In Maple15, in spherical coordinates, what statements plot covariant vector [1,r^2*sin(theta),sin^2(theta)] and its contravariant equivalent [1,sin(theta),1/r^2] within their respective bases vectors. Assume r = 2, theta = pi/6 and phi = pi/4. I presume each plot will display the same space vector.

Hi I'm new to maple

I wanted to use dsolve to solve and equation but instead of getting an answer, maple returns an integration.

What could the promblem be?

Thanks

I try to save results of numeric integration of ODE, returned by dsolve. I address very simple equation and before saving all works as needed:

S1 := dsolve([diff(z(x), x$2)+z(x) = -2, z(0)=0, z(1)=1], z(x), 'numeric', 'output' = listprocedure);

F1 := unapply(rhs(S1[2])(x), x); plot(F1, 0..1, thickness=3);

Next I save solution S1 by save operator:

save S1,  filename;

S1 saved and likely looks correctly:

S1 := [x = proc (x) local _res, _dat, _solnproc; option
`Copyright (c) 1993 by the University of Waterloo. All rights reserved.`; _dat
:= Array(1..4, {1 = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; ........................................................

Operator read reads S1 from file:
read filename;

but

F1 := unapply(rhs(S1[2])(x), x);

returns an error:

Error, (in unknown) invalid input: the 1st argument to pointto is not a valid pointer handle

How to save solution correctly?

M := Matrix([[0,1,1,1,1],[1,0,1,1,1],[1,1,0,1,1],[1,1,1,0,1],[1,1,1,1,0]]);

how to multiply M[1] which is [0,1,1,1,1] with Matrix([[x0], [x1], [x2], [x3], [x4]])
to become [0,x1,x2,x3,x4]

may not use Matrix([[x0], [x1], [x2], [x3], [x4]])

just want to use first element as x0 when it is not 0

second element as x1, etc

Hello friends,

I try to write a loop in Maple.

The equation is f (x) = x + 3

x is a variable and should be from 50 to 70 with dx = 5 can be used in the function, so that f (x) is to be determined.

How can I write such a loop?

Hi

y''+(4/x)*y'-a*y^n=0

that a=constant

LM:=proc(n)
local L;
uses combinat;
L:=permute([1$(n*(n-1)/2), 0$(n*(n-1)/2)], n*(n-1)/2);
[seq(Matrix(n,{seq(seq((i+1,j)=L[k][(i-1)*i/2+j], j=1..i), i=1..n-1)}, shape=symmetric), k=1..nops(L))];
end proc:
M := LM(5);
N := nops(M);
append("E:\\mm.txt");
for i from 1 to N do
ExportMatrix( "E://mm.txt", M[i]);
od:

hope to export to a text file

and show

for example

matrix([[1,1,1],[1,1,0],[0,0,0]]);

matrix([[1,1,1],[1,1,0],[0,0,0]]);

matrix([[1,1,1],[1,1,0],[0,0,0]]);

...

etc

is it possible to generalize a function to a combinatorial level for approximate axioms

for example, first 100 or 1000 data points satisfy axioms

or 100% satisfy a axioms which means satisfy to infinity

because i find data always not exactly satisfy the axioms,
i guess it only satisfy to some limit, this may explain why data has decimal number

or conversely is it possible to generalize some axioms which approximate the original exact axioms
then data can exactly satisfy the approximate axioms

can generalize a nested forloop to achieve this goal?

how can it be done in algebra point of view?

For example:

x*y = for loop -> for loop -> i*j

it can change for loop expression into algebra

for i from 1 to 10 do
for j from 1 to 10 do
print i*j
od:
od:

how to solve this eq by maple:

P:=Matrix([[ 0 , .5 , .5 , 0 , 0 , 0 ], [ 1/3 , 0 , 0 , 1/3 , 1/3 , 0 ], [ 1/3 , 0 , 0 , 0 , 1/3 , 1/3 ], [ 0 , 1 , 0 , 0 , 0 , 0 ], [ 0 , .5 , .5 , 0 , 0 , 0 ], [ 0 , 0 , 1 , 0 , 0 , 0 ]]);

pii:=Vector[row]([ a , b , c , d , e , f ])

how to find

pii.P=pii

Silaws

Hi

 Mt := 1-(sum(4*l^2*exp(-beta[n]^2*tau)/(beta[n]^2*(l^2+beta[n]^2)), n = 1 .. infinity))

where the beta[n]s   are  roots of :

beta[n]*BesselJ(1, beta[n])-l*BesselJ(0, beta[n]) = 0

for  l=1,10,20,40,50,100

I want to plot Mt vs. tou for these l 's  in one diagram

with(combinat); 

L:=permute([1$(n*(n-1)/2), 0$(n*(n-1)/2)], n*(n-1)/2);

Error, (in combinat:-permute) 2nd argument must be a non-negative integer

what is $ in permute?

let m3 = [[0; 1; 0]; [1; 0; 1]; [0; 1; 0]]

1. Firstly, express this matrix into sequence function expression

2. how to express this matrix in terms of forloop code

3. for complicated case such as 1 is not in easy pattern, can it intelligently express the matrix in terms of for loop code

is there exist extra tools to express matrix in terms of for loop code or sequence function code?

Hi,

I have a problem solving two equations.  They are as follows:

s := 1/(273.16+50); s1 := 1/(273.16+145); s3 := 1/(273.16+250); s2 := 1/(273.16+197.5); gamma0 := 0.1e-3; gamma1 := .5; gamma2 := 0.15e-2; beta := -3800:

c := 300; n := 200; tau1 := 99; tau2 := 120;

Delta := solve(1-exp(-(gam0*tau1+(1/2)*gam1*tau1^2)*exp(beta*s1)) = 1-exp(-(gam0*a+(1/2)*gam1*a^2)*exp(beta*s2)), a);
a := Delta[1];

Theta := solve(1-exp(-(gam0*(a+tau2-tau1)+(1/2)*gam1*(a+tau2-tau1)^2)*exp(beta*s2)) = 1-exp(-(gam0*b+(1/2)*gam1*b^2)*exp(beta*s3)), b);
b := Theta[1];

n1 := int((gam1*t+gam0)*exp(beta*s1)*exp(-(gam0*t+(1/2)*gam1*t^2)*exp(beta*s1)), t = 0 .. tau1);
n22 := (n-n1)*(int((gam1*t+gam0)*exp(beta*s2)*exp(-(gam0*t+(1/2)*gam1*t^2)*exp(beta*s2)), t = a1 .. a1+tau2-tau1));
n2 := eval(n22, a1 = a);
n33 := (n-n1-n2)*(Int((gam1*t+gam0)*exp(beta*s3)*exp(-(gam0*t+(1/2)*gam1*t^2)*exp(beta*s3)), t = b1 .. c));
n3 := eval(n33, a1 = a);
n4 := n-n1-n2-n3;

g1 := -n1*(Int((1/(gam1*t+gam0)-t*exp(beta*s1))*(gamma2*t^2+gamma1*t+gamma0)*exp(beta*s1)*exp(-(gamma0*t+(1/2)*gamma1*t^2+(1/3)*gamma2*t^3)*exp(beta*s1)), t = 0 .. tau1))-n2*(Int((1/(gam0+gam1*(a+t-tau1))-(a+t-tau1)*exp(beta*s2))*(gamma0+gamma1*(a+t-tau1)+gamma2*(a+t-tau1)^2)*exp(beta*s2)*exp(-(gamma0*(a+t-tau1)+(1/2)*gamma1*(a+t-tau1)^2+(1/3)*gamma2*(a+t-tau1)^3)*exp(beta*s2)), t = tau1 .. tau2))-n3*(Int((1/(gam0+gam1*(b+t-tau2))-(b+t-tau2)*exp(s3))*(gamma0+gamma1*(b+t-tau2)+gamma2*(b+t-tau2)^2)*exp(beta*s3)*exp(-(gamma0*(b+t-tau2)+(1/2)*gamma1*(b+t-tau2)^2+(1/3)*gamma2*(b+t-tau2)^3)*exp(beta*s3)), t = tau2 .. c))+(n-n1-n2-n3)*(1/(gam0+gam1*(b+c-tau2))-(b+c-tau2)*exp(s3))*(gamma0+gamma1*(b+c-tau2)+gamma2*(b+c-tau2)^2)*exp(beta*s3)*exp(-(gamma0*(b+c-tau2)+(1/2)*gamma1*(b+c-tau2)^2+(1/3)*gamma2*(b+c-tau2)^3)*exp(beta*s3));

g2 := -n1*(Int((t/(gam1*t+gam0)-(1/2)*t^2*exp(beta*s1))*(gamma2*t^2+gamma1*t+gamma0)*exp(beta*s1)*exp(-(gamma0*t+(1/2)*gamma1*t^2+(1/3)*gamma2*t^3)*exp(beta*s1)), t = 0 .. tau1))-n2*(Int(((a+t-tau1)/(gam0+gam1*(a+t-tau1))-(1/2)*(a+t-tau1)^2*exp(beta*s2))*(gamma0+gamma1*(a+t-tau1)+gamma2*(a+t-tau1)^2)*exp(beta*s2)*exp(-(gamma0*(a+t-tau1)+(1/2)*gamma1*(a+t-tau1)^2+(1/3)*gamma2*(a+t-tau1)^3)*exp(beta*s2)), t = tau1 .. tau2))-n3*(Int(((b+t-tau2)/(gam0+gam1*(b+t-tau2))-(1/2)*(b+t-tau2)^2*exp(s3))*(gamma0+gamma1*(b+t-tau2)+gamma2*(b+t-tau2)^2)*exp(beta*s3)*exp(-(gamma0*(b+t-tau2)+(1/2)*gamma1*(b+t-tau2)^2+(1/3)*gamma2*(b+t-tau2)^3)*exp(beta*s3)), t = tau2 .. c))+(n-n1-n2-n3)*((b+c-tau2)/(gam0+gam1*(b+c-tau2))-(1/2)*(b+c-tau2)^2*exp(s3))*(gamma0+gamma1*(b+c-tau2)+gamma2*(b+c-tau2)^2)*exp(beta*s3)*exp(-(gamma0*(b+c-tau2)+(1/2)*gamma1*(b+c-tau2)^2+(1/3)*gamma2*(b+c-tau2)^3)*exp(beta*s3));

solve({g1 = 0, g2 = 0}, {gam0, gam1});

Warning, solutions may have been lost.

What do I do wrong?

Thanks for advice in advance.

Hello, I am new user of Maple and I have simple problem. I have different results after pasting and typing text. Can you help me?

I am attempting to reproduce the the direction field for the the diferential equation below that I found in a book. I am using the dfieldplot command in the window x=0..3 and y=-1..1 but Maple is only plotting the field above the x-axis. I am aware that this is neither a linear DE nor does it posses a unique solution. Is the type of DE the problem here? Do I need to use a different command?