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19 years, 310 days
Ontario, Canada

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These are answers submitted by acer

something...

acer 32303
May 24 2022
2 5

Here is one way, using a legend on the side.

Dynamisches_Modell_Final_filled_conts.mw

Alternatively you could use a seq of implicitplots to get the contours as (ncely rendered) dotted lines, and a corresponding seq of 0-length thick curves and textplots for a faked "legend" inside the main plotting region. It's more effort than I have right now, sorry.

implicitplot...

acer 32303
May 24 2022
2 1

The general approach is to pass implicitplot the relevant inequality and add the filledregions options. However, with all other options at defaults there is not numeric difficulties and ensuing artefacts in the result.

One way around that is to (keep the default Digits=10 working precision and) start the E range from a small poitive number to avoid numeric issues.

plots:-implicitplot(0 <= Vth/E - Vps/E, E = 0.1e-8 .. 1000000, T = 0 .. 15,
                                filledregions, rangeasview);

Dynamisches_Modell_Final_ac1.mw

Another (slower) way is to increase working precision.

Digits:=16:
plots:-implicitplot(0 <= Vth/E - Vps/E, E = 0 .. 1000000, T = 0 .. 15,
                            filledregions, rangeasview);

Dynamisches_Modell_Final_ac.mw

code...

acer 32303
May 24 2022
2 1

At default Digits=10 the call evalf(Zeta(3)) is computed by the internal procedure `evalhf/Zeta`.

restart; evalf(Zeta(3));

          1.202056903

restart; evalf(evalhf(`evalhf/Zeta`(3)));

          1.202056903

You can see how that approximation is computed by examing the source code:

   showstat(`evalhf/Zeta`);

More generally you can also examine (ie. showstat) additional procedures, eg.
   `evalf/Zeta/real`
   `evalf/Zeta/complex`
and so on.

one way...

acer 32303
May 24 2022
1 0

You can get overwriting in a Task-region that gets embedded right below where output (of an Execution Group or Document Block normally appears).

The DocumentTools:-Tabulate command overwrites that region. This can be done within a loop. This provides a mechanism to show how the loops are progressing, without taking up a large amount of vertically-scrolled space.

You can adjust, to get various formatting effects.

For example, using Threads:-Sleep to get a slight pause (or else the example runs too fast to see the effects...):

> 

for i from 1 to 15 do

res1:='res1';
for j from 1 to 100 do

x:= 5*i*j:
if (j mod 10) =0 then
  res1[j] := j/100;
  DocumentTools:-Tabulate(widthmode=pixels,width=400,
                          <sprintf("i=%a, j=%a",i,j),
                          eval('Typesetting:-Typeset'(convert(res1,list)))>):
  Threads:-Sleep(0.05); # sleep 0.05 seconds
fi;

od:
## clear the printing here ##
if (i mod 5) =0 then
  DocumentTools:-Tabulate(widthmode=pixels,width=200,
                          exterior=all, interior=none,
                          ["outer",sprintf("i=%a",i)]):
  Threads:-Sleep(1.0); # sleep 1.0 seconds
fi;

od:
DocumentTools:-Tabulate(widthmode=pixels,width=200,
                        exterior=all, interior=none,
                        [["finished"]]): # or [[]] to show blank
> 

 

Download Tab_loop.mw

palette. command-completion...

acer 32303
May 21 2022
0 0

I don't really understand what you intend by differentiating w.r.t a name appearing in the subscript.

As far as getting nicely typeset derivatives, I suspect that in Maple Flow you could try the Expression palette (on left panel), or command-completion templates.

In order to get the command-completion, one can press the Esc key after first typing the start of the word, eg. after typing diff .

add...

acer 32303
May 21 2022
2 11

You should use add for adding up this particular finite number of terms, and not sum, since it's not an attempt to perform symbolic summation.

> 

restart;
> 

f := (x,y)->1/(2+x*y^2);

proc (x, y) options operator, arrow; 1/(2+x*y^2) end proc

> 

P := (x,y,x0,y0,N) -> sum(1/factorial(n)*sum(binomial(n,k)
                          *D[1$(n-k), 2$k](f)(x0,y0)
                          *(x-x0)^(n-k)*(y-y0)^k, k=0..n),
                          n=0..N):
> 

add(D[1$(3-k),2$k](f)(0,0), k=0..3);

-1/2

Calling the sum command follows usual evaluation rules, in which the arguments are evaluated up front. Here's what the sum command receives for your example:

> 

D[1$(3-k),2$k](f)(0,0);

pochhammer(-3+k, 3-k)*(Sum(0, _k1 = 0 .. k))


In contrast, the add command has special evaluation rules, in which case full evaluation of the first argument is delayed until the index attains actual numeric values.

You could also delay the first argument to sum using a (double, for this example) pair of unevaluation quotes. That's fragile.

> 

sum(''D''[1$(3-k),2$k](f)(0,0), k=0..3);

-1/2

plots:-display...

acer 32303
May 21 2022
0 0

Try either using it like,

   plots:-display (P1,P2);

or, alternatively, first loading the plots package, ie,

   with(plots):
   display(P1,P2);

Don't put a space between the word display and the opening bracket (.

alternatives...

acer 32303
May 20 2022
3 1

Your simplification example is straightforward enough to be handled by several different commands.

Those commands can act differently on more involved examples. Ie,

> 

restart;
> 

ee := (x^2 - 2)/(x - sqrt(2));

(x^2-2)/(x-2^(1/2))

> 

radnormal(ee);

x+2^(1/2)

> 

evala(ee);

x+2^(1/2)

> 

rationalize(ee);

x+2^(1/2)

> 

factor(ee);

x+2^(1/2)

> 

ff := (x^3 - 5*x^2 - 2*x + 10)/(x - sqrt(2));

(x^3-5*x^2-2*x+10)/(x-2^(1/2))

> 

radnormal(ff);

x^2-5*x+x*2^(1/2)-5*2^(1/2)

> 

evala(ff);

x^2-5*x+x*2^(1/2)-5*2^(1/2)

> 

simplify(radnormal(ff));

(x-5)*(x+2^(1/2))

> 

rationalize(ff);

(x-5)*(x+2^(1/2))

> 

factor(ff);

(x-5)*(x+2^(1/2))

Download rad_ex.mw

It is worthwhile familiarizing yourself with these commands.

various...

acer 32303
May 18 2022
3 1

Here are a few ways, using an interpolating function of your data which can then be used with several plotting commands. 

You did not originally show how you wanted it colored/shaded. So I illustrate a few. Let me know if you really need the restricted/reversed hue-shading (particular color gradient scheme) as shown in your followup reply to Carl.

I used Maple 17, which you've indicated. In later releases there are several easier and more flexible techniques, eg. the `colorscheme` option.

The colorbar is also easier in later versions. I might find a moment to retrofit some mechanisms. I just don't have the 20 minutes right now, to construct all the pieces in Maple 17.

I have not really bothered to optimize for speed.

> 

restart;
> 

x := [0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4]:
> 

y := [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4]:
> 

z := [0, 0, 0, 0, 0,
      0, .689376362, 1.378752724, 2.068129087, 2.757505449,
      0, 1.02920355, 2.0584071, 3.087610649, 4.116814199,
      0, 1.216469264, 2.432938529, 3.649407793, 4.865877057,
      0, 1.325720912, 2.651441823, 3.977162735, 5.302883646]:
> 

interfunc:=subs(__M=Matrix(Matrix(5,5,z),datatype=float[8]),
                (x,y)->CurveFitting:-ArrayInterpolation([[0,1,2,3,4],[0,1,2,3,4]],
                                                   __M,[[x],[y]],
                                                   method=cubic)[1,1]):
> 

Pdens:=plots:-densityplot(interfunc,0..4,0..4,
                          colorstyle=HUE,style=patchnogrid):
Pdens;

 

  
> 

plots:-contourplot(interfunc,0..4,0..4,coloring=["Orange","Blue"],filled);

 

  
> 

Pcont:=plots:-contourplot(interfunc,0..4,0..4,grid=[51,51],color=black):
> 

plots:-display(Pdens,Pcont);

 

  
> 

 

Download listcontdens_M17.mw

something...

acer 32303
May 12 2022
2 1

Here are a few ways, using fsolve. I don't know whether it is fast enough for you, or if you need it much faster.

I used Maple 2019.2.

> 

restart;
> 

Digits:=15:
> 

eq[1] := d[0] = 1:
eq[2] := d[0] + d[1] + d[2] + d[3] + d[4] + d[5] + d[6] + d[7] = 0:
eq[3] := b[0] = 1:
eq[4] := b[0] + b[1] + b[2] + b[3] + b[4] + b[5] + b[6] + b[7] = 0:
eq[5] := a[0] = -0.5:
eq[6] := d[1] = 1 + 1.0*a[2]:
eq[7] := a[0] + a[1] + a[2] + a[3] + a[4] + a[5] + a[6] + a[7] + a[8] + a[9] = 0.5:
eq[8] := d[1] + 2*d[2] + 3*d[3] + 4*d[4] + 5*d[5] + 6*d[6] + 7*d[7] = 1.0*a[2] + 3.0*a[3] + 6.0*a[4] + 10.0*a[5] + 15.0*a[6] + 21.0*a[7] + 28.0*a[8] + 36.0*a[9]:
eq[9] := 24*a[4] - 2.104513094*a[1]*a[2] + 6.313539282*a[0]*a[3] + 5.165076420*b[1] + 5.261282735*d[1] = 0:
eq[10] := -88.3895499*a[7]^2 - 191.5106915*a[7]*a[8] - 176.7790999*a[7]*a[9] - 117.8527333*a[8]^2 - 252.5415715*a[8]*a[9] - 151.5249428*a[9]^2 + 25.25415713*a[0]*a[4] + 63.13539282*a[0]*a[5] + 126.2707856*a[0]*a[6] + 220.9738749*a[0]*a[7] + 353.5581998*a[0]*a[8] + 530.3372997*a[0]*a[9] + 12.62707857*a[1]*a[4] + 42.09026188*a[1]*a[5] + 94.70308919*a[1]*a[6] + 176.7790999*a[1]*a[7] + 294.6318332*a[1]*a[8] + 454.5748283*a[1]*a[9] - 4.209026188*a[2]^2 - 12.62707857*a[2]*a[3] - 8.41805237*a[2]*a[4] + 10.52256547*a[2]*a[5] + 50.50831422*a[2]*a[6] + 117.8527333*a[2]*a[7] + 218.8693618*a[2]*a[8] + 359.8717391*a[2]*a[9] - 12.62707857*a[3]^2 - 31.56769641*a[3]*a[4] - 25.25415713*a[3]*a[5] + 50.5083143*a[3]*a[7] + 132.5843249*a[3]*a[8] + 252.5415713*a[3]*a[9] - 25.25415713*a[4]^2 - 58.92636665*a[4]*a[5] - 50.5083142*a[4]*a[6] - 18.9406178*a[4]*a[7] + 42.0902619*a[4]*a[8] + 138.8978642*a[4]*a[9] - 42.09026188*a[5]^2 - 94.7030892*a[5]*a[6] - 84.1805237*a[5]*a[7] - 46.2992881*a[5]*a[8] + 25.2541571*a[5]*a[9] - 63.1353929*a[6]^2 - 138.8978642*a[6]*a[7] - 126.2707857*a[6]*a[8] - 82.0760107*a[6]*a[9] - 2.104513094*a[1]*a[2] + 6.313539282*a[0]*a[3] + 26.30641368*d[5] + 31.56769641*d[6] + 36.82897914*d[7] + 15.78384820*d[3] + 21.04513094*d[4] + 5.261282735*d[1] + 10.52256547*d[2] + 36.15553494*b[7] + 25.82538210*b[5] + 30.99045852*b[6] + 10.33015284*b[2] + 15.49522926*b[3] + 20.66030568*b[4] + 5.165076420*b[1] + 3024.*a[9] + 360.*a[6] + 840.*a[7] + 1680.*a[8] + 24.*a[4] + 120.*a[5] = 0:
eq[11] := 120.*a[5] - 4.209026188*a[2]^2 + 25.25415713*a[0]*a[4] + 10.33015284*b[2] + 10.52256547*d[2] = 0:
eq[12] := -972.2850495*a[7]^2 - 2298.128299*a[7]*a[8] - 2298.128298*a[7]*a[9] - 1532.085532*a[8]^2 - 3535.581998*a[8]*a[9] - 2272.874142*a[9]^2 + 25.25415713*a[0]*a[4] + 126.2707856*a[0]*a[5] + 378.8123569*a[0]*a[6] + 883.8954995*a[0]*a[7] + 1767.790999*a[0]*a[8] + 3182.023798*a[0]*a[9] + 25.25415713*a[1]*a[4] + 126.2707856*a[1]*a[5] + 378.8123569*a[1]*a[6] + 883.8954995*a[1]*a[7] + 1767.790999*a[1]*a[8] + 3182.023798*a[1]*a[9] - 4.209026188*a[2]^2 - 25.25415713*a[2]*a[3] - 25.25415713*a[2]*a[4] + 42.09026184*a[2]*a[5] + 252.5415713*a[2]*a[6] + 707.1163996*a[2]*a[7] + 1532.085532*a[2]*a[8] + 2878.973912*a[2]*a[9] - 37.88123569*a[3]^2 - 126.2707857*a[3]*a[4] - 126.2707857*a[3]*a[5] + 353.5581998*a[3]*a[7] + 1060.674599*a[3]*a[8] + 2272.874141*a[3]*a[9] - 126.2707857*a[4]^2 - 353.5581998*a[4]*a[5] - 353.5581998*a[4]*a[6] - 151.5249424*a[4]*a[7] + 378.812357*a[4]*a[8] + 1388.978642*a[4]*a[9] - 294.6318332*a[5]^2 - 757.6247134*a[5]*a[6] - 757.624714*a[5]*a[7] - 462.992880*a[5]*a[8] + 277.795729*a[5]*a[9] - 568.2185354*a[6]^2 - 1388.978642*a[6]*a[7] - 1388.978642*a[6]*a[8] - 984.912128*a[6]*a[9] + 105.2256547*d[5] + 157.8384820*d[6] + 220.9738748*d[7] + 31.56769640*d[3] + 63.13539282*d[4] + 10.52256547*d[2] + 216.9332096*b[7] + 103.3015284*b[5] + 154.9522926*b[6] + 10.33015284*b[2] + 30.99045852*b[3] + 61.98091704*b[4] + 15120.*a[9] + 720.*a[6] + 2520.*a[7] + 6720.*a[8] + 120.*a[5] = 0:
eq[13] := 720.*a[6] - 25.25415713*a[2]*a[3] + 25.25415713*a[1]*a[4] + 126.2707856*a[0]*a[5] + 30.99045852*b[3] + 31.56769640*d[3] = 0:
eq[14] := -9722.850492*a[7]^2 - 25279.41129*a[7]*a[8] - 27577.53959*a[7]*a[9] - 18385.02639*a[8]^2 - 45962.56593*a[8]*a[9] - 31820.23799*a[9]^2 + 126.2707856*a[0]*a[5] + 757.6247138*a[0]*a[6] + 2651.686498*a[0]*a[7] + 7071.163996*a[0]*a[8] + 15910.11899*a[0]*a[9] + 25.25415713*a[1]*a[4] + 252.5415712*a[1]*a[5] + 1136.437071*a[1]*a[6] + 3535.581998*a[1]*a[7] + 8838.954995*a[1]*a[8] + 19092.14279*a[1]*a[9] - 25.25415713*a[2]*a[3] - 50.50831424*a[2]*a[4] + 126.2707856*a[2]*a[5] + 1010.166285*a[2]*a[6] + 3535.581998*a[2]*a[7] + 9192.513195*a[2]*a[8] + 20152.81739*a[2]*a[9] - 75.76247138*a[3]^2 - 378.8123569*a[3]*a[4] - 505.0831425*a[3]*a[5] + 2121.349198*a[3]*a[7] + 7424.722196*a[3]*a[8] + 18182.99313*a[3]*a[9] - 505.0831426*a[4]^2 - 1767.790999*a[4]*a[5] - 2121.349199*a[4]*a[6] - 1060.674600*a[4]*a[7] + 3030.498859*a[4]*a[8] + 12500.80778*a[4]*a[9] - 1767.790999*a[5]^2 - 5303.372998*a[5]*a[6] - 6060.997709*a[5]*a[7] - 4166.935929*a[5]*a[8] + 2777.95729*a[5]*a[9] - 4545.748282*a[6]^2 - 12500.80779*a[6]*a[7] - 13889.78642*a[6]*a[8] - 10834.03341*a[6]*a[9] + 315.6769641*d[5] + 631.3539280*d[6] + 1104.869374*d[7] + 31.56769640*d[3] + 126.2707856*d[4] + 1084.666048*b[7] + 309.9045852*b[5] + 619.8091704*b[6] + 30.99045852*b[3] + 123.9618341*b[4] + 60480.*a[9] + 720.*a[6] + 5040.*a[7] + 20160.*a[8] - 2.*10^(-7)*a[3]*a[6] = 0:
eq[15] := 2.*d[2] + 5.261282735*a[0]*d[1] - 2.630641368*d[0] = 0:
eq[16] := 17.36935863*d[5] + 27.36935863*d[6] + 39.36935863*d[7] + 3.369358632*d[3] + 9.369358632*d[4] - 2.630641368*d[0] - 2.630641368*d[1] - 0.630641368*d[2] + 36.82897914*a[6]*d[7] + 5.261282735*a[7]*d[1] + 10.52256547*a[7]*d[2] + 15.78384820*a[7]*d[3] + 21.04513094*a[7]*d[4] + 26.30641368*a[7]*d[5] + 31.56769641*a[7]*d[6] + 36.82897914*a[7]*d[7] + 5.261282735*a[8]*d[1] + 10.52256547*a[8]*d[2] + 15.78384820*a[8]*d[3] + 21.04513094*a[8]*d[4] + 26.30641368*a[8]*d[5] + 31.56769641*a[8]*d[6] + 36.82897914*a[8]*d[7] + 5.261282735*a[9]*d[1] + 10.52256547*a[9]*d[2] + 15.78384820*a[9]*d[3] + 21.04513094*a[9]*d[4] + 26.30641368*a[9]*d[5] + 31.56769641*a[9]*d[6] + 36.82897914*a[9]*d[7] + 10.52256547*a[0]*d[2] + 15.78384820*a[0]*d[3] + 21.04513094*a[0]*d[4] + 26.30641368*a[0]*d[5] + 31.56769641*a[0]*d[6] + 36.82897914*a[0]*d[7] + 5.261282735*a[1]*d[1] + 10.52256547*a[1]*d[2] + 15.78384820*a[1]*d[3] + 21.04513094*a[1]*d[4] + 26.30641368*a[1]*d[5] + 31.56769641*a[1]*d[6] + 36.82897914*a[1]*d[7] + 5.261282735*a[2]*d[1] + 10.52256547*a[2]*d[2] + 15.78384820*a[2]*d[3] + 21.04513094*a[2]*d[4] + 26.30641368*a[2]*d[5] + 31.56769641*a[2]*d[6] + 36.82897914*a[2]*d[7] + 5.261282735*a[3]*d[1] + 10.52256547*a[3]*d[2] + 15.78384820*a[3]*d[3] + 21.04513094*a[3]*d[4] + 26.30641368*a[3]*d[5] + 31.56769641*a[3]*d[6] + 36.82897914*a[3]*d[7] + 5.261282735*a[4]*d[1] + 10.52256547*a[4]*d[2] + 15.78384820*a[4]*d[3] + 21.04513094*a[4]*d[4] + 26.30641368*a[4]*d[5] + 31.56769641*a[4]*d[6] + 36.82897914*a[4]*d[7] + 5.261282735*a[5]*d[1] + 10.52256547*a[5]*d[2] + 15.78384820*a[5]*d[3] + 21.04513094*a[5]*d[4] + 26.30641368*a[5]*d[5] + 31.56769641*a[5]*d[6] + 36.82897914*a[5]*d[7] + 5.261282735*a[6]*d[1] + 10.52256547*a[6]*d[2] + 15.78384820*a[6]*d[3] + 21.04513094*a[6]*d[4] + 26.30641368*a[6]*d[5] + 31.56769641*a[6]*d[6] + 5.261282735*a[0]*d[1] = 0:
eq[17] := 6.*d[3] + 5.261282735*a[1]*d[1] + 10.52256547*a[0]*d[2] - 2.630641368*d[1] = 0:
eq[18] := 46.84679316*d[5] + 104.2161518*d[6] + 191.5855104*d[7] - 1.891924104*d[3] + 13.47743453*d[4] - 2.630641368*d[1] - 5.261282736*d[2] + 441.9477498*a[6]*d[7] + 36.82897914*a[7]*d[1] + 84.18052376*a[7]*d[2] + 142.0546338*a[7]*d[3] + 210.4513094*a[7]*d[4] + 289.3705504*a[7]*d[5] + 378.8123569*a[7]*d[6] + 478.7767289*a[7]*d[7] + 42.09026188*a[8]*d[1] + 94.70308923*a[8]*d[2] + 157.8384820*a[8]*d[3] + 231.4964403*a[8]*d[4] + 315.6769641*a[8]*d[5] + 410.3800533*a[8]*d[6] + 515.6057081*a[8]*d[7] + 47.35154462*a[9]*d[1] + 105.2256547*a[9]*d[2] + 173.6223302*a[9]*d[3] + 252.5415713*a[9]*d[4] + 341.9833778*a[9]*d[5] + 441.9477497*a[9]*d[6] + 552.4346872*a[9]*d[7] + 10.52256547*a[0]*d[2] + 31.56769641*a[0]*d[3] + 63.13539282*a[0]*d[4] + 105.2256547*a[0]*d[5] + 157.8384820*a[0]*d[6] + 220.9738749*a[0]*d[7] + 5.261282735*a[1]*d[1] + 21.04513094*a[1]*d[2] + 47.35154461*a[1]*d[3] + 84.18052376*a[1]*d[4] + 131.5320684*a[1]*d[5] + 189.4061784*a[1]*d[6] + 257.8028540*a[1]*d[7] + 10.52256547*a[2]*d[1] + 31.56769641*a[2]*d[2] + 63.13539282*a[2]*d[3] + 105.2256547*a[2]*d[4] + 157.8384820*a[2]*d[5] + 220.9738748*a[2]*d[6] + 294.6318332*a[2]*d[7] + 15.78384820*a[3]*d[1] + 42.09026188*a[3]*d[2] + 78.91924103*a[3]*d[3] + 126.2707856*a[3]*d[4] + 184.1448957*a[3]*d[5] + 252.5415712*a[3]*d[6] + 331.4608123*a[3]*d[7] + 21.04513094*a[4]*d[1] + 52.61282735*a[4]*d[2] + 94.70308923*a[4]*d[3] + 147.3159166*a[4]*d[4] + 210.4513094*a[4]*d[5] + 284.1092676*a[4]*d[6] + 368.2897915*a[4]*d[7] + 26.30641368*a[5]*d[1] + 63.13539282*a[5]*d[2] + 110.4869374*a[5]*d[3] + 168.3610475*a[5]*d[4] + 236.7577231*a[5]*d[5] + 315.6769640*a[5]*d[6] + 405.1187706*a[5]*d[7] + 31.56769641*a[6]*d[1] + 73.65795829*a[6]*d[2] + 126.2707856*a[6]*d[3] + 189.4061784*a[6]*d[4] + 263.0641367*a[6]*d[5] + 347.2446605*a[6]*d[6] = 0:
eq[19] := 24.*d[4] + 10.52256547*a[2]*d[1] + 21.04513094*a[1]*d[2] + 31.56769641*a[0]*d[3] - 5.261282736*d[2] = 0:
eq[20] := 67.38717264*d[5] + 281.0807590*d[6] + 729.5130625*d[7] - 15.78384821*d[3] - 7.56769641*d[4] - 5.261282736*d[2] + 4861.425246*a[6]*d[7] + 220.9738749*a[7]*d[1] + 589.2636663*a[7]*d[2] + 1136.437070*a[7]*d[3] + 1894.061785*a[7]*d[4] + 2893.705504*a[7]*d[5] + 4166.935926*a[7]*d[6] + 5745.320746*a[7]*d[7] + 294.6318332*a[8]*d[1] + 757.6247138*a[8]*d[2] + 1420.546338*a[8]*d[3] + 2314.964404*a[8]*d[4] + 3472.446605*a[8]*d[5] + 4924.560640*a[8]*d[6] + 6702.874204*a[8]*d[7] + 378.8123569*a[9]*d[1] + 947.0308923*a[9]*d[2] + 1736.223302*a[9]*d[3] + 2777.957285*a[9]*d[4] + 4103.800534*a[9]*d[5] + 5745.320747*a[9]*d[6] + 7734.085620*a[9]*d[7] + 31.56769641*a[0]*d[3] + 126.2707856*a[0]*d[4] + 315.6769641*a[0]*d[5] + 631.3539282*a[0]*d[6] + 1104.869374*a[0]*d[7] + 21.04513094*a[1]*d[2] + 94.70308923*a[1]*d[3] + 252.5415712*a[1]*d[4] + 526.1282735*a[1]*d[5] + 947.0308923*a[1]*d[6] + 1546.817124*a[1]*d[7] + 10.52256547*a[2]*d[1] + 63.13539282*a[2]*d[2] + 189.4061784*a[2]*d[3] + 420.9026188*a[2]*d[4] + 789.1924103*a[2]*d[5] + 1325.843249*a[2]*d[6] + 2062.422832*a[2]*d[7] + 31.56769641*a[3]*d[1] + 126.2707856*a[3]*d[2] + 315.6769641*a[3]*d[3] + 631.3539281*a[3]*d[4] + 1104.869374*a[3]*d[5] + 1767.790999*a[3]*d[6] + 2651.686498*a[3]*d[7] + 63.13539282*a[4]*d[1] + 210.4513094*a[4]*d[2] + 473.5154462*a[4]*d[3] + 883.8954995*a[4]*d[4] + 1473.159166*a[4]*d[5] + 2272.874141*a[4]*d[6] + 3314.608123*a[4]*d[7] + 105.2256547*a[5]*d[1] + 315.6769641*a[5]*d[2] + 662.9216246*a[5]*d[3] + 1178.527333*a[5]*d[4] + 1894.061784*a[5]*d[5] + 2841.092676*a[5]*d[6] + 4051.187706*a[5]*d[7] + 157.8384820*a[6]*d[1] + 441.9477497*a[6]*d[2] + 883.8954995*a[6]*d[3] + 1515.249428*a[6]*d[4] + 2367.577230*a[6]*d[5] + 3472.446605*a[6]*d[6] = 0:
eq[21] := 2.119408818*b[2] + 6.176017503*a[0]*b[1] + 42.07215928*a[2] + 0.5*d[0] = 0:
eq[22] := 0.5*d[5] + 0.5*d[6] + 0.5*d[7] + 0.5*d[3] + 0.5*d[4] + 0.5*d[0] + 0.5*d[1] + 0.5*d[2] + 44.50758518*b[7] + 21.19408818*b[5] + 31.79113227*b[6] + 2.119408818*b[2] + 6.358226454*b[3] + 12.71645291*b[4] + 1514.597734*a[9] + 631.0823892*a[6] + 883.5153448*a[7] + 1178.020460*a[8] + 126.2164778*a[3] + 252.4329557*a[4] + 420.7215928*a[5] + 42.07215928*a[2] + 12.35203501*a[0]*b[2] + 18.52805251*a[0]*b[3] + 24.70407001*a[0]*b[4] + 30.88008752*a[0]*b[5] + 37.05610502*a[0]*b[6] + 43.23212252*a[0]*b[7] + 6.176017503*a[1]*b[1] + 12.35203501*a[1]*b[2] + 18.52805251*a[1]*b[3] + 24.70407001*a[1]*b[4] + 30.88008752*a[1]*b[5] + 37.05610502*a[1]*b[6] + 43.23212252*a[1]*b[7] + 6.176017503*a[2]*b[1] + 12.35203501*a[2]*b[2] + 18.52805251*a[2]*b[3] + 24.70407001*a[2]*b[4] + 30.88008752*a[2]*b[5] + 37.05610502*a[2]*b[6] + 43.23212252*a[2]*b[7] + 6.176017503*a[3]*b[1] + 12.35203501*a[3]*b[2] + 18.52805251*a[3]*b[3] + 24.70407001*a[3]*b[4] + 30.88008752*a[3]*b[5] + 37.05610502*a[3]*b[6] + 43.23212252*a[3]*b[7] + 6.176017503*a[4]*b[1] + 12.35203501*a[4]*b[2] + 18.52805251*a[4]*b[3] + 24.70407001*a[4]*b[4] + 30.88008752*a[4]*b[5] + 37.05610502*a[4]*b[6] + 43.23212252*a[4]*b[7] + 6.176017503*a[5]*b[1] + 12.35203501*a[5]*b[2] + 18.52805251*a[5]*b[3] + 24.70407001*a[5]*b[4] + 30.88008752*a[5]*b[5] + 37.05610502*a[5]*b[6] + 43.23212252*a[5]*b[7] + 6.176017503*a[6]*b[1] + 12.35203501*a[6]*b[2] + 18.52805251*a[6]*b[3] + 24.70407001*a[6]*b[4] + 30.88008752*a[6]*b[5] + 37.05610502*a[6]*b[6] + 43.23212252*a[6]*b[7] + 6.176017503*a[7]*b[1] + 12.35203501*a[7]*b[2] + 18.52805251*a[7]*b[3] + 24.70407001*a[7]*b[4] + 30.88008752*a[7]*b[5] + 37.05610502*a[7]*b[6] + 43.23212252*a[7]*b[7] + 6.176017503*a[8]*b[1] + 12.35203501*a[8]*b[2] + 18.52805251*a[8]*b[3] + 24.70407001*a[8]*b[4] + 30.88008752*a[8]*b[5] + 37.05610502*a[8]*b[6] + 43.23212252*a[8]*b[7] + 6.176017503*a[9]*b[1] + 12.35203501*a[9]*b[2] + 18.52805251*a[9]*b[3] + 24.70407001*a[9]*b[4] + 30.88008752*a[9]*b[5] + 37.05610502*a[9]*b[6] + 43.23212252*a[9]*b[7] + 6.176017503*a[0]*b[1] = 0:
eq[23] := 6.358226454*b[3] + 6.176017503*a[1]*b[1] + 12.35203501*a[0]*b[2] + 126.2164778*a[3] + 0.5*d[1] = 0:
eq[24] := 2.5*d[5] + 3.0*d[6] + 3.5*d[7] + 1.5*d[3] + 2.0*d[4] + 0.5*d[1] + d[2] + 222.5379259*b[7] + 63.58226454*b[5] + 127.1645291*b[6] + 6.358226454*b[3] + 25.43290582*b[4] + 10602.18414*a[9] + 2524.329557*a[6] + 4417.576724*a[7] + 7068.122760*a[8] + 126.2164778*a[3] + 504.8659114*a[4] + 1262.164778*a[5] + 12.35203501*a[0]*b[2] + 37.05610502*a[0]*b[3] + 74.11221004*a[0]*b[4] + 123.5203501*a[0]*b[5] + 185.2805251*a[0]*b[6] + 259.3927351*a[0]*b[7] + 6.176017503*a[1]*b[1] + 24.70407002*a[1]*b[2] + 55.58415753*a[1]*b[3] + 98.81628005*a[1]*b[4] + 154.4004376*a[1]*b[5] + 222.3366301*a[1]*b[6] + 302.6248576*a[1]*b[7] + 12.35203501*a[2]*b[1] + 37.05610502*a[2]*b[2] + 74.11221004*a[2]*b[3] + 123.5203501*a[2]*b[4] + 185.2805251*a[2]*b[5] + 259.3927351*a[2]*b[6] + 345.8569801*a[2]*b[7] + 18.52805251*a[3]*b[1] + 49.40814003*a[3]*b[2] + 92.64026255*a[3]*b[3] + 148.2244201*a[3]*b[4] + 216.1606126*a[3]*b[5] + 296.4488402*a[3]*b[6] + 389.0891027*a[3]*b[7] + 24.70407001*a[4]*b[1] + 61.76017503*a[4]*b[2] + 111.1683151*a[4]*b[3] + 172.9284901*a[4]*b[4] + 247.0407002*a[4]*b[5] + 333.5049452*a[4]*b[6] + 432.3212252*a[4]*b[7] + 30.88008752*a[5]*b[1] + 74.11221004*a[5]*b[2] + 129.6963676*a[5]*b[3] + 197.6325601*a[5]*b[4] + 277.9207877*a[5]*b[5] + 370.5610502*a[5]*b[6] + 475.5533477*a[5]*b[7] + 37.05610502*a[6]*b[1] + 86.46424505*a[6]*b[2] + 148.2244201*a[6]*b[3] + 222.3366301*a[6]*b[4] + 308.8008752*a[6]*b[5] + 407.6171552*a[6]*b[6] + 518.7854702*a[6]*b[7] + 43.23212252*a[7]*b[1] + 98.81628005*a[7]*b[2] + 166.7524726*a[7]*b[3] + 247.0407001*a[7]*b[4] + 339.6809627*a[7]*b[5] + 444.6732602*a[7]*b[6] + 562.0175927*a[7]*b[7] + 49.40814002*a[8]*b[1] + 111.1683151*a[8]*b[2] + 185.2805251*a[8]*b[3] + 271.7447701*a[8]*b[4] + 370.5610502*a[8]*b[5] + 481.7293652*a[8]*b[6] + 605.2497153*a[8]*b[7] + 55.58415753*a[9]*b[1] + 123.5203501*a[9]*b[2] + 203.8085776*a[9]*b[3] + 296.4488401*a[9]*b[4] + 401.4411377*a[9]*b[5] + 518.7854703*a[9]*b[6] + 648.4818378*a[9]*b[7] = 0:
eq[25] := 25.43290582*b[4] + 12.35203501*a[2]*b[1] + 24.70407002*a[1]*b[2] + 37.05610502*a[0]*b[3] + 504.8659114*a[4] + d[2] = 0:
eq[26] := 10.0*d[5] + 15.0*d[6] + 21.0*d[7] + 3.0*d[3] + 6.0*d[4] + d[2] + 890.1517036*b[7] + 127.1645291*b[5] + 381.4935873*b[6] + 25.43290582*b[4] + 63613.10484*a[9] + 7572.988671*a[6] + 17670.30690*a[7] + 35340.61380*a[8] + 504.8659114*a[4] + 2524.329556*a[5] + 37.05610502*a[0]*b[3] + 148.2244201*a[0]*b[4] + 370.5610502*a[0]*b[5] + 741.1221004*a[0]*b[6] + 1296.963676*a[0]*b[7] + 24.70407002*a[1]*b[2] + 111.1683151*a[1]*b[3] + 296.4488402*a[1]*b[4] + 617.6017504*a[1]*b[5] + 1111.683151*a[1]*b[6] + 1815.749146*a[1]*b[7] + 12.35203501*a[2]*b[1] + 74.11221005*a[2]*b[2] + 222.3366301*a[2]*b[3] + 494.0814003*a[2]*b[4] + 926.4026256*a[2]*b[5] + 1556.356411*a[2]*b[6] + 2420.998862*a[2]*b[7] + 37.05610502*a[3]*b[1] + 148.2244201*a[3]*b[2] + 370.5610503*a[3]*b[3] + 741.1221006*a[3]*b[4] + 1296.963676*a[3]*b[5] + 2075.141881*a[3]*b[6] + 3112.712822*a[3]*b[7] + 74.11221004*a[4]*b[1] + 247.0407002*a[4]*b[2] + 555.8415753*a[4]*b[3] + 1037.570941*a[4]*b[4] + 1729.284901*a[4]*b[5] + 2668.039561*a[4]*b[6] + 3890.891028*a[4]*b[7] + 123.5203501*a[5]*b[1] + 370.5610502*a[5]*b[2] + 778.1782055*a[5]*b[3] + 1383.427921*a[5]*b[4] + 2223.366301*a[5]*b[5] + 3335.049452*a[5]*b[6] + 4755.533478*a[5]*b[7] + 185.2805251*a[6]*b[1] + 518.7854703*a[6]*b[2] + 1037.570941*a[6]*b[3] + 1778.693041*a[6]*b[4] + 2779.207876*a[6]*b[5] + 4076.171553*a[6]*b[6] + 5706.640175*a[6]*b[7] + 259.3927351*a[7]*b[1] + 691.7139604*a[7]*b[2] + 1334.019781*a[7]*b[3] + 2223.366302*a[7]*b[4] + 3396.809627*a[7]*b[5] + 4891.405863*a[7]*b[6] + 6744.211115*a[7]*b[7] + 345.8569802*a[8]*b[1] + 889.3465205*a[8]*b[2] + 1667.524727*a[8]*b[3] + 2717.447702*a[8]*b[4] + 4076.171553*a[8]*b[5] + 5780.752383*a[8]*b[6] + 7868.246300*a[8]*b[7] + 444.6732602*a[9]*b[1] + 1111.683151*a[9]*b[2] + 2038.085777*a[9]*b[3] + 3260.937242*a[9]*b[4] + 4817.293653*a[9]*b[5] + 6744.211114*a[9]*b[6] + 9078.745732*a[9]*b[7] = 0:
> 

ans1:=CodeTools:-Usage(
   fsolve([seq(eval(eq[i],[eq[1],eq[3],eq[5]]), i = {$1..26} minus {1,3,5})],
          {seq(a[i], i = 1 .. 9),seq(b[i], i = 1 .. 7),seq(d[i], i = 1 .. 7)})
):
% union eval({eq[1],eq[3],eq[5]},%);
max(abs~([seq(evalf[5](evalf[50](eval((rhs-lhs)(eq[i]),%))),i=1..26)]));

memory used=101.54MiB, alloc change=36.00MiB, cpu time=748.00ms, real time=749.00ms, gc time=69.62ms

{a[0] = -.5, a[1] = 4.32375717286124, a[2] = -10.3916808893481, a[3] = -4.37793022080622, a[4] = 20.9848616428886, a[5] = 2.88811154030335, a[6] = -27.7320234280139, a[7] = 18.9496346647742, a[8] = -3.37842933403158, a[9] = -.266301148627605, b[0] = 1, b[1] = -108.924352850057, b[2] = 47.3439092349469, b[3] = 591.097526763819, b[4] = -734.087769795466, b[5] = -7.21902282081380, b[6] = 312.721961795463, b[7] = -101.932252327892, d[0] = 1, d[1] = -9.39168088934813, d[2] = -11.0377514449392, d[3] = 21.8113102540731, d[4] = 10.9837400537900, d[5] = .274415898348425, d[6] = -25.2503779587453, d[7] = 11.6103440868212}

0.31195e-8

> 

ans2:=CodeTools:-Usage(
   fsolve([seq(eval(eq[i],[eq[1],eq[3],eq[5]]), i = {$1..26} minus {1,3,5})],
          {seq(a[i], i = 1 .. 9),seq(b[i], i = 1 .. 7),seq(d[i], i = 1 .. 7)},
   avoid={ans1})
):
% union eval({eq[1],eq[3],eq[5]},%);
max(abs~([seq(evalf[5](evalf[50](eval((rhs-lhs)(eq[i]),%))),i=1..26)]));

memory used=1.47GiB, alloc change=16.00MiB, cpu time=13.64s, real time=12.38s, gc time=2.64s

{a[0] = -.5, a[1] = 473.614434960278, a[2] = -1.21088206676893, a[3] = -814.465012328412, a[4] = -162.479922733996, a[5] = -22.1634383721724, a[6] = 2499.68873209887, a[7] = -3483.73233012660, a[8] = 1889.85415576583, a[9] = -378.105737197022, b[0] = 1, b[1] = 23.7420373170795, b[2] = 58.3936620178671, b[3] = 5302.26159219180, b[4] = -19761.5068929739, b[5] = 26397.3280786320, b[6] = -15175.8506105258, b[7] = 3154.63213334095, d[0] = 1, d[1] = -.210882066768931, d[2] = 1.03794313974688, d[3] = 88.3976988001500, d[4] = -372.809908888624, d[5] = 560.251387803974, d[6] = -366.530299437831, d[7] = 88.8640606493531}

0.49749e-5

> 

CodeTools:-Usage(
   fsolve([seq(eval(eq[i],[eq[1],eq[3],eq[5]]), i = {$1..26} minus {1,3,5})],
          {seq(a[i], i = 1 .. 9),seq(b[i], i = 1 .. 7),seq(d[i], i = 1 .. 7)},
   avoid={ans1, ans2})
):
% union eval({eq[1],eq[3],eq[5]},%);
max(abs~([seq(evalf[5](evalf[50](eval((rhs-lhs)(eq[i]),%))),i=1..26)]));

memory used=1.57GiB, alloc change=-4.00MiB, cpu time=14.71s, real time=13.49s, gc time=2.53s

{a[0] = -.5, a[1] = -1.47913389976148, a[2] = -10.0135460083299, a[3] = 25.0840073123551, a[4] = -3.07976713388045, a[5] = -18.6004959448165, a[6] = -1.91533710533566, a[7] = 16.1443983642844, a[8] = -5.17425515311063, a[9] = 0.341295685951660e-1, b[0] = 1, b[1] = 44.8574953217569, b[2] = 263.899930958965, b[3] = -176.445025694700, b[4] = 530.321442269004, b[5] = -1781.68764750668, b[6] = 1434.90149310926, b[7] = -316.847688457609, d[0] = 1, d[1] = -9.01354600832993, d[2] = -10.5403828146886, d[3] = -24.8853388211367, d[4] = -71.9204338581995, d[5] = 384.191239090326, d[6] = -380.703374127638, d[7] = 111.871836539667}

0.19993e-7

> 

small:={seq(eq[i],i=1..8)}:
foo:=eliminate(small,{a[0],b[0],d[0],a[1],b[1],d[1],a[2],b[2],d[2]}):
> 

alt1:=CodeTools:-Usage(
   fsolve([seq(eval(eq[i],foo[1]), i = {$9..26})],
          {seq(a[i], i = 3 .. 9),seq(b[i], i = 2 .. 7),seq(d[i], i = 3 .. 7)})
):
% union eval(foo[1],%);
max(abs~([seq(evalf[5](evalf[50](eval((rhs-lhs)(eq[i]),%))),i=1..26)]));

memory used=76.70MiB, alloc change=0 bytes, cpu time=698.00ms, real time=592.00ms, gc time=221.39ms

{58.3936620178671 = 58.3936620178671, a[0] = -.500000000000000, a[1] = 473.61443496043, a[2] = -1.210882066767, a[3] = -814.465012328412, a[4] = -162.479922733996, a[5] = -22.1634383721724, a[6] = 2499.68873209887, a[7] = -3483.73233012660, a[8] = 1889.85415576583, a[9] = -378.105737197022, b[0] = 1, b[1] = 23.74203731705, b[2] = 58.3936620178671, b[3] = 5302.26159219180, b[4] = -19761.5068929739, b[5] = 26397.3280786320, b[6] = -15175.8506105258, b[7] = 3154.63213334095, d[0] = 1, d[1] = -.210882066767, d[2] = 1.037943139737, d[3] = 88.3976988001500, d[4] = -372.809908888624, d[5] = 560.251387803974, d[6] = -366.530299437831, d[7] = 88.8640606493531}

0.14028e-4

> 

alt2:=CodeTools:-Usage(
   fsolve([seq(eval(eq[i],foo[1]), i = {$9..26})],
          {seq(a[i], i = 3 .. 9),seq(b[i], i = 2 .. 7),seq(d[i], i = 3 .. 7)},
           avoid={alt1})
):
% union eval(foo[1],%);
max(abs~([seq(evalf[5](evalf[50](eval((rhs-lhs)(eq[i]),%))),i=1..26)]));

memory used=328.98MiB, alloc change=0 bytes, cpu time=2.61s, real time=2.35s, gc time=531.75ms

{33.6836392815204 = 33.6836392815204, a[0] = -.500000000000000, a[1] = -564.3391522566, a[2] = -1.239554618808, a[3] = 435.240596218131, a[4] = 117.265319932553, a[5] = 9.40586196156122, a[6] = 2527.90909984453, a[7] = -5405.84246231077, a[8] = 3783.96364953286, a[9] = -901.363358303432, b[0] = 1, b[1] = 6.39203588489, b[2] = 33.6836392815204, b[3] = -5103.27594542278, b[4] = 12422.4664804907, b[5] = -7331.36147713295, b[6] = -2436.22948761474, b[7] = 2407.32475451336, d[0] = 1, d[1] = -.239554618808, d[2] = 1.000229538753, d[3] = -117.773461803074, d[4] = 417.605706594865, d[5] = -573.430608689689, d[6] = 354.595274441364, d[7] = -82.7575854634121}

0.88648e-5

> 

alt3:=CodeTools:-Usage(
   fsolve([seq(eval(eq[i],foo[1]), i = {$9..26})],
          {seq(a[i], i = 3 .. 9),seq(b[i], i = 2 .. 7),seq(d[i], i = 3 .. 7)},
           avoid={alt1,alt2})
):
% union eval(foo[1],%);
max(abs~([seq(evalf[5](evalf[50](eval((rhs-lhs)(eq[i]),%))),i=1..26)]));

memory used=1.26GiB, alloc change=0 bytes, cpu time=11.10s, real time=9.94s, gc time=2.38s

{47.3439092349469 = 47.3439092349469, a[0] = -.500000000000000, a[1] = 4.32375717286122, a[2] = -10.3916808893474, a[3] = -4.37793022080622, a[4] = 20.9848616428886, a[5] = 2.88811154030335, a[6] = -27.7320234280139, a[7] = 18.9496346647742, a[8] = -3.37842933403158, a[9] = -.266301148627605, b[0] = 1, b[1] = -108.924352850057, b[2] = 47.3439092349469, b[3] = 591.097526763819, b[4] = -734.087769795466, b[5] = -7.21902282081380, b[6] = 312.721961795463, b[7] = -101.932252327892, d[0] = 1, d[1] = -9.3916808893474, d[2] = -11.0377514449400, d[3] = 21.8113102540731, d[4] = 10.9837400537900, d[5] = .274415898348425, d[6] = -25.2503779587453, d[7] = 11.6103440868212}

0.58610e-8

> 

 

Download fsolve_sys_pared.mw

various...

acer 32303
May 12 2022
2 1

Here are some alternatives.

You could choose which of the three flavours you prefer.

The results assigned to Nstep are used to apply seven single steps of Newton's method, to get an approximate root (for both examples).

You might prefer to apply Nstep in a loop, so that you could bail out early is adequate convergence to a root were discovered. (What you don't want to do is redo the differentiation inside a loop. It's only needed once, before the loop, ie. to create Nstep.)

> 

restart
> 

"f(x) := x^2"

proc (x) options operator, arrow, function_assign; x^2 end proc

> 

unapply(diff(f(x), x), x)

proc (x) options operator, arrow; 2*x end proc

> 

D(f)

proc (x) options operator, arrow, function_assign; 2*x end proc

> 

unapply(diff(f(x), x), x)

proc (x) options operator, arrow; 2*x end proc

> 

unapply(x-f(x)/(diff(f(x), x)), x)

proc (x) options operator, arrow; (1/2)*x end proc

> 

unapply(x-f(x)/(D(f))(x), x)

proc (x) options operator, arrow; (1/2)*x end proc

> 

Nstep := unapply(x-f(x)/(diff(f(x), x)), x)

proc (x) options operator, arrow; (1/2)*x end proc

> 

(Nstep@@7)(3.0); f(%)

0.2343750000e-1

0.5493164062e-3

> 

restart
> 

f := proc (x) options operator, arrow; 5*x^3+x-7 end proc

proc (x) options operator, arrow; 5*x^3+x-7 end proc

> 

unapply(diff(f(x), x), x)

proc (x) options operator, arrow; 15*x^2+1 end proc

> 

D(f)

proc (x) options operator, arrow; 15*x^2+1 end proc

> 

unapply(diff(f(x), x), x)

proc (x) options operator, arrow; 15*x^2+1 end proc

> 

unapply(x-f(x)/(diff(f(x), x)), x)

proc (x) options operator, arrow; x-(5*x^3+x-7)/(15*x^2+1) end proc

> 

unapply(x-f(x)/(D(f))(x), x)

proc (x) options operator, arrow; x-(5*x^3+x-7)/(15*x^2+1) end proc

> 

Nstep := unapply(x-f(x)/(diff(f(x), x)), x)

proc (x) options operator, arrow; x-(5*x^3+x-7)/(15*x^2+1) end proc

> 

(Nstep@@7)(3.0); f(%)

1.059154735

-0.5e-8

> 

 

Download diff_variants.mw

like this?...

acer 32303
May 10 2022
1 0

Perhaps you have been instructed to do something like this, using the given f:

> 

f:=n->n/(n+1);

proc (n) options operator, arrow; n/(n+1) end proc

> 

seq(f(2*n), n=0..4);

0, 2/3, 4/5, 6/7, 8/9

> 

seq(f(7*n-5), n=1..3);

2/3, 9/10, 16/17

> 

seq(f(2*n-1)^2, n=1..4);

1/4, 9/16, 25/36, 49/64

> 

seq(f(n^2-1), n=1..6);

0, 3/4, 8/9, 15/16, 24/25, 35/36

Download seq_fun.mw

Is it possible that you mis-copied the last example, and inadvertantly omitted the term 15/16?

rad, or radian...

acer 32303
May 09 2022
1 1

You could just use rad (or radian) in the place where you would normally specify some other unit name.

Compare also with  arcdeg  as unit name (supported by Maple, not sure about Flow).

Explode...

acer 32303
May 06 2022
4 0

Here is one way:

> 

ee := xxtt;

xxtt

> 

parse~(StringTools:-Explode(ee))[];

x, x, t, t

N__2...

acer 32303
May 06 2022
1 1

You appear to be defining N__2 as N__1 where x=200. And so your N__2 doesn't depend on x.

So what then do you intend by eval(N__2, x = x - 200) as appearing in your piecewise?!

That aspect aside, you can evaluate as follows (and, naturally, this changes if you make some correction related to my query):

> 

restart;
> 

N__1 := dsolve([diff(y(x), x, x) + 3*diff(y(x), x) + 2*y(x) = x^2 + 5,
                y(0) = 1, D(y)(0)], y(x));

y(x) = (7/4)*exp(-2*x)+17/4-(3/2)*x+(1/2)*x^2-5*exp(-x)

> 

NN__1 := eval(y(x), N__1);

(7/4)*exp(-2*x)+17/4-(3/2)*x+(1/2)*x^2-5*exp(-x)

> 

NN__2 := eval(NN__1, x=200);

(7/4)*exp(-400)+78817/4-5*exp(-200)

> 

N := piecewise(0 <= x and x <= 200, NN__1,
               200 <= x and x <= 1000, eval(NN__2, x = x - 200));

N := piecewise(0 <= x and x <= 200, 7*exp(-2*x)*(1/4)+17/4-3*x*(1/2)+(1/2)*x^2-5*exp(-x), 200 <= x and x <= 1000, 7*exp(-400)*(1/4)+78817/4-5*exp(-200))

> 

plot(N, x = 0 .. 1000);

Download ThomasBH_2.mw

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