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

Download err_subs.mw

Much of this topic is developed using traditional techniques. Maple modernizes and optimizes solutions by displaying the necessary operators and simple commands to solve large problems. Using the conditions of equilibrium for both moment and force we find the forces and moments of reactions for any type of structure. In spanish.

Equlibrium.mw

https://www.youtube.com/watch?v=7zC8pGC4F2c

Lenin Araujo Castillo

Ambassador of Maple

Hello. I have a question on plotting discrete time plot. When I try to plot the equation below I get an error. Can't figure out where is the problem. If for example I choose for vector A () there is no error. I would appreciate your help.

Error, invalid input: DynamicSystems:-DiscretePlot expects its 2nd argument, v2, to be of type {realcons, list(extended_numeric), ('Vector')(extended_numeric)}, but received Vector(4, {(1) = 1+sin(1), (2) = 1+sin(2), (3) = 1+sin(3), (4) = 1+sin(4)})

Regards,

Tadej

test_sections.mw

Hi, I'm getting some unusual behaviour between the Explore() command / graphs and collapsed sections, as exemplified in the attached (linked) worksheet.  I'm trying to develop some worksheets with several sections where some of the sections have an explore() graph in them.  To keep things simple, I'd like some sections to be collapsed with the graphs hidden (and remain collapsed: View - Section - Autoexpanding - Uncheck) when the worksheet is evaluated.  In the attached, the section remains collapsed, so does the normal graph, but the explore "graph" gets published outside the collapsed section and when there is other information on the worksheet, the explore window appears almost randomly.

So is there any way to ensure the explore graph remains inside the collapsed section?

Sorry for the slightly longwinded explanation :-)

Thanks,

Maple:

how exp into ?

exp2: 

into

Help

Is is possible to tell the latex output what to do if it finds a symbol?

Suppose I have the following expression:

O3^2 + k_O3NO

The normal latex output just takes it as it is and also translates k_O3NO to k_O3NO with the underscore.

I however want it to read (latex notation in math mode)

\left[ \text{O}_3 \right]^2 + k_{\text{O}_3\text{NO}}

So is that possible without changing everything manually?

edit: Just as a remark, the output at the moment for this expression reads

{{\it O3}}^{2}+{\it k\_O3NO}

and is kinda awful if compiled in latex...

Is it also possible for maple to latex realizing where a line-break is necessary?

# Bending Moment Envelope Curve for Isostatic Two-Span Beam

restart:

with(plots):

with(Optimization):
PD:= proc (L1, L2, L3, N)

local l, R, Y, M, M1, M2, V:

R[1]:= piecewise(x <= L1, (L1-x)/L1, 0):

l[1]:=L1:

l[2]:=L2:

l[3]:=L3:

solve([add(R[i], i = 1 .. 3) = 1, add(R[j]*add(l[i], i = 1 .. j), j = 2 .. 3) = x], [R[2], R[3]]):

R[2]:=rhs(%[1][1]):

R[3]:= rhs(`%%`[1][2]):

M1:=piecewise(y <= add(l[i], i = 1 .. 2), R[1]*y, `and`(add(l[i], i = 1 .. 2) < y, y <= add(l[i], i = 1 .. 3)), R[1]*y+R[2]*(y-add(l[i], i = 1 .. 2))):

M2:=piecewise(y <= x, 0, x-y):

for Y to N do eval(M1+M2, y = Y*add(l[j], j = 1 .. 3)/N):

M[Y]:=Maximize(abs(%),x=0..add(l[j],j=1..3))[1]

end do:

pointplot(`<,>`(seq(i*add(l[j], j = 1 .. 3)/N, i = 1 .. N)), `<,>`(seq(M[i], i = 1 .. N)), color = red, symbol = asterisk):

display(%, axis = [gridlines = [10, color = black]], size = [700, "golden"], axesfont = [Times, 16])

end proc:

Hello everyone,

I am trying to solve a differential equation using dsolve command for laplace transform.

In Equation 2, a is a constant and x(t), b(t), u(t) are functions.

What is the "_U1" in the output (4)? Is it because I have defined x(t), b(t), u(t) as functions?

Thank you in advance!

Since 2002, the Texas A&M Math Department has sponsored a Summer Educational Enrichment in Math (SEE-Math) Program for gifted middle school students entering the 6th, 7th or 8th grade under the direction of Philip Yasskin and David Manuel.  Students spend two weeks exploring ideas from algebra, geometry, graph theory, topology, and other mathematical topics. 

The program’s primary goal is to help students find excitement in the discovery of mathematics and science concepts, and to provide them with the knowledge and confidence to continue their studies in math and science related fields. “I love working with the bright young kids who come to SEE-Math, they keep me young,” said Yasskin, one of the programs directors.

Maplesoft has been a sponsor of SEE-Math for many years and are happy to see the students explore math at this young age. Research into the importance of early math skills shows that children who are taught math early and learn the basics at a young age are set up for a lifetime of achievement in all aspects of their academic performance.  Every year, Maplesoft commits time, funds and people to various organizations to enhance the quality of math-based learning and discovery and to encourage students to strengthen their math skills.

One of the major activities of the SEE-Math program, and something the students really enjoy doing, is creating computer animations in Maple. The kids are divided into 3 groups; the Euler group is mostly made up of 6th graders with a few younger, the Fibonacci group is mostly 6th and 7th graders, and the Gauss group is 7th and 8th graders.

 Here are the 2017 first place winners from each group and their animations:

Euler Group - Nigel M "Buckets"

Fibonacci Group - Gabriel M "Skillz"

Gauss Group - Michael C - "Newton's Castle"

To learn more about this program visit: http://see-math.math.tamu.edu/2017/

I have a problem for dsolve for equations.How can I remove it?

"too few boundary conditions: expected %1, got %2\"",20,19

thanks

FEW_BCS.mw
 

Download FEW_BCS.mw

Anybody know how to put this in coding for Jacobian Matrix? 

     Hi,

i want to solve equation system u0(x,t),u1(x,t),v1(x,t),v0(x,t)v2(x,t) dependent on f(x,t).

I attached file. 

Thanks in advance.

worksheet.mwworksheet.mw

Maple gives me a null output for an equation that has a real solution.

solve(4/x^(1/3)+1=0)

The following command seems to work

solve(4/surd(x,3)+1=0)

-64

Why doesn't this have a solution over the complex numbers, when real numbers are a subset of the complex numbers. Mathematica has the same result too.