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tomleslie

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15 years, 172 days
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These are answers submitted by tomleslie

Any numerical method...

tomleslie 13876
August 12 2019
2 0

requires that the variable be 'L' be given a value.

The attached uses L=10, althogh it can easily be changed

> 

  restart;
#
# Have to give 'L' a value to enable
# numeric solution
#
  L:=10:
  PDE := 35139.16048*(diff(w(x, t), x, x, x, x))+98646.00937*(diff(w(x, t), t, t))-2771.636*(diff(w(x, t), x, x)) = 24883.20000:
  bcs:= w(0,t)=0, D[1](w)(0,t)=0, D[1,1](w)(L,t)=0, D[1,1,1](w)(L,t)=0:
  ics:= w(x,0)=0, D[2](w)(x,0)=0:
  sol:=pdsolve(PDE, [bcs, ics], numeric):
#
# Plot w(x,t) for x=L/2 and t=0..10
#
  sol:-plot(x=L/2, t=0..10);
#
# Plot w(x,t) for x=0..L and t=5
#
  sol:-plot(t=0.5, x=0..L);
#
# 3D plot of w(x,t) for x=0..L, and t=0..10)
#
  sol:-plot3d( x=0..L, t=0..10);

 

 

 
> 

 

> 

 

> 

 


 

Download solvePDE2.mw

Two possibilities...

tomleslie 13876
August 10 2019
1 0

You cannot really expect the drawing tool within Maple to have the capabilities of a serious drawing program. Maple is a system for mathemetical calculation - not drawing.

You have two choices

  1. Use an external drawing packing (Gimp/Visio/whatever). Export from that package into a format understood by the Maple drawing tool, and then use an "import" command
  2. Use the plottoools() package within Maple to produce a suitable drawing, export the result in an appropriate format. Then use an import command in the target worksheet as in (1) above

Firstly...

tomleslie 13876
August 10 2019
0 0

upload actual worksheet using the big green up-arrow in the Mapleprimes toolbar.

The code you present in your oriignal post cannot produce the output you present for three reasons

  1. the variable 'q' is undefined
  2. you have two first order differential equations, which obviously require two initlal conditions in order for a numeric solution to be feasible. No initial conditions are supplied

Not sure I understand the problem...

tomleslie 13876
August 10 2019
1 0

What is wrong with a simple function definition, as in the attached; the function may be called from top-level or from within a package. Scoping is pretty much the same as any other function definition

> 

  restart;
  r:= (x,y)-> Record( 'name'=x, 'age'=y):
  myModule:= module()
                    global r;
                    option package;
                    export makeRec;
                    makeRec:= proc( a, b )
                                    return r(a,b)
                              end proc;
             end module:
  with(myModule):
> 

  s1:=r("JohnDoe1", 26):
  s2:=r("JohnDoe2", 28):
  s3:=makeRec("JohnDoe3", 30):
  s1:-name;
  s2:-age;
  s3:-age;

"JohnDoe1"

  

28

  

30

 (1)
> 

 

> 

 


 

Download makeRec.mw

+ve and -ve...

tomleslie 13876
August 09 2019
0 3

With R=0.5, the integrand is positive over some of the domain z=-R..R, y=0..R and negative over the rest. My "calibrated eyeball" thnks that, overall, the integral ought to be negative - which it is. See the attached

No idea what your plot command is doing because 'phi' is undefined


 

> 

Integrand := parse(FileTools[Text][ReadFile]("C:/Users/TomLeslie/Desktop/1.txt")):
#
# Evaluate the integral
#
  R:=0.5:
  evalf(Int(Integrand, [z = -R .. R, y = 0 .. R]));
#
# Plot the integrand over the region specified
# by the limits of integration
#
  plot3d(Integrand, z=-R..R, y=0..R);

-0.1342931338e-2

  

 
> 

 


 

Download posNegInt.mw

 

An alternative...

tomleslie 13876
August 09 2019
0 0

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

Pretty much...

tomleslie 13876
August 08 2019
2 0

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

I like making guesses...

tomleslie 13876
August 08 2019
1 0

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

More like observations really...

tomleslie 13876
August 06 2019
1 1

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

Investigate freeze/thaw...

tomleslie 13876
August 06 2019
1 4

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"

Using guesswork...

tomleslie 13876
August 05 2019
0 0
  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

 

Quick and dirty...

tomleslie 13876
August 05 2019
1 1

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

Or possibly...

tomleslie 13876
August 05 2019
0 1

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

It is trivial...

tomleslie 13876
August 04 2019
0 1

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)
> 

 


 

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Obvious question - why????...

tomleslie 13876
August 01 2019
0 1

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

  
> 

 


 

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