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How to use the Liebniz notation in a complex expre...

Asked by: mmcdara 7891
derivative 2dmath diff
January 04 2020
1  4

Hi

I would like to use  the Liebniz notation that someone from the technical support posted here
Writing Derivatives at a Point Using Leibniz Notation
to display a formula that is not just a partial derivative but a more complex expression invoking partial derivatives. 
Typically an expression like this one:

2*(Diff(f(mu__1, mu__2), mu__1))^2*lambda__1^2-(Diff(f(mu__1, mu__2), mu__1))^2*mu__1^2+2*(Diff(f(mu__1, mu__2), mu__2))^2*lambda__2^2-(Diff(f(mu__1, mu__2), mu__2))^2*mu__2^2+2*(Diff(f(mu__1, mu__2), mu__1))*(Diff(f(mu__1, mu__2), mu__2))*lambda__1*lambda__2-2*(Diff(f(mu__1, mu__2), mu__1))*mu__1*(Diff(f(mu__1, mu__2), mu__2))*mu__2

Could anyone help me to do this?
Thanks in advance

(PS: I'm still using Maple 2015.2)

Problem in making animation of multiple solutions...

Asked by: Muhammad Usman 240
animation plotting
December 29 2019
1  4

Dear Users!

Hoped everything going fine with you. I want to make animation of ten solutions as given bellow but fail to do that. Please see it fix the problem. I shall be very thankful to u.
SOLNSuy[1, 1] := 2.5872902469406659197*10^(-20)-.65694549571241255901*y+1.9708364871372376767*y^2-1.3138909914248251176*y^3-1.6010739356637904911*10^(-19)*y^4;
SOLNSuy[2, 1] := -4.002204462000*10^(-20)-1.7879176897079605225*y+5.3637530691192141414*y^2-3.5758353794044226250*y^3-6.8309939211286845440*10^(-12)*y^4;
SOLNSuy[3, 1] := -1.1953264450000*10^(-19)-3.2481690589079594122*y+9.7445071767154794599*y^2-6.4963381177952273213*y^3-1.2292726248071398400*10^(-11)*y^4;
SOLNSuy[4, 1] := -2.6720465500000*10^(-19)-4.9239979672954025921*y+14.771993901873204315*y^2-9.8479959345587718955*y^3-1.9029826928878336000*10^(-11)*y^4;
SOLNSuy[5, 1] := 3.416928541000*10^(-20)-6.7268498492441931137*y+20.180549547714413714*y^2-13.453699698443639810*y^3-2.6580790570532587008*10^(-11)*y^4;
SOLNSuy[6, 1] := -2.554122292000*10^(-20)-8.5884528335125514887*y+25.765358500514014457*y^2-17.176905666966875698*y^3-3.4587270427710613504*10^(-11)*y^4;
SOLNSuy[7, 1] := -9.206107680000*10^(-20)-10.456823708331499352*y+31.370471124965259849*y^2-20.913647416590986491*y^3-4.2774005353527132160*10^(-11)*y^4;
SOLNSuy[8, 1] := 1.9644186790000*10^(-19)-12.293003938471349390*y+36.879011815379230436*y^2-24.586007876856948223*y^3-5.0932823222176363520*10^(-11)*y^4;
SOLNSuy[9, 1] := -3.775112769000*10^(-19)-14.068404975282556550*y+42.205214925807397100*y^2-28.136809950465931724*y^3-5.8908824448577377280*10^(-11)*y^4;
SOLNSuy[10, 1] := 1.146281780000*10^(-19)-15.762658869974768890*y+47.287976609878780960*y^2-31.525317739837422477*y^3-6.6589592851037286400*10^(-11)*y^4;
plots[animate](plot, [SOLNSuy[A, 1], y = 0 .. 1], A = 1 .. 10);

Special request:
@acer @Carl Love @Kitonum @Preben Alsholm

Drawing fireworks with Maple

by: mmcdara 7891 Maple 2015
animation
December 25 2019
10  3

Here is a little animation to wish all of you a Merry Christmas

FireWorks.mw


How to follow an hyperlink ?...

Asked by: mmcdara 7891
documenttools hyperlink
December 24 2019
0  4

Hi, 

 

In help page DocumentTools:-Layout:-Font, there is an example which shows how to inser a hyperlink in a Layout.

F := Font( "Some text", size=16, color=blue, style=:-Hyperlink ):
InsertContent(Worksheet(Group(Input(Textfield( F ))))):
 

When this id done, how can we activate this hyperlink ?
5I'm presently working with Maple 2015.2 under Mac OS Mojave)

Thanks in advance

 

Why don't the sliders work?...

Asked by: mmcdara 7891
explore
December 16 2019
0  8

Hi, 

Moving the sliders clean the plot.
Does any one can show me how to fix this (PS: this piece of code is a part of a procedure whose arguments are RV and SliderRanges and I need this unusual coding to make the procedure generic ... at least I guess so)

Thanks in advance


 

> 

restart:
> 

interface(version);

`Standard Worksheet Interface, Maple 2015.2, Mac OS X, December 21 2015 Build ID 1097895`

 (1)
> 

with(Statistics):
> 

RV   := RandomVariable(Normal(a, b)):
law  := [attributes(RV)][3]:
pars := law:-Parameters;

[a, b]

 (2)
> 

SliderRanges := [-5.0..5.0, 1.0..3.0]:
[seq(pars[k]=SliderRanges[k], k=1..numelems(pars))]

[a = -5.0 .. 5.0, b = 1.0 .. 3.0]

 (3)
> 

f := PDF(RV, x);
# Explore(plot(f, x=-3..3), parameters=[seq(pars[k]=SliderRanges[k], k=1..numelems(pars))]);

(1/2)*2^(1/2)*exp(-(1/2)*(x-a)^2/b^2)/(Pi^(1/2)*b)

 (4)
> 

 


 

Download Explore_Problem.mw

Why doesn't dsolve[events] return the good result...

Asked by: mmcdara 7891
events dsolve numeric
December 12 2019
1  3

Hi,

Why extracting the features of the events doesn't return the good results when executed within a loop (see the pink test) ?

Thanks in advance.

PS: please, spare me  replies of the type "you can solve this equation formally"

 

> 

restart;
> 

interface(version);

`Standard Worksheet Interface, Maple 2015.2, Mac OS X, December 21 2015 Build ID 1097895`

 (1)
> 

sys := { diff(x(t), t) = 1, x(0) = 0 }:
evs := [ [x(t)-0.1, none],  [x(t)-0.3, none], [x(t)-0.5, none] ]:
sol := dsolve(sys, numeric, events=evs):

plots:-odeplot(sol, [t, x(t)], t=0..0.5, gridlines=true);

 
> 

# times that fired the events

sol(1): # initialization

sol(eventfired=[1]);
sol(eventfired=[2]);
sol(eventfired=[3]);
 

[HFloat(0.1)]

  

[HFloat(0.3)]

  

[HFloat(0.49999999999999994)]

 (2)
> 

# Same times computed  within a loop

for i from 1 to 3 do
  te := op(sol(eventfired=[i]));
end do;

HFloat(0.1)

  

HFloat(0.3)

  

HFloat(0.49999999999999994)

 (3)
> 

# Values of x(t) computed  within a loop
#
# Why are calues for events 2 and 3 wrong ?
for i from 1 to 3 do
  te := op(sol(eventfired=[i]));
# xe := sol(te);             # this doesn't return the correct result,
# xe := subs(sol(te), x(t)); # this doesn't work neither
  xe := eval(x(t), sol(te)); # this doesn't work neither
end do;

HFloat(0.1)

  

HFloat(0.1)

  

HFloat(0.0)

  

HFloat(0.0)

  

HFloat(0.0)

  

HFloat(0.0)

 (4)
> 

 


 

Download Incomprehensible.mw

 

How do I plot a hyperbola in polar with no asympto...

Asked by: dhamill 15
asymptote polarplot plotting
December 06 2019
3  3

I would like to plot a hyperbola using the polarplot command, such as the following:

polarplot(3/(1-1.5*sin(theta)), coordinateview = [0 .. 10, 0 .. 2*Pi])

But the graph includes the asymptotes, which I would not like to be included. I have tried the discont=true command, but it completely changes the shape of the graph and no longer looks like a hyperbola:

polarplot(3/(1-1.5*sin(theta)), coordinateview = [0 .. 10, 0 .. 2*Pi], discont = true)

 How would I get the hyperbola above to display with no asymptotes?

Thanks

is there any library or tools to design index of G...

Asked by: LeeHoYeung 535
November 16 2019
0  0

is there any library or tools to design index of Grassmannian and its k and n for Schubert use?

is there any library to relate poset with index of Grassmannian and its k and n for Schubert use

how I solve a Hard Triple Integral?...

Asked by: AYOUB ED-DAHMOUNY 5
integration numeric
November 09 2019
1  0

hello everyone,
   INGT.mw
 

L__d := 100:

L__b := 200:

L__c := L__d+(1/2)*L__b;

200

 (1)

X := .3;

.3

 (2)

Error, (in plot) procedure expected, as range contains no plotting variable

  

`ΔE__g` := 1.155*X+.37*X^2;

.3798

 (3)

V__0 := .6*`ΔE__g`;

.22788

 (4)

m__D := 0.67e-1*m[e];

0.67e-1*m[e]

 (5)

m__B := (0.67e-1+0.83e-1*X)*m[e];

0.919e-1*m[e]

 (6)

Sol := solve(2*cos(L__d*sqrt(E__x))+(m__D*sqrt((V__0-E__x)/E__x)/m__B-m__B*sqrt(E__x/(V__0-E__x))/m__D)*sin(L__d*sqrt(E__x))-(m__D*sqrt((V__0-E__x)/E__x)/m__B+m__B*sqrt(E__x/(V__0-E__x))/m__D)*sin(L__d*sqrt(E__x))*exp(-sqrt(V__0-E__x)*L__b) = 0, E__x);

0.1110897170e-2, 0.3531161505e-2, -.2585338615+0.9991335677e-27*I

 (7)

 

0.1110897170e-2, 0.3531161505e-2, -.2585338615+0.9991335677e-27*I

 (8)

E__1 := 0.1110897170e-2:

K__1 := sqrt(E__1);

0.3333012406e-1

 (9)

K__2 := sqrt(V__0-E__1);

.4762027959

 (10)

C := cosh((1/2)*K__2*L__b);

0.2399908351e21

 (11)

beta := m__D*K__2/(m__B*K__1);

10.41631973

 (12)

B := -beta*sinh((1/2)*K__2*L__b);

-0.2499821271e22

 (13)

A := -B*sin(K__1*L__d)+C*cos(K__1*L__d);

-0.7112056933e21

 (14)

h := proc (x) options operator, arrow; piecewise(x <= -L__c, A*exp(K__2*(x+L__c)), -L__c < x and x < -(1/2)*L__b, -B*sin(K__1*(x+(1/2)*L__b))+C*cos(K__1*(x+(1/2)*L__b)), abs(x) <= (1/2)*L__b, (1/2)*exp(K__2*x)+(1/2)*exp(-K__2*x), (1/2)*L__b < x and x < L__c, -B*sin(K__1*(x-(1/2)*L__b))+C*cos(K__1*(x-(1/2)*L__b)), L__c <= x, A*exp(K__2*(x-L__c))) end proc:

'h(x)' = h(x);

h(x) = piecewise(x <= -200, -7.112056933*10^20*exp(95.24055918+.4762027959*x), -200 < x and x < -100, 2.499821271*10^21*sin(3.333012406+0.3333012406e-1*x)+2.399908351*10^20*cos(3.333012406+0.3333012406e-1*x), abs(x) <= 100, (1/2)*exp(.4762027959*x)+(1/2)*exp(-.4762027959*x), 100 < x and x < 200, 2.499821271*10^21*sin(0.3333012406e-1*x-3.333012406)+2.399908351*10^20*cos(0.3333012406e-1*x-3.333012406), 200 <= x, -7.112056933*10^20*exp(-95.24055918+.4762027959*x))

 (15)

L__y := 200:

L__z := 200:

P := proc (x, y, z) options operator, arrow; h(x)*cos(Pi*y/L__y)*cos(Pi*z/L__z) end proc:

'Psi(x, y, z)' = P(x, y, z);

Psi(x, y, z) = piecewise(x <= -200, -7.112056933*10^20*exp(95.24055918+.4762027959*x), -200 < x and x < -100, 2.499821271*10^21*sin(3.333012406+0.3333012406e-1*x)+2.399908351*10^20*cos(3.333012406+0.3333012406e-1*x), abs(x) <= 100, (1/2)*exp(.4762027959*x)+(1/2)*exp(-.4762027959*x), 100 < x and x < 200, 2.499821271*10^21*sin(0.3333012406e-1*x-3.333012406)+2.399908351*10^20*cos(0.3333012406e-1*x-3.333012406), 200 <= x, -7.112056933*10^20*exp(-95.24055918+.4762027959*x))*cos((1/200)*Pi*y)*cos((1/200)*Pi*z)

 (16)

INGT := proc (x__i) `assuming`([evalf(int(int(int(P(x, y, z)^2*exp(-lambda*sqrt((x-x__i)^2+y^2+z^2)), x = -infinity .. infinity), y = -L__y .. L__y), z = -L__z .. L__z))], [0 < lambda]) end proc

evalf(INGT(2))

``

Warning,  computation interrupted

  

``


 

Download INGT.mw
 

L__d := 100:

L__b := 200:

L__c := L__d+(1/2)*L__b;

200

 (1)

X := .3;

.3

 (2)

Error, (in plot) procedure expected, as range contains no plotting variable

  

`&Delta;E__g` := 1.155*X+.37*X^2;

.3798

 (3)

V__0 := .6*`&Delta;E__g`;

.22788

 (4)

m__D := 0.67e-1*m[e];

0.67e-1*m[e]

 (5)

m__B := (0.67e-1+0.83e-1*X)*m[e];

0.919e-1*m[e]

 (6)

Sol := solve(2*cos(L__d*sqrt(E__x))+(m__D*sqrt((V__0-E__x)/E__x)/m__B-m__B*sqrt(E__x/(V__0-E__x))/m__D)*sin(L__d*sqrt(E__x))-(m__D*sqrt((V__0-E__x)/E__x)/m__B+m__B*sqrt(E__x/(V__0-E__x))/m__D)*sin(L__d*sqrt(E__x))*exp(-sqrt(V__0-E__x)*L__b) = 0, E__x);

0.1110897170e-2, 0.3531161505e-2, -.2585338615+0.9991335677e-27*I

 (7)

 

0.1110897170e-2, 0.3531161505e-2, -.2585338615+0.9991335677e-27*I

 (8)

E__1 := 0.1110897170e-2:

K__1 := sqrt(E__1);

0.3333012406e-1

 (9)

K__2 := sqrt(V__0-E__1);

.4762027959

 (10)

C := cosh((1/2)*K__2*L__b);

0.2399908351e21

 (11)

beta := m__D*K__2/(m__B*K__1);

10.41631973

 (12)

B := -beta*sinh((1/2)*K__2*L__b);

-0.2499821271e22

 (13)

A := -B*sin(K__1*L__d)+C*cos(K__1*L__d);

-0.7112056933e21

 (14)

h := proc (x) options operator, arrow; piecewise(x <= -L__c, A*exp(K__2*(x+L__c)), -L__c < x and x < -(1/2)*L__b, -B*sin(K__1*(x+(1/2)*L__b))+C*cos(K__1*(x+(1/2)*L__b)), abs(x) <= (1/2)*L__b, (1/2)*exp(K__2*x)+(1/2)*exp(-K__2*x), (1/2)*L__b < x and x < L__c, -B*sin(K__1*(x-(1/2)*L__b))+C*cos(K__1*(x-(1/2)*L__b)), L__c <= x, A*exp(K__2*(x-L__c))) end proc:

'h(x)' = h(x);

h(x) = piecewise(x <= -200, -7.112056933*10^20*exp(95.24055918+.4762027959*x), -200 < x and x < -100, 2.499821271*10^21*sin(3.333012406+0.3333012406e-1*x)+2.399908351*10^20*cos(3.333012406+0.3333012406e-1*x), abs(x) <= 100, (1/2)*exp(.4762027959*x)+(1/2)*exp(-.4762027959*x), 100 < x and x < 200, 2.499821271*10^21*sin(0.3333012406e-1*x-3.333012406)+2.399908351*10^20*cos(0.3333012406e-1*x-3.333012406), 200 <= x, -7.112056933*10^20*exp(-95.24055918+.4762027959*x))

 (15)

L__y := 200:

L__z := 200:

P := proc (x, y, z) options operator, arrow; h(x)*cos(Pi*y/L__y)*cos(Pi*z/L__z) end proc:

'Psi(x, y, z)' = P(x, y, z);

Psi(x, y, z) = piecewise(x <= -200, -7.112056933*10^20*exp(95.24055918+.4762027959*x), -200 < x and x < -100, 2.499821271*10^21*sin(3.333012406+0.3333012406e-1*x)+2.399908351*10^20*cos(3.333012406+0.3333012406e-1*x), abs(x) <= 100, (1/2)*exp(.4762027959*x)+(1/2)*exp(-.4762027959*x), 100 < x and x < 200, 2.499821271*10^21*sin(0.3333012406e-1*x-3.333012406)+2.399908351*10^20*cos(0.3333012406e-1*x-3.333012406), 200 <= x, -7.112056933*10^20*exp(-95.24055918+.4762027959*x))*cos((1/200)*Pi*y)*cos((1/200)*Pi*z)

 (16)

INGT := proc (x__i) `assuming`([evalf(int(int(int(P(x, y, z)^2*exp(-lambda*sqrt((x-x__i)^2+y^2+z^2)), x = -infinity .. infinity), y = -L__y .. L__y), z = -L__z .. L__z))], [0 < lambda]) end proc

evalf(INGT(2))

``

Warning,  computation interrupted

  

``


 

Download INGT.mw

 

I'm trying to calculate a triple integral complicated by a procedure that changes each time a variable xi, while the program takes a lot of time and it gives me the message "Warning, computation interrupted". If anyone can help me I will be very happy

i can't find our where my error is......

Asked by: mmcdara 7891
linear-algebra dot-product
October 20 2019
2  9

Hi,

Sorry to ask such a stupid question but I can't find out where my error is. Probably it's so huge it blinds me!

The double loop and the matrix product F^+ . F should give the same result, no? (it seems that F^+ . F has its rows reordered ?)


 

> 

restart:
> 

N   := 3:
P   := 2:
niv := [seq(Z[i], i=1..N)];
f   := Matrix(N^P, P, (i,j) -> `if`(j=P, niv[(i mod 3)+1], niv[iquo(i-1,3)+1]));

niv := [Z[1], Z[2], Z[3]]

  

f := Matrix(9, 2, {(1, 1) = Z[1], (1, 2) = Z[2], (2, 1) = Z[1], (2, 2) = Z[3], (3, 1) = Z[1], (3, 2) = Z[1], (4, 1) = Z[2], (4, 2) = Z[2], (5, 1) = Z[2], (5, 2) = Z[3], (6, 1) = Z[2], (6, 2) = Z[1], (7, 1) = Z[3], (7, 2) = Z[2], (8, 1) = Z[3], (8, 2) = Z[3], (9, 1) = Z[3], (9, 2) = Z[1]})

 (1)
> 

ds := subs(niv =~ [$0..N-1], f);

ds := Matrix(9, 2, {(1, 1) = 0, (1, 2) = 1, (2, 1) = 0, (2, 2) = 2, (3, 1) = 0, (3, 2) = 0, (4, 1) = 1, (4, 2) = 1, (5, 1) = 1, (5, 2) = 2, (6, 1) = 1, (6, 2) = 0, (7, 1) = 2, (7, 2) = 1, (8, 1) = 2, (8, 2) = 2, (9, 1) = 2, (9, 2) = 0})

 (2)
> 

vs := [ seq(V__||i, i=1..P)]:
es := unapply( sort( [ seq( mul(vs ^~ [entries(ds[i,..], nolist)]), i=1..N^P) ] ), vs);
 

proc (V__1, V__2) options operator, arrow; [1, V__1, V__2, V__1^2, V__2^2, V__1*V__2, V__1*V__2^2, V__1^2*V__2, V__1^2*V__2^2] end proc

 (3)
> 

ff := convert([ seq(es(entries(ffd[i,..], nolist)), i=1..N^P) ], Matrix);


UnityRoots := [solve(z^3=1, z)]:
F := simplify(subs(niv =~ UnityRoots, ff)) /~ sqrt(N^P):

ff := Matrix(9, 9, {(1, 1) = 1, (1, 2) = Z[1], (1, 3) = Z[2], (1, 4) = Z[1]^2, (1, 5) = Z[2]^2, (1, 6) = Z[1]*Z[2], (1, 7) = Z[1]*Z[2]^2, (1, 8) = Z[1]^2*Z[2], (1, 9) = Z[1]^2*Z[2]^2, (2, 1) = 1, (2, 2) = Z[1], (2, 3) = Z[3], (2, 4) = Z[1]^2, (2, 5) = Z[3]^2, (2, 6) = Z[1]*Z[3], (2, 7) = Z[1]*Z[3]^2, (2, 8) = Z[1]^2*Z[3], (2, 9) = Z[1]^2*Z[3]^2, (3, 1) = 1, (3, 2) = Z[1], (3, 3) = Z[1], (3, 4) = Z[1]^2, (3, 5) = Z[1]^2, (3, 6) = Z[1]^2, (3, 7) = Z[1]^3, (3, 8) = Z[1]^3, (3, 9) = Z[1]^4, (4, 1) = 1, (4, 2) = Z[2], (4, 3) = Z[2], (4, 4) = Z[2]^2, (4, 5) = Z[2]^2, (4, 6) = Z[2]^2, (4, 7) = Z[2]^3, (4, 8) = Z[2]^3, (4, 9) = Z[2]^4, (5, 1) = 1, (5, 2) = Z[2], (5, 3) = Z[3], (5, 4) = Z[2]^2, (5, 5) = Z[3]^2, (5, 6) = Z[2]*Z[3], (5, 7) = Z[2]*Z[3]^2, (5, 8) = Z[2]^2*Z[3], (5, 9) = Z[2]^2*Z[3]^2, (6, 1) = 1, (6, 2) = Z[2], (6, 3) = Z[1], (6, 4) = Z[2]^2, (6, 5) = Z[1]^2, (6, 6) = Z[1]*Z[2], (6, 7) = Z[1]^2*Z[2], (6, 8) = Z[1]*Z[2]^2, (6, 9) = Z[1]^2*Z[2]^2, (7, 1) = 1, (7, 2) = Z[3], (7, 3) = Z[2], (7, 4) = Z[3]^2, (7, 5) = Z[2]^2, (7, 6) = Z[2]*Z[3], (7, 7) = Z[2]^2*Z[3], (7, 8) = Z[2]*Z[3]^2, (7, 9) = Z[2]^2*Z[3]^2, (8, 1) = 1, (8, 2) = Z[3], (8, 3) = Z[3], (8, 4) = Z[3]^2, (8, 5) = Z[3]^2, (8, 6) = Z[3]^2, (8, 7) = Z[3]^3, (8, 8) = Z[3]^3, (8, 9) = Z[3]^4, (9, 1) = 1, (9, 2) = Z[3], (9, 3) = Z[1], (9, 4) = Z[3]^2, (9, 5) = Z[1]^2, (9, 6) = Z[1]*Z[3], (9, 7) = Z[1]^2*Z[3], (9, 8) = Z[1]*Z[3]^2, (9, 9) = Z[1]^2*Z[3]^2})

 (4)

Scalar products of pairs of comumn vectors

F must be an orthogonal array

> 

for i1 from 1 to N^P do
  for i2 from 1 to N^P do
    printf("%a ", simplify(add(F[..,i1] . F[.., i2])))
  end do:
  printf("\n"):
end do:
printf("\n");

1 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0
0 0 0 0 1 0 0 0 0
0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 1
 

  

or more simply:

> 

simplify(F^+ . F)

Matrix([[1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0]])

 (5)
> 

 


 

Download Too_Blind_To_Find_My_Mistake.mw

How to put a symbol (like greek) before a variable...

Asked by: RHERWOLF 62
October 17 2019
2  4

Can I do something like it?

op command does not work!!!...

Asked by: Muhammad Usman 240
assign assignment set
October 15 2019
0  5

Dear Users!
Hope everyone is fine here. I have some questions about the following code:

Sol := {u[1, 1, 1, 1] = 0.2754389666e-1, u[1, 1, 1, 2] = 0.1305849194e-1, u[1, 1, 1, 3] = 0.2886163307e-2, u[1, 1, 1, 4] = -0.7346547512e-3, u[1, 1, 2, 1] = 0.4659732849e-1, u[1, 1, 2, 2] = 0.1466736306e-1, u[1, 1, 2, 3] = 0.2615590961e-3, u[1, 1, 2, 4] = -0.2999417306e-2, u[1, 2, 1, 1] = 0.4659732850e-1, u[1, 2, 1, 2] = 0.1466736306e-1, u[1, 2, 1, 3] = 0.2615590934e-3, u[1, 2, 1, 4] = -0.2999417305e-2, u[1, 2, 2, 1] = 0.7816751150e-1, u[1, 2, 2, 2] = 0.1319905841e-1, u[1, 2, 2, 3] = -0.3594991974e-2, u[1, 2, 2, 4] = -0.6810219469e-2, u[2, 1, 1, 1] = 0.4277449264e-1, u[2, 1, 1, 2] = -0.7962732407e-2, u[2, 1, 1, 3] = -0.1373208839e-1, u[2, 1, 1, 4] = -0.2756504221e-2, u[2, 1, 2, 1] = 0.7104313232e-1, u[2, 1, 2, 2] = -0.2934293200e-1, u[2, 1, 2, 3] = -0.1500623941e-1, u[2, 1, 2, 4] = -0.3113543133e-2, u[2, 2, 1, 1] = 0.7104313230e-1, u[2, 2, 1, 2] = -0.2934293199e-1, u[2, 2, 1, 3] = -0.1500623942e-1, u[2, 2, 1, 4] = -0.3113543128e-2, u[2, 2, 2, 1] = .1180017068, u[2, 2, 2, 2] = -0.7162229544e-1, u[2, 2, 2, 3] = -0.8898045960e-2, u[2, 2, 2, 4] = -0.9223166732e-2};
My aim is to write all the entries in Sol like the following way

u[1, 1, 1, 1] := 0.2754389666e-1;

u[1, 1, 1, 2] := 0.1305849194e-1;

u[1, 1, 1, 3] := 0.2886163307e-2;

and so on. For this I used the following logic (op command)

for i from 1 by 1 while i <= 32 do

lhs(op(i, Sol)) := rhs(op(i, Sol))

end do;
But it cant work. Please help me to solve my matter. I shall be greatful to you for your positive response. Please take care and thanks in advance.

Special request

@acer @Carl Love @Kitonum @Preben Alsholm

How to plot selected point from a set of points...

Asked by: Muhammad Usman 240
norm pointplot3d pointplot
October 10 2019
0  0

Dear Users!

Hoped everyone fine here. I have three main questions regarding the maple code given bellow:

restart; with(LinearAlgebra); with(plots);

alpha := 1; beta := 1; theta := 1/2;

UU := sinh(x)*sinh(y)*sinh(z)*exp(-1.*t);

NN := 3; L := 0; R := 1; T := 1; N := NN; Mx := NN; My := NN; Mz := NN; `&Delta;x` := (R-L)/Mx; `&Delta;y` := (R-L)/My; `&Delta;z` := (R-L)/Mz; `&Delta;t` := (R-L)/N;

kappa[1] := 1; kappa[2] := 2/x^2; kappa[3] := 1/x^2; kappa[X] := x^2+y^2+z^2+1; kappa[Y] := x^2+y^2+z^2+1; kappa[Z] := x^2+y^2+z^2+1; kappa[4] := 0; NL := 3;

ics := [seq(seq(seq([u[i, j, k, 0] = eval(UU, [x = i*`&Delta;x`, y = j*`&Delta;y`, z = k*`&Delta;z`, t = 0]), u[i, j, k, -1] = eval(u[i, j, k, 1]-2*`&Delta;t`*(eval(diff(UU, t), t = 0)), [x = i*`&Delta;x`, y = j*`&Delta;y`, z = k*`&Delta;z`, t = 0])][], i = 0 .. Mx), j = 0 .. My), k = 0 .. Mz)];

bcs := [seq(seq(seq([u[0, j, k, n] = eval(UU, [x = 0, y = j*`&Delta;y`, z = k*`&Delta;z`, t = n*`&Delta;t`]), u[Mx, j, k, n] = eval(UU, [x = L, y = j*`&Delta;y`, z = k*`&Delta;z`, t = n*`&Delta;t`])][], j = 0 .. My), k = 0 .. Mz), n = 1 .. N), seq(seq(seq([u[i, 0, k, n] = eval(UU, [x = i*`&Delta;x`, y = 0, z = k*`&Delta;z`, t = n*`&Delta;t`]), u[i, My, k, n] = eval(UU, [x = i*`&Delta;x`, y = L, z = k*`&Delta;z`, t = n*`&Delta;t`])][], i = 1 .. Mx-1), k = 0 .. Mz), n = 1 .. N), seq(seq(seq([u[i, j, 0, n] = eval(UU, [x = i*`&Delta;x`, y = j*`&Delta;y`, z = 0, t = n*`&Delta;t`]), u[i, j, Mz, n] = eval(UU, [x = i*`&Delta;x`, y = j*`&Delta;y`, z = L, t = n*`&Delta;t`])][], i = 1 .. Mx-1), j = 1 .. My-1), n = 1 .. N)];
Sol := {u[1, 1, 1, 1] = 0.2366497936e-1, u[1, 1, 1, 2] = 0.7589975856e-2, u[1, 1, 1, 3] = 0.6029906475e-3, u[1, 1, 2, 1] = 0.3778786317e-1, u[1, 1, 2, 2] = 0.7126415819e-2, u[1, 1, 2, 3] = -0.1197885714e-2, u[1, 2, 1, 1] = 0.3778786315e-1, u[1, 2, 1, 2] = 0.7126415820e-2, u[1, 2, 1, 3] = -0.1197885718e-2, u[1, 2, 2, 1] = 0.6038763054e-1, u[1, 2, 2, 2] = 0.4264591907e-2, u[1, 2, 2, 3] = -0.3509477851e-2, u[2, 1, 1, 1] = 0.3171958616e-1, u[2, 1, 1, 2] = -0.1327161715e-1, u[2, 1, 1, 3] = -0.4628647419e-2, u[2, 1, 2, 1] = 0.4979852397e-1, u[2, 1, 2, 2] = -0.3060811899e-1, u[2, 1, 2, 3] = -0.344914876e-4, u[2, 2, 1, 1] = 0.4979852397e-1, u[2, 2, 1, 2] = -0.3060811898e-1, u[2, 2, 1, 3] = -0.3449150010e-4, u[2, 2, 2, 1] = 0.7882396741e-1, u[2, 2, 2, 2] = -0.6192340018e-1, u[2, 2, 2, 3] = 0.1156615222e-1}

Using set of points given in ics, bcs and Sol

1. I want to contruct a vector at any time level (by fixing fourth suffix like u[i,j,k,n]) for i = 0..Mx,j=0..My,k=0..Mz and then find its L2 and L[infinity] norms.

2. Next I want contruct a vector by fixing two suffixes like u[i,j,k,n]) for i = 0..Mx,j=0..My and plot a surface in 3D

3. Finally I want to construct a vector by fixing three suffixes like u[i,j,k,n]) for i = 0..Mx, and plot a curve in 2D.

I'm waiting for your positive respone. I shall be very thankfull to you in advance.

Special request to:
@acer @Carl Love @Kitonum @Preben Alsholm

How to define an absolute color scale in matrixplo...

Asked by: mmcdara 7891
matrixplot plotting surfdata
September 21 2019
0  5

Hi, 

I need to plot some correlation matrices C1, C2, ... and I use matrixplot for this.
I would like to use the same absolute scale (-1..+1) for all of them.
For instance is I decide to uses colorscheme=["blue", "white", "red"] I would like blue to correspond to value -1, white to value 0 and red to value 1.
Unfortunately colorscheme set to blue the cell with the mininum value (not necessarily -1) and to red the maximum one (not necessarily +1).
Here is an example

restart:
with(plots):
with(Statistics):
randomize():
N := 10:
P := 3:
A := Sample(Uniform(0, 1), [N, P]):
C := CorrelationMatrix(A):
matrixplot(
  C,
 heights=histogram,
 axes=frame,
​​​​​​​  gap=0.25,
​​​​​​​  color=((x,y)->(C[x,y]+1)/2),
​​​​​​​  orientation=[0, 0, 0],
​​​​​​​  lightmodel=none,
​​​​​​​  tickmarks=[[seq(i+1/2=A||i, i=1..P)], [seq(i+1/2=A||i, i=1..P)], default],
​​​​​​​  labels=[("")$3]​​​​​​​
​​​​​​​  );


​​​​​​​I also tried to use color=((x,y) -> (C[x, y]+1)/2) instead of colorscheme but here again matrixplot uses a local scale defined by the reange of the correlation matrix to plot.

I fixed this by using something like seq(seq(PLOT(POLYGONS(...), i=1..P), j=1..P) instead of matrixplot, but I think it is a shame to do so.

So my question: is it possible to force matrixplot not to use a scale defined by the matrix to plot, but a "user" scale?

PS: I'm using Maple 2015 

Thanks in advance

Problem in finding the solution of linear algebrai...

Asked by: Muhammad Usman 240
fsolve
September 09 2019
0  2

Dear Users!

Hope you would be fine with everything. I want to find the solution of linear algebric equations but fsolve command not working please see and fix this problem. I shall be very thankful.

C[0] := 3.19153824321146142351956847947*tau[1]-19.1492294592687685411174108768*tau[2]+111.703838512401149823184896781*tau[3]+3.19153824321146142351956847947*tau[4]-44.6815354049604599292739587124*tau[5]+622.349957426234977586315853494*tau[6];
C[1] := 51.0646118913833827763130956714*tau[2]-612.775342696600593315757148056*tau[3]+51.0646118913833827763130956714*tau[5]-1429.80913295873471773676667880*tau[6];
C[2] := -1.06073680388443795908856507616+3.19153824321146142351956847947*tau[1]+53.1609155734306093706448370717*tau[2]+1672.89412862088744108725223170*tau[3]+3.19153824321146142351956847947*tau[4]+27.6286096277389179824882892361*tau[5]+1026.57792701153122226218722129*tau[6];
C[3] := -1.08847004231036963538035920033+3.19153824321146142351956847947*tau[1]+62.6399144226357196540662623767*tau[2]+2040.52109049201342887896297462*tau[3]+3.19153824321146142351956847947*tau[4]+37.1076084769440282659097145411*tau[5]+1242.54090729537544551915515930*tau[6];
C[4] := -1.05523181556926815105314303389+3.19153824321146142351956847947*tau[1]+72.7671212023804312453829273862*tau[2]+2472.93216226733267613216245895*tau[3]+3.19153824321146142351956847947*tau[4]+47.2348152566887398572263795506*tau[5]+1512.91667059477930731128800348*tau[6];
C[5] := -.922876006485286011069063957991+3.19153824321146142351956847947*tau[1]+82.9822841707707093164204255644*tau[2]+2971.36790137532483139495115633*tau[3]+3.19153824321146142351956847947*tau[4]+57.4499782250790179282638777288*tau[5]+1847.90980220852701343747673000*tau[6];

fsolve({seq(`$`(C[l1], l1 = 0 .. 5))});

Special request to:
@acer @Carl Love @Kitonum @Preben Alsholm

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