but simply A^(-1). There is the MatrixInverse function but that needs a declared matrix. And since I dont have explicit matrices I can't use Matrix or the like to declare that A is a matrix. Any help here would appreciated. I tried to work with assume, but that didn't work either and I am kind of out of options (that I find on the web) right now. In essence I just want Maple to write A^(-1) and only cancel that if an A is next to it... (albeit with not just A but of course A also being setup by addition and multiplication of matrices...).

A smaller, related interest would be a general identity matrix. One that basically just fulfills A.I=I.A=A and I^(-1)=I. At least to me that seems kind of similar but I can't just define a Mtrix as being a Matrix and not having elements...

Thank you in advance and have a nice weekend y'all! :)

differentiate output of pdsolve...

Asked by: mehdi jafari 749
differentiation pde numeric
April 21 2023
2  1

Hi. I want to differentiate output of pdsolve, CA(y,z) with respect to z. how can i get the result? thnx in advance.

> 

restart
> 

CA0 := 0:CAi := 0.0336:L := 3:`Γ_1` := 0.05:mu := 0.000894:rho := 998:Dab := 0.196e-8:
Re_1 := 4*`Γ_1`*rho/mu:g := 9.8:delta := evalf(3*mu*`Γ_1`/(rho^2*g))^(1/3):
> 

Eq1 := mu*diff(uy(z), z, z) = -rho*g;

0.894e-3*(diff(diff(uy(z), z), z)) = -9780.4

 (1)
> 

Bcs := uy(delta) = 0., D[1](uy)(0) = 0.;

uy(0.2395046078e-3) = 0., (D(uy))(0) = 0.

 (2)
> 

sol:=dsolve({Bcs, Eq1}):UY:=rhs(sol);

-(2445100000/447)*z^2+35064235998909136283971/111750000000000000000000

 (3)
> 

uy_bar := rho*g*delta^2/(3*mu):
> 

Eq2 := UY*diff(CA(y, z), y) = Dab*diff(CA(y, z), z, z);

(-(2445100000/447)*z^2+35064235998909136283971/111750000000000000000000)*(diff(CA(y, z), y)) = 0.196e-8*(diff(diff(CA(y, z), z), z))

 (4)
> 

IBC := {CA(0, z) = 0, CA(y, 0) = 0.0336, D[2](CA)(y, delta) = 0};

{CA(0, z) = 0, CA(y, 0) = 0.336e-1, (D[2](CA))(y, 0.2395046078e-3) = 0}

 (5)
> 

sol2:= pdsolve(Eq2, IBC, numeric)

_m1045849856

 (6)
> 

sol2:-value(output=listprocedure);

[y = proc () option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; evalf(args[1]) end proc, z = proc () option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; evalf(args[2]) end proc, CA(y, z) = proc () local tv, xv, solnproc, stype, ndsol, vals; option `Copyright (c) 2001 by Waterloo Maple Inc. All rights reserved.`; Digits := trunc(evalhf(Digits)); solnproc := proc (tv, xv) local INFO, errest, nd, dvars, dary, daryt, daryx, vals, msg, i, j; option `Copyright (c) 2001 by Waterloo Maple Inc. All rights reserved.`; table( [( "soln_procedures" ) = array( 1 .. 1, [( 1 ) = (36893488148465195156) ] ) ] ) INFO := table( [( "leftwidth" ) = 1, ( "vectorhf" ) = true, ( "timeadaptive" ) = false, ( "extrabcs" ) = [0], ( "solmat_is" ) = 0, ( "spaceadaptive" ) = false, ( "pts", z ) = [0, 0.2395046078e-3], ( "linear" ) = true, ( "mixed" ) = false, ( "solvec3" ) = Vector(21, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0}, datatype = float[8]), ( "theta" ) = 1/2, ( "solution" ) = Array(1..3, 1..21, 1..1, {(1, 1, 1) = .0, (1, 2, 1) = .0, (1, 3, 1) = .0, (1, 4, 1) = .0, (1, 5, 1) = .0, (1, 6, 1) = .0, (1, 7, 1) = .0, (1, 8, 1) = .0, (1, 9, 1) = .0, (1, 10, 1) = .0, (1, 11, 1) = .0, (1, 12, 1) = .0, (1, 13, 1) = .0, (1, 14, 1) = .0, (1, 15, 1) = .0, (1, 16, 1) = .0, (1, 17, 1) = .0, (1, 18, 1) = .0, (1, 19, 1) = .0, (1, 20, 1) = .0, (1, 21, 1) = .0, (2, 1, 1) = .0, (2, 2, 1) = .0, (2, 3, 1) = .0, (2, 4, 1) = .0, (2, 5, 1) = .0, (2, 6, 1) = .0, (2, 7, 1) = .0, (2, 8, 1) = .0, (2, 9, 1) = .0, (2, 10, 1) = .0, (2, 11, 1) = .0, (2, 12, 1) = .0, (2, 13, 1) = .0, (2, 14, 1) = .0, (2, 15, 1) = .0, (2, 16, 1) = .0, (2, 17, 1) = .0, (2, 18, 1) = .0, (2, 19, 1) = .0, (2, 20, 1) = .0, (2, 21, 1) = .0, (3, 1, 1) = .0, (3, 2, 1) = .0, (3, 3, 1) = .0, (3, 4, 1) = .0, (3, 5, 1) = .0, (3, 6, 1) = .0, (3, 7, 1) = .0, (3, 8, 1) = .0, (3, 9, 1) = .0, (3, 10, 1) = .0, (3, 11, 1) = .0, (3, 12, 1) = .0, (3, 13, 1) = .0, (3, 14, 1) = .0, (3, 15, 1) = .0, (3, 16, 1) = .0, (3, 17, 1) = .0, (3, 18, 1) = .0, (3, 19, 1) = .0, (3, 20, 1) = .0, (3, 21, 1) = .0}, datatype = float[8], order = C_order), ( "solmat_i2" ) = 0, ( "depdords" ) = [[[1, 2]]], ( "matrixproc" ) = proc (v, vp, vpp, t, x, k, h, n, mat) local _s1, _s2, _s3, xi; _s1 := -(49/50000000000)/h^2; _s2 := -(2445100000/447)/k; _s3 := (49/111750000000000000000000)*(715596653038961964979*h^2+4470000000000*k)/(k*h^2); mat[4] := 1; mat[8*n-4] := (3/2)/h; mat[8*n-6] := (1/2)/h; mat[8*n-5] := -2/h; for xi from 2 to n-1 do mat[8*xi-4] := _s2*x[xi]^2+_s3; mat[8*xi-5] := _s1; mat[8*xi-3] := _s1 end do end proc, ( "totalwidth" ) = 8, ( "solmatrix" ) = Matrix(21, 8, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (9, 8) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (10, 8) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (11, 8) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (12, 7) = .0, (12, 8) = .0, (13, 1) = .0, (13, 2) = .0, (13, 3) = .0, (13, 4) = .0, (13, 5) = .0, (13, 6) = .0, (13, 7) = .0, (13, 8) = .0, (14, 1) = .0, (14, 2) = .0, (14, 3) = .0, (14, 4) = .0, (14, 5) = .0, (14, 6) = .0, (14, 7) = .0, (14, 8) = .0, (15, 1) = .0, (15, 2) = .0, (15, 3) = .0, (15, 4) = .0, (15, 5) = .0, (15, 6) = .0, (15, 7) = .0, (15, 8) = .0, (16, 1) = .0, (16, 2) = .0, (16, 3) = .0, (16, 4) = .0, (16, 5) = .0, (16, 6) = .0, (16, 7) = .0, (16, 8) = .0, (17, 1) = .0, (17, 2) = .0, (17, 3) = .0, (17, 4) = .0, (17, 5) = .0, (17, 6) = .0, (17, 7) = .0, (17, 8) = .0, (18, 1) = .0, (18, 2) = .0, (18, 3) = .0, (18, 4) = .0, (18, 5) = .0, (18, 6) = .0, (18, 7) = .0, (18, 8) = .0, (19, 1) = .0, (19, 2) = .0, (19, 3) = .0, (19, 4) = .0, (19, 5) = .0, (19, 6) = .0, (19, 7) = .0, (19, 8) = .0, (20, 1) = .0, (20, 2) = .0, (20, 3) = .0, (20, 4) = .0, (20, 5) = .0, (20, 6) = .0, (20, 7) = .0, (20, 8) = .0, (21, 1) = .0, (21, 2) = .0, (21, 3) = .0, (21, 4) = .0, (21, 5) = .0, (21, 6) = .0, (21, 7) = .0, (21, 8) = .0}, datatype = float[8], order = C_order), ( "eqnords" ) = [[1, 2]], ( "multidep" ) = [false, false], ( "maxords" ) = [1, 2], ( "errorest" ) = false, ( "norigdepvars" ) = 1, ( "spacevar" ) = z, ( "eqndep" ) = [1], ( "spaceidx" ) = 2, ( "dependson" ) = [{1}], ( "bandwidth" ) = [2, 3], ( "spacestep" ) = 0.119752303900000e-4, ( "solvec5" ) = 0, ( "matrixhf" ) = true, ( "depords" ) = [[1, 2]], ( "erroraccum" ) = true, ( "depeqn" ) = [1], ( "stages" ) = 1, ( "startup_only" ) = false, ( "spacepts" ) = 21, ( "vectorproc" ) = proc (v, vp, vpp, t, x, k, h, n, vec) local _s1, _s2, _s3, _s4, xi; _s2 := (49/50000000000)/h^2; _s3 := -(2445100000/447)/k; _s4 := (35064235998909136283971/111750000000000000000000)/k; vec[1] := 0.336e-1; vec[n] := 0; for xi from 2 to n-1 do _s1 := vp[xi-1]-2*vp[xi]+vp[xi+1]; vec[xi] := _s2*_s1+(_s3*x[xi]^2+_s4)*vp[xi] end do end proc, ( "t0" ) = 0, ( "allocspace" ) = 21, ( "initialized" ) = false, ( "method" ) = theta, ( "depvars" ) = [CA], ( "BCS", 1 ) = {[[1, 0, 0], b[1, 0, 0]-0.336e-1], [[1, 1, 0.2395046078e-3], b[1, 1, 0.2395046078e-3]]}, ( "timeidx" ) = 1, ( "solmat_v" ) = Vector(168, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0, (25) = .0, (26) = .0, (27) = .0, (28) = .0, (29) = .0, (30) = .0, (31) = .0, (32) = .0, (33) = .0, (34) = .0, (35) = .0, (36) = .0, (37) = .0, (38) = .0, (39) = .0, (40) = .0, (41) = .0, (42) = .0, (43) = .0, (44) = .0, (45) = .0, (46) = .0, (47) = .0, (48) = .0, (49) = .0, (50) = .0, (51) = .0, (52) = .0, (53) = .0, (54) = .0, (55) = .0, (56) = .0, (57) = .0, (58) = .0, (59) = .0, (60) = .0, (61) = .0, (62) = .0, (63) = .0, (64) = .0, (65) = .0, (66) = .0, (67) = .0, (68) = .0, (69) = .0, (70) = .0, (71) = .0, (72) = .0, (73) = .0, (74) = .0, (75) = .0, (76) = .0, (77) = .0, (78) = .0, (79) = .0, (80) = .0, (81) = .0, (82) = .0, (83) = .0, (84) = .0, (85) = .0, (86) = .0, (87) = .0, (88) = .0, (89) = .0, (90) = .0, (91) = .0, (92) = .0, (93) = .0, (94) = .0, (95) = .0, (96) = .0, (97) = .0, (98) = .0, (99) = .0, (100) = .0, (101) = .0, (102) = .0, (103) = .0, (104) = .0, (105) = .0, (106) = .0, (107) = .0, (108) = .0, (109) = .0, (110) = .0, (111) = .0, (112) = .0, (113) = .0, (114) = .0, (115) = .0, (116) = .0, (117) = .0, (118) = .0, (119) = .0, (120) = .0, (121) = .0, (122) = .0, (123) = .0, (124) = .0, (125) = .0, (126) = .0, (127) = .0, (128) = .0, (129) = .0, (130) = .0, (131) = .0, (132) = .0, (133) = .0, (134) = .0, (135) = .0, (136) = .0, (137) = .0, (138) = .0, (139) = .0, (140) = .0, (141) = .0, (142) = .0, (143) = .0, (144) = .0, (145) = .0, (146) = .0, (147) = .0, (148) = .0, (149) = .0, (150) = .0, (151) = .0, (152) = .0, (153) = .0, (154) = .0, (155) = .0, (156) = .0, (157) = .0, (158) = .0, (159) = .0, (160) = .0, (161) = .0, (162) = .0, (163) = .0, (164) = .0, (165) = .0, (166) = .0, (167) = .0, (168) = .0}, datatype = float[8], order = C_order, attributes = [source_rtable = (Matrix(21, 8, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (9, 8) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (10, 8) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (11, 8) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (12, 7) = .0, (12, 8) = .0, (13, 1) = .0, (13, 2) = .0, (13, 3) = .0, (13, 4) = .0, (13, 5) = .0, (13, 6) = .0, (13, 7) = .0, (13, 8) = .0, (14, 1) = .0, (14, 2) = .0, (14, 3) = .0, (14, 4) = .0, (14, 5) = .0, (14, 6) = .0, (14, 7) = .0, (14, 8) = .0, (15, 1) = .0, (15, 2) = .0, (15, 3) = .0, (15, 4) = .0, (15, 5) = .0, (15, 6) = .0, (15, 7) = .0, (15, 8) = .0, (16, 1) = .0, (16, 2) = .0, (16, 3) = .0, (16, 4) = .0, (16, 5) = .0, (16, 6) = .0, (16, 7) = .0, (16, 8) = .0, (17, 1) = .0, (17, 2) = .0, (17, 3) = .0, (17, 4) = .0, (17, 5) = .0, (17, 6) = .0, (17, 7) = .0, (17, 8) = .0, (18, 1) = .0, (18, 2) = .0, (18, 3) = .0, (18, 4) = .0, (18, 5) = .0, (18, 6) = .0, (18, 7) = .0, (18, 8) = .0, (19, 1) = .0, (19, 2) = .0, (19, 3) = .0, (19, 4) = .0, (19, 5) = .0, (19, 6) = .0, (19, 7) = .0, (19, 8) = .0, (20, 1) = .0, (20, 2) = .0, (20, 3) = .0, (20, 4) = .0, (20, 5) = .0, (20, 6) = .0, (20, 7) = .0, (20, 8) = .0, (21, 1) = .0, (21, 2) = .0, (21, 3) = .0, (21, 4) = .0, (21, 5) = .0, (21, 6) = .0, (21, 7) = .0, (21, 8) = .0}, datatype = float[8], order = C_order))]), ( "depshift" ) = [1], ( "PDEs" ) = [(-(2445100000/447)*z^2+35064235998909136283971/111750000000000000000000)*(diff(CA(y, z), y))-(49/25000000000)*(diff(diff(CA(y, z), z), z))], ( "periodic" ) = false, ( "soltimes" ) = Vector(3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8]), ( "adjusted" ) = false, ( "timevar" ) = y, ( "banded" ) = true, ( "explicit" ) = false, ( "solspace" ) = Vector(21, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = 0.2395046078e-3}, datatype = float[8]), ( "ICS" ) = [0], ( "inputargs" ) = [(-(2445100000/447)*z^2+35064235998909136283971/111750000000000000000000)*(diff(CA(y, z), y)) = 0.196e-8*(diff(diff(CA(y, z), z), z)), {CA(0, z) = 0, CA(y, 0) = 0.336e-1, (D[2](CA))(y, 0.2395046078e-3) = 0}], ( "solmat_i1" ) = 0, ( "fdepvars" ) = [CA(y, z)], ( "solvec2" ) = Vector(21, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0}, datatype = float[8]), ( "minspcpoints" ) = 4, ( "IBC" ) = b, ( "indepvars" ) = [y, z], ( "intspace" ) = Matrix(21, 1, {(1, 1) = .0, (2, 1) = .0, (3, 1) = .0, (4, 1) = .0, (5, 1) = .0, (6, 1) = .0, (7, 1) = .0, (8, 1) = .0, (9, 1) = .0, (10, 1) = .0, (11, 1) = .0, (12, 1) = .0, (13, 1) = .0, (14, 1) = .0, (15, 1) = .0, (16, 1) = .0, (17, 1) = .0, (18, 1) = .0, (19, 1) = .0, (20, 1) = .0, (21, 1) = .0}, datatype = float[8], order = C_order), ( "rightwidth" ) = 0, ( "timestep" ) = 0.119752303900000e-4, ( "solvec1" ) = Vector(21, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0}, datatype = float[8]), ( "solvec4" ) = 0, ( "solmat_ne" ) = 0, ( "autonomous" ) = true ] ); if xv = "left" then return INFO["solspace"][1] elif xv = "right" then return INFO["solspace"][INFO["spacepts"]] elif tv = "start" then return INFO["t0"] elif not (type(tv, 'numeric') and type(xv, 'numeric')) then error "non-numeric input" end if; if xv < INFO["solspace"][1] or INFO["solspace"][INFO["spacepts"]] < xv then error "requested %1 value must be in the range %2..%3", INFO["spacevar"], INFO["solspace"][1], INFO["solspace"][INFO["spacepts"]] end if; dary := Vector(3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8]); daryt := 0; daryx := 0; dvars := []; errest := false; nd := nops(INFO["depvars"]); if dary[nd+1] <> tv then try `pdsolve/numeric/evolve_solution`(INFO, tv) catch: msg := StringTools:-FormatMessage(lastexception[2 .. -1]); if tv < INFO["t0"] then error cat("unable to compute solution for %1<%2: ", msg), INFO["timevar"], INFO["failtime"] else error cat("unable to compute solution for %1>%2: ", msg), INFO["timevar"], INFO["failtime"] end if end try end if; if dary[nd+1] <> tv or dary[nd+2] <> xv then `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["solspace"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, dary); if errest then `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["err_t"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, daryt); `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["err_x"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, daryx) end if end if; dary[nd+1] := tv; dary[nd+2] := xv; if dvars = [] then [seq(dary[i], i = 1 .. INFO["norigdepvars"])] else vals := NULL; for i to nops(dvars) do j := eval(dvars[i]); try if errest then vals := vals, evalhf(j(tv, xv, dary, daryt, daryx)) else vals := vals, evalhf(j(tv, xv, dary)) end if catch: userinfo(5, `pdsolve/numeric`, `evalhf failure`); try if errest then vals := vals, j(tv, xv, dary, daryt, daryx) else vals := vals, j(tv, xv, dary) end if catch: vals := vals, undefined end try end try end do; [vals] end if end proc; stype := "1st"; if nargs = 1 then if args[1] = "left" then return solnproc(0, "left") elif args[1] = "right" then return solnproc(0, "right") elif args[1] = "start" then return solnproc("start", 0) else error "too few arguments to solution procedure" end if elif nargs = 2 then if stype = "1st" then tv := evalf(args[1]); xv := evalf(args[2]) else tv := evalf(args[2]); xv := evalf(args[1]) end if; if not (type(tv, 'numeric') and type(xv, 'numeric')) then if procname <> unknown then return ('procname')(args[1 .. nargs]) else ndsol := pointto(solnproc("soln_procedures")[1]); return ('ndsol')(args[1 .. nargs]) end if end if else error "incorrect arguments to solution procedure" end if; vals := solnproc(tv, xv); vals[1] end proc]

 (7)
> 

U:= subs(sol2:-value(output=listprocedure), CA(y, z));

proc () local tv, xv, solnproc, stype, ndsol, vals; option `Copyright (c) 2001 by Waterloo Maple Inc. All rights reserved.`; Digits := trunc(evalhf(Digits)); solnproc := proc (tv, xv) local INFO, errest, nd, dvars, dary, daryt, daryx, vals, msg, i, j; option `Copyright (c) 2001 by Waterloo Maple Inc. All rights reserved.`; table( [( "soln_procedures" ) = array( 1 .. 1, [( 1 ) = (36893488148465189476) ] ) ] ) INFO := table( [( "leftwidth" ) = 1, ( "vectorhf" ) = true, ( "timeadaptive" ) = false, ( "extrabcs" ) = [0], ( "solmat_is" ) = 0, ( "spaceadaptive" ) = false, ( "pts", z ) = [0, 0.2395046078e-3], ( "linear" ) = true, ( "mixed" ) = false, ( "solvec3" ) = Vector(21, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0}, datatype = float[8]), ( "theta" ) = 1/2, ( "solution" ) = Array(1..3, 1..21, 1..1, {(1, 1, 1) = .0, (1, 2, 1) = .0, (1, 3, 1) = .0, (1, 4, 1) = .0, (1, 5, 1) = .0, (1, 6, 1) = .0, (1, 7, 1) = .0, (1, 8, 1) = .0, (1, 9, 1) = .0, (1, 10, 1) = .0, (1, 11, 1) = .0, (1, 12, 1) = .0, (1, 13, 1) = .0, (1, 14, 1) = .0, (1, 15, 1) = .0, (1, 16, 1) = .0, (1, 17, 1) = .0, (1, 18, 1) = .0, (1, 19, 1) = .0, (1, 20, 1) = .0, (1, 21, 1) = .0, (2, 1, 1) = .0, (2, 2, 1) = .0, (2, 3, 1) = .0, (2, 4, 1) = .0, (2, 5, 1) = .0, (2, 6, 1) = .0, (2, 7, 1) = .0, (2, 8, 1) = .0, (2, 9, 1) = .0, (2, 10, 1) = .0, (2, 11, 1) = .0, (2, 12, 1) = .0, (2, 13, 1) = .0, (2, 14, 1) = .0, (2, 15, 1) = .0, (2, 16, 1) = .0, (2, 17, 1) = .0, (2, 18, 1) = .0, (2, 19, 1) = .0, (2, 20, 1) = .0, (2, 21, 1) = .0, (3, 1, 1) = .0, (3, 2, 1) = .0, (3, 3, 1) = .0, (3, 4, 1) = .0, (3, 5, 1) = .0, (3, 6, 1) = .0, (3, 7, 1) = .0, (3, 8, 1) = .0, (3, 9, 1) = .0, (3, 10, 1) = .0, (3, 11, 1) = .0, (3, 12, 1) = .0, (3, 13, 1) = .0, (3, 14, 1) = .0, (3, 15, 1) = .0, (3, 16, 1) = .0, (3, 17, 1) = .0, (3, 18, 1) = .0, (3, 19, 1) = .0, (3, 20, 1) = .0, (3, 21, 1) = .0}, datatype = float[8], order = C_order), ( "solmat_i2" ) = 0, ( "depdords" ) = [[[1, 2]]], ( "matrixproc" ) = proc (v, vp, vpp, t, x, k, h, n, mat) local _s1, _s2, _s3, xi; _s1 := -(49/50000000000)/h^2; _s2 := -(2445100000/447)/k; _s3 := (49/111750000000000000000000)*(715596653038961964979*h^2+4470000000000*k)/(k*h^2); mat[4] := 1; mat[8*n-4] := (3/2)/h; mat[8*n-6] := (1/2)/h; mat[8*n-5] := -2/h; for xi from 2 to n-1 do mat[8*xi-4] := _s2*x[xi]^2+_s3; mat[8*xi-5] := _s1; mat[8*xi-3] := _s1 end do end proc, ( "totalwidth" ) = 8, ( "solmatrix" ) = Matrix(21, 8, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (9, 8) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (10, 8) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (11, 8) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (12, 7) = .0, (12, 8) = .0, (13, 1) = .0, (13, 2) = .0, (13, 3) = .0, (13, 4) = .0, (13, 5) = .0, (13, 6) = .0, (13, 7) = .0, (13, 8) = .0, (14, 1) = .0, (14, 2) = .0, (14, 3) = .0, (14, 4) = .0, (14, 5) = .0, (14, 6) = .0, (14, 7) = .0, (14, 8) = .0, (15, 1) = .0, (15, 2) = .0, (15, 3) = .0, (15, 4) = .0, (15, 5) = .0, (15, 6) = .0, (15, 7) = .0, (15, 8) = .0, (16, 1) = .0, (16, 2) = .0, (16, 3) = .0, (16, 4) = .0, (16, 5) = .0, (16, 6) = .0, (16, 7) = .0, (16, 8) = .0, (17, 1) = .0, (17, 2) = .0, (17, 3) = .0, (17, 4) = .0, (17, 5) = .0, (17, 6) = .0, (17, 7) = .0, (17, 8) = .0, (18, 1) = .0, (18, 2) = .0, (18, 3) = .0, (18, 4) = .0, (18, 5) = .0, (18, 6) = .0, (18, 7) = .0, (18, 8) = .0, (19, 1) = .0, (19, 2) = .0, (19, 3) = .0, (19, 4) = .0, (19, 5) = .0, (19, 6) = .0, (19, 7) = .0, (19, 8) = .0, (20, 1) = .0, (20, 2) = .0, (20, 3) = .0, (20, 4) = .0, (20, 5) = .0, (20, 6) = .0, (20, 7) = .0, (20, 8) = .0, (21, 1) = .0, (21, 2) = .0, (21, 3) = .0, (21, 4) = .0, (21, 5) = .0, (21, 6) = .0, (21, 7) = .0, (21, 8) = .0}, datatype = float[8], order = C_order), ( "eqnords" ) = [[1, 2]], ( "multidep" ) = [false, false], ( "maxords" ) = [1, 2], ( "errorest" ) = false, ( "norigdepvars" ) = 1, ( "spacevar" ) = z, ( "eqndep" ) = [1], ( "spaceidx" ) = 2, ( "dependson" ) = [{1}], ( "bandwidth" ) = [2, 3], ( "spacestep" ) = 0.119752303900000e-4, ( "solvec5" ) = 0, ( "matrixhf" ) = true, ( "depords" ) = [[1, 2]], ( "erroraccum" ) = true, ( "depeqn" ) = [1], ( "stages" ) = 1, ( "startup_only" ) = false, ( "spacepts" ) = 21, ( "vectorproc" ) = proc (v, vp, vpp, t, x, k, h, n, vec) local _s1, _s2, _s3, _s4, xi; _s2 := (49/50000000000)/h^2; _s3 := -(2445100000/447)/k; _s4 := (35064235998909136283971/111750000000000000000000)/k; vec[1] := 0.336e-1; vec[n] := 0; for xi from 2 to n-1 do _s1 := vp[xi-1]-2*vp[xi]+vp[xi+1]; vec[xi] := _s2*_s1+(_s3*x[xi]^2+_s4)*vp[xi] end do end proc, ( "t0" ) = 0, ( "allocspace" ) = 21, ( "initialized" ) = false, ( "method" ) = theta, ( "depvars" ) = [CA], ( "BCS", 1 ) = {[[1, 0, 0], b[1, 0, 0]-0.336e-1], [[1, 1, 0.2395046078e-3], b[1, 1, 0.2395046078e-3]]}, ( "timeidx" ) = 1, ( "solmat_v" ) = Vector(168, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0, (25) = .0, (26) = .0, (27) = .0, (28) = .0, (29) = .0, (30) = .0, (31) = .0, (32) = .0, (33) = .0, (34) = .0, (35) = .0, (36) = .0, (37) = .0, (38) = .0, (39) = .0, (40) = .0, (41) = .0, (42) = .0, (43) = .0, (44) = .0, (45) = .0, (46) = .0, (47) = .0, (48) = .0, (49) = .0, (50) = .0, (51) = .0, (52) = .0, (53) = .0, (54) = .0, (55) = .0, (56) = .0, (57) = .0, (58) = .0, (59) = .0, (60) = .0, (61) = .0, (62) = .0, (63) = .0, (64) = .0, (65) = .0, (66) = .0, (67) = .0, (68) = .0, (69) = .0, (70) = .0, (71) = .0, (72) = .0, (73) = .0, (74) = .0, (75) = .0, (76) = .0, (77) = .0, (78) = .0, (79) = .0, (80) = .0, (81) = .0, (82) = .0, (83) = .0, (84) = .0, (85) = .0, (86) = .0, (87) = .0, (88) = .0, (89) = .0, (90) = .0, (91) = .0, (92) = .0, (93) = .0, (94) = .0, (95) = .0, (96) = .0, (97) = .0, (98) = .0, (99) = .0, (100) = .0, (101) = .0, (102) = .0, (103) = .0, (104) = .0, (105) = .0, (106) = .0, (107) = .0, (108) = .0, (109) = .0, (110) = .0, (111) = .0, (112) = .0, (113) = .0, (114) = .0, (115) = .0, (116) = .0, (117) = .0, (118) = .0, (119) = .0, (120) = .0, (121) = .0, (122) = .0, (123) = .0, (124) = .0, (125) = .0, (126) = .0, (127) = .0, (128) = .0, (129) = .0, (130) = .0, (131) = .0, (132) = .0, (133) = .0, (134) = .0, (135) = .0, (136) = .0, (137) = .0, (138) = .0, (139) = .0, (140) = .0, (141) = .0, (142) = .0, (143) = .0, (144) = .0, (145) = .0, (146) = .0, (147) = .0, (148) = .0, (149) = .0, (150) = .0, (151) = .0, (152) = .0, (153) = .0, (154) = .0, (155) = .0, (156) = .0, (157) = .0, (158) = .0, (159) = .0, (160) = .0, (161) = .0, (162) = .0, (163) = .0, (164) = .0, (165) = .0, (166) = .0, (167) = .0, (168) = .0}, datatype = float[8], order = C_order, attributes = [source_rtable = (Matrix(21, 8, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (9, 8) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (10, 8) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (11, 8) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (12, 7) = .0, (12, 8) = .0, (13, 1) = .0, (13, 2) = .0, (13, 3) = .0, (13, 4) = .0, (13, 5) = .0, (13, 6) = .0, (13, 7) = .0, (13, 8) = .0, (14, 1) = .0, (14, 2) = .0, (14, 3) = .0, (14, 4) = .0, (14, 5) = .0, (14, 6) = .0, (14, 7) = .0, (14, 8) = .0, (15, 1) = .0, (15, 2) = .0, (15, 3) = .0, (15, 4) = .0, (15, 5) = .0, (15, 6) = .0, (15, 7) = .0, (15, 8) = .0, (16, 1) = .0, (16, 2) = .0, (16, 3) = .0, (16, 4) = .0, (16, 5) = .0, (16, 6) = .0, (16, 7) = .0, (16, 8) = .0, (17, 1) = .0, (17, 2) = .0, (17, 3) = .0, (17, 4) = .0, (17, 5) = .0, (17, 6) = .0, (17, 7) = .0, (17, 8) = .0, (18, 1) = .0, (18, 2) = .0, (18, 3) = .0, (18, 4) = .0, (18, 5) = .0, (18, 6) = .0, (18, 7) = .0, (18, 8) = .0, (19, 1) = .0, (19, 2) = .0, (19, 3) = .0, (19, 4) = .0, (19, 5) = .0, (19, 6) = .0, (19, 7) = .0, (19, 8) = .0, (20, 1) = .0, (20, 2) = .0, (20, 3) = .0, (20, 4) = .0, (20, 5) = .0, (20, 6) = .0, (20, 7) = .0, (20, 8) = .0, (21, 1) = .0, (21, 2) = .0, (21, 3) = .0, (21, 4) = .0, (21, 5) = .0, (21, 6) = .0, (21, 7) = .0, (21, 8) = .0}, datatype = float[8], order = C_order))]), ( "depshift" ) = [1], ( "PDEs" ) = [(-(2445100000/447)*z^2+35064235998909136283971/111750000000000000000000)*(diff(CA(y, z), y))-(49/25000000000)*(diff(diff(CA(y, z), z), z))], ( "periodic" ) = false, ( "soltimes" ) = Vector(3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8]), ( "adjusted" ) = false, ( "timevar" ) = y, ( "banded" ) = true, ( "explicit" ) = false, ( "solspace" ) = Vector(21, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = 0.2395046078e-3}, datatype = float[8]), ( "ICS" ) = [0], ( "inputargs" ) = [(-(2445100000/447)*z^2+35064235998909136283971/111750000000000000000000)*(diff(CA(y, z), y)) = 0.196e-8*(diff(diff(CA(y, z), z), z)), {CA(0, z) = 0, CA(y, 0) = 0.336e-1, (D[2](CA))(y, 0.2395046078e-3) = 0}], ( "solmat_i1" ) = 0, ( "fdepvars" ) = [CA(y, z)], ( "solvec2" ) = Vector(21, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0}, datatype = float[8]), ( "minspcpoints" ) = 4, ( "IBC" ) = b, ( "indepvars" ) = [y, z], ( "intspace" ) = Matrix(21, 1, {(1, 1) = .0, (2, 1) = .0, (3, 1) = .0, (4, 1) = .0, (5, 1) = .0, (6, 1) = .0, (7, 1) = .0, (8, 1) = .0, (9, 1) = .0, (10, 1) = .0, (11, 1) = .0, (12, 1) = .0, (13, 1) = .0, (14, 1) = .0, (15, 1) = .0, (16, 1) = .0, (17, 1) = .0, (18, 1) = .0, (19, 1) = .0, (20, 1) = .0, (21, 1) = .0}, datatype = float[8], order = C_order), ( "rightwidth" ) = 0, ( "timestep" ) = 0.119752303900000e-4, ( "solvec1" ) = Vector(21, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0}, datatype = float[8]), ( "solvec4" ) = 0, ( "solmat_ne" ) = 0, ( "autonomous" ) = true ] ); if xv = "left" then return INFO["solspace"][1] elif xv = "right" then return INFO["solspace"][INFO["spacepts"]] elif tv = "start" then return INFO["t0"] elif not (type(tv, 'numeric') and type(xv, 'numeric')) then error "non-numeric input" end if; if xv < INFO["solspace"][1] or INFO["solspace"][INFO["spacepts"]] < xv then error "requested %1 value must be in the range %2..%3", INFO["spacevar"], INFO["solspace"][1], INFO["solspace"][INFO["spacepts"]] end if; dary := Vector(3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8]); daryt := 0; daryx := 0; dvars := []; errest := false; nd := nops(INFO["depvars"]); if dary[nd+1] <> tv then try `pdsolve/numeric/evolve_solution`(INFO, tv) catch: msg := StringTools:-FormatMessage(lastexception[2 .. -1]); if tv < INFO["t0"] then error cat("unable to compute solution for %1<%2: ", msg), INFO["timevar"], INFO["failtime"] else error cat("unable to compute solution for %1>%2: ", msg), INFO["timevar"], INFO["failtime"] end if end try end if; if dary[nd+1] <> tv or dary[nd+2] <> xv then `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["solspace"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, dary); if errest then `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["err_t"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, daryt); `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["err_x"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, daryx) end if end if; dary[nd+1] := tv; dary[nd+2] := xv; if dvars = [] then [seq(dary[i], i = 1 .. INFO["norigdepvars"])] else vals := NULL; for i to nops(dvars) do j := eval(dvars[i]); try if errest then vals := vals, evalhf(j(tv, xv, dary, daryt, daryx)) else vals := vals, evalhf(j(tv, xv, dary)) end if catch: userinfo(5, `pdsolve/numeric`, `evalhf failure`); try if errest then vals := vals, j(tv, xv, dary, daryt, daryx) else vals := vals, j(tv, xv, dary) end if catch: vals := vals, undefined end try end try end do; [vals] end if end proc; stype := "1st"; if nargs = 1 then if args[1] = "left" then return solnproc(0, "left") elif args[1] = "right" then return solnproc(0, "right") elif args[1] = "start" then return solnproc("start", 0) else error "too few arguments to solution procedure" end if elif nargs = 2 then if stype = "1st" then tv := evalf(args[1]); xv := evalf(args[2]) else tv := evalf(args[2]); xv := evalf(args[1]) end if; if not (type(tv, 'numeric') and type(xv, 'numeric')) then if procname <> unknown then return ('procname')(args[1 .. nargs]) else ndsol := pointto(solnproc("soln_procedures")[1]); return ('ndsol')(args[1 .. nargs]) end if end if else error "incorrect arguments to solution procedure" end if; vals := solnproc(tv, xv); vals[1] end proc

 (8)
> 

U(1e-5,1e-6)

HFloat(0.02593255728999584)

 (9)
> 

CA_DZ:=diff(eval(CA(y,z), sol2:-value(output=listprocedure)),z);

Error, non-algebraic expressions cannot be differentiated

  
> 

 

Download Hw-02-01_problem.mw

`evala/Minpoly` and PolynomialTools:-MinimalPolyno...

Asked by: sursumCorda 922
polynomial minpoly
April 21 2023
1  4

Here are three algebraic numbers: (In fact, they are solutions to some equation. See the attachment below.)

bSol := {RootOf(1216*_Z^4 + (264*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^8 + 408*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^7 - 1580*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^6 - 6832*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^5 + 3508*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^4 + 9944*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^3 + 9948*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^2 - 10752*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266) + 5204)*_Z^3 + (891*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^8 + 1652*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^7 - 4748*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^6 - 24076*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^5 + 5354*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^4 + 35356*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^3 + 29668*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^2 - 196*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266) + 3971)*_Z^2 + (506*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^8 + 980*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^7 - 2264*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^6 - 12420*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^5 + 3676*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^4 + 11596*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^3 + 33800*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^2 - 7772*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266) + 1210)*_Z - 473*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^8 - 720*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^7 + 2560*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^6 + 10960*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^5 - 8034*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^4 - 13840*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^3 - 9304*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^2 + 1104*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266) - 1133, index = real[2]), RootOf(1216*_Z^4 + (264*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^8 + 408*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^7 - 1580*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^6 - 6832*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^5 + 3508*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^4 + 9944*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^3 + 9948*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^2 - 10752*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68) + 5204)*_Z^3 + (891*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^8 + 1652*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^7 - 4748*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^6 - 24076*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^5 + 5354*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^4 + 35356*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^3 + 29668*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^2 - 196*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68) + 3971)*_Z^2 + (506*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^8 + 980*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^7 - 2264*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^6 - 12420*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^5 + 3676*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^4 + 11596*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^3 + 33800*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^2 - 7772*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68) + 1210)*_Z - 473*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^8 - 720*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^7 + 2560*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^6 + 10960*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^5 - 8034*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^4 - 13840*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^3 - 9304*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^2 + 1104*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68) - 1133, index = real[2]), RootOf(1216*_Z^4 + (264*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^8 + 408*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^7 - 1580*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^6 - 6832*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^5 + 3508*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^4 + 9944*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^3 + 9948*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^2 - 10752*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657) + 5204)*_Z^3 + (891*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^8 + 1652*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^7 - 4748*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^6 - 24076*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^5 + 5354*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^4 + 35356*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^3 + 29668*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^2 - 196*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657) + 3971)*_Z^2 + (506*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^8 + 980*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^7 - 2264*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^6 - 12420*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^5 + 3676*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^4 + 11596*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^3 + 33800*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^2 - 7772*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657) + 1210)*_Z - 473*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^8 - 720*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^7 + 2560*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^6 + 10960*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^5 - 8034*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^4 - 13840*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^3 - 9304*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^2 + 1104*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657) - 1133, index = real[2])}:

One may check that 11_X9－47_X8＋96_X7－376_X6－370_X5－142_X4＋280_X3＋64_X2－17_X－11 is an “annihilating” polynomial of each of them (using another computer algebra system); accordingly, the degree of the minimal polynomial cannot be greater than 9. However, Maple's output indicates that the minimal polynomial is of degree 36! 

> 

restart;
> 

alias(`~`[`=`](alpha__ || (1 .. 3), ` $`, RootOf(11*_Z^9+17*_Z^8-64*_Z^7-280*_Z^6+142*_Z^5+370*_Z^4+376*_Z^3-96*_Z^2+47*_Z-11, .2246 .. .2266), RootOf(11*_Z^9+17*_Z^8-64*_Z^7-280*_Z^6+142*_Z^5+370*_Z^4+376*_Z^3-96*_Z^2+47*_Z-11, 1.671 .. 1.68), RootOf(11*_Z^9+17*_Z^8-64*_Z^7-280*_Z^6+142*_Z^5+370*_Z^4+376*_Z^3-96*_Z^2+47*_Z-11, 2.648 .. 2.657)))
> 

({PDETools:-Solve})({`~`[`>=`](a, b, ` $`, 0), a^5*b+4*a^4*b^2+4*a^3*b^3-7*a^4*b-6*a^2*b^3-7*a*b^4+b^5-6*a^3*b+12*a^2*b^2+4*b^4+4*a^3-6*a*b^2+4*b^3+4*a^2-7*a*b+a = 0, a <> b})
bSol := `~`[subs](%, b)
> 

evalf[2*Digits](`~`[eval](11*_X^9-47*_X^8+96*_X^7-376*_X^6-370*_X^5-142*_X^4+280*_X^3+64*_X^2-17*_X-11, `~`[`=`](_X, bSol)))

{RootOf(1216*_Z^4+(264*alpha__1^8+408*alpha__1^7-1580*alpha__1^6-6832*alpha__1^5+3508*alpha__1^4+9944*alpha__1^3+9948*alpha__1^2-10752*alpha__1+5204)*_Z^3+(891*alpha__1^8+1652*alpha__1^7-4748*alpha__1^6-24076*alpha__1^5+5354*alpha__1^4+35356*alpha__1^3+29668*alpha__1^2-196*alpha__1+3971)*_Z^2+(506*alpha__1^8+980*alpha__1^7-2264*alpha__1^6-12420*alpha__1^5+3676*alpha__1^4+11596*alpha__1^3+33800*alpha__1^2-7772*alpha__1+1210)*_Z-473*alpha__1^8-720*alpha__1^7+2560*alpha__1^6+10960*alpha__1^5-8034*alpha__1^4-13840*alpha__1^3-9304*alpha__1^2+1104*alpha__1-1133, index = real[2]), RootOf(1216*_Z^4+(264*alpha__2^8+408*alpha__2^7-1580*alpha__2^6-6832*alpha__2^5+3508*alpha__2^4+9944*alpha__2^3+9948*alpha__2^2-10752*alpha__2+5204)*_Z^3+(891*alpha__2^8+1652*alpha__2^7-4748*alpha__2^6-24076*alpha__2^5+5354*alpha__2^4+35356*alpha__2^3+29668*alpha__2^2-196*alpha__2+3971)*_Z^2+(506*alpha__2^8+980*alpha__2^7-2264*alpha__2^6-12420*alpha__2^5+3676*alpha__2^4+11596*alpha__2^3+33800*alpha__2^2-7772*alpha__2+1210)*_Z-473*alpha__2^8-720*alpha__2^7+2560*alpha__2^6+10960*alpha__2^5-8034*alpha__2^4-13840*alpha__2^3-9304*alpha__2^2+1104*alpha__2-1133, index = real[2]), RootOf(1216*_Z^4+(264*alpha__3^8+408*alpha__3^7-1580*alpha__3^6-6832*alpha__3^5+3508*alpha__3^4+9944*alpha__3^3+9948*alpha__3^2-10752*alpha__3+5204)*_Z^3+(891*alpha__3^8+1652*alpha__3^7-4748*alpha__3^6-24076*alpha__3^5+5354*alpha__3^4+35356*alpha__3^3+29668*alpha__3^2-196*alpha__3+3971)*_Z^2+(506*alpha__3^8+980*alpha__3^7-2264*alpha__3^6-12420*alpha__3^5+3676*alpha__3^4+11596*alpha__3^3+33800*alpha__3^2-7772*alpha__3+1210)*_Z-473*alpha__3^8-720*alpha__3^7+2560*alpha__3^6+10960*alpha__3^5-8034*alpha__3^4-13840*alpha__3^3-9304*alpha__3^2+1104*alpha__3-1133, index = real[2])}

  

{-0.7765721e-11, -0.40e-16, -0.2e-17}

 (1)
> 

`~`[`@`(evala, Minpoly)](bSol, _X)

{-17799961-(10941904462/121)*_X+(61823634144236824/14641)*_X^9-(31748793508955524/14641)*_X^8-(101389427707536/14641)*_X^7+(2187899683524768/14641)*_X^6+(660533278629392/14641)*_X^5-(35195970681077/1331)*_X^4+(4540912173250/1331)*_X^3-(226104907168/1331)*_X^2+_X^36+(562/11)*_X^35+(1306112/1331)*_X^34-(18882494/14641)*_X^33-(1885893201/14641)*_X^32-(8021957456/14641)*_X^31+(128807680096/14641)*_X^30+(601684442192/14641)*_X^29+(136952065956/14641)*_X^28-(7313279407608/14641)*_X^27-(20755313257248/14641)*_X^26-(72279502775080/14641)*_X^25-(235147325265588/14641)*_X^24+(407012808852624/14641)*_X^23-(2003920103008/1331)*_X^22-(2647129453154576/14641)*_X^21-(5329535956015778/14641)*_X^20-(11189597881735324/14641)*_X^19+(18014890583299168/14641)*_X^18-(25692630236542548/14641)*_X^17+(57603516516708946/14641)*_X^16-(875402744452912/121)*_X^15+(36990665431348512/14641)*_X^14+(67887070781490608/14641)*_X^13+(643327218250876/1331)*_X^12-(81888059180050616/14641)*_X^11+(306280599794336/14641)*_X^10}

 (2)
> 

`~`[PolynomialTools[MinimalPolynomial]](bSol, _X)

{14641*_X^36+748022*_X^35+14367232*_X^34-18882494*_X^33-1885893201*_X^32-8021957456*_X^31+128807680096*_X^30+601684442192*_X^29+136952065956*_X^28-7313279407608*_X^27-20755313257248*_X^26-72279502775080*_X^25-235147325265588*_X^24+407012808852624*_X^23-22043121133088*_X^22-2647129453154576*_X^21-5329535956015778*_X^20-11189597881735324*_X^19+18014890583299168*_X^18-25692630236542548*_X^17+57603516516708946*_X^16-105923732078802352*_X^15+36990665431348512*_X^14+67887070781490608*_X^13+7076599400759636*_X^12-81888059180050616*_X^11+306280599794336*_X^10+61823634144236824*_X^9-31748793508955524*_X^8-101389427707536*_X^7+2187899683524768*_X^6+660533278629392*_X^5-387155677491847*_X^4+49950033905750*_X^3-2487153978848*_X^2-1323970439902*_X-260609229001}

 (3)
> 

factor({{-260609229001-1323970439902*_X+407012808852624*_X^23-22043121133088*_X^22-2647129453154576*_X^21-5329535956015778*_X^20-11189597881735324*_X^19+18014890583299168*_X^18-25692630236542548*_X^17+57603516516708946*_X^16-105923732078802352*_X^15+36990665431348512*_X^14+67887070781490608*_X^13+7076599400759636*_X^12-81888059180050616*_X^11+306280599794336*_X^10+61823634144236824*_X^9-31748793508955524*_X^8-101389427707536*_X^7+2187899683524768*_X^6+660533278629392*_X^5-387155677491847*_X^4+49950033905750*_X^3-2487153978848*_X^2+14641*_X^36+748022*_X^35+14367232*_X^34-18882494*_X^33-1885893201*_X^32-8021957456*_X^31+128807680096*_X^30+601684442192*_X^29+136952065956*_X^28-7313279407608*_X^27-20755313257248*_X^26-72279502775080*_X^25-235147325265588*_X^24}[], {-17799961-(10941904462/121)*_X+(407012808852624/14641)*_X^23-(2003920103008/1331)*_X^22-(2647129453154576/14641)*_X^21-(5329535956015778/14641)*_X^20-(11189597881735324/14641)*_X^19+(18014890583299168/14641)*_X^18-(25692630236542548/14641)*_X^17+(57603516516708946/14641)*_X^16-(875402744452912/121)*_X^15+(36990665431348512/14641)*_X^14+(67887070781490608/14641)*_X^13+(643327218250876/1331)*_X^12-(81888059180050616/14641)*_X^11+(306280599794336/14641)*_X^10+(61823634144236824/14641)*_X^9-(31748793508955524/14641)*_X^8-(101389427707536/14641)*_X^7+(2187899683524768/14641)*_X^6+(660533278629392/14641)*_X^5-(35195970681077/1331)*_X^4+(4540912173250/1331)*_X^3-(226104907168/1331)*_X^2+_X^36+(562/11)*_X^35+(1306112/1331)*_X^34-(18882494/14641)*_X^33-(1885893201/14641)*_X^32-(8021957456/14641)*_X^31+(128807680096/14641)*_X^30+(601684442192/14641)*_X^29+(136952065956/14641)*_X^28-(7313279407608/14641)*_X^27-(20755313257248/14641)*_X^26-(72279502775080/14641)*_X^25-(235147325265588/14641)*_X^24}[]})

{(11*_X^9-47*_X^8+96*_X^7-376*_X^6-370*_X^5-142*_X^4+280*_X^3+64*_X^2-17*_X-11)*(83746429305*_X-163433814*_X^23-1409885474*_X^22+7323055726*_X^21+92878340298*_X^20+291711433585*_X^19-28358008525*_X^18-1146850616945*_X^17+2003142623069*_X^16+7054039060380*_X^15+10860482240404*_X^14+4410674835220*_X^13-23715924119108*_X^12+39935154074341*_X^11-76564178781009*_X^10+246946329497683*_X^9-303627746551159*_X^8+41661161235738*_X^7+181533634595246*_X^6-146573328877410*_X^5+44279227597786*_X^4-3813039868649*_X^3+234521505317*_X^2+1331*_X^27+73689*_X^26+1609349*_X^25+4562111*_X^24+23691748091), (1/14641)*(11*_X^9-47*_X^8+96*_X^7-376*_X^6-370*_X^5-142*_X^4+280*_X^3+64*_X^2-17*_X-11)*(83746429305*_X-163433814*_X^23-1409885474*_X^22+7323055726*_X^21+92878340298*_X^20+291711433585*_X^19-28358008525*_X^18-1146850616945*_X^17+2003142623069*_X^16+7054039060380*_X^15+10860482240404*_X^14+4410674835220*_X^13-23715924119108*_X^12+39935154074341*_X^11-76564178781009*_X^10+246946329497683*_X^9-303627746551159*_X^8+41661161235738*_X^7+181533634595246*_X^6-146573328877410*_X^5+44279227597786*_X^4-3813039868649*_X^3+234521505317*_X^2+1331*_X^27+73689*_X^26+1609349*_X^25+4562111*_X^24+23691748091)}

 (4)
> 

``


 

Download minpoly.mw

Isn't the results incorrect? 

Normalize the matrix of columns of independent va...

Asked by: vs140580 490
linearalgebra do-loop statistics
April 21 2023
0  6

I have a n cross n matrix M I need help to write a function f say which takes the Matrix M as input function and Normalize each column of independent data.

Here normalization is  subtract by mean and divide by Standard deviation kind help if possible

If anyone has  idea of other different types of normalization please help it will help me a lot 

Kind help your ideas will all be acknowledge Please help

Installation issue of Maple on Intel Evo laptop...

Asked by: adamsmithad 5
installation
April 20 2023
1  0

Hello everyone,

I am facing an issue while installing Maple on my Intel Evo laptop. The installation process starts but then it fails and I get an error message. I have tried to install it multiple times but the issue persists. I have also checked for any updates or patches but there are none available.I am not sure what could be causing this issue. Has anyone else faced a similar problem? If so, could you please share your experience and any solutions that worked for you? I would appreciate any help or suggestions on how to resolve this issue.

Thank you in advance for your time and assistance.

Can a colored shape in the xy plane be projected o...

Asked by: Earl 930
sphere projection plotting
April 20 2023
2  3

Is there any simple way that the colored shape created in the xy plane by the uploaded code can be projected in the z direction onto the surface of the unit sphere centred at the origin?

Projection.mw

Can maplesim facilitate rigid-flexible coupling an...

Asked by: Maxie 25
multiple connected
April 20 2023
1  10

I am now using maplesim to do research on railway vehicles. When I replace the rails with flexible beams in maplesim, I try to connect the rails and two sleepers with moving pairs, and I find that there are over-constraint problems. How to replace the rails with flexible bodies? Are the rails connected with multiple sleepers?

I hope you can give me some advice, thank you very much.

Generally speaking, will eliminating the need for ...

Asked by: sursumCorda 922
April 20 2023
0  5

Let us begin with the official descriptions of loops. The Maple® documentation claims that: 

Note that the examples above don't necessarily illustrate the best way to perform these operations. Often a functional form like seq, map, add, or mul is far more efficient.

Mma's tech tutorial also claims that: 

If you have a big program full of If, Do, Return, etc., you're probably not doing things right. 
Often, however, you can make more elegant and efficient programs using the functional programming constructs ….

Also, MatLab's Techniques to Improve Performance and Measure and Improve GPU Performance claims that: 

You can achieve better performance by rewriting loops to make use of higher-dimensional operations. The performance of a wide variety of element-wise functions can be improved … instead of looping over the matrices.

Well, I'm confused. Why did the official help page say like this? Actually, I find that lots of users in this forum still (and usually) use traditional for-loops instead of something which fits in with the alleged functional programming ideas. Did I misconstrue those statements? 
(For instance, as for the functional operations, it's unfortunate that Maple's built-in map cannot operate on arbitrary expression trees of any depth; so I have to use the loops to apply some procedure indirectly, which is not so convenient. In my opinion, owing to such limitation, people have to, and then gradually tend to, use the loops.) 

How do I access the Google Maps and Geocoding pack...

Asked by: Teep 195
google-maps-and-geocoding
April 20 2023
0  2

Good day! 

I attempted to download the geocoding package for Maple and I cannot get it to work. Executing the worksheet produces no results.

I am using Maple 2022. 

Can anyone shed some light on this please?

Thanks for reading ..

https://maple.cloud/app/5769608062566400/Google+Maps+and+Geocoding?activeGroup=MathApps

How to extract the coefficients of the random var...

Asked by: MaPal93 90
collect coeff randomvariable
April 20 2023
1  9

How to use collect() or coeffs() on random variables instead of standard variables?

I need to re-organize a linear combination of RVs nu[1], nu[2], u[1], u[2], u[3] by collecting the coefficients on each of these 5 RVs. Note that the Xs are correlated with each other and the Ys are correlated with each other (but Xs and Ys are uncorrelated).

For example, nu is a 2D gaussian vector where nu[1] and nu[2] are defined in terms of _R1, _R2, means, standard deviations and correlation coefficient. They are quite "nested" and the 3D gaussian vector u is even worse, so when these enter a linear combination it becomes hard to identify them back as simply nu[1], nu[2], u[1], u[2], u[3].

Is there a way to "isolate" them in a linear combination by using collect()-like or coeffs()-like functions (i) directly on the RVs or (ii) indireclty on the explicit expressions of _Rs, means, standard devs, correlation coeffs? 

(I already checked the answers to these two somewhat similar questions but did not help for my case:

https://mapleprimes.com/questions/235215-Reduce-Length-Of-Sum-Of-Products

https://mapleprimes.com/questions/234292-Re-How-To-Collect-Using-A-Term-By-Multiplication

)

See my script below: 

For example, I would want collect() on nu[1] (or equivalently on _R1*sigma__v[1]+nu__0[1]) to give me X__1+X__3 (as you easily see from my definition of Omega).

> 

# 2.2.1 Define the Omega random variable as Omega__1+Omega__2+Omega__3:
> 

`&Omega;__1` := X__1*(nu[1]-`&mu;__1`-`&lambda;__1`*(u[1]+X__1)); `&Omega;__2` := X__2*(nu[2]-`&mu;__2`-`&lambda;__2`*(u[2]+X__2)); `&Omega;__3` := X__3*(nu[1]+nu[2]-`&mu;__3`-`&lambda;__3`*(u[3]+X__3)); Omega := `&Omega;__1`+`&Omega;__2`+`&Omega;__3`

X__1*(sigma__v[1]*_R1+nu__0[1]-mu__1-lambda__1*(_R3*sigma__u[1]+X__1))+X__2*(sigma__v[2]*rho__v[1, 2]*_R1+(-rho__v[1, 2]^2+1)^(1/2)*sigma__v[2]*_R2+nu__0[2]-mu__2-lambda__2*(rho__u[1, 2]*sigma__u[2]*_R3+(-rho__u[1, 2]^2+1)^(1/2)*sigma__u[2]*_R4+X__2))+X__3*(sigma__v[1]*_R1+nu__0[1]+sigma__v[2]*rho__v[1, 2]*_R1+(-rho__v[1, 2]^2+1)^(1/2)*sigma__v[2]*_R2+nu__0[2]-mu__3-lambda__3*(rho__u[1, 3]*sigma__u[3]*_R3-sigma__u[3]*(rho__u[1, 2]*rho__u[1, 3]-rho__u[2, 3])*_R4/(-rho__u[1, 2]^2+1)^(1/2)+((-2*rho__u[1, 2]*rho__u[1, 3]*rho__u[2, 3]+rho__u[1, 2]^2+rho__u[1, 3]^2+rho__u[2, 3]^2-1)/(rho__u[1, 2]^2-1))^(1/2)*sigma__u[3]*_R5+X__3))

 (1)
> 

# 2.2.2 Simplify and re-arrange the Omega RV to obtain the easy-to-read version (a,b,c,d,e,f are the coefficients):
#Omega__* = a + b*nu[1] + c*nu[2] + d*u[1] + e*u[2] + f*u[3];
# How to do it? Collect() does not work...simplify() doesn't make it any easier...
> 

`&Omega;__*` := collect(Omega, [_R1*`&sigma;__v`[1]+`&nu;__0`[1], `&sigma;__v`[2]*`&rho;__v`[1, 2]*_R1+sqrt(-`&rho;__v`[1, 2]^2+1)*`&sigma;__v`[2]*_R2+`&nu;__0`[2], `&sigma;__u`[1]*_R3, `&sigma;__u`[2]*`&rho;__u`[1, 2]*_R3+sqrt(-`&rho;__u`[1, 2]^2+1)*`&sigma;__u`[2]*_R4, `&sigma;__u`[3]*`&rho;__u`[1, 3]*_R3-`&sigma;__u`[3]*(`&rho;__u`[1, 2]*`&rho;__u`[1, 3]-`&rho;__u`[2, 3])*_R4/sqrt(-`&rho;__u`[1, 2]^2+1)+sqrt((-2*`&rho;__u`[1, 2]*`&rho;__u`[1, 3]*`&rho;__u`[2, 3]+`&rho;__u`[1, 2]^2+`&rho;__u`[1, 3]^2+`&rho;__u`[2, 3]^2-1)/(`&rho;__u`[1, 2]^2-1))*`&sigma;__u`[3]*_R5])

Error, (in collect) cannot collect _R1*sigma__v[1]+nu__0[1]

  
> 

`&Omega;__col` := collect(Omega, [nu[1], nu[2], u[1], u[2], u[3]])

Error, (in collect) cannot collect _R1*sigma__v[1]+nu__0[1]

  
> 

 

Download collect.mw

why Maple dsolve with series requires IC to be sam...

Asked by: nm 8552
dsolve series differential-equations
April 20 2023
0  1

Is there a mathematical reason why Maple does not allow expansion point for solving an ode using series solution to be different than where initial conditions are located?

I do not see why this restriction is there. Here is first order ode, where expansion point is x=1 and initial condiitons are also at x=1

restart;
ode:=diff(y(x),x)=x^3;
dsolve([ode,y(1)=1],y(x),'series',x=1)

            y(x) = (1 + (x - 1)) + 3/2*(x - 1)^2 + (x - 1)^3 + 1/4*(x - 1)^4 + O((x - 1)^6)

No problem. But when expansion point at x=0, it complains

restart;
ode:=diff(y(x),x)=x^3;
dsolve([ode,y(1)=1],y(x),'series',x=0)

Error, (in dsolve/SERIES) conflicting specifications of the series expansion point: 1 v.s. 0

I know help mentions that it uses initial conditions point for expansion if given, and if no IC is given, then it uses x=point if given and if no x=point is given then it default to x=0.

But my question is, why it does not handle the case when the expansion point is given explicitly and is at a different location than where IC are given? Is this simply just a feature missing that could be added in a future release if needed, or is it due to some mathematical reason that I do not see?

I would have expected it to first find the series solution around the given expansion point, then use the IC to determine the unknown constant after that, just like we normally do when solving an ode using standard methods not using series expansion.

I am using Maple 2023

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