Hi all,

I am using Maple 2016.

I have defined 5 polynomials: f1, f2, f3, f4 and f5 with 5 unknowns q1,q2 ,q3, q4 and lamda.

After this, I generated the Gröbner basis. But when I try to find the normal set I got an error.

with(Groebner);

f1 := lamda*q1-(3380075947548081*q1*(1/140737488355328)-259050600068343*q2*(1/140737488355328)-1826834460600733*q3*(1/1125899906842624)+4414049272733425*q4*(1/9007199254740992))*(q2*(8289619202186977*q1*(1/9007199254740992)+3380075947548081*q2*(1/281474976710656)-4414049272733425*q3*(1/18014398509481984)-1826834460600733*q4*(1/2251799813685248))+q3*(1826834460600733*q1*(1/2251799813685248)-4414049272733425*q2*(1/18014398509481984)+843667886835955*q3*(1/70368744177664)-215663898201129*q4*(1/9007199254740992))-q4*(4414049272733425*q1*(1/18014398509481984)+1826834460600733*q2*(1/2251799813685248)+431327796402257*q3*(1/18014398509481984)+843667886835955*q4*(1/70368744177664))-q1*(3380075947548081*q1*(1/281474976710656)-259050600068343*q2*(1/281474976710656)-1826834460600733*q3*(1/2251799813685248)+4414049272733425*q4*(1/18014398509481984)));
f2 := lamda*q2+(259050600068343*q1*(1/140737488355328)+3380075947548081*q2*(1/140737488355328)-4414049272733425*q3*(1/9007199254740992)-1826834460600733*q4*(1/1125899906842624))*(q2*(8289619202186977*q1*(1/9007199254740992)+3380075947548081*q2*(1/281474976710656)-4414049272733425*q3*(1/18014398509481984)-1826834460600733*q4*(1/2251799813685248))+q3*(1826834460600733*q1*(1/2251799813685248)-4414049272733425*q2*(1/18014398509481984)+843667886835955*q3*(1/70368744177664)-215663898201129*q4*(1/9007199254740992))-q4*(4414049272733425*q1*(1/18014398509481984)+1826834460600733*q2*(1/2251799813685248)+431327796402257*q3*(1/18014398509481984)+843667886835955*q4*(1/70368744177664))-q1*(3380075947548081*q1*(1/281474976710656)-259050600068343*q2*(1/281474976710656)-1826834460600733*q3*(1/2251799813685248)+4414049272733425*q4*(1/18014398509481984)));
f3 := (1826834460600733*q1*(1/1125899906842624)-4414049272733425*q2*(1/9007199254740992)+843667886835955*q3*(1/35184372088832)-862655592804515*q4*(1/18014398509481984))*(q2*(8289619202186977*q1*(1/9007199254740992)+3380075947548081*q2*(1/281474976710656)-4414049272733425*q3*(1/18014398509481984)-1826834460600733*q4*(1/2251799813685248))+q3*(1826834460600733*q1*(1/2251799813685248)-4414049272733425*q2*(1/18014398509481984)+843667886835955*q3*(1/70368744177664)-215663898201129*q4*(1/9007199254740992))-q4*(4414049272733425*q1*(1/18014398509481984)+1826834460600733*q2*(1/2251799813685248)+431327796402257*q3*(1/18014398509481984)+843667886835955*q4*(1/70368744177664))-q1*(3380075947548081*q1*(1/281474976710656)-259050600068343*q2*(1/281474976710656)-1826834460600733*q3*(1/2251799813685248)+4414049272733425*q4*(1/18014398509481984)))+lamda*q3;
f4 := lamda*q4-(4414049272733425*q1*(1/9007199254740992)+1826834460600733*q2*(1/1125899906842624)+862655592804515*q3*(1/18014398509481984)+843667886835955*q4*(1/35184372088832))*(q2*(8289619202186977*q1*(1/9007199254740992)+3380075947548081*q2*(1/281474976710656)-4414049272733425*q3*(1/18014398509481984)-1826834460600733*q4*(1/2251799813685248))+q3*(1826834460600733*q1*(1/2251799813685248)-4414049272733425*q2*(1/18014398509481984)+843667886835955*q3*(1/70368744177664)-215663898201129*q4*(1/9007199254740992))-q4*(4414049272733425*q1*(1/18014398509481984)+1826834460600733*q2*(1/2251799813685248)+431327796402257*q3*(1/18014398509481984)+843667886835955*q4*(1/70368744177664))-q1*(3380075947548081*q1*(1/281474976710656)-259050600068343*q2*(1/281474976710656)-1826834460600733*q3*(1/2251799813685248)+4414049272733425*q4*(1/18014398509481984)));
f5 := q1^2+q2^2+q3^2+q4^2-1;
ord := tdeg(q1, q2, q3, q4, lamda);
                  tdeg(q1, q2, q3, q4, lamda)
G := Basis([f1, f2, f3, f4, f5], ord);

IsZeroDimensional(G);
                             false
ns, rv := NormalSet(G, ord);
Error, (in Groebner:-NormalSet) The case of non-zero-dimensional varieties is not handled.

Any help please ?

Thank you.

Hello,

I was wondering if it is possible to use units in Maple so I can always check if the result I have at the end of calculation is the meter.  For example:

The answer is of course 3.10^8 m^3*kg/s^3

I try to do something with the units but I am unable to crreate something that will simplify the m/s ffactor to 1.

Any idea?

Thank you in advance for your help.

how to convert a nested for loop to iterative version with stack

#my testing for wildcard to one
#after testing, it loop a very long time and not stop
ppp := [[0,0,0,x],[0,0,1,0],[0,1,0,0],[1,0,0,0]]:
check1 := [seq(0,ii=1..nops(ppp))];
ttt1 := [[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]]:
mmmeaght1 := [seq(0,ii=1..nops(ppp[1]))]:
bbb1 := [seq(0,ii=1..nops(ppp[1]))]:
emap := [(xx) -> if [xx < 0 assuming x > 0] then 0 else 1 end if, (xx) -> evalf(1/(1+exp(xx)))]:
#trace(perceptronrule1);
MM(ppp, ttt1, mmmeaght1, bbb1, check1, emap);
 

when test wildcard variable for input, would like to assume x > 0 then

i try assuming x > 0 , got error

I have expression h1 as below:

Download simplifymore.mw

How can i simplify h1 more in Maple?

Funny, I can't seem to find a list of all available units in the help file.

Is there not a listed table of units somewhere?

**edit add**  conversion of units I mean.  ie.  meters, miles, gallons, litres, Pa, etc...

I wish to solve for k interms of x, e is a constant in the equation k=x+e*sin(k). Using the solve function, i got 

RootOf(_Z-x-e*sin(_Z)) and using the function allvalues(RootOf(_Z-x-e*sin(_Z))) still gave the same expression in _Z. Please is there a way out because I need the value of k  as a substitute to another equation. Any help will be highly appreciated.
 

The maple I used at school is a much older version and when I do Definite Integrals there and copy it to Word as part of the project, it just copies perfectly.

Now I have Maple 16 at home and when I have a definite integral, I have to copy it using copy special and take it as an image to MS Word. That's not the problem. The problem is the limits sometimes seem to be cut off. The left hand-side image is the older version of Maple. Limits look perfect and even the integral sign is darker and so on. The right hand-side image is the Maple 2016. Can anyone help me change the style on Maple 2016 so it's like the old one so the integrals look better on my project. Thanks alot

I am trying to model a disease. The equation is as follows:

S*X - f(X,S,Sp) = 100

I have data for S, I have data for X and I have data for f(X,S,Sp) however I want to find an equation for f(X,S,Sp) that has the best fit with the data because I need to use it later on in my calculation. If anyone is intrested S is the sensitivity of the blood test, Sp is the specificity of the blood test. This means that X*(1-Sp) is the number of false positives.

I currently dont have access to Maple hence I am doing all my modeling in excel 2016. So I am severly limited because excel is useless at algebra.

Maple.xlsx

I have a non-linear function to be optimized. It involves infinite sums. Maple plots the function so I can see where the minimum is. However the NLP solve keeps on evaluating without providing the solution. I have tried to write the function as a procedure but it does not work either.

I'd appreciate any suggestion

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

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

How do I do this?

Tom Dean

So i got this code, im trying to iterate with jacobi and gaussseidel method.

H := HilbertMatrix(n, n, 1); b := Matrix(n, 1, proc (i) options operator, arrow; add(1/(i+j-1), j = 1 .. n) end proc); A := Matrix(n, 1, 1); Multiply(H, A); norm1H := norm(H, 1); norm2H := norm(H, 2); normHinf := norm(H, infinity); norm1b := norm(b, 1); norm2b := norm(b, 2); norminfb := norm(b, infinity); IterativeApproximate(H, initialapprox = Vector(n, 0), tolerance = 10^(-7), maxiterations = 10, method = gaussseidel)

But sadly no iteration gave me an answer, anyone knows wheres my mistake? i really help with this! 


thanks in advance

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

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

Thanks in advance!

Friends

I have plotted some figures and saved them yesterfay!

now once i opened them some nonsence digits appear on the figure! see the picture please. anyone has similar experience? how to solve it!

Dont make me disappointed maple! two days work is invain now !

> restart;
> with(plots); with(StringTools); with(plottools);
> INF := 999999999999999999999;
                     999999999999999999999
> NULL;
> MinoxAngle := 200; MikromaAngle := 350; MinicordAngle := 290; GamiAngle := 280; GamiFocal := 0.25e-1; SummitarDial := [1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 2, 2.2, 3, 4, 5, 6, 7, 10, 20, INF]; Minox35MLDial := [3, 4, 6, 10, 20, INF]; Minox35Angle := 100; MinicordDial := [.35, .4, .5, .6, .7, .8, .9, 1, 1.2, 1.5, 2, 3, 4, 8, INF]; Mini := nops(MinicordDial); MikromaDial := [.5, .6, .7, .8, .9, 1, 1.2, 1.5, 2, 2.5, 3.5, 6, INF]; MinoxLXDial := [.2, .24, .3, .4, .6, 1, 2, 30]; MinoxLXAngle := 270; GamiDial := [.5, .6, .7, .8, 1, 1.2, 1.5, 2, 3, 5, 99990000000000]; MinoxBDial := [8*(1/12), 10*(1/12), 1, 1.5, 2, 3, 6, INF]; MinoxBAngle := 270;
                              200
                              350
                              290
                              280
                             0.025
[1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 2, 2.2, 3, 4, 5, 6, 7, 10, 

  20, 999999999999999999999]
            [3, 4, 6, 10, 20, 999999999999999999999]
                              100
 [0.35, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 1.2, 1.5, 2, 3, 4, 8, 

   999999999999999999999]
                               15
    [0.5, 0.6, 0.7, 0.8, 0.9, 1, 1.2, 1.5, 2, 2.5, 3.5, 6, 

      999999999999999999999]
              [0.2, 0.24, 0.3, 0.4, 0.6, 1, 2, 30]
                              270
   [0.5, 0.6, 0.7, 0.8, 1, 1.2, 1.5, 2, 3, 5, 99990000000000]
         [2  5                                        ]
         [-, -, 1, 1.5, 2, 3, 6, 999999999999999999999]
         [3  6                                        ]
                              270
> 
> NULL;
> dd := GamiDial; N := nops(dd); dstx := [seq(convert(dd[i], string), i = 1 .. N)];
   [0.5, 0.6, 0.7, 0.8, 1, 1.2, 1.5, 2, 3, 5, 99990000000000]
                               11
  [".5", ".6", ".7", ".8", "1", "1.2", "1.5", "2", "3", "5", 

    "99990000000000"]
> NULL;
> MinicordAngle := 290;
                              290
> NULL;
> 
> LensDial := proc (LensName, focal, Angle, scale, dr) local p1, p2, p3, p8, pk, pt, rk, R, R2, R3, Rc, c1, ds2; R := 1600; R2 := 1400; R3 := 1200; Rc := 1500; CaptionTail1 := "EXTENSION ANGLE"; CaptionTail2 := "LENS FOCUSING DIAL"; Caption1 := Join([LensName, CaptionTail1]); Caption2 := Join([LensName, CaptionTail2]); q := 180/Pi; rotation := 90; dir := dr; ds := scale; N := nops(ds); dstx := [seq(convert(ds[i], string), i = 1 .. N)]; ds2 := subs(dstx[N] = infinity, dstx); MaxAngle := Angle; f := focal; degr := -(-ds[1]+f)*Angle/(D-f)+rotation; g1 := degr/q; for j to N do deg[j] := subs(D = ds[j], degr) end do; for i to N do rdn[i] := evalf(deg[i]/q); xv[i] := R2*cos(rdn[i]); yv[i] := R2*sin(rdn[i]); wx[i] := R3*cos(rdn[i]); wy[i] := R3*sin(rdn[i]) end do; pk := {seq([ds[i], deg[i]], i = 1 .. N)}; rk := {seq([dir*xv[i], yv[i]], i = 1 .. N)}; txt := {seq([dir*wx[i], wy[i], ds2[i]], i = 1 .. N)}; p3 := pointplot(rk, caption = Caption2, captionfont = ["ROMAN", bold, 22], symbol = solidcircle, symbolsize = 15, color = red, axes = none); c1 := circle([0, 0], Rc, thickness = 8); p8 := textplot(txt, 'font' = ["times", "bold", 14]); display(p3, c1, p8, scaling = constrained) end proc;
Warning, `CaptionTail1` is implicitly declared local to procedure `LensDial`
Warning, `CaptionTail2` is implicitly declared local to procedure `LensDial`
Warning, `Caption1` is implicitly declared local to procedure `LensDial`
Warning, `Caption2` is implicitly declared local to procedure `LensDial`
Warning, `q` is implicitly declared local to procedure `LensDial`
Warning, `rotation` is implicitly declared local to procedure `LensDial`
Warning, `dir` is implicitly declared local to procedure `LensDial`
Warning, `ds` is implicitly declared local to procedure `LensDial`
Warning, `N` is implicitly declared local to procedure `LensDial`
Warning, `dstx` is implicitly declared local to procedure `LensDial`
Warning, `MaxAngle` is implicitly declared local to procedure `LensDial`
Warning, `f` is implicitly declared local to procedure `LensDial`
Warning, `degr` is implicitly declared local to procedure `LensDial`
Warning, `g1` is implicitly declared local to procedure `LensDial`
Warning, `j` is implicitly declared local to procedure `LensDial`
Warning, `deg` is implicitly declared local to procedure `LensDial`
Warning, `i` is implicitly declared local to procedure `LensDial`
Warning, `rdn` is implicitly declared local to procedure `LensDial`
Warning, `xv` is implicitly declared local to procedure `LensDial`
Warning, `yv` is implicitly declared local to procedure `LensDial`
Warning, `wx` is implicitly declared local to procedure `LensDial`
Warning, `wy` is implicitly declared local to procedure `LensDial`
Warning, `txt` is implicitly declared local to procedure `LensDial`
> ;
> NULL;
> LensDial("MEOPTA MICROMA  HELGOR 25mm", 0.25e-1, 350, MikromaDial, 1);

> LensDial("GOERZ MINICORD  25mm", 0.25e-1, 335, MinicordDial, 1);

> 
> ;
> LensDial("MINOX LX MINOX 15mm", 0.15e-1, 270, MinoxLXDial, 1);

> LensDial("GAMI ESAMITAR 25mm", 0.25e-1, 290, GamiDial, 1);