a+c^2

5*a+b^5

2*a+b^2*c+3*c

assume system of polynomials are above, how to test whether inverse exist

and find inverse of them

Let a planar polygon P without selfintersections be given through the plottools:-polygon command.
How to find its triangulation as a set of triangles (The indication of common sides is desired too.) in an optimal way with Maple? This is used in the finite element method.

properties of operations on sets?

Example:

is((A minus B) intersect (A minus C) = A minus (B union C)) assuming A::set, B::set, C::set;

                                                                  FAIL

how to calculate the RicciTensor for system of 3 polynomials equations in 3 variables

i find examples using differential expression, how to do for system of polynomial equations

Riemannian metric of constant sectional curvature

expect to test whether metric of constant sectional curvature g(t) = 1 when t tends to infinity or finite T

with(DifferentialGeometry):
with(Tensor):
DGSetup([x,y,z],M);
C1 := Connection();
R1 := CurvatureTensor(C1);
Ric1 := RicciTensor(R1);

sys := Diff(g(t), t) = -2*Ric1;

I have a large system of linear algebraic equations that I want to solve (2005 Unknowns, 2005 Equations). I was wondering that what are the proper commands to use in maple for solving the system as fast as possible. Take a look at the files in the download link if you want to see the system of linear algebraic equations.

http://pc.cd/h79

Please provide me any suggesitons that you may think will be helpful like using other sofwares that are good in doing this work such as MATLAB or something else.


Thanks in Advance

how to convert legendre polynomials into system of polynomials of 3 variables for drawing sphere with this ideal?

is possible to draw sphere from system of monomial polynomials?

Hi,

I have coded up a vector that is of my interest. The code runs witout any problem and gives me exactly what I want.

newtest.mw

All I want to know, is that if there are more efficient way to do so?

Any tricks, or better use of a particular function that I wasn't aware?

The only tiny bit of unsatisfactory is that, the (1-w) term is at the first term of the addition, is that possible to move it to the last term? Which is more conventional to read.

Thanks,

casper

Hello Dears

I have this equation

                                          (Napla)^4 * F(x,y) + k^2 *  (Napla)^2 * F(x,y)= 0,      (1)

which may be written as a non-homgeneous Helmholtz equation as

                                          (Napla)^2 * F(x,y) + k^2 * F(x,y)= g(x,y),                (2)

where the function g(x,y) is a harmonic function and (Napla)^2 is the laplace's operator in two dimension.

Can Maple solve equation (1), it will be better. If not may be solve equation (2).

how to calculate the cobordism between two ideals

do graph have invariant for invariant of cayley graph

for example, how to convert below word relation into graph

a^2 = 1

a*b = b*a

my code can only do for one variable, 

how to make divisible checking for multivariable cases with the ordering such as plex

IsDivisible(LP(h, t), LP(g[i], t), x)

it is not only x when multivariable

f:=LP(y^2*x,plex(x, y))[2];
g:=LP(y*x-y,plex(x, y))[2];
Remainder(f, g, gcd(f,g));
degree(Remainder(f, g, x),x);
degree(g, x);

remainder has error expect its 3rd argument x, to be of type or but received y*x

how to do if have ordering

do it need to check whether both f and g have variable x using indets and then apply remainder?

do it need to check each variable starting from the first variable in the ordering? 

how about if f has variable x but g do not have variable x, or f do not have variable x and g have variable x

if so, i try to replace below code in the bottom code, it has error

Error, (in FindDivisble) cannot determine if this expression is true or false: 0 < Search(x, {x, y})

FindDivisble := proc(g, h, t)
with(ListTools):
result := 0;
for i from 1 to nops(g) do
mainvariable := 0;
for j from 1 to nops(t) do
mainvariable := op(j, t);
if mainvariable <> 0 then
if Search(mainvariable, indets(h)) > 0 and Search(mainvariable, indets(g[i])) > 0 then
if IsDivisible(LP(h,t), LP(g[i],t), mainvariable) = 0 then
return i;
else
result := 0;
end if:
end if:
end if:
od:
od:
return result;
end proc:

with(Groebner):
LP := proc(f, t)
return LeadingTerm(f, t)/LeadingCoefficient(f, t);
end proc:
IsDivisible := proc(f, g, x)
with(Algebraic):
if Remainder(f, g, x) = 0 or degree(Remainder(f, g, x),x) < degree(g, x) then
return 0;
else
return 1;
end if:
end proc:
FindDivisble := proc(g, h, t)
result := 0;
for i from 1 to nops(g) do
if IsDivisible(LP(h, t), LP(g[i], t), x) = 0 then
return i;
else
result := 0;
end if:
od:
return result;
end proc:
MD := proc(f, g, t)
r := 0;
u := Matrix(nops(g), 1);
for j from 1 to nops(g) do
u[j] := 0;
od:
h := f;
while h <> 0 do
i := FindDivisble(g, h, t);
if i > 0 then
u[i] := u[i] + LeadingTerm(h, t)/LeadingTerm(f[i], t);
h := h - LeadingTerm(h, t)/LeadingTerm(f[i], t)*f[i];
else
r := r + LeadingTerm(h, t);
h := h - LeadingTerm(h, t);
end if:
od:
end proc:
f:=y^2*x;
f1 := y*x-y;
f2 := y^2-x;
MD(f,[f1,f2],plex(x, y));

From some scientific experiments, the following set of data is available
(1.0, 2.33),(2.0, 0.0626),(3.0, −2.16),(4.0, −2.45),(5.0, −0.357),(6.0, 2.21),(7.0, 2.75),(8.0, 0.636),(9.0, −2.45).

We need to use least squares method to fit the curve to the data
y = a + b cos(x) + c sin(x) + d cos(2x) + e sin(2x)

Show your solution procedure in Maple and get the best fit for the coefficients. Finally
plot the data and the y curve together on the same graph to visualize the fitting. For the
data, use blue circles while for the y curve, use red solid line style. Use the leastsquares
command we learned in LinearAlgebra package.

Find the eigenvalues and eigenvectors for

A =
2 0.37 0
0 1.1 −4.29
1.6 0 2.2

Can you estimate the largest eigenvalues (in absolute value) using Power method for this
problem? Try to explain why if you can

If I have a list, how can I write a program to see is that list is graphical? So far I have

graphicalseq := proc (L::list)

local i::integer, N;

N := convert(L, `+`);

if type(N, odd) then print("Sequence is not graphical")

else if numelems(L)-1 < L[1] then print("Sequence is not graphical")
end if;

end if;

end proc;

I know I still have to keep going to determine whether the sequence is graphical, but I'm not sure how.

 I was thinking of trying to somehow use Havel-Hakimi's theorem, but again I'm not sure how. Any hints would be appreciated.  I can't use the is Graph Sequence function