Maple 2015 Questions and Posts

These are Posts and Questions associated with the product, Maple 2015

I have a polynomial of 4th order and I wanted to use allvalues on the RootOf expression. It then says:
 

Error, (in evala/Normal/preproc) reducible RootOf detected.  Substitutions are {RootOf(4678560000000000000000000000000000000000+(16573041*CO^2+70122975000000000000*CO-623180900000000000000000000000000)*_Z^4+(-19887649200*CO^2-82987335000000000000000*CO+745755960000000000000000000000000000)*_Z^3+(5966294760000*CO^2+23851989000000000000000000*CO-221858784000000000000000000000000000000)*_Z^2+(417684600000000000000000000*CO-757598400000000000000000000000000000000)*_Z) = 600, RootOf(4678560000000000000000000000000000000000+(16573041*CO^2+70122975000000000000*CO-623180900000000000000000000000000)*_Z^4+(-19887649200*CO^2-82987335000000000000000*CO+...
Error, (in allvalues) numeric exception: division by zero

So apparently the expression is reducible but how do I do that?

 I have in my Maple documents many good quality plots resulting from simulations. I need to export (or paste) them to templates of transactions in Word without loosing quality, and beeing flexible to some degree to fit the dimension.

Until now when I paste such plots the quality is lost and especially on descripltion on axes (vertical).

What I have to do? Do I need to go throuhg pdf format ? 

Hello dear!

Hope you all are fine. I am trying to sloution the system of nonlinear system of ODEs (see attached file) but my solutions not converging please see and fix the problem. I am waiting your quick response.

Graph.mw

restart;
with(Groebner):

DoExist := proc(tau, n)
if rtable_num_elems(tau) >= n then
	return tau[n];
else
	return 0;
end if;
end proc;

IsZero := proc(a, b)
if a=0 then 
	return 0;
else 
	return a/b;
end if
end proc;

g1 := x^2-w*y;
g2 := x*y - w*z;
g3 := y^2 - x*z;
gro := Basis([g1,g2,g3],plex(x,y,z,w));

X1 := `*`(LeadingTerm(g1, tdeg(x, y, z, w)));
X2 := `*`(LeadingTerm(g2, tdeg(x, y, z, w)));
X3 := `*`(LeadingTerm(g3, tdeg(x, y, z, w)));
X12 := lcm(X1,X2);
X13 := lcm(X1,X3);
X23 := lcm(X2,X3);
S12 := SPolynomial(g1, g2, lexdeg([x, y, z, w]));
S23 := SPolynomial(g2, g3, lexdeg([x, y, z, w]));
S13 := SPolynomial(g1, g3, lexdeg([x, y, z, w]));
e1 := Vector([1,0,0]);
e2 := Vector([0,1,0]);
e3 := Vector([0,0,1]);
eq1:= S12 = h121*g1 + h122*g2 + h123*g3;
eq1 := S12 - expand(h121*g1 + h122*g2 + h123*g3):
NormalForm(eq1, Basis([g1, g2, g3], tdeg(x, y, z, w, h121, h122, h123)), tdeg(x, y, z, w, h121, h122, h123), 'Q');
h121 := 0;
h122 := 0;
h123 := 0;
s12 := IsZero(X12,X1)*e1-IsZero(X12,X2)*e2-Vector([DoExist(<Q>,3), DoExist(<Q>,2), DoExist(<Q>,1)]);

eq1 := S13-expand(h131*g1+h132*g2+h133*g3):
NormalForm(eq1, Basis([g1, g2, g3], tdeg(x, y, z, w, h131, h132, h133)), tdeg(x, y, z, w, h131, h132, h133), 'Q');
h131 := 0;
h132 := 0;
h133 := 0;
s13 := IsZero(X13,X1)*e1-IsZero(X13,X3)*e3-Vector([DoExist(<Q>,3), DoExist(<Q>,2), DoExist(<Q>,1)]);

eq1:= S23 - expand(h231*g1 + h232*g2 + h233*g3);
NormalForm(eq1, Basis([g1, g2, g3], tdeg(x, y, z, w, h231, h232, h233)), tdeg(x, y, z, w, h231, h232, h233), 'Q');
h231 := 0;
h232 := 0;
h233 := 0;
s23 := IsZero(X23,X2)*e2-IsZero(X23,X3)*e3-Vector([DoExist(<Q>,3), DoExist(<Q>,2), DoExist(<Q>,1)]);

with(LinearAlgebra):
#F = Syz*GrobnerBasis
F := simplify(MatrixMatrixMultiply(Matrix([[s12[1],s13[1],s23[1]],[s12[2],s13[2],s23[2]],[s12[3],s13[3],s23[3]]]), Matrix([[gro[1]],[gro[2]],[gro[3]]])));
F[1][1] - g1 = 0; 
F[2][1] - g2 = 0;
F[3][1] - g3 = 0;
F := simplify(MatrixMatrixMultiply(Matrix([[s12[1],0,s23[1]],[s12[2],0,s23[2]],[s12[3],0,s23[3]]]), Matrix([[gro[1]],[gro[2]],[gro[3]]])));
F[1][1] - g1 = 0; 
F[2][1] - g2 = 0;
F[3][1] - g3 = 0;

#F = GrobnerBasis*Syz
F := simplify(MatrixMatrixMultiply(Matrix([[gro[1],gro[2],gro[3]]]), Matrix([[s12[1],s13[1],s23[1]],[s12[2],s13[2],s23[2]],[s12[3],s13[3],s23[3]]])));
F[1][1] - g1 = 0; 
F[1][2] - g2 = 0;
F[1][3] - g3 = 0;
F := simplify(MatrixMatrixMultiply(Matrix([[gro[1],gro[2],gro[3]]]), Matrix([[s12[1],0,s23[1]],[s12[2],0,s23[2]],[s12[3],0,s23[3]]])));
F[1][1] - g1 = 0; 
F[1][2] - g2 = 0;
F[1][3] - g3 = 0;

#F = GrobnerBasis*Syz
F := simplify(MatrixMatrixMultiply(Matrix([[gro[1],gro[2],gro[3]]]), Matrix([[s12[1],s12[1],s12[1]],[s13[2],s13[2],s13[2]],[s23[3],s23[3],s23[3]]])));
F[1][1] - g1 = 0; 
F[1][2] - g2 = 0;
F[1][3] - g3 = 0;
F := simplify(MatrixMatrixMultiply(Matrix([[gro[1],gro[2],gro[3]]]), Matrix([[s12[1],0,s12[1]],[s13[2],0,s13[2]],[s23[3],0,s23[3]]])));
F[1][1] - g1 = 0; 
F[1][2] - g2 = 0;
F[1][3] - g3 = 0;

syz result is s12, s23

but after verify, F is not equal to GrobnerBasis*Syz

How to find the range of poset?

i would like to search the range of range is equal to the range of domain after solve system.

it may not exactly equal but around 80% of elements in range belong to the range of domain

if it is not factorisation domain,

how to generate ideal with function in maple?

If I enter the following I do not get the residue... how do I make the residue command work?

 

ode1a := diff(y1(tt),tt) = round(rhs(odeparm1[1][1]))*y1(tt) + round(rhs(odeparm1[1][2]))*y2(tt) + round(rhs(odeparm1[1][3]))*y3(tt);
ode2a := diff(y2(tt),tt) = round(rhs(odeparm1[1][4]))*y1(tt) + round(rhs(odeparm1[1][5]))*y2(tt) + round(rhs(odeparm1[1][6]))*y3(tt);
ode3a := diff(y3(tt),tt) = round(rhs(odeparm1[1][7]))*y1(tt) + round(rhs(odeparm1[1][8]))*y2(tt) + round(rhs(odeparm1[1][9]))*y3(tt);
sys := subs(y3(tt)=1,[ode1a,ode2a]);
print(DEplot(sys, [y1(tt), y2(tt)], tt = 0 .. 16, y1 = -16 .. 16, y2 = -16 .. 16, color = magnitude, title = `Stable Limit Cycles`, arrows = curve, dirfield = 800, axes = none));

 

how to mirror the vector field graph mathematically?

mirror the graph about x=0 this line,

so that the graph looked flip

i find curl can do, but how to do ?

 

restart;
with(VectorCalculus):
SetCoordinates('cartesian'[x(t), y(t), z(t)]);
Curl((x(t),y(t),z(t)),(Diff(x(t),t) - a11*x(t) - a12*y(t) - a13*z(t),Diff(x(t),t) - a21*x(t) - a22*y(t) - a23*z(t),Diff(x(t),t) - a31*x(t) - a32*y(t) - a33*z(t)));
Error, (in VectorCalculus:-SetCoordinates) coordinate system `cartesian[x(t), y(t), z(t)]` does not exist
Error, (in Vector) dimension parameter is required for this form of initializer

 

Hello everybody

I'm using discrete distributions from the Statistics package and I found a rather strange result.

In short the theoritical values of some statistics of a NegativeBinomial(1, P) Random Variable (P being the probability of success equal to 1e-4) are correctly computed, but their empirical estimators computed from a sample of this RV are roughly wrong.

For NegativeBinomial(1, P) is similar to Geometric(P) I asked Maple to compute the theoritical values of some statistics of Geometric(P) and next to assess their empirical values from a sample of Geometric(P).
Some discrepancies still remain but they can be explained by statistical fluctuations.

Could you please look to the attached file (an error on my part is still possible) and help me to fix this ?

Thanks in advance


PS : the histogram of Sample(NegativeBinomial(K, P), AnySizeYouWant) is obviously wrong (it should look like a decreasing exponential) 


 

Download NegativeBinomial.mw

From clues:
a1 := subs(y=n,1/y!*x^y); # diff make it equal to the left term
a2 := subs(y=n-1,1/y!*x^y);
simplify(factor(a1 - a2));
 
To find limit of below
nterm := sum(tanh(product(sum(kk, kk=1..jj),jj=1..y))*1/y!*x^y, y=n..n);
n2term := sum(tanh(product(sum(kk, kk=1..jj),jj=1..y))*1/y!*x^y, y=(n+1)..(n+1));
simplify(factor(n2term - nterm));
simplify(limit((subs(x=x+h, n2term)-n2term)/h, h=0)) = nterm;
 
question is to find a limit make n2term equal nterm after calculation

g3 := tanh(x+1);
a:=eval(diff(g3,x$n)/n!, x=0) assuming n>=0:
tanhx := sum(a*x^n, n=0..infinity):
tanhx2 := subs(x^n=subs(_C1=0, subs(t=n!, g2))*x^n, tanhx):
diff(tanhx2, x) - tanhx2;
 

would like to find a operator to make it equalt to itself , a new differential operator for new transcendental function tanhx2

 i need a help on how to find the local truncation error of a hybird block method of three order IVP. here is the one of the discrete methods i need to find the local truncation error. please any solution should put here thanks 

dear all,

I have a problem when I try to find points on boundary of the surface.

the surface ploted from a matrix as follow:

 

please help me to generate a bondary curve of this surface.

Thanks

 

 

 

Hello,

I am trying to solve analytically a simple system of partial differential equations with boundary conditions and I am not able to do it. Even in the very simple case of

pdsolve([diff(u(x, y, t), y, y) = 0, diff(p(x, y, t), y) = 0, u(x, 0, t) = 1, (D[2](u))(x, 1, t) = 0, p(x, 1, t) = 2], [p(x, y, t), u(x, y, t)]);

I don't get any answer.  However if I remove the boundary conditions I get the right answer

pdsolve([diff(u(x, y, t), y, y) = 0, diff(p(x, y, t), y) = 0], [{p(x, y, t), u(x, y, t)}]);
 {p(x, y, t) = _F3(x, t), u(x, y, t) = _F1(x, t) y + _F2(x, t)}

Can maple 2015 solve analytically systems of partial differential equations with boundary conditions? I have not been able to find any example anywhere.

Thanks a lot for your help.

Javier

All the 3d plot in my maple are upside down.....the tickmarks..the numbering even the lebeling are also upside down...how do i solve it....plz help

I have a list of coefficients each assigned a triple of indices. E.g. CF_{x,y,z}. These indicies are also able to take other values between +-2. E.g. CF_{x+2,y-1,z} or CF_{x,y-2,z+1} as examples. I have a working loop that cycles through the list of these coefficients and I am able to call a particular one by specifying the triple of indicies. This script has been attached:

triple_index_script.mw

I would like to modify this script to have more control over single indexes. As an example, say I want to add up all the coefficients which have z as a subscript (so not z+1,z-2 etc...) and I don't care what the x and y subscripts are; I want to be able to call that sum using the same notation in the script but with a single index. e.g. (using a new example function called RR_MapZ):

RR_MapZ[0]; ## This would return the sum of all coefficients that had z in their subscript

and this would return the sum of all the coefficients which have subscript Z. If I wanted to add up all the coefficients which had index Z+1 I would do:

RR_MapN[1]; ## This would return the sum of all coefficients that had z+1 in their subscript

What would be the most efficient way to do this?

-Yeti

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