Still in Maple 2017 the palette is almost not readable without the help of a magnifier under a UHD screen (3840x2160) resolution. I have set all things which could be set for scaling and sizing, no effect on the palette. With the trend to higher resoluiton screen this should be fixed in the near future - or is there any work around?

https://gist.github.com/hoyeunglee/b0c6b61fafd1bee988fcafef3cfe6025
https://gist.github.com/hoyeunglee/a1e0ca335be8bbc8fde301c6aded66f8

test1 = o(a(x,y),z)

test1.args[0]

python sympy can not get function name o and a

Hi. I am using JetCalclulus to prolong infinitesimal generators.

Then I want to find invariants, it means I want to act on some function by these differential operators and to solve linear PDEs.

Is it possible to do it automatically?

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

Hi!

I am using solve() to solve a system of equations. Fortunately, the system is linear. Since it has more than 700 variables and more than 300 equations, I actually don't know if the solution exists.

I called solve() to solve the problem, and the solution I got indicates that all the variables are free variables. (That is, the solution is given as x_k = x_k for all variables.) Obviously, my system is not homogeneous, and 0 is not a solution to my problem. (I plugged in 0 and verified it.)

Since all the coefficients to my system are fractions, so I suppose the solve() function is using some symbolic algorithms? I don't know why this happens. Does this mean there is no solution to my system?

Thanks!

William

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

v := x -> `if`(x::numeric, x^2, 'procname(args)'):
u := x -> `if`(x::numeric, x^2, 'procname(args)'):

Optimization:-NLPSolve(v(x), {-1 <= x, x <= 1});
Error, (in Optimization:-NLPSolve) unsupported type of index, HFloat(1.0)

Optimization:-NLPSolve(u(x), {-1 <= x, x <= 1});
      [1.83670992315982423*10^(-40), [x = -1.35525271560688*10^(-20)]]

u and v are identical.

f := proc(x, rec := true)
  if rec then Optimization:-NLPSolve(2, y -> (y -~ 1/4).(y -~ 1/4), [], [<-1, -1>, <1, 1>],
    maximize = false) end if;
  (x -~ 1/4).(x -~ 1/4)
end proc:

fgrad := proc(x, g) g[1 .. 2] := 2*~(x -~ 1/4) end proc:

Optimization:-NLPSolve(2, f, [], [<-1, -1>, <1, 1>],
  maximize = false, objectivegradient = fgrad);
Warning, no iterations performed as initial point satisfies first-order conditions
        [0.125000000000000000, Vector[column](2, [0., 0.])]


Optimization:-NLPSolve(2, x -> f(x, false), [],  [<-1, -1>, <1, 1>],
  maximize = false, objectivegradient = fgrad);
        [0., Vector[column](2, [.250000000000000, .250000000000000])]

The inner NLPSolve doesn't do anything, except it breaks the outer NLPSolve.

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!