MaplePrimes Questions

"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); `ρc` := 60; `ρs` := 7900; L := 20*10^(-12); `ζc` := 1; `ζs` := 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("≔", 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("⋅", 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("−", 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("⋅", 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("−", 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("⋅", 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("−", 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("⋅", 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("−", 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("⋅", 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("−", 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("≔", 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("≔", 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("⋅", 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

 

I am attempting to build a text field at the bottom of this worksheet MathApps-ResistorsMark.mw  that asks users for the resistance.

I am hoping to have the value of the text field evaluated using the Module() at the bottom of the startup code, for use as a question within MapleTA.  For some reason I can get the code to work for a slider, but not a textbox.

I have limited knowledge about startup code.

Notice: I will be removing the resistance from the diagram for students after I know it works.

I appreciate any help that can be offered.

I am trying to understand the use of "events" in solving ode's, specifically the possible actions.
From the help pages:

Events are specified by the events=[event1,event2,...] option in the call to dsolve[numeric], where each event is a list of [trigger,action] pairs, where the trigger describes the trigger of the event, and the action describes the action to perform when the event is triggered.

It then goes on to list possible actions, for example,

u(t) = -u(t): execute statement when triggered
– [u(t) = -u(t), y(t) = -y(t)]: execute statements when triggered
[If(y(t) < 0, y(t) = -y(t), halt)]: execute statements conditionally when triggered

I tried to use the first one unsuccessfully several ways:
This works:dsolve({eq, y(0) = 1, (D(y))(0) = -1}, numeric, events = [[x+y(x) = 15, halt]])

but dsolve({eq, y(0) = 1, (D(y))(0) = -1}, numeric, events = [[y(x) = 0,[ 'print("Yes'")', halt]]]) does not

nor does any variant of that using print.

Also, I cannot get at the result of any assingment, e.g.,

dsolve({eq, y(0) = 1, (D(y))(0) = -1}, numeric, events = [[y(x) = 0, [z = diff(y(x), x), halt]]]) does not work either; z does not have a value. What commands can be executed as actions after an event is triggered?

 

 

 

 

I experience an issued with a 3d plot. This is my code and I get: "Warning, expecting only range variables [H[s], H[j]] in expression eq to be plotted but found name eq." as a return from Maple.

restart;

eq = c[1]-abs(H[s])^2*sigma^2/abs(H[j])^2;

c[1] := 2;

c[2] := 4;

sigma := 1;

tmp := plot3d(eq, H[s] = .1 .. 2, H[j] = 0 .. 5, view = 0 .. 8,

axes = boxed, labels = [H[s], H[j], P[j]],

filled = [style = surface, transparency = .2]); plots:-display(tmp, view = 0.1e-1 .. 8)

I have two square matrices (LS,RS) in the form of generalized eigen-value problem as below:

LS*z=omega*RS*z

One time, I am using inverse of RS multiplying by LS to get the eigen values as
MS := MatrixInverse(RS) . LS:
VL1, VR1 := Eigenvectors(MS):

Next time, I am using direct method as below to get the eigen values 

VL2, VR2 := Eigenvectors(LS, RS);
 

I am wondering there are meaningful differences between VL1 and VL2 as well as VR1 and VR2.

Does anybody know why?

RS.mw

LS.mw

 

 

 

there is a problem with users tab and web page of mapleprimes, and it just does display the first page and not other pages ...
for example :
https://www.mapleprimes.com/users/?page=2
is not displayed ...

i have started using maple toolbox on MATLAB and i have alot of questions...
first of all, why there is not a good document for using maple toolbox on matlab ? how commands should be use and so on?
MY FIRST QUESTION : can we increase number of digits for using solve or fsolve command in maple toolbox on matlab?
MY SECOND QUESTION : when using maple toolbox, the output is displayed just like when using 'pretty print' command, can we deactivate this option ?
for example, i used fsolve , and want output and the calculations be done using 50 Digits, but it does not ! :(

The object in the above display consists of a thin red disk and attached thin blue disk. They have radii 1.0 and 0.2 and masses 1.0 and 0.2 respectively.

Starting from rest at the above position they are given an initial angular velocity of Omega radians/second which starts the object rolling along the positive x axis.

If Omega is great enough that, at some time during the roll, the vertical component of the centrifugal force on the blue disk exceeds the downward force of gravity on the object, will the object begin a spinning projectile motion above the x axis?

Assuming both disks have negligible thickness, what Physics laws will govern the rolling and (possible) spinning projectile motions and what mathematics describes these motions? 

I have a big vector (1*10000) composed of negative, positive and HFloat(infinity) elements. How to extract only positive elements of this messy big vector with corresponding number of element,except positive infinities?

For example, suppose only the 111,181, 206th elemenst of this vector are positive values as: 101.2109e11,19211.129,87211.

How to get both 111,181, 206 and their corresponding values, 101.2109e11,19211.129,87211?

Dear Maple users,

I am solving a system of linear equations Ax=b where A is a matrix (243*241) which contains a rational polynomial of unknown "kappa" along with floating numbers. As suggested in some other posts I am using Linear algebra package with the LinearSolve command and option "solve" to find out unknown vector x. b is a vector having entries zero and 1. The system is such that two equations are redundant but it is difficult to recognise which two are redundant and hence for the time being I am keeping them in the matrix. (For a known value of kappa (say kappa=2) I have checked that two equations are redundant.) For the reference, the matrix and the right-hand vector b is attached as text.

There are two issues

1) Maple takes very long time (12 hours and so) to get x=b\A;

2) The result is a long expression i.e.  x[i] is a rational polynomial in kappa; a very long rational polynomial which I am importing as a text. I am not sure if maple exports all terms in the polynomial as for the different value of kappa I see Ax-b >0. 

How can I overcome this problem? Any help will be greatly appreciated. 

for example, a__b+b__a+a__b^2,how i can choose the first and third.

I posted a similar question about typesetting:-delayDotProduct. I used two different methods to solve the same vector calculus problem and came up with two seperate problems, though both are using the with(Physics[Vectors]) package. Below is my code showing the error.

Thanks for any help you all can give on this.

Cheers,

Dave
 

``

Problem 3-1

 

basis issue

 

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

[mathematicalnotation = true]

 

Coordinates(cartesian)

 

Coordinates(X = [x, y, z, t])

(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:=Nabla.D1=0;
f3:=Nabla.(epsilon*E)=0;

Physics:-Vectors:-Divergence(D1_(t, x, y, z)) = 0

 

epsilon*Physics:-Vectors:-Divergence(E_(t, x, y, z)) = 0

(1.1.4)

poisson equation and assume sigma is sigma__p

f4:=epsilon__0*(Nabla.E)=sigma__p(t);

epsilon__0*Physics:-Vectors:-Divergence(E_(t, x, y, z)) = sigma__p(t)

(1.1.5)

f5:=diff(sigma__p(t),t)+Nabla.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)+Physics:-Vectors:-Divergence(j__p_(t, x, y, z)) = 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, x, y, z), t))/Physics:-Vectors:-Norm(B_)^2

 

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

(1.1.6)

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

Physics:-Vectors:-Divergence(diff(D1_(t, x, y, z), t)) = 0

 

epsilon*Physics:-Vectors:-Divergence(diff(E_(t, x, y, z), t)) = 0

 

epsilon__0*Physics:-Vectors:-Divergence(diff(E_(t, x, y, z), t)) = diff(sigma__p(t), t)

(1.1.7)

f12:=isolate(f11,diff(sigma__p(t),t));
f13:=subs(f12,f5);
f14:=subs(f8,f13);
f15:=isolate(f14,Nabla.diff(E_(t,x,y,z),t));

diff(sigma__p(t), t) = epsilon__0*Physics:-Vectors:-Divergence(diff(E_(t, x, y, z), t))

 

epsilon__0*Physics:-Vectors:-Divergence(diff(E_(t, x, y, z), t))+Physics:-Vectors:-Divergence(j__p_(t, x, y, z)) = 0

 

epsilon__0*Physics:-Vectors:-Divergence(diff(E_(t, x, y, z), t))+Physics:-Vectors:-Divergence(rho*(diff(E_(t, x, y, z), t))/Physics:-Vectors:-Norm(B_(t, x, y, z))^2) = 0

 

Error, (in Physics:-Vectors:-+) vectors projected over different basis

 

 

NULL


 

Download Different_basis.mw

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

 

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