Maple Questions and Posts

Problem with element properties...

Asked by: Mac Dude 1576

August 14 2017

3 9

I am trying to use the element properties Maple has in its ScientificConstants package. I am running into problems with the density of gaseous elements:

with(ScientificConstants);

Units:-UsingSystem(); # returns SI as expected

GetValue(Element('Si',density)); # returns 2329.0000 [kg/m^3] which is 2.329 g/cm^3, which is correct

GetValue(Element('H',density(gas))); # returns 88 [kg/m^3], which is incorrect.

PDG gives the density of hydrogen as 8.376E-5 g/cm^3, which is 0.08376 kg/m^3.

Even more crazy for Krypton:

GetValue(Element('Kr',density(gas))); # returns 3677.000 [kg/m^3]. Heavy little buggers, these Kypton atoms! Should be 3.486 in the same units.

What gives? Am I missing something here?

Mac Dude

Maple use of symbols...

Asked by: Wtolrud 75

August 14 2017

1 2

What is the meaning of the "0" in the series expansion

series(x/(-x²-x+1), x = 0); ( this is the Maple command)

x + x² + 2 x³ + 3 x⁴+ 5 x⁵ + O(x⁶) This is the results

This is use in Maple I've seen quite a bit for series. I assume the the series continues on. But I am not sure

Also is there any listing of what some of the symbols that maple uses???

Specify color for output variables...

Asked by: mohkam7 45

August 14 2017

3 12

Is there a way to specify different colors for different output variables? For example, if x,y, and z appear in the entire document as variables, I want x to be red, y to be blue, and z to be green whenever an output is displayed.

Thanks

how i can reduce the runtime of the program ?...

Asked by: torabi 90

August 14 2017

1 6

hi..how i can rewrite section of this code as another form i,e ''for section''

I have a lot of line as this and runnig cise is time consuming.

is there another way to write this section in order to the runtime of the program is reduced??

thanks

for.mw

>

restart;

>	with(LinearAlgebra):

>	with(VectorCalculus):

>	#Digits:=5: k:=6:

>

l:=0:

>

h:=1:

>

m:=4:

>

n:=4:

>

l1:=2*h:

>

l2:=2*h:

>

N:=0.5:

>

nu:=.3:

>	E_m:=70e9:

>	E_c:=380e9:

>	rho_m:=2702:

>	rho_c:=3800:

>	lambda_m:=nuE_m/((1+nu)(1-2*nu)):

>	lambda_c:=nuE_c/((1+nu)(1-2*nu)):

>	mu_m:=E_m/(2*(1+nu)):

>	mu_c:=E_c/(2*(1+nu)):

>	with(orthopoly):

>	for i from 0 to 5 do: L(i):=sqrt((2i+1)/2)P(i,z): end do:

>	Z:=rho_m+(rho_c-rho_m)*((1/2)+(z/h))^N;

(1)

>	U:=lambda_m+(lambda_c-lambda_m)*((1/2)+(z/h))^N;

(2)

>	S:=mu_m+(mu_c-mu_m)*((1/2)+(z/h))^N;

(3)

>	d:=Matrix([[0,0,0,0,0,0,0,0],[sqrt(3),0,0,0,0,0,0,0],[0,sqrt(15),0,0,0,0,0,0],[sqrt(7),0,sqrt(35),0,0,0,0,0],[0,sqrt(27),0,sqrt(63),0,0,0,0],[sqrt(11),0,sqrt(55),0,sqrt(99),0,0,0],[0,sqrt(39),0,sqrt(91),0,sqrt(143),0,0],[sqrt(15),0,sqrt(75),0,sqrt(135),0,sqrt(195),0]]);

$d := Matrix(8, 8, {(1, 1) = 0, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (2, 1) = 3^(1/2), (2, 2) = 0, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (2, 6) = 0, (2, 7) = 0, (2, 8) = 0, (3, 1) = 0, (3, 2) = 15^(1/2), (3, 3) = 0, (3, 4) = 0, (3, 5) = 0, (3, 6) = 0, (3, 7) = 0, (3, 8) = 0, (4, 1) = 7^(1/2), (4, 2) = 0, (4, 3) = 35^(1/2), (4, 4) = 0, (4, 5) = 0, (4, 6) = 0, (4, 7) = 0, (4, 8) = 0, (5, 1) = 0, (5, 2) = 3*3^(1/2), (5, 3) = 0, (5, 4) = 3*7^(1/2), (5, 5) = 0, (5, 6) = 0, (5, 7) = 0, (5, 8) = 0, (6, 1) = 11^(1/2), (6, 2) = 0, (6, 3) = 55^(1/2), (6, 4) = 0, (6, 5) = 3*11^(1/2), (6, 6) = 0, (6, 7) = 0, (6, 8) = 0, (7, 1) = 0, (7, 2) = 39^(1/2), (7, 3) = 0, (7, 4) = 91^(1/2), (7, 5) = 0, (7, 6) = 143^(1/2), (7, 7) = 0, (7, 8) = 0, (8, 1) = 15^(1/2), (8, 2) = 0, (8, 3) = 5*3^(1/2), (8, 4) = 0, (8, 5) = 3*15^(1/2), (8, 6) = 0, (8, 7) = 195^(1/2), (8, 8) = 0})$

(4)

>

e2 := 0;

(5)

Download for.mw

how I can dsolve this differential equation...

Asked by: torabi 90

August 14 2017

0 12

hi...

how I can dsolve this differential equations. parameter p is unkown.

I want to gain w(x) and u(x) and psi(x) and p.

thanks

sade.mw

>

restart; eq1 := (diff(psi(x), x))^2+(diff(u(x), x)+(8*(1/2))*(diff(w(x), x))^2)((diff(psi(x), x))^2)+3*(diff(w(x), x, x))+5*(diff(w(x), x, x))*(diff(psi(x), x))-7*(diff(u(x), x, x, x)+(8*(1/2))*(diff(w(x), x, x))^2+(3/2)*(diff(w(x), x, x, x))*(diff(w(x), x)))+3 = p

(diff(psi(x), x))^2+(diff(u(x), x))((diff(psi(x), x))^2)+4*(diff(w(x), x))((diff(psi(x), x))^2)^2+3*(diff(diff(w(x), x), x))+5*(diff(diff(w(x), x), x))*(diff(psi(x), x))-7*(diff(diff(diff(u(x), x), x), x))-28*(diff(diff(w(x), x), x))^2-(21/2)*(diff(diff(diff(w(x), x), x), x))*(diff(w(x), x))+3 = p

(1)

>

70+8*(diff(diff(diff(diff(psi(x), x), x), x), x))-7*(diff(w(x), x))+7*psi(x) = 0

(2)

>

4*(diff(diff(w(x), x), x))-4*(diff(psi(x), x))+34+26*(diff(diff(diff(diff(w(x), x), x), x), x)) = 0

(3)

>

dsys3 := {eq1, eq2, eq3, psi(0) = 0, psi(1) = 0, u(0) = 0, u(1) = 0, w(0) = 0, w(1) = 0, ((D@@1)(psi))(0) = 0, ((D@@1)(psi))(1) = 0, ((D@@1)(w))(0) = 0, ((D@@1)(w))(1) = 0}; dsol5 := dsolve(dsys3, 'maxmesh' = 1200, numeric, abserr = .1, output = array([.5]))

Error, (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 12, got 10

>

>	with(PDEtools, casesplit, declare);

(4)

>

Download sade.mw

how i can dsolve this differential equations........

Asked by: 9009134 110

August 14 2017

0 5

hi...

how i can dsolve this differential equations and obtain w(x) and U(x) and phi(x) analytical or numerically?

thanks

zah.mw

Download zah.mw

a look at recursive functions

by: Matt C Anderson 190 Product: Maple 13

August 14 2017

1 0

Hi MaplePrimes,

another_recursive_sequence.mw

another_recursive_sequence.pdf

These two files have the same content. One is a .pdf and the other is a Maple Worksheet. I explore integer sequences of the form -

a(r) = c*a(r-1)+d*a(r-2) with a(1) and a(2) given.

Some of these sequences are in (the Online Encyclopedia of Integer Sequences) OEIS.org and some are not. If we restrict c to 1 and assume that a(1)=1 and a(2) = 2 we have the parameter d remaining. See additional webpage -

https://sites.google.com/site/recrusivefunction/

Let me know if you like the code.

Regards,

Matt

fix error and identify any other wrong and explain...

Asked by: bashar27 55

August 14 2017

0 1

> {w = -4*mu, a[-1] = -12*mu/(a+b), a[0] = a[0], a[1] = 0, b[-1] = 0, b[0] = 0, b[1] = 0};
/ 12 mu
{ w = -4 mu, a[-1] = - -----, a[0] = a[0], a[1] = 0, b[-1] = 0, b[0] = 0,
\ a + b

           \
   b[1] = 0 }
           /
> restart;
>
> w := -4*mu;
                                    -4 mu
> a[-1] := -12*mu/(a+b);
                                     12 mu
                                   - -----
                                     a + b
> a[0] := a[0];
                                    a[0]
> a[1] := 0;
                                      0
> b[-1] := 0;
                                      0
> b[0] := 0;
                                      0
> b[1] := 0;
                                      0
> xi := x+w*t;
                                 x - 4 mu t
> P := sqrt(mu)*tan(A-sqrt(mu)*xi);
                      (1/2)    /      (1/2)             \
                    mu      tan\A - mu      (x - 4 mu t)/
> u := a[0]+a[1]*P/(1+lambda*P)+a[-1]*(1+lambda*P)/P+b[0]*sqrt(sigma*(1+P^2/mu))/P+b[1]*sqrt(sigma*(1+P^2/mu))+b[-1]*sqrt(sigma*(1+P^2/mu))/P^2;
                (1/2) /             (1/2)    /      (1/2)             \\
           12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//
    a[0] - -------------------------------------------------------------
                                  /      (1/2)             \
                       (a + b) tan\A - mu      (x - 4 mu t)/
> Diff(u, x, t)+a*(Diff(u, x))*(Diff(u, x, y))+b*(Diff(u, `$`(x, 2)))*(Diff(u, y))+Diff(u, `$`(x, 3), y);
/   2   /            (1/2) /             (1/2)    /      (1/2)             \\\
| d    |       12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//|
|------ |a[0] - -------------------------------------------------------------|
| dt dx |                              /      (1/2)             \            |
\       \                   (a + b) tan\A - mu      (x - 4 mu t)/            /

\     /    /
|     | d |
| + a |--- |a[0]
|     | dx |
/     \    \

          (1/2) /             (1/2)    /      (1/2)             \\\\ /   2   /
     12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//|| | d    |
   - -------------------------------------------------------------|| |------ |
                            /      (1/2)             \            || | dy dx |
                 (a + b) tan\A - mu      (x - 4 mu t)/            // \       \

              (1/2) /             (1/2)    /      (1/2)             \\\\     /
         12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//||     |
a[0] - -------------------------------------------------------------|| + b |
                                /      (1/2)             \            ||     |
                     (a + b) tan\A - mu      (x - 4 mu t)/            //     \

   2 /            (1/2) /             (1/2)    /      (1/2)             \\\\ /
d |       12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//|| |
-- |a[0] - -------------------------------------------------------------|| |
     |                              /      (1/2)             \            || |
     \                   (a + b) tan\A - mu      (x - 4 mu t)/            // \

      /            (1/2) /             (1/2)    /      (1/2)             \\\\
   d |       12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//||
--- |a[0] - -------------------------------------------------------------||
   dy |                              /      (1/2)             \            ||
      \                   (a + b) tan\A - mu      (x - 4 mu t)/            //

     / 4 /            (1/2) /             (1/2)    /      (1/2)             \\
     |d |       12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//
   + |-- |a[0] - -------------------------------------------------------------
     |   |                              /      (1/2)             \
     \   \                   (a + b) tan\A - mu      (x - 4 mu t)/

\\
||
||
||
//
> value(%);
                       /                                 2\
              3        |       /      (1/2)             \ |
         96 mu lambda \1 + tan\A - mu      (x - 4 mu t)/ /
         --------------------------------------------------
                               a + b

                                                                2
                            /                                 2\
                   3        |       /      (1/2)             \ |
              96 mu lambda \1 + tan\A - mu      (x - 4 mu t)/ /
            - --------------------------------------------------- +
                                                         2
                               /      (1/2)             \
                    (a + b) tan\A - mu      (x - 4 mu t)/

                                                  /
                                                  |
                             1                    |     (5/2) /
           -------------------------------------- \96 mu      \1
                                                3
                      /      (1/2)             \
           (a + b) tan\A - mu      (x - 4 mu t)/

(1/2) / (1/2) \\
+ lambda mu tan\A - mu (x - 4 mu t)//

                                               2\
           /                                 2\ |
           |       /      (1/2)             \ | |
           \1 + tan\A - mu      (x - 4 mu t)/ / / -

                                                 /
                             1                   |     (5/2) /
           ------------------------------------- \96 mu      \1
                      /      (1/2)             \
           (a + b) tan\A - mu      (x - 4 mu t)/

                                                            /
                       (1/2)    /      (1/2)             \\ |
            + lambda mu      tan\A - mu      (x - 4 mu t)// \1

                                           2\\
                 /      (1/2)             \ ||
            + tan\A - mu      (x - 4 mu t)/ //
> simplify(%);
Error, (in simplify/tools/_zn) too many levels of recursion
>

plot an indefinite integral ...

Asked by: mehdi jafari 774

August 14 2017

0 7

hi every one, i want to plot an indefinite integral , it is some what complex and maple can not compute the answer, ( but numeric integration can be computed) , but we want to plot the output, what should we do ? tnx for help in advance

corrected.mw

weighted norm of an expression...

Asked by: mehdi jafari 774

August 14 2017

0 3

how can we compute wighted norm of a matrix or a vector in maple?

How can I convert a result to a trigonometric iden...

Asked by: Gillee 237

August 13 2017

1 5

Download trigonometric_id.mw

how to dsolve for this equation?...

Asked by: LeeHoYeung 535

August 13 2017

0 5

this equation is complicated

how to dsolve for this equation for function f ?

f(t,x,diff(x,t)) - f(t,x,p) - (diff(x,t)-p)*diff(f(t,x,p), p) = tan(t)

how to find the contour of time series data? and c...

Asked by: LeeHoYeung 535

August 12 2017

0 1

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

search value plot maximize...

Asked by: lucaud 45

August 12 2017

0 1

In this fuction the maximize is about at t=46 and x=46 but in the plot I look other max at other value, why?because is discontinus fuction?I need not the local max (it is potential energy but I think don't matter)optimization2enerpot.mws

how to solve this system?...

Asked by: LeeHoYeung 535

August 12 2017

0 0

updated:

P := evalm(p2 + c*vector([cos(q1+q2+q3), sin(q1+q2+q3)]));

restart:
with(Groebner):
p1 := vector([a*cos(q1), a*sin(q1)]);
p2 := evalm(p1 + b*vector([cos(q1+q2), sin(q1+q2)]));
P := evalm(p2 + c*vector([cos(q1+q2+q3), sin(q1+q2+q3)]));
Pe := map(expand, P);
A := {cos(q1) = c1, sin(q1) =s1, cos(q2)=c2, sin(q2)=s2, cos(q3)=c3, sin(q3)=s3};
P := subs(A, op(Pe));
F1 := [x - P[1], y - P[2], s1^2+c1^2-1, s2^2+c2^2-1, s3^2+c3^2-1 ];

F2 := subs({a=1, b=1, c=1}, F1);

g2 := Basis(F2, plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[1], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[2], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[3], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[4], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[5], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[6], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[7], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[8], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[9], plex(c3, s3, c2, s2, c1, s1));

                                   1, c1
                               2       2    2   2
                           16 y + 16 x , s1 s2
                                           2
                                 8 x, c1 s2
                                2      2    2
                             2 y + 2 x , s1 c2
                                 2 x, c1 c2
                            3            2
                         2 x - 2 x + 2 y x, s2 c2
                                        2
                                   1, c2
                                   2 x, s3
                                    2, c3

originally i think

g2[1], g2[7], g2[9] have single variables c1, c2, c3 respectively

can be used to solve system

but without x and y, these equations can not be used

if choose leading term has x and y , but there is no single variable s1 or c1.

originally expect solve as follows

g2spec := subs({x=1, y=1/2}, [g2[3],g2[5],g2[6]]);
S1 := [solve([g2spec[1]])];
q1a := evalf(arccos(S1[1]));
q1b := evalf(arccos(S1[2]));

S2 := [solve(subs(s1=S1[1], g2spec[2])), solve(subs(s1=S1[2], g2spec[2])) ];
q2a := evalf(arccos(S2[1]));
q2b := evalf(arccos(S2[2]));

S3 := [solve(subs(s1=S2[1], g2spec[2])), solve(subs(s1=S2[2], g2spec[2])) ];
q2a := evalf(arccos(S3[1]));
q2b := evalf(arccos(S3[2]));

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