Maple 18 Questions and Posts

These are Posts and Questions associated with the product, Maple 18

Hi,

 

I am completely new to Maple (and this kind of software in general).

I am just on my first steps of learning...but I quickly noticed, that if I write Pi and hit enter, I do not get

the well-known greek Pi-symbol. I get an ordinary "p" as the result.

I checked the greek-palette...nearly all items in this palette are ordinary letters.

Does anyone have an idea whats wrong?

BTW: I don`t know if it could have to do with that, but I use a german windows 7 installation.

 

Thank you,

regards,

Kai

Please see the attached worksheet for the error at the end, any idea what happens?

Besides, anyone know how to make plot array with each element has a plot and scatterplot in it?  I made my plot by making table first and then type the cmd individually.

Raw Data

restart

avicel102_aero200 := Matrix(12, 3, {(1, 1) = 50, (1, 2) = 1.6621, (1, 3) = .22, (2, 1) = 100, (2, 2) = 3.33221, (2, 3) = .103, (3, 1) = 150, (3, 2) = 4.95533, (3, 3) = 0.43e-1, (4, 1) = 200, (4, 2) = 5.62147, (4, 3) = 0.37e-1, (5, 1) = 50, (5, 2) = 1.88627, (5, 3) = .207, (6, 1) = 50, (6, 2) = 1.90375, (6, 3) = .199, (7, 1) = 100, (7, 2) = 4.04708, (7, 3) = 0.89e-1, (8, 1) = 100, (8, 2) = 4.20413, (8, 3) = 0.87e-1, (9, 1) = 150, (9, 2) = 5.50509, (9, 3) = 0.41e-1, (10, 1) = 150, (10, 2) = 4.90453, (10, 3) = 0.49e-1, (11, 1) = 200, (11, 2) = 6.22001, (11, 3) = 0.16e-1, (12, 1) = 200, (12, 2) = 6.24435, (12, 3) = 0.23e-1}); avicel102_syloid := Matrix(13, 3, {(1, 1) = 50, (1, 2) = 1.76578, (1, 3) = .235, (2, 1) = 100, (2, 2) = 4.08314, (2, 3) = .128, (3, 1) = 150, (3, 2) = 4.85921, (3, 3) = 0.73e-1, (4, 1) = 200, (4, 2) = 5.66786, (4, 3) = 0.51e-1, (5, 1) = 50, (5, 2) = 2.06221, (5, 3) = .224, (6, 1) = 50, (6, 2) = 2.17294, (6, 3) = .216, (7, 1) = 100, (7, 2) = 4.03728, (7, 3) = .109, (8, 1) = 100, (8, 2) = 3.67978, (8, 3) = .116, (9, 1) = 150, (9, 2) = 5.78427, (9, 3) = 0.6e-1, (10, 1) = 150, (10, 2) = 5.43599, (10, 3) = 0.59e-1, (11, 1) = 200, (11, 2) = 6.26332, (11, 3) = 0.38e-1, (12, 1) = 200, (12, 2) = 6.10814, (12, 3) = 0.39e-1, (13, 1) = 200, (13, 2) = 6.83857, (13, 3) = 0.25e-1}); avicel301_101_aero200 := Matrix(12, 3, {(1, 1) = 50, (1, 2) = 1.106, (1, 3) = .2597543205, (2, 1) = 50, (2, 2) = 1.06, (2, 3) = .2564849561, (3, 1) = 50, (3, 2) = 1.129, (3, 3) = .2552025392, (4, 1) = 100, (4, 2) = 2.865, (4, 3) = .1280363098, (5, 1) = 100, (5, 2) = 2.793, (5, 3) = .127659333, (6, 1) = 100, (6, 2) = 3.088, (6, 3) = .1347147061, (7, 1) = 150, (7, 2) = 4.216, (7, 3) = 0.802489497e-1, (8, 1) = 150, (8, 2) = 4.044, (8, 3) = 0.838493001e-1, (9, 1) = 150, (9, 2) = 4.071, (9, 3) = 0.855901289e-1, (10, 1) = 200, (10, 2) = 4.826, (10, 3) = 0.627298821e-1, (11, 1) = 200, (11, 2) = 4.924, (11, 3) = 0.614759445e-1, (12, 1) = 200, (12, 2) = 4.76, (12, 3) = 0.61001365e-1})

NULL

 

with(LinearAlgebra):

X[1] := Column(avicel102_aero200, 3):

X[2] := Column(avicel102_syloid, 3):

X[3] := Column(avicel301_101_aero200, 3):

S := Array(1 .. 3):

S[1] := ScatterPlot(X[1], Y[1], labels = [Porocity, Tensile*Strength], title = Compactability*of*Avicel102*with*Aerosil200):

with(plots):NULL

 

vSST := Array(1 .. 3):

tpfit := proc (x, y) options operator, arrow; Fit(a*exp(-k*p)+c, x, y, p, output = [leastsquaresfunction, residualsumofsquares, degreesoffreedom]) end proc:SST := proc (y) options operator, arrow; Variance(y)*(NumElems(y)-1) end proc:NULL

for i to 3 do fnTP[i] := tpfit(X[i], Y[i])[1] end do:

for i to 3 do fnPC[i] := Fit(c*p^2+b*p+a, P[i], X[i], p, output = [leastsquaresfunction, residualsumofsquares, degreesoffreedom])[1] end do:

NULL

for i to 3 do vSST[i] := SST(Y[i]) end do:

for i to 3 do pSST[i] := SST(X[i]) end do:

NULL

for i to 3 do vSSR[i] := tpfit(X[i], Y[i])[2] end do:

for i to 3 do Rsquare[i] := 1-vSSR[i]/vSST[i] end do:

NULL

``

s := Array(1 .. 3):

for i to 3 do s[i] := plot(fnTP[i], p = 0 .. .26, legend = typeset(fnTP[i], R^2, "= ", Rsquare[i])) end do

for i to 3 do ps[i] := plot(fnPC[i], p = 0 .. 200, legend = typeset(fnPC[i], R^2, "= ", pRsquare[i])) end do

G := Array(1 .. 3):

G[1] := [S[1], s[1]]:

pG := [[PS[1], ps[1]], [PS[2], ps[2]], [PS[3], ps[3]]]:NULL

NULL

Table 1: Compactability Curve

display(G[1])

 

NULL

display(G[2])

 

NULL

display(G[3])

 

NULL

NULL

NULL

Table 2: Compressibility Curve

display(pG[1])

 

NULL

display(pG[2])

 

NULL

display(pG[3])

 

NULL

``

ff := proc (x) options operator, arrow; unapply(x, p) end proc:

gtp := map(ff, fnTP):

gpc := map(ff, fnPC):

TS1 := proc (pressure) options operator, arrow; (`@`(gtp[1], gpc[1]))(pressure/Unit('MPa'))*Unit('MPa') end proc:

TS2 := proc (pressure) options operator, arrow; (`@`(gtp[2], gpc[2]))(pressure/Unit('MPa'))*Unit('MPa') end proc:

TS3 := proc (pressure) options operator, arrow; (`@`(gtp[3], gpc[2]))(pressure/Unit('MPa'))*Unit('MPa') end proc:

por1 := proc (p) options operator, arrow; gpc[1](p/Unit('MPa')) end proc:

(1)

por1(x*Unit('MPa'))

HFloat(0.36333333333333295)-HFloat(0.0036139999999999957)*x+HFloat(9.666666666666651e-6)*x^2

(2)

por1(x);

HFloat(0.36333333333333295)-HFloat(0.0036139999999999957)*x/Units:-Unit('MPa')+HFloat(9.666666666666651e-6)*x^2/Units:-Unit('MPa')^2

(3)

``

NULL

 

(4)

ts := 2/3*(10*P/(Pi*D^2*(2.84*t/D-.126*t/W+3.15*W/D+0.1e-1))):

Target Weight of Tablet, m__t:

m__t := 700*Unit('mg')

700*Units:-Unit('mg')

(5)

Tablet True Density:NULL

`ρ__true1` := 1.8*Unit('g'/'cm'^3)

1800.0*Units:-Unit(('kg')/('m')^3)

(6)

Width of tablet w;

d := 7.747*Unit('mm')

7.747*Units:-Unit('mm')

(7)

Length of tablet, l:

l := 17.018*Unit('mm')

17.018*Units:-Unit('mm')

(8)

Cup Depth, h:

hh := 1.6764*Unit('mm')

1.6764*Units:-Unit('mm')

(9)

Cup Volume", `v__cup`"

v__cup := 119.789438*Unit('mm'^3)

119.789438*Units:-Unit(('mm')^3)

(10)

Die cross sectional area, v__die:

a__die := 118.9610524*Unit('mm'^2)

118.9610524*Units:-Unit(('mm')^2)

(11)

Equation to solve tablet thickness using tablet dimension and porocity:

Tablet bulk density:

`ρ__bulk` := `ρ__true`*sf

`ρ__true`*sf

(12)

Tablet volume:``

V__tablet := 2*V__cup+A__die*(t-2*H)

2*V__cup+A__die*(t-2*H)

(13)

NULL

Tablet bulk Density:``

`ρ__bulk` := m__tablet/V__tablet

m__tablet/(2*V__cup+A__die*(t-2*H))

(14)

NULL

eq1 := m__tablet/(2*V__cup+A__die*(t-2*H)) = `ρ__true`*sf

m__tablet/(2*V__cup+A__die*(t-2*H)) = `ρ__true`*sf

(15)

Function for thickness:

thickness := unapply(simplify(solve(eq1, t), size), sf, A__die, H, V__cup, `ρ__true`, m__tablet)

proc (sf, A__die, H, V__cup, `ρ__true`, m__tablet) options operator, arrow; (2*sf*(A__die*H-V__cup)*`ρ__true`+m__tablet)/(A__die*sf*`ρ__true`) end proc

(16)

simplify(thickness(1-por[1](100*Unit(MPa)), a__die, hh, v__cup, `ρ__true1`, m__t))

HFloat(0.005719286791216391)*Units:-Unit('m')

(17)

t2 := proc (cc, A__die, H, V__cup, `ρ__true`, m__tablet) options operator, arrow; simplify(thickness(1-cc, A__die, H, V__cup, `ρ__true`, m__tablet)) end proc:

``

``

``

Tablet tensile strength:NULL

eq2 := `σ__t` = ts

`σ__t` = (20/3)*P/(Pi*D^2*(2.84*t/D-.126*t/W+3.15*W/D+0.1e-1))

(18)

Break force of tablet (N)

breakforce := unapply(subs(W = t-2*h, solve(eq2, P)), `σ__t`, D, h, t)

proc (`σ__t`, D, h, t) options operator, arrow; 0.9424777961e-3*`σ__t`*D*(5.*D*(t-2*h)-63.*t*D+1575.*(t-2*h)^2+1420.*t*(t-2*h))/(t-2*h) end proc

(19)

 

kp := simplify(breakforce(TS[1](100*Unit('MPa')), d, hh, 0.5719e-2*Unit('m')))

HFloat(286.99924404612904)*Units:-Unit('N')

(20)

convert(kp, units, kilopond)

HFloat(29.265778226624693)*Units:-Unit('kilopond')

(21)

t2(por[1](100*Unit('MPa')), a__die, hh, v__cup, `ρ__true1`, m__t)

HFloat(0.005719286791216391)*Units:-Unit('m')

(22)

``

hh

1.6764*Units:-Unit('mm')

(23)

simplify(breakforce(TS[1](100*Unit('MPa')), d, hh, t2(por[1](100*Unit('MPa')), a__die, hh, v__cup, `ρ__true1`, m__t)))

HFloat(287.02451456724083)*Units:-Unit('N')

(24)

Encounter problem while chaning variable

 BF:= 
proc (`σ__t`, D, p, A__die, hhh, V__cup, `ρ__true`, m__tablet) options operator, arrow; breakforce(`σ__f`, D, hhh, t2(p, A__die, hhh, V__cup, `ρ__true`, m__tablet)) end proc:

BF(TS1(100*Unit('MPa')), d, por1(100*Unit('MPa')), a__die, hh, v__cup, `ρ__true1`, m__t)

BF(HFloat(3.6712504621161846)*Units:-Unit('MPa'), 7.747*Units:-Unit('mm'), HFloat(0.09859999999999991), 118.9610524*Units:-Unit(('mm')^2), 1.6764*Units:-Unit('mm'), 119.789438*Units:-Unit(('mm')^3), 1420.00*Units:-Unit(('kg')/('m')^3), 667*Units:-Unit('mg'))

(25)

evalf(TS[1](100*Unit(MPa)))

HFloat(3.6712504621161846)*Units:-Unit('MPa')

(26)

plot(breakforce(TS1(x), d, hh, t2(por1(x), a__die, hh, v__cup, `ρ__true1`, m__t)), x = Unit('MPa') .. 200*Unit('MPa'), useunits = true)

Error, (in Units:-Standard:-+) the units `1` and `1/MPa` have incompatible dimensions

 

plot(t2(por1(x), a__die, hh, v__cup, `ρ__true1`, m__t), x = Unit('MPa') .. 200*Unit('MPa'), useunits = true)

Error, (in Units:-Standard:-+) the units `1` and `1/MPa` have incompatible dimensions

 

plot(evalf(por1(xx)), xx = 10 .. 200)

 

but por1 works fine on its own with units

por1(Units:-Standard:-`*`(200, Unit('MPa')))

HFloat(0.02719999999999989)

(27)

plot(evalf(por1(xx)), xx = 10 .. 200);

 

Unloading Units:-Standard

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Fitting_worksheet.mw

I also used a lot for for loop in this worksheet, can anyone suggest another way of doing it? And I think I initiated many Array(1..3) that is of no use.  But if I do not initiate and do the following

A[1]:=a : 

A[2]:=b:

A[3]:=c:

A;

output: A

Only if I initiate A:=Array(1..3) and then define the element I can see the complete A array at the end.

 

Please advise as to the proper coding entries needed in the triple integration palette  to transform from the Cartesian placeholders x;y;z to spherical coordinates rho; theta; phi so that the triple integration palette can be used in spherical coordinmates. Dr. Lopez alreadyb has a standalone template which does this but I would like to set a palette option for spherical  calculations.

 

Thanx

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