tomleslie

4918 Reputation

15 Badges

9 years, 185 days

MaplePrimes Activity


These are answers submitted by tomleslie

which doesn't use the 'background' option. (and just because I like alternatives)

Rendering is better in the worksheet than it is on this site - honest!

Differential Geometry

restart;

with(VectorCalculus):with(LinearAlgebra):with(plots):

Digits:=10:
interface(displayPrecision=10):
with(VectorCalculus):BasisFormat(false):

Frenet Frame

 

frenet := proc(p)
               local vel, speed, unitT, curv, kappa, unitN, unitB, tors:
               vel := diff(p,s):
               speed := simplify(Norm(vel)):
               unitT := simplify(vel/speed):
               curv := simplify(diff(unitT,s)):
               kappa := simplify(Norm(curv)):
               unitN := simplify(curv/kappa):
               unitB := simplify(unitT &x unitN):
               tors := diff(unitB,s)/~unitN:
              # print("Velocity",vel,"Speed",speed,"T",unitT,"Curvature",curv,"Kappa",kappa,"N",unitN,"B",unitB,"Torsion",tors);
               return([vel,curv,unitB]):
          end proc:

Testing

 

p :=unapply( <3*arcsinh(s/5), (25+s^2)^(1/2), 4*arcsinh(s/5)>, s):
ptan:=unapply(frenet(p(s))[1],s):
display( [ spacecurve
           ( p(s),
             s = 0 .. 16*Pi,
             numpoints = 1000
           ),
           display
           ( [ seq
               ( arrow
                 ( p(A),
                   ptan(A),
                   width=0.3,
                   length=4
                 ),
                 A=0..50
               )
             ],
             insequence=true
           )
         ]
       );

 

 

Download anim.mw

the same way as you would generate any other subGraph - see the attached

  restart;
  with(GraphTheory):
  with(RandomGraphs):
#
# Create some random weighted graph
# and draw it
#
  G := RandomDigraph(10, .5, weights=1..5);
  DrawGraph(G);

GRAPHLN(directed, weighted, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], Array(%id = 18446744074329129078), `GRAPHLN/table/1`, Matrix(%id = 18446744074329130638))

 

 

#
# Output the edges of the above graph then
# select a few of these
#
  E:=Edges(G);
  e:=E[1..5];
#
# Create a subgraph on the restricted set of edges
# then draw it
#
  s:=Subgraph(G, e);
  DrawGraph(s);
  

{[1, 2], [1, 6], [1, 9], [1, 10], [2, 3], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [3, 2], [3, 6], [3, 9], [3, 10], [4, 1], [4, 2], [4, 5], [4, 7], [4, 8], [5, 4], [5, 7], [5, 8], [6, 1], [6, 2], [6, 3], [6, 4], [6, 8], [6, 9], [6, 10], [7, 1], [7, 2], [7, 4], [7, 6], [7, 8], [7, 10], [8, 1], [8, 2], [8, 3], [8, 4], [8, 5], [8, 6], [8, 9], [9, 2], [9, 5], [9, 10], [10, 3], [10, 4], [10, 7], [10, 8]}

 

{[1, 2], [1, 6], [1, 9], [1, 10], [2, 3]}

 

GRAPHLN(directed, weighted, [1, 2, 3, 6, 9, 10], Array(%id = 18446744074347199174), `GRAPHLN/table/5`, Matrix(%id = 18446744074347200374))

 

 

 


 

Download subG.mw

so I'm going to "fix" all of your typos by pure guesswork - in which case I get the attached

restart;
w:=(x)->sin(lambda*x)+b*cos(lambda*x)-sinh(lambda*x)-b*cosh(lambda*x);
b := -(sin(lambda*L)+sinh(lambda*L))/(cos(lambda*L)+cosh(lambda*L));

proc (x) options operator, arrow; sin(lambda*x)+b*cos(lambda*x)-sinh(lambda*x)-b*cosh(lambda*x) end proc

 

-(sin(lambda*L)+sinh(lambda*L))/(cos(lambda*L)+cosh(lambda*L))

(1)

expr:=eval(int(w(x)^2,x=0..L), L=10);
plot( expr, lambda=-1..1)

(1/8)*(20*lambda*exp(40*lambda)+80*sin(10*lambda)*lambda*exp(30*lambda)-80*cos(10*lambda)^2*lambda*exp(20*lambda)-6*sin(10*lambda)*cos(10*lambda)*exp(40*lambda)+6*exp(40*lambda)*cos(10*lambda)^2+40*lambda*exp(20*lambda)-80*sin(10*lambda)*lambda*exp(10*lambda)+exp(40*lambda)-10*sin(10*lambda)*exp(30*lambda)+14*cos(10*lambda)*exp(30*lambda)-12*sin(10*lambda)*cos(10*lambda)*exp(20*lambda)-4*exp(20*lambda)*sin(10*lambda)*cosh(10*lambda)-4*exp(20*lambda)*sinh(10*lambda)*cos(10*lambda)-4*exp(20*lambda)*sinh(10*lambda)*cosh(10*lambda)+20*lambda-10*sin(10*lambda)*exp(10*lambda)-14*cos(10*lambda)*exp(10*lambda)-6*sin(10*lambda)*cos(10*lambda)-6*cos(10*lambda)^2-1)*exp(-20*lambda)/(lambda*(cos(10*lambda)^2+2*cos(10*lambda)*cosh(10*lambda)+cosh(10*lambda)^2))

 

 

fsolve( expr=1, lambda=-0.5..0);
fsolve( expr=1, lambda= 0..0.5);

-.1007127230

 

.1007127230

(2)

 


 

Download solveEq2.mw

with a large numeber of points (eg 1000) you are going to run out of labels in the dataframe quite quickly - in fact after about 26 entries. Generating appropriate labels for your 'dataframe' will probably become more cumbersome than generating the data - so why bother??? For your requirement a 2X1000(ish) matrix would suffice.

If your datapoints have integer values, then Maple will calculate exact distances which will (almost certainly) contain square root symbols. Trust me, Excel isn't going to like these! It is probably a good idea to "force" a floating point conversion within the ExcelTools:-Export() command.

The attached illustrates the technique

  restart;
  with(Student:-Calculus1):
#
# Specify the "reference" points
#
  refpts:=[ [1,1],
            [2,4]
          ];
#
# Generate 'n' random points whose x-coordinates
# are in the range -xRange..xRange and y-coordinates
# are in the range -yRange..yRange.
#
# Specific values chose below are just for illustration
#
  n:=100: xRange:=10: yRange:=20:
  xR:=rand(-xRange..xRange):
  yR:=rand(-yRange..yRange):
  pts:=[seq([xR(), yR()],j=1..n)]:
#
# Produce a matrix
#
#  1. first row is the distance from refpts[1] to
#     each of the random points generated above
#  2. second row is the distance from refpts[2] to
#     each of the random points generated above
#
  d:= Matrix
      ( 2,
        n,
        (i,j)-> Distance
                ( refpts[i],
                  pts[j]
                )
      );
#
# Export the distance matrix to Excel. Note that if
# integers have been used in the above calculations
# then the computed distance value is likely to contain
# a square root symbol, whihc Excel isn't going to like!
# Best to force a floating point evaluation at this point
#
# OP will also have to change the file path to something
# appropriate for his/her machine
#
  ExcelTools:-Export( evalf~(d),
                      "C:/Users/TomLeslie/Desktop/test.xlsx",
                       1, "B2"
                    );

refpts := [[1, 1], [2, 4]]

 

_rtable[18446744074399240054]

(1)

 


Download toXL.mw

On my machine this produces the file

test.xlsx

as in the attached

restart;
expr1:=(x^2-1)*y/x^2+(x^2-1)/x^2;
thaw(algsubs((y+1)=freeze((y+1)), expr1));

(x^2-1)*y/x^2+(x^2-1)/x^2

 

(y+1)*(x^2-1)/x^2

(1)

 

Download frth2.mw

Although, I do admit that working out exactly which sub-expression to "freeze", can sometimes be a bit of a "black art"

  1. Please upload a worksheet using the big green up-arrow in the MaplePrimes toolbar
  2. By using a lot of guesswork, I managed to come up with the attached - but this did involve butchery on the code you originally presented
  3. Main syntax-type changes I made were
    1. Using square brackets ( ie [] not () ) when one wants to access an indexaxable quantity
    2. Realising that when one uses Statistics:-Mean() to compute the "mean" of a Matrix, the result is returned as a vector. Hence the quantity 'MeanY' in your worksheet  can only be used with a single index - so MeanY[1] rather than MeanY[1,1] everywhere it is used

For what it is worth, and bearing in mind the outright butchery I performed on the code you posted, the attached now actually runs without error. Whether or not it bears any relation to what you want, I have no idea


 

restart:               

interface(rtablesize = 50); with(LinearAlgebra): with(plots):with(Statistics): with(ArrayTools):
Y := Matrix(12, 1, [2, 3, 2, 7, 6, 8, 10, 7, 8, 12, 11, 14]);
MeanY := Mean(Y);
n := ArrayNumElems(Y);
type(Y, Matrix);
X := Matrix(12, 3, [1, 0, 2, 1, 2, 6, 1, 2, 7, 1, 2, 5, 1, 4, 9, 1, 4, 8, 1, 4, 7, 1, 6, 10, 1, 6, 11, 1, 6, 9, 1, 8, 15, 1, 8, 13]);
 k := NumElems(X)/n;
Xprimed := Transpose(X);
XprimedX := Xprimed . X;
XprimedXinverse := MatrixInverse(XprimedX);
XprimedY := Xprimed . Y;
Betahat := XprimedXinverse . XprimedY;
Betahat := convert(Betahat, float);
fit := plot3d(5.38+3.01*X1-1.29*X2, X1 = 0 .. 8, X2 = 2 .. 15);
data := pointplot3d({[0, 2, 2], [2, 5, 7], [2, 6, 3], [2, 7, 2], [4, 7, 10], [4, 8, 8], [4, 9, 6], [6, 9, 12], [6, 10, 7], [6, 11, 8], [8, 13, 14], [8, 15, 11]}, axes = normal, color = red, symbol = soliddiamond, symbolsize = 40, scaling = unconstrained, title = `\` Data vs Best Fit ' `);

display({data, fit});
Yprimed := Transpose(Y);
 YprimedY := Yprimed . Y;
 BetahatPrime := Transpose(Betahat);
SSE := YprimedY-BetahatPrime . XprimedY;
SampleVariance := (YprimedY-BetahatPrime . XprimedY)/(n-k-1);
SSR := Transpose(Betahat) . Transpose(X) . Y-n*MeanY(1, 1)^2;

SST := SSR+SSE;
 F := SSR[1, 1]*(n-k-1)/(k*SSE);

RsquaredNonCentered := Determinant(SSR)/Determinant(SST);
 R := sqrt(%);
RsquaredCentered:= ((Transpose(Betahat) . Transpose(X) . Y) - n*MeanY[1]^2) .(1/((Yprimed . Y) - n*MeanY[1]^2));
F := SSR[1, 1]*(n-k-1)/(k*SSE[1, 1]);
 SSE; SSR; SSR+SSE;
 Total := Yprimed . Y-n*MeanY[1]^2;

[10, 10]

 

Vector(12, {(1) = 2, (2) = 3, (3) = 2, (4) = 7, (5) = 6, (6) = 8, (7) = 10, (8) = 7, (9) = 8, (10) = 12, (11) = 11, (12) = 14})

 

Vector(1, {(1) = 7.5})

 

n := 12

 

true

 

Matrix(12, 3, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 2, (2, 1) = 1, (2, 2) = 2, (2, 3) = 6, (3, 1) = 1, (3, 2) = 2, (3, 3) = 7, (4, 1) = 1, (4, 2) = 2, (4, 3) = 5, (5, 1) = 1, (5, 2) = 4, (5, 3) = 9, (6, 1) = 1, (6, 2) = 4, (6, 3) = 8, (7, 1) = 1, (7, 2) = 4, (7, 3) = 7, (8, 1) = 1, (8, 2) = 6, (8, 3) = 10, (9, 1) = 1, (9, 2) = 6, (9, 3) = 11, (10, 1) = 1, (10, 2) = 6, (10, 3) = 9, (11, 1) = 1, (11, 2) = 8, (11, 3) = 15, (12, 1) = 1, (12, 2) = 8, (12, 3) = 13})

 

k := 3

 

Matrix(3, 12, {(1, 1) = 1, (1, 2) = 1, (1, 3) = 1, (1, 4) = 1, (1, 5) = 1, (1, 6) = 1, (1, 7) = 1, (1, 8) = 1, (1, 9) = 1, (1, 10) = 1, (1, 11) = 1, (1, 12) = 1, (2, 1) = 0, (2, 2) = 2, (2, 3) = 2, (2, 4) = 2, (2, 5) = 4, (2, 6) = 4, (2, 7) = 4, (2, 8) = 6, (2, 9) = 6, (2, 10) = 6, (2, 11) = 8, (2, 12) = 8, (3, 1) = 2, (3, 2) = 6, (3, 3) = 7, (3, 4) = 5, (3, 5) = 9, (3, 6) = 8, (3, 7) = 7, (3, 8) = 10, (3, 9) = 11, (3, 10) = 9, (3, 11) = 15, (3, 12) = 13})

 

Matrix(3, 3, {(1, 1) = 12, (1, 2) = 52, (1, 3) = 102, (2, 1) = 52, (2, 2) = 296, (2, 3) = 536, (3, 1) = 102, (3, 2) = 536, (3, 3) = 1004})

 

Matrix(3, 3, {(1, 1) = 309/317, (1, 2) = 77/317, (1, 3) = -145/634, (2, 1) = 77/317, (2, 2) = 411/2536, (2, 3) = -141/1268, (3, 1) = -145/634, (3, 2) = -141/1268, (3, 3) = 53/634})

 

Vector(3, {(1) = 90, (2) = 482, (3) = 872})

 

Vector(3, {(1) = 1704/317, (2) = 3819/1268, (3) = -815/634})

 

Vector(3, {(1) = 5.375394322, (2) = 3.011829653, (3) = -1.285488959})

 

 

 

 

Vector[row](12, {(1) = 2, (2) = 3, (3) = 2, (4) = 7, (5) = 6, (6) = 8, (7) = 10, (8) = 7, (9) = 8, (10) = 12, (11) = 11, (12) = 14})

 

Vector(1, {(1) = 840})

 

Vector[row](3, {(1) = 5.375394322, (2) = 3.011829653, (3) = -1.285488959})

 

Vector(1, {(1) = 25.458990522000022})

 

Vector(1, {(1) = 3.1823738152500027})

 

Vector(1, {(1) = 139.54100947799998})

 

Vector(1, {(1) = 165.0})

 

Vector(1, {(1) = 14.616029582415962})

 

RsquaredNonCentered := .845703087745454

 

R := .919621165342259

 

Vector(1, {(1) = .8457030877454544})

 

F := 14.6160295824160

 

Vector(1, {(1) = 25.458990522000022})

 

Vector(1, {(1) = 139.54100947799998})

 

Vector(1, {(1) = 165.0})

 

Matrix(%id = 18446744074376644238)

(1)

 


 

Download matProb.mw

 

Just put the desired values of Mh in a list and add another loop, which will permit a sequence of plots to be obtained. Thes can then be displayed together. Just make sure that the number of entries in the list 'colors' is the same as the number of entries in the list 'Mh'

Code changes are highlighted in the attached

restart:
with(plots):
m:=10:H:=1:b:=0.02:a:=0.05:V:=Array(0..m): V[0]:=1-exp(-t):
plts:=NULL:
Mh:=[1,2,3,4]:
colors:=[red, blue, green, black]:
for zz from 1 to 4 by 1 do
    for k from 1 to m do
        if   k=1
        then chi:=0:
        else chi:=1: # OP's code here didn't make sense
        fi:
        p:=0:
        for j from 0 to k-1 do
            p:=p+(V[k-1-j]*diff(V[j],t$2)-diff(V[k-1-j],t)*diff(V[j],t)-a*(2*diff(V[k-1-j],t)*diff(V[j],t$3)-diff(V[k-1-j],t$2)*diff(V[j],t$2)-V[k-1-j]*diff(V[j],t$4))):
        od:
        p:=(p+diff(V[k-1],t$3)-b*(diff(V[k-1],t$2)+t*diff(V[k-1],t$3))-Mh[zz]*diff(V[k-1],t))*h*H:
        p:=factor(p):
        V[k]:=(-int(p,t)+0.5*exp(t)*int(exp(-t)*p,t)+0.5*exp(-t)*int(exp(t)*p,t)+chi*V[k-1]+C1+C3*exp(-t)):
        v:=unapply(V[k],t):
        V[k]:=frontend(expand,[V[k]]):
        V[k]:=subs(C3=solve(eval(subs(t=0,diff(V[k],t))),C3),V[k]):
        V[k]:=frontend(expand,[V[k]]):
        V[k]:=subs(C1=solve(eval(subs(t=0,-V[k]-diff(V[k],t))),C1),V[k]):
    od:
    appr:=0:
    for k from 0 to m do
        appr:=appr+V[k]:
    od:
    u_appr:=unapply(appr,(h,t)):
    u_appr_1:=unapply(diff(u_appr(h,t),t),(h,t)):
    evalf(u_appr_1(-0.4,t)):
    plts:=plts, plot([u_appr_1(-0.4,t)],t=0..4,0..1.2,color=colors[zz],axes=frame):
od:
display([plts]);

 

 

 


 

Download odeProb.mw

something like

restart;
f := a*x+b;
g := (p, q) -> unapply( eval(f, [a=p, b=q]), x):
g(a, b)(x);
g(2, 3)(t);

a*x+b

 

a*x+b

 

2*t+3

(1)

 


Download funcomp.mw

to generate all the data which you want.

The only difficulty seems to be how you want data to be saved and then accessed - only you know this

Amongst other things, the attached will output all values of -R(0)[3])  and also demonstrate how to access/display a value corresponding to a specific combination of 'bi' and 'pr'.

It is trivial to organise this data any way you want. You just have to be able to specify how you want it!!

  restart:
  with(plots):
  fcns:= {T(eta), f(eta)}:
  m:= .5: bet:= 1: na:= 1/6: N:= 5:
  eq1:= diff(f(eta), eta$3)*pr+m-m*(diff(f(eta), eta))+((m+1)*(1/2))*(diff(f(eta), eta$2))*f(eta) = 0:
  eq2:= diff(T(eta), eta$2)+((m+1)*(1/2))*(diff(T(eta), eta))*f(eta) = 0:
  bc:= f(0) = 0, D(f)(0) = 0, D(f)(N) = 1, D(T)(0) = -bi*(1-T(0)), T(N) = 0:
  plts:=NULL:
  for bi from 1 to 4 by 0.1 do    
      for pr from 1 to 2 by 0.1 do  
          R:= dsolve
              ( {bc, eq1, eq2},
                fcns,
                type = numeric,
                method = bvp[midrich],
                maxmesh=2400
              ):
          X1[bi, pr]:= -R(0)[3]:
          plts:= plts,
                 odeplot
                 ( R,
                   [ [ eta, T(eta)],
                     [ eta, diff(T(eta),eta)],
                     [ eta, f(eta)],
                     [ eta, diff(f(eta), eta)]
                   ],
                   eta =0..N,
                   color=[red, blue, green, grey]
                 ):
      end do:  
  end do:
#
# Display all plots
#
  display([plts]);
#
# Output all values of -R(0)[3]
#
  X1();
#
# Output the value of -R(0)[3] for
# bi=3.7, pr=1.2 (just as an example)
#
  X1[3.7, 1.2]

 

(table( [( 1.9, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.3685471185517967), ( 2.1, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.3566056707899961), ( 4.0, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.4063555123062397), ( 2.3, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.3598368356117598), ( 2.7, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.37059028404251043), ( 1.3, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.32286620738758504), ( 3.2, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.3865857817486042), ( 1.8, 1 ) = -(diff(T(eta), eta)) = HFloat(0.36804774565588166), ( 3.6, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.39492554189970075), ( 4.0, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.38546715936994363), ( 3.9, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.3869313670902811), ( 1.9, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.3653348257498673), ( 2.6, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.38885436707254006), ( 3.4, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.3768095431377291), ( 2.3, 1 ) = -(diff(T(eta), eta)) = HFloat(0.3851685693796018), ( 2.3, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.3691357324117606), ( 3.3, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.3777454974137787), ( 3.5, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.39063075394660707), ( 4.0, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.38789347061256635), ( 1.3, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.3382638404805423), ( 2.0, 1 ) = -(diff(T(eta), eta)) = HFloat(0.37573034018595075), ( 2.3, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.3779743868095872), ( 1.7, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.35179304049512566), ( 2.0, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.3536033621581177), ( 2.5, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.3865419283936697), ( 1.9, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.35244584182886457), ( 2.9, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.38473780714072997), ( 2.8, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.37479258580492053), ( 2.1, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.3545539547959186), ( 2.7, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.39102032086987887), ( 1.2, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.321793665926088), ( 4.0, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.3932207957938002), ( 1.2, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.31317761068874317), ( 3.4, 1 ) = -(diff(T(eta), eta)) = HFloat(0.40723230179133924), ( 2.4, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.3840676244365858), ( 3.1, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.39125827860964574), ( 3.9, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.3982865144973882), ( 1, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.30541363725338794), ( 2.6, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.36864418784988556), ( 1.4, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.328697264397516), ( 3.4, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.3813671546811552), ( 1, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.3020235978500463), ( 2.7, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.38407676304619276), ( 3.6, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.39823920996118556), ( 1.7, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.3603244234728465), ( 2.2, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.3572959611729115), ( 3.1, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.3749762774891147), ( 3.4, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.38385988650143804), ( 1.2, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.3238679200134328), ( 1.7, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.34706124579439357), ( 3.2, 1 ) = -(diff(T(eta), eta)) = HFloat(0.40420645762960516), ( 1, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.3137706271733252), ( 1.5, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.3423471283438797), ( 2.7, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.3781263901888064), ( 2.8, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.3829234582291056), ( 3.4, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.3865155334849777), ( 3.7, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.4069487730117626), ( 1.5, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.35042125985954675), ( 1.3, 1 ) = -(diff(T(eta), eta)) = HFloat(0.34121377991131435), ( 2.5, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.36886763496416), ( 2.9, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.37413178088547927), ( 3.9, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.38224061058665876), ( 3.5, 1 ) = -(diff(T(eta), eta)) = HFloat(0.40863068507444056), ( 2.4, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.36219792535626677), ( 2.8, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.3773238353192568), ( 1.6, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.3386355296322837), ( 4.0, 1 ) = -(diff(T(eta), eta)) = HFloat(0.4146825424884372), ( 1.2, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.32849000634897485), ( 1.2, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.3147041036872464), ( 1.5, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.34751592381768215), ( 2.4, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.3690353920191932), ( 1.7, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.3572532740134888), ( 2.8, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.3930532814172942), ( 2.8, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.37241586206570343), ( 1.6, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.33678484790971086), ( 1.4, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.334612249292344), ( 2.5, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.37131922424305897), ( 3.2, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.37871222084608863), ( 1.9, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.3483628064613999), ( 3.8, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.38352196043007053), ( 2.3, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.3578424954891447), ( 3.0, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.3734704435606725), ( 2.6, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.3643839023617166), ( 2.7, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.366285161840364), ( 2.2, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.35937962775126775), ( 1.5, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.33042453837685737), ( 1.7, 1 ) = -(diff(T(eta), eta)) = HFloat(0.3636735874534946), ( 3.1, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.37971123630146947), ( 1.6, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.34059950522842625), ( 1.4, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.3269533364595742), ( 1, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.3036651914095638), ( 1.9, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.3503432946508047), ( 2.5, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.36656523184049145), ( 3.9, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.4092571122590745), ( 2.0, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.35158595032730894), ( 3.4, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.3956645508412699), ( 3.5, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.39698448941014014), ( 3.9, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.39515410474112506), ( 1.1, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.30891672890295835), ( 1.4, 1 ) = -(diff(T(eta), eta)) = HFloat(0.3477330830463698), ( 2.9, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.39496513287872526), ( 3.0, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.38349714542020613), ( 2.2, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.37517190913970366), ( 3.6, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.40181990862712075), ( 2.4, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.37438996419239506), ( 3.5, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.4044071054842335), ( 3.7, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.4030357327934403), ( 3.7, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.38247865344742626), ( 2.3, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.36419494878582065), ( 1.3, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.3195936082090132), ( 3.8, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.4041943727139419), ( 1, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.29764181576423043), ( 2.1, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.35878428940294954), ( 3.3, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.40159484907645293), ( 2.0, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.36306271123728656), ( 2.7, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.38099367758642233), ( 3.4, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.40303743155023797), ( 3.7, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.3874062229183938), ( 3.1, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.39846636352015974), ( 3.2, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.3895833058517508), ( 3.5, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.3780064881037774), ( 3.7, 1 ) = -(diff(T(eta), eta)) = HFloat(0.4112258899131765), ( 1.7, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.3544200112627842), ( 2.1, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.363578387317663), ( 3.5, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.38023261702883665), ( 2.4, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.3773666809488808), ( 2.6, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.3761005562049321), ( 1.6, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.33503722669472785), ( 1.8, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.3488507831697624), ( 2.1, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.3721498277720235), ( 3.3, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.380075281000164), ( 1.1, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.31055028071881824), ( 4.0, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.3993059900807851), ( 2.5, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.3643976599399065), ( 1.5, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.3378644111695954), ( 3.4, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.3923934147435261), ( 2.5, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.3830097916407869), ( 2.2, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.3720485474076505), ( 3.2, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.3928075650180713), ( 3.8, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.3812572637027126), ( 2.2, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.3639479050584537), ( 3.7, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.39011133854393143), ( 1.6, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.3556135323470227), ( 2.5, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.3767407635419642), ( 2.2, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.36159237733249944), ( 2.4, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.36017740089977307), ( 2.6, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.3709728639050683), ( 3.2, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.3763990670019762), ( 3.3, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.38518860497208984), ( 3.1, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.39471399733718954), ( 2.0, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.36045803614789024), ( 1.6, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.342688673879741), ( 1.8, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.3510427269752175), ( 3.7, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.3802262252308929), ( 1.3, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.33073421488058646), ( 1.5, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.3358334754857911), ( 1.8, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.3533814156603244), ( 3.3, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.3977836113541952), ( 3.5, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.4005425596402157), ( 1.3, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.3246510460110759), ( 2.1, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.36622851883207386), ( 3.6, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.3889721310461709), ( 3.8, 1 ) = -(diff(T(eta), eta)) = HFloat(0.41243216858828297), ( 2.2, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.3785603228758816), ( 3.6, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.38375854196516357), ( 3.8, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.39721899110022213), ( 3.0, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.39304581794356863), ( 3.3, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.3755483115285272), ( 1.2, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.3180324833997474), ( 1.7, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.34934701240835236), ( 1.8, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.34485014671142067), ( 2.4, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.3666137690948643), ( 3.5, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.38777503832374033), ( 3.6, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.3813835253994172), ( 1, 1 ) = -(diff(T(eta), eta)) = HFloat(0.3163072299330439), ( 2.5, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.37975512983086623), ( 3.9, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.4016570644919745), ( 3.3, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.3880062143784469), ( 3.9, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.389497613042579), ( 1, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.2990202854243228), ( 1.3, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.3265486010270545), ( 1.4, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.34185871693758163), ( 2.6, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.3789370873515808), ( 3.6, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.3791439394364868), ( 3.0, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.38074440525362274), ( 3.4, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.37902155520890407), ( 3.8, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.38592376918072846), ( 2.0, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.3721565188173238), ( 2.2, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.36915481801438305), ( 3.0, 1 ) = -(diff(T(eta), eta)) = HFloat(0.4008310721278625), ( 3.8, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.38847662305765734), ( 1, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.3004782952076783), ( 2.7, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.3874062474583827), ( 3.2, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.39629082731924675), ( 2.5, 1 ) = -(diff(T(eta), eta)) = HFloat(0.3903988075273821), ( 1.8, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.3646179115878063), ( 1.2, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.31631948489453166), ( 1.1, 1 ) = -(diff(T(eta), eta)) = HFloat(0.3256719939432692), ( 1.1, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.30737588763760404), ( 2.7, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.37544994364370754), ( 2.6, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.36645203320105985), ( 2.3, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.37480438589252574), ( 1.2, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.32609307015762823), ( 3.2, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.38378868426040913), ( 3.9, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.38451703956376165), ( 3.5, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.3825932765957472), ( 2.4, 1 ) = -(diff(T(eta), eta)) = HFloat(0.38787504168927445), ( 3.1, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.37727192360263034), ( 1.1, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.31611197119666096), ( 1.4, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.3305473392940528), ( 1.3, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.3355558224488306), ( 2.6, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.3852800381773658), ( 3.5, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.38510211551544343), ( 1, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.3114392278325224), ( 1.1, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.3141355723317724), ( 3.1, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.3880592995534765), ( 3.1, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.3823095905835051), ( 3.2, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.4000733774409443), ( 2.6, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.38198684465838234), ( 1.4, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.344669848418153), ( 2.8, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.3800271613355227), ( 3.0, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.3781672111665577), ( 3.6, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.39184557085753946), ( 2.9, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.3765305272852101), ( 3.2, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.3742174712037255), ( 3.9, 1 ) = -(diff(T(eta), eta)) = HFloat(0.4135831469305623), ( 2.9, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.36974446993189164), ( 1.1, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.32298360647457947), ( 1.2, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.3310847383610217), ( 1.6, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.34491702237039507), ( 2.2, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.3664623264968471), ( 2.9, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.3718740760344962), ( 1.9, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.3623724602690272), ( 2.9, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.38181410382365494), ( 3.1, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.3728110959578103), ( 2.7, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.3729436899300281), ( 1.5, 1 ) = -(diff(T(eta), eta)) = HFloat(0.35358804777262876), ( 1.7, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.3449185897589872), ( 1.3, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.32118344645902996), ( 1.8, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.3585731319644271), ( 2.6, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.37345261088488585), ( 2.8, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.36806846894995554), ( 2.9, 1 ) = -(diff(T(eta), eta)) = HFloat(0.3989928110636767), ( 1.4, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.33685562578796946), ( 1.9, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.3570709547588308), ( 2.9, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.3912781142179875), ( 2.4, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.3716208507983714), ( 2.7, 1 ) = -(diff(T(eta), eta)) = HFloat(0.39496754396155204), ( 2.0, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.368881277728723), ( 3.2, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.3811702547181832), ( 1.7, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.33921552922483195), ( 3.7, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.38486737184532166), ( 3.8, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.39119676024932254), ( 1.6, 1 ) = -(diff(T(eta), eta)) = HFloat(0.3588752983264506), ( 1.3, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.32857137000406), ( 3.0, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.37574763294930563), ( 1.9, 1 ) = -(diff(T(eta), eta)) = HFloat(0.37205162751761583), ( 3.0, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.3967663844289941), ( 3.0, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.3896191204763884), ( 3.6, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.3862827369241901), ( 2.2, 1 ) = -(diff(T(eta), eta)) = HFloat(0.3822588050767603), ( 2.8, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.386037982872599), ( 2.1, 1 ) = -(diff(T(eta), eta)) = HFloat(0.37912195009157135), ( 3.6, 1 ) = -(diff(T(eta), eta)) = HFloat(0.4099602273343711), ( 3.1, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.3850850920173563), ( 3.5, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.3936915826803844), ( 1.4, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.3253060104247713), ( 1.5, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.34003026305275075), ( 1.1, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.3182314735147397), ( 4.0, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.3961575874128777), ( 2.8, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.3894017058089653), ( 2.1, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.36907637577365987), ( 2.8, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.37017875729098837), ( 2.8, 1 ) = -(diff(T(eta), eta)) = HFloat(0.3970418646833052), ( 2.0, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.3658613571136523), ( 2.2, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.3553296094640667), ( 2.7, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.368374992797939), ( 1.8, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.34301804710187034), ( 1.2, 1 ) = -(diff(T(eta), eta)) = HFloat(0.3339102682255454), ( 2.9, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.37908538642631023), ( 3.8, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.39410328469630357), ( 4.0, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.41033359905916317), ( 1.9, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.34649329422995595), ( 3.0, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.3864467805537068), ( 3.7, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.39943342958153755), ( 1.4, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.33926348582563653), ( 2.9, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.38788203704965574), ( 3.4, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.38935266047337647), ( 3.3, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.3942741737124612), ( 1.9, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.3596267360315394), ( 2.3, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.3814138435292724), ( 2.4, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.3805803582828228), ( 4.0, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.383179500106091), ( 1.1, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.32051382561549696), ( 3.3, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.38255109844856033), ( 1.5, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.34483442530962616), ( 3.1, 1 ) = -(diff(T(eta), eta)) = HFloat(0.40256613677874253), ( 3.8, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.40813005339209757), ( 1, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.30728148449883236), ( 1.5, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.33392392531117804), ( 1.6, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.34986126735407697), ( 3.8, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.40057142116439926), ( 3.9, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.40529977004143064), ( 3.3, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.3910258925933461), ( 1.7, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.3410071285143856), ( 1.8, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.36147345615835635), ( 3.0, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.37132256722603857), ( 1.2, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.3198532403645723), ( 2.1, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.37548363019999353), ( 2.0, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.358025065490636), ( 2.3, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.37186779804032405), ( 2.5, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.3623525877663485), ( 3.3, 1 ) = -(diff(T(eta), eta)) = HFloat(0.40575958871173634), ( 1, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.3092838505060341), ( 2.3, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.36195033078560784), ( 3.6, 1.1 ) = -(diff(T(eta), eta)) = HFloat(0.405709261875519), ( 1.3, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.33305505619179404), ( 2.0, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.349681778175179), ( 3.4, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.39919889455893887), ( 2.1, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.3526175863486376), ( 1.4, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.3325146556271503), ( 2.0, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.35574534089036086), ( 1.7, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.3429046359334747), ( 2.1, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.3611032563226344), ( 3.7, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.3930016967901932), ( 4.0, 1.7 ) = -(diff(T(eta), eta)) = HFloat(0.39047253688520034), ( 1.9, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.3546833411641723), ( 2.6, 1 ) = -(diff(T(eta), eta)) = HFloat(0.39275776382186073), ( 4.0, 1.3 ) = -(diff(T(eta), eta)) = HFloat(0.4026938904273606), ( 1.1, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.3122861394663878), ( 1.1, 2.0 ) = -(diff(T(eta), eta)) = HFloat(0.3059194943965801), ( 1.6, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.3473011969639276), ( 1.8, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.3467907851593792), ( 3.9, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.39223211742615066), ( 2.5, 1.5 ) = -(diff(T(eta), eta)) = HFloat(0.3739368965926833), ( 3.7, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.39609994117837094), ( 1.8, 1.4 ) = -(diff(T(eta), eta)) = HFloat(0.355884467914531), ( 2.4, 1.8 ) = -(diff(T(eta), eta)) = HFloat(0.36433932968600935), ( 1.6, 1.2 ) = -(diff(T(eta), eta)) = HFloat(0.35262182912593965), ( 2.3, 1.6 ) = -(diff(T(eta), eta)) = HFloat(0.3665846185344934), ( 1.5, 1.9 ) = -(diff(T(eta), eta)) = HFloat(0.332124247381247) ] ))()

 

-(diff(T(eta), eta)) = HFloat(0.4030357327934403)

(1)

 

-(diff(T(eta), eta)) = HFloat(0.3163072299330439)

(2)

 


 

Download odeSol.mw

You (as author) have control over the order of arguments in the function call, so why use an order that you do not want? This seems perverse

The only(?) way I can think of doing this is to use some kind of "wrapper" procedure which accepts both the target procedure name and its arguments, then checks the latter, before invoking the former.

The attached will "work" for the example you posted, but can probably be "beaten" for some argument combinations

foo := proc(a::expects(integer):=0, b::expects(integer):=0, {c::integer:= 1, d::integer:= 1},$)
    print("a=",a," b=",b," c=",c," d=",d);
end proc:
foo(1,2);                                #case 1                                             
foo(1, 2,'c' = 1, 'd' = 2);              #case 2
foo('c' = 1, 1, 'd' = 2, 2);             #case 3
foo('c' = 1, 1, 2);                      #case 4
foo(1, 'c'=1, 2);                        #case 5       

"a=", 1, " b=", 2, " c=", 1, " d=", 1

 

"a=", 1, " b=", 2, " c=", 1, " d=", 2

 

"a=", 1, " b=", 2, " c=", 1, " d=", 2

 

"a=", 1, " b=", 2, " c=", 1, " d=", 1

 

"a=", 1, " b=", 2, " c=", 1, " d=", 1

(1)

checkPar:= proc()
               local p:=selectremove(not type, [_passed][2..-1], `=`);
               if [ p[1][], p[2][] ]=[_passed][2..-1]
               then _passed[1]( _passed[2..-1] )
               else error "Wrong parameter order";
               fi;
           end proc:
checkPar( foo, 1,2);                                #case 1                                             
checkPar( foo, 1, 2,'c' = 1, 'd' = 2);              #case 2
checkPar( foo, 'c' = 1, 1, 'd' = 2, 2);             #case 3
checkPar( foo, 'c' = 1, 1, 2);                      #case 4
checkPar( foo, 1, 'c'=1, 2);                        #case 5  

"a=", 1, " b=", 2, " c=", 1, " d=", 1

 

"a=", 1, " b=", 2, " c=", 1, " d=", 2

 

Error, (in checkPar) Wrong parameter order

 

Error, (in checkPar) Wrong parameter order

 

Error, (in checkPar) Wrong parameter order

 

 


 

Download parChk.mw

 

which I have fixed in the attached (I also removed some stuff which you didn't seem to be using)

  restart;
  d1 := 1; d2 := 1; AA := 0.2e-2; BB := 0.79e-1; L := 1;
  PDE1:= diff(u(x, t), t) = d1*(diff(u(x, t), x, x))-u(x, t)*v(x, t)^2+AA*(1-u(x, t));
  PDE2:= diff(v(x, t), t) = d1*(diff(v(x, t), x, x))+u(x, t)*v(x, t)^2-BB*v(x, t);

  IBC1:= u(0, t) = 1, u(1, t) = 1,
         u(x, 0) = 1-(1/2)*sin(Pi*(x-L)/(2*L))^100;
  IBC2:= v(0, t) = 0, v(1, t) = 0,
         v(x, 0) = (1/4)*sin(Pi*(x-L)/(2*L))^100;     

  pds:= pdsolve( [PDE1,PDE2], [IBC1,IBC2], numeric, time = t, range = 0 .. 1);

  p1:= pds:-plot(t = 0, numpoints = 50);

  p2:= pds:-plot(t = 1/8, numpoints = 50, color = blue);

  p3:= pds:-plot(t = 1/4, numpoints = 50, color = green);

1

 

1

 

0.2e-2

 

0.79e-1

 

1

 

diff(u(x, t), t) = diff(diff(u(x, t), x), x)-u(x, t)*v(x, t)^2+0.2e-2-0.2e-2*u(x, t)

 

diff(v(x, t), t) = diff(diff(v(x, t), x), x)+u(x, t)*v(x, t)^2-0.79e-1*v(x, t)

 

u(0, t) = 1, u(1, t) = 1, u(x, 0) = 1-(1/2)*sin((1/2)*Pi*(x-1))^100

 

v(0, t) = 0, v(1, t) = 0, v(x, 0) = (1/4)*sin((1/2)*Pi*(x-1))^100

 

_m708780480

 

 

 

 

 

Download pdeProb.mw

  1. Open the file 1.mw as a worksheet in whatever is your normal method for opening Maple worksheets
  2. Don't execute anything, don't do anything other than use the menu operation File->Export As dialogue. When presented with the "Export As" pop-up, choose any directory you want, and any filename you want, but ensure that the "Files of Type" field is set to Maple Input (.mpl)
  3. Having save the file 1.mw as a .mpl change the read statement in the 2.mw file to correspond with the filepath and filename chosen in (2) above
  4. I have performed this operation on your files. I chose to "Export" your file 1.mw to my Desktop withe the name 1.mpl, and hence I change the read statement in the file 2.mw to read C:/Users/TomLeslie/Desktop/1.mpl. Obviously yu will have to chnage this to correspond with thefilepath/filename whihc ou chose in (2) above
  5. The attached shows the file 2.mw running correctly after these adjustments

restart:                 
with(Optimization):      
with(MTM):               
interface(warnlevel=0):  

#read "1.mw";
read "C:/Users/TomLeslie/Desktop/1.mpl":

 

BO:=[2,1,4,3,8];
OW:=[4,8,4,2,1];

[2, 1, 4, 3, 8]

 

[4, 8, 4, 2, 1]

(1)

with(BWM):   # call BWM package
BWM(BO,OW);  # use BWM function to solve given problem

"the number of the criteria", 5

 

"the best criterion", C[2]

 

"the worst criterion", C[5]

 

"the value of the best-worst comparison", 8

 

"the Euclidean BWM results are as follows:"

 

        
 w1=.216334313277441        
 w2=.443058029942151        
 w3=.154326427504539        
 w4=.132526090111623        
 w5=.0537551391642455        
 xi=1.716258440        
 consistency index=11.61895004        
 the consistency ratio=xi/consistency index=.1477120079        
 Total Deviation=.300418064406966

 

"the linear Chebyshev BWM results are as follows:"

 

        
 w1=.246153845963213        
 w2=.43076923146822        
 w3=.123076922981606        
 w4=.153846153210709        
 w5=.0461538463762519        
 xi=.615384604582054e-1        
 max xi=.256880733528126        
 the actual consistency ratio=xi/max xi=.2395604358        
 Total Deviation=.92413885935391

 

 


 

Download run2.mw

it sounds as if there are a couple of things you need to change

  1. Maple input: From the menus, use Tools->Options->Display and toggle the "Input Display" field to Maple Notation. Then check "Apply Globally" at the bottom of this pop-up. Thius should give you old-fashioned, plaintext, Maple Input in the current and all subsequent Maple sessions
  2. Maple Input Font: From the menus, use Format->Input Styles. In the Style Management pop-up, scroll down the available styles to "Maple Input" - it is generally two or three from the bottom (may be version dependent?). Select (ie right-click) the "Maple Input" field, then click "Modify". At this point you will get a new pop-up headed "Character style" where you can select the font family, font size, etc etc. My default setting here is "Times New Roman", 14pt, bold, and the color is one of the "brownish" ones, which I find restful. Just play with the settings in this pop-up and go back to the main worksheet to examine the result - after a couple of adjustments you ought to be able to get the font-style you want

where solve() is used to generate all roots - and results are presented in both rational and floating-point forms.

It *ought* to work for any value of the parameter 'n' in the expression cos( n * arccos(x) )

  restart;
#
# procedure which finds the "roots" of the
# expression cos(n*arccos(x)), for any (integer)
# supplied value of 'n'
#
  getSol:= proc( n::integer )
                 local Z, expr, j, sol1, sol2, sol3, sol4;
                 expr:= cos(n*arccos(x));
                 sol1:= solve( expr,
                               allsolutions=true
                             ):
                 sol2:= subs( `minus`( indets(sol1, 'name'),
                                       {Pi}
                                     )[]
                              = Z,
                              sol1
                            );
                 sol3:= [ { seq
                            ( simplify
                              ( eval
                                ( sol2,
                                  Z = j
                                ),
                                trig
                              ),
                              j = -n .. n-1
                            )
                          }[]
                        ]:
                 sol4:= evalf(sol3);
                 return expr,
                        sol2,
                        sol3,
                        sol4;
           end proc:
#
# Return values for each of the following are
#
# 1. the expression being solved
# 2. the general (ie closed-form) solution
# 3. the distinct (rational) roots
# 4, the distinct (floating point) roots
#
  getSol( 2 );
  getSol( 3 );
  getSol( 4 );
  getSol( 5 );

cos(2*arccos(x)), cos((1/4)*Pi+(1/2)*Pi*Z), [-(1/2)*2^(1/2), (1/2)*2^(1/2)], [-.7071067810, .7071067810]

 

cos(3*arccos(x)), cos((1/6)*Pi+(1/3)*Pi*Z), [0, -(1/2)*3^(1/2), (1/2)*3^(1/2)], [0., -.8660254040, .8660254040]

 

cos(4*arccos(x)), cos((1/8)*Pi+(1/4)*Pi*Z), [-cos((1/8)*Pi), -cos((3/8)*Pi), cos((1/8)*Pi), cos((3/8)*Pi)], [-.9238795325, -.3826834325, .9238795325, .3826834325]

 

cos(5*arccos(x)), cos((1/10)*Pi+(1/5)*Pi*Z), [0, -cos((1/10)*Pi), -cos((3/10)*Pi), cos((1/10)*Pi), cos((3/10)*Pi)], [0., -.9510565163, -.5877852522, .9510565163, .5877852522]

(1)

 

``

``

``

``

``

``

``

``

``

``

``

Download egtRoots.mw

using the geometry() package with triangles, circumcircles, incircles, circumcentres inceentres etc.

See the attached

  restart;
  with(geometry):
  _EnvHorizontalName:=x:
  _EnvVerticalName:=y:
#
# Define a list of sidelengths
#
  sideLength:=[3,5,7]:
#  sideLength:=[3,4,5]:
   
#
# Define three points which will become the triangle
# For the moment one can specify
#
# 1. the first triangle vertex is at the origin
# 2. the second triangle vertex is along the +ve x-axis
# 3. the third triangle vertex is in the positive y-plane
#
  point(A, [0, 0]):
  point(B, [x__b, 0]):
  point(C, [x__c, y__c]):
#
# Specify the lengths of the sides of the triangles
# and assign appropriate values to the unknown
# coordinates used in the definition of the vertices
#
  sol:= assign
        ( solve
          ( [ x__b > 0,
              y__c > 0,
              distance(A,B)=sideLength[1],
              distance(A,C)=sideLength[2],
              distance(B,C)=sideLength[3]
            ]
          )
        ):
#
# Construct the triangle from these three points
#
  triangle(T1, [A, B, C]):

#
# Produce the circumcircle of the triangle, and
# draw both
#
  circumcircle(C1, T1):
  draw( [ T1(color=red),
          C1(color=blue)
        ],
        axes=normal
      );
#
# Translate the circumcircle to the origin.
# Apply the same translation to the triangle
#
  dsegment( ds1,
            point(P1, coordinates(center(C1))),
            point(OO, [0,0])
          ):
  translation(C2, C1, ds1):
  translation(T2, T1, ds1):
  draw( [ T2(color=red),
          C2(color=blue)
        ],
        axes=normal
      );
#
# Get the coordinates of translated triangle
#
  map(coordinates, DefinedAs(T2));

 

 

[[-3/2, -(13/6)*3^(1/2)], [3/2, -(13/6)*3^(1/2)], [-4, (1/3)*3^(1/2)]]

(1)

#
# Observe that rotations, reflections etc are also "solutions".
#
# Successively rotate the triangle by Pi/8, and draw the results
#
  draw( [ C2(color=blue),
          seq
          ( rotation( cat(TR, j),
                      T2,
                      j*Pi/4,
                      clockwise
                    ),
            j=0..7
          )
        ],
        axes=normal
      );
#
# Now with a few reflections
#
  draw( [ C2(color=blue),
          T2,
          reflection( TF1,
                      T2,
                      line(x_axis, y=0 )
                    ),
          reflection( TF2,
                      T2,
                      line(y_axis, x=0 )
                    ),
          reflection( TF3,
                      TF2,
                      line(x_axis, y=0 )
                    )
        ]
      );
#
# Get the coordinates of (some of) these triangles
#
  map(coordinates, DefinedAs(TR3));
  map(coordinates, DefinedAs(TR6));
  map(coordinates, DefinedAs(TF1));
  map(coordinates, DefinedAs(TF3));

 

 

[[(3/4)*2^(1/2)-(13/12)*3^(1/2)*2^(1/2), (3/4)*2^(1/2)+(13/12)*3^(1/2)*2^(1/2)], [-(3/4)*2^(1/2)-(13/12)*3^(1/2)*2^(1/2), -(3/4)*2^(1/2)+(13/12)*3^(1/2)*2^(1/2)], [2*2^(1/2)+(1/6)*3^(1/2)*2^(1/2), 2*2^(1/2)-(1/6)*3^(1/2)*2^(1/2)]]

 

[[(13/6)*3^(1/2), -3/2], [(13/6)*3^(1/2), 3/2], [-(1/3)*3^(1/2), -4]]

 

[[-3/2, (13/6)*3^(1/2)], [3/2, (13/6)*3^(1/2)], [-4, -(1/3)*3^(1/2)]]

 

[[3/2, (13/6)*3^(1/2)], [-3/2, (13/6)*3^(1/2)], [4, -(1/3)*3^(1/2)]]

(2)

#
# Produce the incircle of the triangle, Draw both
# of these. NB center of the incircle is the incenter
#
  incircle(C3, T1):
  draw([T1(color=red), C3(color=blue)], axes=normal);
#
# Translate the centre of the incircle to the
# origin. Apply the same translation to the triangle
#
  dsegment( ds2,
            point(P1, coordinates(center(C3))),
            point(OO, [0,0])
          ):
  translation(C4, C3, ds1):
  translation(T3, T1, ds1):
  draw( [ T3(color=red),
          C4(color=blue)
        ],
        axes=normal
      );
#
# Get the coordinates of translated triangle
#
  map(coordinates, DefinedAs(T3));

 

 

[[-1/2, -(1/2)*3^(1/2)], [5/2, -(1/2)*3^(1/2)], [-3, 2*3^(1/2)]]

(3)

#
# Observe that rotations, reflections etc are also "solutions".
#
# Successively rotate the triangle by Pi/8,, and draw the results
#
  draw( [ C4(color=blue),  seq( rotation( cat(TIR, j), T3, j*Pi/4, clockwise), j=0..7)], axes=normal);
#
# Now with a few reflections
#
  draw( [ C4(color=blue),
          T3,
          reflection( TF4,
                      T3,
                      line(x_axis, y=0 )
                    ),
          reflection( TF5,
                      T3,
                      line(y_axis, x=0 )
                    ),
          reflection( TF6,
                      TF5,
                      line(x_axis, y=0 )
                    )
        ]);
#
# Get the coordinates of (some of) these triangles
#
  map(coordinates, DefinedAs(TIR3));
  map(coordinates, DefinedAs(TIR6));
  map(coordinates, DefinedAs(TF4));
  map(coordinates, DefinedAs(TF6));

 

 

[[(1/4)*2^(1/2)-(1/4)*3^(1/2)*2^(1/2), (1/4)*2^(1/2)+(1/4)*3^(1/2)*2^(1/2)], [-(5/4)*2^(1/2)-(1/4)*3^(1/2)*2^(1/2), -(5/4)*2^(1/2)+(1/4)*3^(1/2)*2^(1/2)], [(3/2)*2^(1/2)+3^(1/2)*2^(1/2), (3/2)*2^(1/2)-3^(1/2)*2^(1/2)]]

 

[[(1/2)*3^(1/2), -1/2], [(1/2)*3^(1/2), 5/2], [-2*3^(1/2), -3]]

 

[[-1/2, (1/2)*3^(1/2)], [5/2, (1/2)*3^(1/2)], [-3, -2*3^(1/2)]]

 

[[1/2, (1/2)*3^(1/2)], [-5/2, (1/2)*3^(1/2)], [3, -2*3^(1/2)]]

(4)

 

Download triFun.mw

1 2 3 4 5 6 7 Last Page 2 of 110