MaplePrimes Questions

I ran into this problem when trying to do some symbolic vector calculus using the with(Physics[Vectors]) package. I have uploaded my document (at least I hope it uploads correctly). I use 1-D math input because I learned maple 13 years ago.

Thanks for any help you all can provide.

Cheers,

Dave
 

``

Problem 3-1

 

typsetting issue

 

restart; with(Physics[Vectors]): Setup(mathematicalnotation=true);
#Coordinates(cartesian); Coordinates(X = [x,y,z,t])

[mathematicalnotation = true]

(1.1.1)

D1:=D1_(t,x,y,z);
B:=B_(t,x,y,z);
E:=E_(t,x,y,z);
j__p:=j__p_(t,x,y,z);

D1_(t, x, y, z)

 

B_(t, x, y, z)

 

E_(t, x, y, z)

 

j__p_(t, x, y, z)

(1.1.2)

f1:=epsilon=epsilon__0+rho/(B_.B_);

epsilon = epsilon__0+rho/Physics:-Vectors:-Norm(B_)^2

(1.1.3)

f2:=%Divergence(D1_)=0;
f3:=%Divergence(epsilon*E_)=0;

%Divergence(D1_) = 0

 

%Divergence(epsilon*E_) = 0

(1.1.4)

poisson equation and assume sigma is sigma__p

f4:=epsilon__0*%Divergence(E_)=sigma__p(t);

epsilon__0*%Divergence(E_) = sigma__p(t)

(1.1.5)

f5:=diff(sigma__p(t),t)+%Divergence(j__p_)=0;
f6:=j__p=n*e(v__i_p-v__e_p);
f7:=j__p=n/(B_.B_)*(m__i+m__e)*Diff(E_,t);
f8:=j__p=rho/(B_.B_)*Diff(E_,t);

diff(sigma__p(t), t)+%Divergence(j__p_) = 0

 

j__p_(t, x, y, z) = n*e(v__i_p-v__e_p)

 

j__p_(t, x, y, z) = n*(m__i+m__e)*(Diff(E_, t))/Physics:-Vectors:-Norm(B_)^2

 

j__p_(t, x, y, z) = rho*(Diff(E_, t))/Physics:-Vectors:-Norm(B_)^2

(1.1.6)

f9:=Diff(f2,t);
f10:=Diff(f3,t);
f11:=Diff(f4,t);

Diff(%Divergence(D1_) = 0, t)

 

Diff(%Divergence(epsilon*E_) = 0, t)

 

Diff(epsilon__0*%Divergence(E_) = sigma__p(t), t)

(1.1.7)

``


 

Download Typesetting-delayDotProduct.mw

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

 

how to mirror the vector field graph mathematically?

mirror the graph about x=0 this line,

so that the graph looked flip

i find curl can do, but how to do ?

 

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

 

I am relatively new to maple and am using it for a multivariate calculus class.

I want to define a function g(x,y) which is the derivative of f(x,y).

I am trying:

which is my function, and

which should be the derivative.

When I try g(x,y) I get

but when I try to put numerical values in the first argument, (eg: f(1,y) I get

"Error, (in g) invalid input: diff received 1, which is not valid for its 2nd argument"
Any tips?

Hi quick question.  When I am writing in maple 2D input the next line seems to add a space and I have to manually go and take the spaces out.  Is there a quick fix for this?  

Thank you.

Why do I get different answers for the same command?

 different_answers.mw


 

``

restart

x := proc (n) options operator, arrow; cos(n*Pi) end proc;

proc (n) options operator, arrow; cos(n*Pi) end proc

(1)

"f:=k->"sum(k*x(n), n = 2 .. 3);f(1);

0

 

f(1)

(2)

f := proc (k) options operator, arrow; sum(k*x(n), n = 2 .. 3) end proc;

proc (k) options operator, arrow; sum(k*x(n), n = 2 .. 3) end proc

 

0

(3)

``


 

Download different_answers.mw

convert(arctan(y, x), abs);
                             / y + I x \
                        -I ln|---------|
                             \|y + I x|/

The output has x and y swapped. Further, for complex x and y it's wrong even if x and y are swapped back, because Maple's definition of arctan has sqrt(x^2+y^2) in the denominator, which isn't the same as abs(x+I*y).

 

Hello everybody

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

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

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

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

Thanks in advance


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


 

Download NegativeBinomial.mw

signum(0, abs(x), 0);
                       signum(0, |x|, 0)

signum(0, abs(tan(Pi/5)-sqrt(5-2*sqrt(5))), 0);
                               1

The second one should give 0 or return unevaluated.

 

I have recently reinstalled the MapleSim 6.4 but the probe windows do not appeaar anymore.

The image below shows that there are 3 probes (none are disabled) and when I run the simulation nothing happens.,

hi..i have a problem with dsolve.

please help me thanks

1.mw
 

restart; Digits := 15; c := 5*10^(-12); b := 5*10^(-12); E[s] := 210*10^9; E[c] := 56*10^6; G[c] := 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); `ρ__c` := 60; `ρ__s` := 7900; L := 20*10^(-12); `ζ__c` := 1; `ζ__s` := 1

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

dsys3 := {f11, f22, f33, f44, f55, 12*(L/d)^3*((D@@1)(f5))(0) = 0, 12*(L/d)^3*((D@@1)(f5))(1) = 0, 12*(L/d)^3*((D@@1)(f4))(0)+(1/5)*Zeta*(diff(w__t(x, t), x, x, x, x))*((D@@4)(f1))(0) = 0, 12*(L/d)^3*((D@@1)(f4))(1)+(1/5)*Zeta*(diff(w__t(x, t), x, x, x, x))*((D@@4)(f1))(1) = 0, (1/120)*zeta__c*(c/d)^4*(c/L)^5*((D@@3)(f3))(0)-((1/12)*zeta__c*(c/d)^4*(c/L)^3*((1/2)*E__c/G__c))*((D@@1)(f3))(0)+(1/24)*zeta__c*(c/d)^4*c*((D@@2)(f1))(0)/L = 0, (1/120)*zeta__c*(c/d)^4*(c/L)^5*((D@@3)(f3))(1)-((1/12)*zeta__c*(c/d)^4*(c/L)^3*((1/2)*E__c/G__c))*((D@@1)(f3))(1)+(1/24)*zeta__c*(c/d)^4*c*((D@@2)(f1))(1)/L = 0, -(1/120)*zeta__c*(c/d)^4*(c/L)^5*((D@@4)(f3))(0)+(1/12)*zeta__c*(c/d)^4*(c/L)^3*(1+(1/2)*E__c/G__c)*((D@@2)(f3))(0)-(1/24)*zeta__c*(c/d)^4*c*(diff(w__t(x, t), x, x, x))*((D@@3)(f1))(0)/L = 0, -(1/120)*zeta__c*(c/d)^4*(c/L)^5*((D@@4)(f3))(1)+(1/12)*zeta__c*(c/d)^4*(c/L)^3*(1+(1/2)*E__c/G__c)*((D@@2)(f3))(1)-(1/24)*zeta__c*(c/d)^4*c*(diff(w__t(x, t), x, x, x))*((D@@3)(f1))(1)/L = 0, -((1/4)*zeta__c*E__c*(c/d)^4*c/(E__s*L)*(E__c/G__c))*((D@@1)(f3))(0)+(1/24)*zeta__c*E__c*(c/d)^4*(c/L)^3*((D@@3)(f3))(0)/E__s+(Zeta*c/d*(L/d)-(1/3)*zeta__c*E__c*(c/d)^3*L/(E__s*d))*((D@@2)(f1))(0)-L*((D@@3)(f1))(0)/d = 0, -((1/4)*zeta__c*E__c*(c/d)^4*c/(E__s*L)*(E__c/G__c))*((D@@1)(f3))(1)+(1/24)*zeta__c*E__c*(c/d)^4*(c/L)^3*((D@@3)(f3))(1)/E__s+(Zeta*c/d*(L/d)-(1/3)*zeta__c*E__c*(c/d)^3*L/(E__s*d))*((D@@2)(f1))(1)-L*((D@@3)(f1))(1)/d = 0, -L*((D@@2)(f2))(0)/d-((1/4)*zeta__c*E__c*(c/d)^4*c/(E__s*L)*(E__c/G__c))*((D@@1)(f3))(0)+(1/24)*zeta__c*E__c*(c/d)^4*(c/L)^3*((D@@3)(f3))(0)/E__s+(3/8)*zeta__c*E__c*(c/d)^3*L*((D@@2)(f1))(0)/(E__s*d)+(Zeta*c/d*(L/d))*((D@@2)(f2))(0) = 0, -L*((D@@2)(f2))(1)/d-((1/4)*zeta__c*E__c*(c/d)^4*c/(E__s*L)*(E__c/G__c))*((D@@1)(f3))(1)+(1/24)*zeta__c*E__c*(c/d)^4*(c/L)^3*((D@@3)(f3))(1)/E__s+(3/8)*zeta__c*E__c*(c/d)^3*L*((D@@2)(f1))(1)/(E__s*d)+(Zeta*c/d*(L/d))*((D@@2)(f2))(1) = 0, (1/120)*zeta__c*(c/d)^4*(c/L)^5*((D@@5)(f3))(0)-(1/12)*zeta__c*(c/d)^4*(c/L)^3*(1+(1/2)*E__c/G__c)*((D@@3)(f3))(0)+(1/24)*zeta__c*(c/d)^4*c*((D@@4)(f1))(0)/L+(1/4)*zeta__c*(c/d)^3*L*E__c*((D@@2)(f1))(0)/(d*G__c)+(1/4)*zeta__c*(c/d)^4*c*(E__c/G__c)^2*((D@@1)(f3))(0)/L = 0, (1/120)*zeta__c*(c/d)^4*(c/L)^5*((D@@5)(f3))(1)-(1/12)*zeta__c*(c/d)^4*(c/L)^3*(1+(1/2)*E__c/G__c)*((D@@3)(f3))(1)+(1/24)*zeta__c*(c/d)^4*c*((D@@4)(f1))(1)/L+(1/4)*zeta__c*(c/d)^3*L*E__c*((D@@2)(f1))(1)/(d*G__c)+(1/4)*zeta__c*(c/d)^4*c*(E__c/G__c)^2*((D@@1)(f3))(1)/L = 0, f1(0) = 0, f1(1) = 0, f2(0) = 0, f2(1) = 0}:

dsys4 := subs(omega^2 = omega2, dsys3):

solve(sys, {diff(f1(x), `$`(x, 4)), diff(f2(x), `$`(x, 4)), diff(f3(x), `$`(x, 6)), diff(f4(x), `$`(x, 2)), diff(f5(x), `$`(x, 2))}):

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")), 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("≔", 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("dsys4", 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:-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:-mn(".0000000000001", mathvariant = "normal")), 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("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("omega2", 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:-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(".000000001", 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 = "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("⋅", 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("&uminus0;", 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("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("⋅", 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("&uminus0;", 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("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("⋅", 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("&uminus0;", 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("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:-msup(Typesetting:-mi("x", italic = "true", mathvariant = "italic"), Typesetting:-mrow(Typesetting:-mi("")), superscriptshift = "0"), 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:-mn("1", mathvariant = "normal"), 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:-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:-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 = "0.0em", 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("⋅", 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("&uminus0;", 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")), 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("2024", 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("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("1e−5", 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:-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("≔", 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 = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", 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("Sol", 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("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("omega2", 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"))

f3(0)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

f3(1)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

f4(0)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

f4(1)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

f5(0)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

f5(1)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

(D(f1))(0)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

(D(f1))(1)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

(D(f2))(0)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

(D(f2))(1)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

(D(f3))(0)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

(D(f3))(1)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

(D(f4))(0)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

(D(f4))(1)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

(D(f5))(0)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

(D(f5))(1)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

((D@@2)(f1))(0)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

((D@@2)(f1))(1)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

((D@@2)(f2))(0)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

((D@@2)(f2))(1)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

((D@@2)(f3))(0)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

((D@@2)(f3))(1)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

((D@@3)(f1))(0)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

((D@@3)(f1))(1)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

((D@@3)(f2))(0)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

((D@@3)(f2))(1)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

((D@@3)(f3))(0)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

((D@@3)(f3))(1)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

((D@@4)(f3))(0)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

((D@@4)(f3))(1)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

((D@@5)(f3))(0)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

((D@@5)(f3))(1)

 

"input system must be an ODE system, found %1", {f3(x), u__ob(x, t), u__ot(x, t), w__b(x, t), w__t(x, t)}

 

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

 

NULL


 

Download 1.mw

 

Hi Maple folks!

I am trying to solve the following PDE in maple:

pde:= diff(c(x,t),t)+c(x,t)*diff(c(x,t),x)=0

bc:=c(x,0)=piecewise(x < 0, 0, x > 0, 1)

I tried the following:

pdsolve({pde,bc}, c(x, 0))

But it gives no solution, i also tried a numeric solution, but i couldn't make it work. Please help.

Thanks! :)

 

I have written a Maple code which extracts terms in a matrix into two new matrices dependent on certain markers. I am running into problems with this particular code as it requires enormous amounts of RAM when going to large matrix sizes (32GB+); and will take 4-5 days to complete for larger matrix sizes, or simply crashes.

Each matrix element is an algebraic expression containing A and B and the markers hh and ss. The example in the attached Maple file (3 x 3 matrix) is a minimal working example and the actual expressions are much longer and the matrices much larger (5000 x 5000 or larger). I utilise the symmetry of the matrix to ease the process, and use the tril command of MTM to extract only the lower triangular matrix; as this is all that is needed for the next stage (I have yet to test how efficient this command is, but use it for now).

The two markers hh and ss are targeted and if found in an expression that term will be extracted accordingly. The matrix elements are expanded and a procedure run over the matrix and will extract terms with hh into one matrix and terms with ss into another matrix. I think the map(expand,...) part is what causes the memory issue; but I believe this needs to be done to correctly extract terms.

Any help or tips are greatly appreciated on how to increase efficiency and improve this method.
 

Sub_matrix_extraction.mw

-Yeti

 

 

seq(alias(a[i] = RootOf(_Z1^6-3*_Z1^2-2*_Z1+11, index = i)), i = 1..6):

ee := a[1]*a[5]+a[2]*a[6]+a[3]*a[4];

evalf(ee);
                       3.999999999 + 0. I

evala(ee);
  -(18/449)*a[1]^2-(196/449)*a[1]^3-(128/449)*a[1]^4+(40/449)*a[1]^5+(110/449)*a[2]^2-
  (324/449)*a[2]^3-(220/449)*a[3]-(680/449)*a[2]-(320/449)*a[1]-(60/449)*a[3]*a[2]^2*a[1]^2+
  (64/449)*a[3]*a[2]*a[1]^2+(128/449)*a[3]*a[2]^2*a[1]-(256/449)*a[3]*a[2]*a[1]-
  (32/449)*a[2]^3*a[3]*a[1]^3-(16/449)*a[3]*a[2]^2*a[1]^5-(16/449)*a[3]*a[2]^3*a[1]^4+
  (32/449)*a[3]*a[2]*a[1]^5-(16/449)*a[3]*a[2]^2*a[1]^4-(24/449)*a[3]*a[2]*a[1]^4-
  (56/449)*a[3]*a[2]^2*a[1]^3-(16/449)*a[3]*a[2]^3*a[1]^2+(40/449)*a[2]^2*a[1]^2+
  (66/449)*a[3]*a[2]^2-(232/449)*a[3]*a[2]+(24/449)*a[3]*a[1]^5+(64/449)*a[3]*a[1]^4+
  (164/449)*a[3]*a[1]^3+(130/449)*a[3]*a[1]^2-(192/449)*a[3]*a[1]+(228/449)*a[2]^3*a[3]-
  (32/449)*a[2]*a[1]^5+(88/449)*a[2]*a[1]^4+(128/449)*a[2]*a[1]^3+(256/449)*a[2]*a[1]-
  (32/449)*a[2]^3*a[1]^5-(48/449)*a[2]^3*a[1]^3-(88/449)*a[2]^3*a[1]^2+(256/449)*a[2]^3*a[1]-
  (256/449)*a[2]^2*a[1]+(32/449)*a[2]^2*a[1]^5-(48/449)*a[2]^2*a[1]^4-(48/449)*a[2]^2*a[1]^3+1780/449

evalf(evala(ee));
                  3.139680582 - 1.737673929 I

I wasn't able to figure out what it depends on, but evala(ee) doesn't always do the same thing. If I don't evaluate evalf(ee) first, then most times I get the correct result evala(ee)=4.

This is in Maple 2017.2, system="X86 64 WINDOWS", wordsize=64.

 

aa := tan(Pi/11)^2;
bb := RootOf(_Z^5-55*_Z^4+330*_Z^3-462*_Z^2+165*_Z-11, index = 1); # bb = aa
ee := (exp(-Pi-I*Pi*aa/bb))^(1+I);

seq((proc() try timelimit(k, signum(Re(ee)-1/k)) catch: lprint(lastexception) end try end proc)(),
    k = 1..10);

`shake/shake`, "time expired"
`expand/sin`, "time expired"
`evalr/tan`, "time expired"
sdmp:-mul, "time expired"
                        1, 1, 1, 1, 1, 1

An explanation: aa/bb=1, so, as we know from here, ee=exp(-2*Pi), and ee is tricky to evaluate numerically. Normally signum(Re(ee)-1/5) just seems to hang indefinitely, which is not the worst thing it could do. But after one of the timelimit interrupts (or after clicking "Interrupt the current operation"), something breaks, and Maple starts returning wrong values.

This is in Maple 2017.2, system="X86 64 WINDOWS", wordsize=64.

Also, is there any way to clear the cached values so that this computation can be repeated without doing restart?

 

Hi, I have a system of 15 polynomial equations (of 15 variables) of 2nd degree. Meaning, every monomial has at most mulplications of 2 different variables or a single variable squared.

I tried to solve them in Maple but it's been 2 hours and Maple is still thinking.. I don't have any indication if Maple is just stuck or it should return a solution at some point.  

Below I wrote the Maple commands that I tried to run (sorry but I'm new here so I didn't know how to write them nicely). I also wrote one of the solutions that I'm expecting to get (15 values for the 15 variables). and you can see that by typing eq7 for example I got -2.5=-2.5 (and the same for the rest of the equations) which means that the values are correct.

I know there is an algorithm for solving any system of numerical polynomial equations of any degree. I don't know if Maple implemented it.

Anyone knows if Maple is able to solve the equations below? and if not, is there any other way that can be done to solve them?

Thanks

David

 

Here's the commands for Maple (including one of the solutions I'm expecting to get).

The variables are: r11, r12, r13, r21, r22, r23, r31, r32, r33, t1, t2, t3, s1, s2, s3

eq1:=r11^2+r21^2+r31^2 = 1;
eq2:=r12^2+r22^2+r32^2 = 1;
eq3:=r13^2+r23^2+r33^2 = 1;
eq4:=r11*r12+r21*r22+r31*r32 = 0;
eq5:=r11*r13+r21*r23+r31*r33 = 0;
eq6:=r12*r13+r22*r23+r32*r33 = 0;
eq7:=-30*r13-.79382581863774e-1*s1*r11-.95259098236529e-1*s1*r12+.992282273297173*s1*r13 = -.83717247687439e-1*t1;
eq8:=-30*r13+.79382581863774e-1*s2*r11+.95259098236529e-1*s2*r12+.992282273297173*s2*r13 = .76364294519742e-1*t2;
eq9:=-30*r13-.86165283952334e-1*s3*r11+.103398340742801*s3*r12+.990900765451843*s3*r13 = -.81460429387834e-1*t3;
eq10:=-30*r23-.79382581863774e-1*s1*r21-.95259098236529e-1*s1*r22+.992282273297173*s1*r23 = -.107930827800543*t1;
eq11:=-30*r23+.79382581863774e-1*s2*r21+.95259098236529e-1*s2*r22+.992282273297173*s2*r23 = .60269029165473e-1*t2;
eq12:=-30*r23-.86165283952334e-1*s3*r21+.103398340742801*s3*r22+.990900765451843*s3*r23 = .105021268850622*t3;
eq13:=-30*r33-.79382581863774e-1*s1*r31-.95259098236529e-1*s1*r32+.992282273297173*s1*r33 = .990627255252918*t1-30;
eq14:=-30*r33+.79382581863774e-1*s2*r31+.95259098236529e-1*s2*r32+.992282273297173*s2*r33 = .995256820446840*t2-30;
eq15:=-30*r33-.86165283952334e-1*s3*r31+.103398340742801*s3*r32+.990900765451843*s3*r33 = .991128009660183*t3-30;


r11 := 1;
r12 := 0;
r13 := 0;
x := .523598775598299;
r21 := 0;
r22 := cos(x);
r23 := -sin(x);
r31 := 0;
r32 := sin(x);
r33 := cos(x);
t1 := 29.862424638395044;
t2 := 32.737813080348531;
t3 := 30.689747387623886;
s1 := 31.493054789905649;
s2 := 31.493054789905628;
s3 := 29.014005238849720;
eq1;
eq2;
eq3;
eq4;
eq5;
eq6;
eq7;
eq8;
eq9;
eq10;
eq11;
eq12;
eq13;
eq14;
eq15;

unassign('r11', 'r12', 'r13', 'r21', 'r22', 'r23', 'r31', 'r32', 'r33', 't1', 't2', 't3', 's1', 's2', 's3');
solve({eq1, eq10, eq11, eq12, eq13, eq14, eq15, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9}, {r11, r12, r13, r21, r22, r23, r31, r32, r33, s1, s2, s3, t1, t2, t3});

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