MaplePrimes Questions

Hi,

I have some matrix valued functions that that I can only define piecewise. Unfortunately I have some problems to manipulate those functions. Piecewise sees to do the job for  scalar valued functions. There I can easily differentiale and add results. For Matrix valued functions however, those features seem to not be availible.
 

I can work around these limitations by manually applying all operations to the operands of the piecewise function. Like I show here:


 

restart:

# a piecewise function

p1:=piecewise(a(t)^2=0,<cos(a(t))^2+sin(a(t))^2,0>,<1,1/a(t)>)

p1 := piecewise(a(t)^2 = 0, Vector(2, {(1) = cos(a(t))^2+sin(a(t))^2, (2) = 0}), Vector(2, {(1) = 1, (2) = 1/a(t)}))

(1)

# differentiation does not work

diff(p1,t)

diff(piecewise(a(t)^2 = 0, Vector(2, {(1) = cos(a(t))^2+sin(a(t))^2, (2) = 0}), Vector(2, {(1) = 1, (2) = 1/a(t)})), t)

(2)

# selecting individual entries does not work

r:=p1(1)+1

r := (piecewise(a(t)^2 = 0, Vector(2, {(1) = cos(a(t))^2+sin(a(t))^2, (2) = 0}), Vector(2, {(1) = 1, (2) = 1/a(t)})))(1)+1

(3)

# strange simplification behaviour

simplify(p1)

piecewise(t = RootOf(a(_Z)), _z1(RootOf(a(_Z))), Vector(2, {(1) = 1, (2) = 1/a(t)}))

(4)

# current workaround, define new piecewise function by using op

r:=piecewise(op(1,p1),op(2,p1)(1)+1,op(3,p1)(1)+1)

r := piecewise(a(t)^2 = 0, cos(a(t))^2+sin(a(t))^2+1, 2)

(5)

 


 

Download Scratch.mw

 

I think my workaround is very cumbersome and error prone. Is there a better way to tackle this probem? Or should I try to overload all needed operations, and is this even possible?

Thanks for all suggestions!

Honigmelone

is it possible to express rational number into fraction in terms of power of 2

input

2.142857143

output

(2^3+2^2+2+1)/(1+2+2^2)

Hi, there.

I have a program, and I want to make an interface where I can text in the figures and show the results. But I have no idea about this. Anyone can give me some instructions? Thanks!

Hello

I'm importing some data from Excel which comes across as L:

L := Matrix(1, 6, [["TC,DB", "PC,JL", "TD,JK", "IW,CM", "CC,PG", "KJ,DJ"]])

M: = convert( L,'list' );

["TC,DB", "PC,JL", "TD,JK", "IW,CM", "CC,PG", "KJ,DJ"

map(convert, M, 'name') ; # remove inverted commas

[`TC,DB`, `PC,JL`, `TD,JK`, `IW,CM`, `CC,PG`, `KJ,DJ`]

How to I add square brackets to each pair in the output?

What I want is a command to display L or M as:

[[TC,DB], [PC,JL], [TD,JK], [IW,CM], [CC,PG], [KJ,DJ]]

 

1.
tanh(1-x) = sum(p(ii)*x^q(ii), ii=0..infinity) or product(p*x^q(ii), ii=0..infinity) ?
2.
tanh(1-x)*1/(1-x) = sum(p(ii)*x^q(ii), ii=0..infinity) or product(p*x^q(ii), ii=0..infinity) ?
3.
tanh(x) = sum(p(ii)*x^q(ii), ii=0..infinity) or product(p*x^q(ii), ii=0..infinity) ?

Remark: it may not be possible to use diff to find p(ii)

update

series(tanh(1-x), x=0);
with(OrthogonalSeries):
Coefficients(series(1/(1-x), x=0));
coeffs(series(tanh(1-x), x=0));
coeffs(series(tanh(1-x), x=0),x);
Error, invalid arguments to coeffs;
 
and is it possible to find q(ii) only if assume p(ii) all are one?

I am trying to solve a vector calculus problem, find r(t) given:

a(t) = < 4t, sin t, cos(2t) > ,  v(0) = <1,0,0>  , r(0) = <0, 1, 0 >

My approach below seems kind of complicated for such a straightforward problem.  I am trying to do this without copying pasting previous results. Also there might be a recursion issue when i defined v in terms of v(t).

 

 

I am a newbie at generating numeric data sets using the Matrix command.  Linked is the code I used to generate a time profile for various values of k.  The output results in 10 separate matrices for each value of k.  Instead I would like one matrix that has all ten data sets included.   Can anyone provide assistance?

untitled5.mw

 

 

 

   ,Hello friends

  .I want to plot a coupled differential equation numerically  but I dont know whats wrong with the loops


 

 


 

numeric4.mw  .pdfnumeric4.pdf

 

Question on the ditto operator, labels, and unapply, using three examples.

 

Example 1:

The ditto operator produces no output. Why is that? I presumed that the ditto operator is equivalent to copying pasting the last output.

 

Example 2:

Here the label approach seems to work, but in example three, both the ditto and label approach fails.

 

Example 3:

Someone earlier said that I should use unapply.

Why isn't    " v := x->% " equivalent to "v:=unapply(%,x)"

And why does the label approach fail in the vector calculus example.

I am trying to avoid having to copy paste an entire line of output.

The context of the problem , I am given an acceleration vector and want to find the position vector.

a:= <4t, sin t, cos 2t) with v(0) = <1,0,0> and r(0) = <0,1,0>

My problem is with an intermediate step, finding the velocity vector.

There is no output.

Another attempt. This time using a label

This time i do get an output, but v(1) should be (2 + c1) e_x + (-cos(1) + c2) e_y + (1/2 sin(2) + c3)e_z

The only way for it to work is to copy paste manually the output from line (21) as shown here

 

Hello people in mapleprimes,

I have a question about how PDEtools:-declare works.

I declared f__1 as a function of k__1 with the command declare, and

defined f__1 as a function of K__1/L__1, which is k__1,

and, differentiated f__1 with K__1.

But, the form I could get is e_1 and e_2, which contains D(f__1)(k__1).
And, the same thing occurs in e7_2.

How can I have it shown as f__1' or f__1'(k__1), which does not include D of D(f__1).

I hope you will give me a help, and thaks in advance.

18_Sep_2017.mw

Dear Maple users

Let's say I want to plot a line containing a parameter, for example (a+2)*x+6, where a is the parameter. When using the following Explore command:

Explore(plot((a+2)*x+6, x = -5 .. 5, view = -10 .. 10), parameters = [a = -4.0 .. 3], initialvalues = [a = 1])

I will be able to change the value of a by using the slider. The actual value of a is currently displayed as well. Now, However, I want to have the current value of the slope of the line displayed as I move the slider. How is this done? When using a print command inside the Explore command the value of a+2 is not displayed, rather "a+2". Can I use some kind of component?

I hope someone can help. 

NB! I constructed this rather doll example, just to make it simple.

Regards, Erik

 


ode1a := diff(y1(t), t) = round(rhs(odeparm1[1][1]))*y1(t)+round(rhs(odeparm1[1][2]))*y2(t)+round(rhs(odeparm1[1][3]))*y3(t);
ode2a := diff(y2(t), t) = round(rhs(odeparm1[1][4]))*y1(t)+round(rhs(odeparm1[1][5]))*y2(t)+round(rhs(odeparm1[1][6]))*y3(t);
ode3a := diff(y3(t), t) = round(rhs(odeparm1[1][7]))*y1(t)+round(rhs(odeparm1[1][8]))*y2(t)+round(rhs(odeparm1[1][9]))*y3(t);
try
ode1a := diff(y1(t), t) = rhs(odeparm1[1][1])*y1(t)+rhs(odeparm1[1][2])*y2(t)+rhs(odeparm1[1][3])*y3(t);
ode2a := diff(y2(t), t) = rhs(odeparm1[1][4])*y1(t)+rhs(odeparm1[1][5])*y2(t)+rhs(odeparm1[1][6])*y3(t);
ode3a := diff(y3(t), t) = rhs(odeparm1[1][7])*y1(t)+rhs(odeparm1[1][8])*y2(t)+rhs(odeparm1[1][9])*y3(t);
sys := DiffEquation([ode1a, ode2a, ode3a], inputvariable = [y1(t)], outputvariable = [y2(t), y3(t)]);
sysz := ToDiscrete(sys, ts); in_t := Sine(1, 1, 0, 0);
sol := Simulate(sys, [in_t]);
try
p1 := plots[odeplot](sol, [[t, y2(t)]], t = 0 .. t_sim, numpoints = 200, color = red);
print("succeed 1 2", i)
catch:
print("error draw at ", i)
end try;
try
p1 := plots[odeplot](sol, [[t, y3(t)]], t = 0 .. t_sim, numpoints = 200, color = red);
print("succeed 1 3", i)
catch:
print("error draw at ", i)
end try
catch: print("error at ", i);
print(lastexception);
print(ode1a);
print(ode2a);
print(ode3a);
end try;
try
ode1a := diff(y1(t), t) = rhs(odeparm1[1][1])*y1(t)+rhs(odeparm1[1][2])*y2(t)+rhs(odeparm1[1][3])*y3(t);
ode2a := diff(y2(t), t) = rhs(odeparm1[1][4])*y1(t)+rhs(odeparm1[1][5])*y2(t)+rhs(odeparm1[1][6])*y3(t);
ode3a := diff(y3(t), t) = rhs(odeparm1[1][7])*y1(t)+rhs(odeparm1[1][8])*y2(t)+rhs(odeparm1[1][9])*y3(t);
sys := DiffEquation([ode1a, ode2a, ode3a], inputvariable = [y2(t)], outputvariable = [y1(t), y3(t)]);
sysz := ToDiscrete(sys, ts);
in_t := Sine(1, 1, 0, 0);
sol := Simulate(sys, [in_t]);
try
p1 := plots[odeplot](sol, [[t, y1(t)]], t = 0 .. t_sim, numpoints = 200, color = red);
print("succeed 2 1", i)
catch:
print("error draw at ", i)
end try;
try
p1 := plots[odeplot](sol, [[t, y3(t)]], t = 0 .. t_sim, numpoints = 200, color = red);
print("succeed 2 3", i)
catch:
print("error draw at ", i)
end try
catch:
print("error at ", i);
print(lastexception);
print(ode1a);
print(ode2a);
print(ode3a)
end try;
try
ode1a := diff(y1(t), t) = rhs(odeparm1[1][1])*y1(t)+rhs(odeparm1[1][2])*y2(t)+rhs(odeparm1[1][3])*y3(t);
ode2a := diff(y2(t), t) = rhs(odeparm1[1][4])*y1(t)+rhs(odeparm1[1][5])*y2(t)+rhs(odeparm1[1][6])*y3(t);
ode3a := diff(y3(t), t) = rhs(odeparm1[1][7])*y1(t)+rhs(odeparm1[1][8])*y2(t)+rhs(odeparm1[1][9])*y3(t);
sys := DiffEquation([ode1a, ode2a, ode3a], inputvariable = [y3(t)], outputvariable = [y1(t), y2(t)]);
sysz := ToDiscrete(sys, ts);
in_t := Sine(1, 1, 0, 0);
sol := Simulate(sys, [in_t]);
try
p1 := plots[odeplot](sol, [[t, y1(t)]], t = 0 .. t_sim, numpoints = 200, color = red);
print("succeed 3 1", i)
catch:
print("error draw at ", i)
end try;
try
p1 := plots[odeplot](sol, [[t, y2(t)]], t = 0 .. t_sim, numpoints = 200, color = red);
print("succeed 3 2", i)
catch:
print("error draw at ", i)
end try
catch:
print("error at ", i);
print(lastexception);
print(ode1a);
print(ode2a);
print(ode3a)
end try

diff(y1(t), t) = 1.052936200*10^5*y1(t)+70106.19000*y2(t)+35169.00000*y3(t)
diff(y2(t), t) = 70106.19000*y1(t)+71031.61000*y2(t)+35511.00000*y3(t)
diff(y3(t), t) = 35169.00000*y1(t)+35511.00000*y2(t)+36100.00000*y3(t)
"the DEs contain functions with undefined values (probably caused by a discontinuity in the input that was differentiated). As a result, the numerical solution cannot be calculated. The DE system is: %1\"",[(&DifferentialD;)/(&DifferentialD;t) y1(t)=1.052936200 10^5 y1(t)+70106.19000 y2(t)+35169.00000 ({[[0,t<0],[sin(t),otherwise]]),(&DifferentialD;)/(&DifferentialD;t) y2(t)=70106.19000 y1(t)+71031.61000 y2(t)+35511.00000 ({[[0,t<0],[sin(t),otherwise]]),{[[0,t<0],[undefined,t=0],[cos(t),0<t]]=35169.00000 y1(t)+35511.00000 y2(t)+36100.00000 ({[[0,t<0],[sin(t),otherwise]]),y2(0)=0,y1(0)=0]
 
it has error when plot

"The account type or email address or password is incorrect."

None of those things is true. Using those same credentials, I am able to log in to Maple Cloud in my office but not from home. 

Has anyone else had this problem or know of a solution?

Thanks!

Running Maple 2017 in office on Windows 7 and at home on Windows 10.

Office copy is through a site license purchased by my university. Home copy is a personal home-use copy obtained through the Maple Adoption program.

I have a problem for converging dsolve?

"matrix is singular" and '"initial Newton iteration is not converging"' 

thanks

dsolve.mw
 

restart; Digits := 15; c := 5*10^(-12); b := 5*10^(-12); Eb := 210*10^9; Ec := 56*10^6; Gc := 22*10^6; d := 2*10^(-12); L[0] := 17.6*10^(-6); L[1] := 17.6*10^(-6); L[2] := 17.6*10^(-6); `&rho;c` := 60; `&rho;s` := 7900; L := 20*10^(-12); `&zeta;c` := 1; `&zeta;s` := 1

wt := proc (x, t) options operator, arrow; f1(x)*exp(I*omega*t) end proc:

sys3 := {f11, f22, f33, f44, f55};

{-(125/393216)*(diff(diff(diff(diff(diff(diff(f3(x), x), x), x), x), x), x))+(15625/135168)*(diff(diff(diff(diff(f3(x), x), x), x), x))-(4375/44)*(diff(diff(diff(f1(x), x), x), x))-(30625/1936)*(diff(diff(f3(x), x), x)), -12000*(diff(diff(f4(x), x), x))-7500*f3(x)-(9540/79)*f4(x)*omega^2-(30/79)*f5(x)*omega^2+(3/79)*(diff(f1(x), x))*omega^2-(3/158)*(diff(f2(x), x))*omega^2, -12000*(diff(diff(f5(x), x), x))+7500*f3(x)-(9540/79)*f5(x)*omega^2-(30/79)*f4(x)*omega^2+(3/158)*(diff(f1(x), x))*omega^2-(3/79)*(diff(f2(x), x))*omega^2, (2/3)*(diff(diff(f2(x), x), x))+(30/79)*f2(x)*omega^2+(9540/79)*f1(x)*omega^2-(23/33792)*(diff(diff(diff(f3(x), x), x), x))+(1/147456)*(diff(diff(diff(diff(diff(f3(x), x), x), x), x), x))+(1079/72)*(diff(diff(diff(diff(f1(x), x), x), x), x))-(3/1580)*(diff(diff(f1(x), x), x))*omega^2+(3/79)*(diff(f4(x), x))*omega^2+(3/158)*(diff(f5(x), x))*omega^2-128*f1(x)+128*f2(x)+(3/3160)*(diff(diff(f2(x), x), x))*omega^2+(7/20)*(diff(f3(x), x))-(2/3)*(diff(diff(f1(x), x), x)), (9540/79)*f2(x)*omega^2+(30/79)*f1(x)*omega^2-(3/1580)*(diff(diff(f2(x), x), x))*omega^2-(3/158)*(diff(f4(x), x))*omega^2-(3/79)*(diff(f5(x), x))*omega^2+128*f1(x)-128*f2(x)+(3/3160)*(diff(diff(f1(x), x), x))*omega^2+15*(diff(diff(diff(diff(f2(x), x), x), x), x))+(7/20)*(diff(f3(x), x))-(2/3)*(diff(diff(f2(x), x), x))+(2/3)*(diff(diff(f1(x), x), x))-(7/4224)*(diff(diff(diff(f3(x), x), x), x))+(1/147456)*(diff(diff(diff(diff(diff(f3(x), x), x), x), x), x))+(1/64)*(diff(diff(diff(diff(f1(x), x), x), x), x))}

(1)

dsys4 := {bcs3, sys3}; -1; dsys4[1]; -1; indets(dsys4, specfunc(diff))

{diff(diff(diff(diff(diff(diff(f3(x), x), x), x), x), x), x), diff(diff(diff(diff(diff(f3(x), x), x), x), x), x), diff(diff(diff(diff(f1(x), x), x), x), x), diff(diff(diff(diff(f2(x), x), x), x), x), diff(diff(diff(diff(f3(x), x), x), x), x), diff(diff(diff(f1(x), x), x), x), diff(diff(diff(f2(x), x), x), x), diff(diff(diff(f3(x), x), x), x), diff(diff(f1(x), x), x), diff(diff(f2(x), x), x), diff(diff(f3(x), x), x), diff(diff(f4(x), x), x), diff(diff(f5(x), x), x), diff(f1(x), x), diff(f2(x), x), diff(f3(x), x), diff(f4(x), x), diff(f5(x), x)}

(2)

extra_bcs := `minus`({seq(seq(((D@@i)(f1))(a), i = 0 .. 3), a = 0 .. 1), seq(seq(((D@@i)(f2))(a), i = 0 .. 3), a = 0 .. 1), seq(seq(((D@@i)(f3))(a), i = 0 .. 5), a = 0 .. 1), seq(seq(((D@@i)(f4))(a), i = 0 .. 1), a = 0 .. 1), seq(seq(((D@@i)(f5))(a), i = 0 .. 1), a = 0 .. 1)}, `~`[lhs](bcs3))

{f3(0), f3(1), f4(0), f4(1), f5(0), f5(1), (D(f1))(0), (D(f1))(1), (D(f2))(0), (D(f2))(1), (D(f3))(0), (D(f3))(1), (D(f4))(0), (D(f4))(1), (D(f5))(0), (D(f5))(1), ((D@@2)(f1))(0), ((D@@2)(f1))(1), ((D@@2)(f2))(0), ((D@@2)(f2))(1), ((D@@2)(f3))(0), ((D@@2)(f3))(1), ((D@@3)(f1))(0), ((D@@3)(f1))(1), ((D@@3)(f2))(0), ((D@@3)(f2))(1), ((D@@3)(f3))(0), ((D@@3)(f3))(1), ((D@@4)(f3))(0), ((D@@4)(f3))(1), ((D@@5)(f3))(0), ((D@@5)(f3))(1)}

(3)

newsys2 := subs(omega^2 = 10*omega3, sys3):

solve(newsys2, {diff(f1(x), `$`(x, 5)), diff(f2(x), `$`(x, 4)), diff(f3(x), `$`(x, 6)), diff(f4(x), x, x), diff(f5(x), x, x)});

SYS := solve({newsys2[1], newsys2[2], newsys2[3], newsys2[5], diff(newsys2[4], x)}, {diff(f1(x), `$`(x, 5)), diff(f2(x), `$`(x, 4)), diff(f3(x), `$`(x, 6)), diff(f4(x), x, x), diff(f5(x), x, x)}):

BCS4 := eval[recurse](convert(newsys2[4], D), `union`({x = 0}, bcs3));

(2/3)*((D@@2)(f2))(0)-(23/33792)*((D@@3)(f3))(0)+(1/147456)*((D@@5)(f3))(0)+(1079/72)*((D@@4)(f1))(0)-(3/158)*((D@@2)(f1))(0)*omega3+(30/79)*(D(f4))(0)*omega3+(15/79)*(D(f5))(0)*omega3+(3/316)*((D@@2)(f2))(0)*omega3+(7/20)*(D(f3))(0)-(2/3)*((D@@2)(f1))(0)

(4)

extra_bcs := {seq(seq(seq(((D@@i)(cat(f, j)))(a), i = 0 .. N[j]-1), j = 1 .. nops(N)), a = 0 .. 1)}

{f1(0), f1(1), f2(0), f2(1), f3(0), f3(1), f4(0), f4(1), f5(0), f5(1), (D(f1))(0), (D(f1))(1), (D(f2))(0), (D(f2))(1), (D(f3))(0), (D(f3))(1), (D(f4))(0), (D(f4))(1), (D(f5))(0), (D(f5))(1), ((D@@2)(f1))(0), ((D@@2)(f1))(1), ((D@@2)(f2))(0), ((D@@2)(f2))(1), ((D@@2)(f3))(0), ((D@@2)(f3))(1), ((D@@3)(f1))(0), ((D@@3)(f1))(1), ((D@@3)(f2))(0), ((D@@3)(f2))(1), ((D@@3)(f3))(0), ((D@@3)(f3))(1), ((D@@4)(f1))(0), ((D@@4)(f1))(1), ((D@@4)(f3))(0), ((D@@4)(f3))(1), ((D@@5)(f3))(0), ((D@@5)(f3))(1)}

(5)

Typesetting:-mrow(Typesetting:-mo("for", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("bb", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("in", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("extra_bcs", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("do", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("try", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("print", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("bb", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-msup(Typesetting:-mn("10", mathvariant = "normal"), Typesetting:-mrow(Typesetting:-mo("&uminus0;", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mn("5", mathvariant = "normal")), superscriptshift = "0")), mathvariant = "normal"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("res", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("bb", italic = "true", mathvariant = "italic")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo("&coloneq;", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("dsolve", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("SYS", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("union", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("bb", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-msup(Typesetting:-mn("10", mathvariant = "normal"), Typesetting:-mrow(Typesetting:-mo("&uminus0;", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mn("5", mathvariant = "normal")), superscriptshift = "0")), mathvariant = "normal", open = "{", close = "}"), Typesetting:-mo("union", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("bcs3", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("union", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("BCS4", italic = "true", mathvariant = "italic")), mathvariant = "normal", open = "{", close = "}"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("numeric", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("method", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("bvp", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("middefer", italic = "true", mathvariant = "italic")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("output", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("listprocedure", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("initmesh", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("3024", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("approxsoln", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("omega3", italic = "false", mathvariant = "normal"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("0.01", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("f1", italic = "false", mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("x", italic = "false", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-msup(Typesetting:-mi("x", italic = "true", mathvariant = "italic"), Typesetting:-mrow(Typesetting:-mn("4", mathvariant = "normal")), superscriptshift = "0"), Typesetting:-mo("&sdot;", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-msup(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("1", mathvariant = "normal"), Typesetting:-mo("&minus;", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mi("x", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mrow(Typesetting:-mn("4", mathvariant = "normal")), superscriptshift = "0"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("f2", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("x", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-msup(Typesetting:-mi("x", italic = "true", mathvariant = "italic"), Typesetting:-mrow(Typesetting:-mn("3", mathvariant = "normal")), superscriptshift = "0"), Typesetting:-mo("&sdot;", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-msup(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("1", mathvariant = "normal"), Typesetting:-mo("&minus;", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mi("x", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mrow(Typesetting:-mn("3", mathvariant = "normal")), superscriptshift = "0"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("f4", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("x", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("x", italic = "true", mathvariant = "italic"), Typesetting:-mo("&sdot;", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("1", mathvariant = "normal"), Typesetting:-mo("&minus;", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mi("x", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("f3", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("x", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-msup(Typesetting:-mi("x", italic = "true", mathvariant = "italic"), Typesetting:-mrow(Typesetting:-mn("5", mathvariant = "normal")), superscriptshift = "0"), Typesetting:-mo("&sdot;", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-msup(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("1", mathvariant = "normal"), Typesetting:-mo("&minus;", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mi("x", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mrow(Typesetting:-mn("5", mathvariant = "normal")), superscriptshift = "0"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("f5", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("x", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("x", italic = "true", mathvariant = "italic"), Typesetting:-mo("&sdot;", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("1", mathvariant = "normal"), Typesetting:-mo("&minus;", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mi("x", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("abserr", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("0.3", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("catch", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("print", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("lasterror", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("end", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("try", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("end", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("do", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("indx", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("&coloneq;", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("indices", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("res", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("nolist", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mi("nops", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("indx", italic = "true", mathvariant = "italic")), mathvariant = "normal", open = "[", close = "]")), mathvariant = "normal"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "auto"), Typesetting:-mi("res", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("indx", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("1", mathvariant = "normal")), mathvariant = "normal", open = "[", close = "]")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("P", italic = "true", mathvariant = "italic"), Typesetting:-mo("&coloneq;", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("seq", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("subs", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("res", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("indx", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("i", italic = "true", mathvariant = "italic")), mathvariant = "normal", open = "[", close = "]")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("omega3", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("0", mathvariant = "normal")), mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("i", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("1", mathvariant = "normal"), Typesetting:-mo("..", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.0em"), Typesetting:-mi("nops", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("indx", italic = "true", mathvariant = "italic")), mathvariant = "normal", open = "[", close = "]")), mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(":", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo("for", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("i", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("from", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("1", mathvariant = "normal"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("by", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("1", mathvariant = "normal"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("to", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("nops", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("indx", italic = "true", mathvariant = "italic")), mathvariant = "normal", open = "[", close = "]")), mathvariant = "normal"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("do", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfrac(Typesetting:-mrow(Typesetting:-mi("sqrt", italic = "false", mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("10", mathvariant = "normal"), Typesetting:-mo("^", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.1111111em", rspace = "0.1111111em"), Typesetting:-mn("1", mathvariant = "normal"), Typesetting:-mo("*", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.1666667em", rspace = "0.1666667em"), Typesetting:-mi("P", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("i", italic = "true", mathvariant = "italic")), mathvariant = "normal", open = "[", close = "]")), mathvariant = "normal")), Typesetting:-mrow(Typesetting:-mn("2", mathvariant = "normal"), Typesetting:-mo("&sdot;", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("Pi", italic = "false", mathvariant = "normal")), linethickness = "1", denomalign = "center", numalign = "center", bevelled = "false"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("od", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(";", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"), Typesetting:-mi("plots", italic = "true", mathvariant = "italic"), Typesetting:-mo(":-", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("odeplot", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("res", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("indx", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("1", mathvariant = "normal")), mathvariant = "normal", open = "[", close = "]")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi(""), Typesetting:-mrow(Typesetting:-mi("seq", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("x", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("cat", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("f", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("i", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("x", italic = "true", mathvariant = "italic")), mathvariant = "normal")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("i", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("1", mathvariant = "normal"), Typesetting:-mo("..", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.0em"), Typesetting:-mn("1", mathvariant = "normal")), mathvariant = "normal")), Typesetting:-mi("")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mn("0", mathvariant = "normal"), Typesetting:-mo("..", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.0em"), Typesetting:-mn("1", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("thickness", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("3", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(";", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"), Typesetting:-mi("plots", italic = "true", mathvariant = "italic"), Typesetting:-mo(":-", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("odeplot", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("res", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("indx", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("1", mathvariant = "normal")), mathvariant = "normal", open = "[", close = "]")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi(""), Typesetting:-mrow(Typesetting:-mi("seq", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("x", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("cat", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("f", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("i", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("x", italic = "true", mathvariant = "italic")), mathvariant = "normal")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("i", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("2", mathvariant = "normal"), Typesetting:-mo("..", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.0em"), Typesetting:-mn("2", mathvariant = "normal")), mathvariant = "normal")), Typesetting:-mi("")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mn("0", mathvariant = "normal"), Typesetting:-mo("..", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.0em"), Typesetting:-mn("1", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("thickness", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("3", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(";", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"), Typesetting:-mi("plots", italic = "true", mathvariant = "italic"), Typesetting:-mo(":-", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("odeplot", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("res", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("indx", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("1", mathvariant = "normal")), mathvariant = "normal", open = "[", close = "]")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi(""), Typesetting:-mrow(Typesetting:-mi("seq", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("x", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("cat", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("f", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("i", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("x", italic = "true", mathvariant = "italic")), mathvariant = "normal")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("i", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("3", mathvariant = "normal"), Typesetting:-mo("..", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.0em"), Typesetting:-mn("3", mathvariant = "normal")), mathvariant = "normal")), Typesetting:-mi("")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mn("0", mathvariant = "normal"), Typesetting:-mo("..", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.0em"), Typesetting:-mn("1", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("thickness", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("3", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(";", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"), Typesetting:-mi("plots", italic = "true", mathvariant = "italic"), Typesetting:-mo(":-", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("odeplot", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("res", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("indx", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("1", mathvariant = "normal")), mathvariant = "normal", open = "[", close = "]")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi(""), Typesetting:-mrow(Typesetting:-mi("seq", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("x", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("cat", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("f", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("i", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("x", italic = "true", mathvariant = "italic")), mathvariant = "normal")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("i", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("4", mathvariant = "normal"), Typesetting:-mo("..", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.0em"), Typesetting:-mn("4", mathvariant = "normal")), mathvariant = "normal")), Typesetting:-mi("")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mn("0", mathvariant = "normal"), Typesetting:-mo("..", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.0em"), Typesetting:-mn("1", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("thickness", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("3", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(";", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"), Typesetting:-mi("plots", italic = "true", mathvariant = "italic"), Typesetting:-mo(":-", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("odeplot", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("res", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("indx", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn("1", mathvariant = "normal")), mathvariant = "normal", open = "[", close = "]")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi(""), Typesetting:-mrow(Typesetting:-mi("seq", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("x", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("cat", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("f", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("i", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("x", italic = "true", mathvariant = "italic")), mathvariant = "normal")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("i", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("5", mathvariant = "normal"), Typesetting:-mo("..", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.0em"), Typesetting:-mn("5", mathvariant = "normal")), mathvariant = "normal")), Typesetting:-mi("")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mn("0", mathvariant = "normal"), Typesetting:-mo("..", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.0em"), Typesetting:-mn("1", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("thickness", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("3", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(";", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"))

f1(0) = 1/100000

 

"matrix is singular"

 

f1(1) = 1/100000

 

"matrix is singular"

 

f2(0) = 1/100000

 

"matrix is singular"

 

f2(1) = 1/100000

 

"matrix is singular"

 

f3(0) = 1/100000

 

"initial Newton iteration is not converging"

 

f3(1) = 1/100000

 

"initial Newton iteration is not converging"

 

f4(0) = 1/100000

 

"initial Newton iteration is not converging"

 

f4(1) = 1/100000

 

"initial Newton iteration is not converging"

 

f5(0) = 1/100000

 

"precision is insufficient for required absolute error, suggest increasing Digits to approximately %1 for this problem", 21

 

f5(1) = 1/100000

 

"initial Newton iteration is not converging"

 

(D(f1))(0) = 1/100000

 

"initial Newton iteration is not converging"

 

(D(f1))(1) = 1/100000

 

"initial Newton iteration is not converging"

 

(D(f2))(0) = 1/100000

 

"initial Newton iteration is not converging"

 

(D(f2))(1) = 1/100000

 

"initial Newton iteration is not converging"

 

(D(f3))(0) = 1/100000

 

"precision is insufficient for required absolute error, suggest increasing Digits to approximately %1 for this problem", 25

 

(D(f3))(1) = 1/100000

 

"initial Newton iteration is not converging"

 

(D(f4))(0) = 1/100000

 

"matrix is singular"

 

(D(f4))(1) = 1/100000

 

"matrix is singular"

 

(D(f5))(0) = 1/100000

 

"matrix is singular"

 

(D(f5))(1) = 1/100000

 

"matrix is singular"

 

((D@@2)(f1))(0) = 1/100000

 

"initial Newton iteration is not converging"

 

((D@@2)(f1))(1) = 1/100000

 

"initial Newton iteration is not converging"

 

((D@@2)(f2))(0) = 1/100000

 

"initial Newton iteration is not converging"

 

((D@@2)(f2))(1) = 1/100000

 

"initial Newton iteration is not converging"

 

((D@@2)(f3))(0) = 1/100000

 

"precision is insufficient for required absolute error, suggest increasing Digits to approximately %1 for this problem", 22

 

((D@@2)(f3))(1) = 1/100000

 

"precision is insufficient for required absolute error, suggest increasing Digits to approximately %1 for this problem", 23

 

((D@@3)(f1))(0) = 1/100000

 

"initial Newton iteration is not converging"

 

((D@@3)(f1))(1) = 1/100000

 

"initial Newton iteration is not converging"

 

((D@@3)(f2))(0) = 1/100000

 

"initial Newton iteration is not converging"

 

((D@@3)(f2))(1) = 1/100000

 

"initial Newton iteration is not converging"

 

((D@@3)(f3))(0) = 1/100000

 

"precision is insufficient for required absolute error, suggest increasing Digits to approximately %1 for this problem", 24

 

((D@@3)(f3))(1) = 1/100000

 

"precision is insufficient for required absolute error, suggest increasing Digits to approximately %1 for this problem", 25

 

((D@@4)(f1))(0) = 1/100000

 

"initial Newton iteration is not converging"

 

((D@@4)(f1))(1) = 1/100000

 

"initial Newton iteration is not converging"

 

((D@@4)(f3))(0) = 1/100000

 

"precision is insufficient for required absolute error, suggest increasing Digits to approximately %1 for this problem", 24

 

((D@@4)(f3))(1) = 1/100000

 

"precision is insufficient for required absolute error, suggest increasing Digits to approximately %1 for this problem", 23

 

((D@@5)(f3))(0) = 1/100000

 

"precision is insufficient for required absolute error, suggest increasing Digits to approximately %1 for this problem", 21

 

((D@@5)(f3))(1) = 1/100000

 

"precision is insufficient for required absolute error, suggest increasing Digits to approximately %1 for this problem", 24

 

Error, invalid input: indices received res, which is not valid for its 1st argument, t

 

Error, invalid input: subs received res[indx[1]](0), which is not valid for its 1st argument

 

(1/2)*10^(1/2)*P[1]^(1/2)/Pi

 

Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

 

Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

 

Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

 

Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

 

Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

 

sys3[5]:

NULL

NULL


 

Download dsolve.mw

 

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