Given a polynomial expression I would like to obtain a list whose entries are the positive entries of the polynomial with multiplicity given by the coefficients:

Example:

Given the polynomial expression: p:=x^2*y-2*y*z+3*x^2+2*y-z

The positive terms are: x^2*y, 3*x^2, 2*y

Thus I would like to obtain the list L:=[x^2*y , x^2 , x^2 , x^2, y , y].

Notice x^2*y appears once since the coefficient is 1.

x^2 appears three times since the coefficient is 3.

y appears two times since the coefficient is 2.

Is there a way to divide two lists entry by entry. I mean the following:

L:=[2,4,6,3];

T:=[2,2,3,1];

L/T=[1,2,2,3]

Given a list I would like to find the position of the positive numbers. Ex: Given L:=[3,8,-5,1,-3,-7], I would like to have as a result P:=[1,2,4].

I want to avoid using a loop for this. Any suggestion?

Hello,

I need to solve the next ode:

diff(u(x, y), x) = -(2/3)*(3*h^3*nu+9*h^2*nu*y-12*nu*y^3+36*x^2*y+56*y^3)/h^3

diff(v(x, y), y) = (2/3)*(36*nu*x^2*y+56*nu*y^3+3*h^3+9*h^2*y-12*y^3)/h^3

diff(u(x, y), y)+diff(v(x, y), x) = -(6*(1+nu))*x*(h^2-4*y^2)/h^3

The inicial conditions are:

u(L, 0) = 0
v(L, 0) = 0
D[1]*u(L, 0) = 0

When I write on Maple this code, he give me a error:

with(PDEtools, casesplit, declare); declare((u, v)(x, y))

sys2 := [diff(u(x, y), x) = -(2/3)*(3*h^3*nu+9*h^2*nu*y-12*nu*y^3+36*x^2*y+56*y^3)/h^3, diff(v(x, y), y) = (2/3)*(36*nu*x^2*y+56*nu*y^3+3*h^3+9*h^2*y-12*y^3)/h^3, diff(u(x, y), y)+diff(v(x, y), x) = -(6*(1+nu))*x*(h^2-4*y^2)/h^3]

sol := pdsolve(sys2)

ics := u(L, 0) = 0, v(L, 0) = 0, D[1]*u(L, 0) = 0

pdsolve([sys2, ics]);

Why Maple can't solve this PDE?

I think that the problem is on sys2. But I don't know how to explain to Maple the function: diff(u(x, y), y)+diff(v(x, y), x) = -(6*(1+nu))*x*(h^2-4*y^2)/h^3; on the system of equations. I think the problem is there.

I'm so sorry by my bad english.

I need to solve this, anyone help me please.

Thanks.

please i need assistance on how to go about contructing a 3d plot of the fuction below:

((Pi*BesselJ(1, x)*HermiteH(0, x)+2*BesselJ(0, x)-Pi*BesselJ(0, x)*BesselJ(1, x)*HermiteH(0, x))*exp(-x^2*D*t/`αk`)*BesselJ(0, x/chi)/BesselJ(1, x)^2)-M[0]*T[2]*`γgr`*exp(-T[g/T[0]]*(t-delta))

please i will appreciate a code or sort of syntax or guidline on how to do it,pls i want to plot the value of the function on the y axis, chai on the x axis and t[2] on the z axis.

M[0]=8,g=9.8,T[2]=300,500,700,900,gamma=1.17,r=1.15,T[g]=1.11111,T[0]=3.666667,t=5e-9,delta=0.002,x=3.478505,alpha=5.36,k=1.2,chi=0.22,0.23,0.24,0.25,r=1.15,D=7.46

In my calculations, I encounter with too small numbers, e.g. 0.4e-10. My question is that how can I make the maple to ignore these small numbers and considers them as zero and not to incorporate them into subsequent calculations???

Thanks in advance.

Hi, the fsolve works perfectly fine when otaining SOL2 below. However, as soon as I change the values of paramters (from 0 values in SOL2 to t_prof = .16, t_r = .16, t_w = .16 in SOL3) fsolve simplmy reproduces the eval results and would not solve! Please your help is highly appreciated. Thanks in advance!

restart;
eq1 := ((1-s)*w)^(1-gamma)*r^gamma-P_v = 0;
eq2 := (1-s)*w*H/M-(1-gamma)*P_v*q/phi = 0;
eq3 := r*(K+K_f)/M-gamma*P_v*q/phi = 0;
eq4 := prof-M*p_d*q+(1-s)*w*H+r*(K+K_f) = 0;
eq5 := -tau*y_x+q-y_d-y_g = 0;
eq6 := p_d-sigma*P_v/((sigma-1)*phi) = 0;
eq7 := y_d-M^(lambda-1)*Y*(p_d/P)^(-sigma) = 0;
eq8 := y_x-F_f*(tau*p_d)^(-sigma_x) = 0;
eq9 := y_f-M_f^(lambda-1)*Y*((1+z)*tau*p_f/P)^(-sigma) = 0;
eq10 := (G*alpha_g+Y)^(-alpha_c)/P-A*H^alpha_h/((1-t_w)*w) = 0;
eq11 := P*Y-(1-t_w)*w*H-(1-t_r)*r*K-(1-t_prof)*prof+T = 0;
eq12 := P*Y-M*p_d*y_d-M_f*(1+z)*tau*p_f*y_f = 0;
eq13 := (1-t_r)*r-r_f = 0;
eq14 := G-y_g*M^((lambda_g-1+sigma_g)/(sigma_g-1)) = 0;
eq15 := s*w*H+M*p_d*y_g-T-t_w*w*H-t_r*r*(K+K_f)-t_prof*prof-z*M_f*tau*p_f*y_f = 0;

SOL2 := fsolve(eval({eq1, eq10, eq11, eq12, eq13, eq14, eq15, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9}, [A = 7.716049383, K = 3.2, K_f = 0, alpha_c = .8, alpha_g = .2, alpha_h = 4, lambda = .5, p_f = 1, phi = .625, s = 0, sigma = 5, sigma_g = 5, sigma_x = 5, t_prof = 0, t_r = 0, t_w = 0, tau = 1.1, y_d = 1, y_f = 1, y_g = .4, y_x = 1, z = 0, lambda_g = .5, gamma = .25, gamma = .25]), {F_f, G, H, M, M_f, P, P_v, T, Y, p_d, prof, q, r, r_f, w}, {F_f = 2 .. 4, G = .1 .. .4, H = .4 .. .8, M = .4 .. .6, M_f = .3 .. .7, P = .8 .. 2, P_v = .4 .. .8, T = -.2 .. .3, Y = .7 .. 3, p_d = .9 .. 1.6, prof = .1 .. .4, q = 1.5 .. 2.7, r = 0.4e-1 .. 0.9e-1, r_f = 0.4e-1 .. 0.9e-1, w = .8 .. 3});

SOL3 := fsolve(eval({eq1, eq10, eq11, eq12, eq13, eq14, eq15, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9}, [A = 7.716049383, K = 3.2, K_f = 0, alpha_c = .8, alpha_g = .2, alpha_h = 4, lambda = .5, p_f = 1, phi = .625, s = 0, sigma = 5, sigma_g = 5, sigma_x = 5, t_prof = .16, t_r = .16, t_w = .16, tau = 1.1, y_d = 1, y_f = 1, y_g = .4, y_x = 1, z = 0, lambda_g = .5, gamma = .25, gamma = .25]), {F_f, G, H, M, M_f, P, P_v, T, Y, p_d, prof, q, r, r_f, w}, {F_f = 2 .. 4, G = .1 .. .4, H = .4 .. .8, M = .4 .. .6, M_f = .3 .. .7, P = .8 .. 2, P_v = .4 .. .8, T = -.2 .. .3, Y = .7 .. 3, p_d = .9 .. 1.6, prof = .1 .. .4, q = 1.5 .. 2.7, r = 0.4e-1 .. 0.9e-1, r_f = 0.4e-1 .. 0.9e-1, w = .8 .. 3});

I have started to use Maple 18 and I have found that my scale starts at 2.*10^16 for all functions I graph no matter if its 3D or 2D. Is there a way to change this scale?

Dear, my attached file take alot time to exicute the result, Please solve this problem. I am waiting your kind response. 

Hirota_Bilinear_Method-3.mw

With my best regards and sincerely.

Muhammad Usman

PhD (Scholar) Mathematics

HITEC University, Taxila

Lecturer of Mathematics

Govt. Degree College Taxila Pakistan.

Visiting Lecturer of Mathematics

University of Wah, Pakistan.

Email: mughal1103@gmail.com

Mob #: +923152329276

1.

similar gap system, which function can output coset table ?

if find example below,

f := FreeGroup( "a", "b" );

g := f / [f.1^2, f.2^3, (f.1*f.2)^5];
tab := CosetTable(g, Subgroup(g, [g.1, g.2*g.1*g.2*g.1*g.2^-1]));

2.

if quotient group is for equivalence relations, what do relations [g.1, g.2*g.1*g.2*g.1*g.2^-1] for? which kind of relations is for input to subgroup parameter which is like relations?

3. equalivance relations in wiki mentioned is to partition cells, how do they satisfy symmetric, reflexive and transitive after partition? how to test these partition?

how to implement a free group with symmetric properties?

i find that equivalence relations = relexive, symmetric and transitive , is only these three ?

if implement symmetric properties, does it mean that adding equivalence relations to group?

how to implement free group with this?

i guess something like

f := FreeGroup( "a", "b" );
g := f / [equivalence relations....];

is there a library storing all kinds of equivalence relations?
https://en.wikipedia.org/wiki/Equivalence_relation
For quotient groups, is there IsEquivalenceRelation and IsEquivalenceClass like gap system?
www.gap-system.org/Manuals/doc/ref/chap33.html
like
f := FreeGroup( "a", "b" );
g := f / [f.1^2, f.2^3, (f.1*f.2)^5];

when i paste words here, most words missing, is there being hacked?

I want to calculate

Lim _x-->1⁺ ([X²]-1)/([X]-1)

I let  x=1+c  and  _c-->0⁺  then we have [X²]=[c²+2c+1]=[2c]+1

Lim _x-->1⁺ ([X²]-1)/([X]-1) = Lim _c-->0⁺ [2c]/[c]

Maple shows the both limitations equal to zero

I want know how maple claculates it

I'd like to pay attention to Maple packages for symmetric functions, posets, root systems, and finite Coxeter groups by John Stembridge. That was estimated as well qualified in Mathoverflow.

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