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RezaZanjirani

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Maple 2D implicitplot with three functio...

RezaZanjirani 40 Maple 2021
performance implicitplot inequal
January 02 2024
1 12

Dear Maple users/ experts

I have three functions, each with two parameters, alpha and delta, changing over 0..1. I want to partition the region in terms of what part gets the highest value. In the attached maple file, I used "implicit plot" and did it for any pair of functions in a reasonable time. But I don't know how these three plots can be consolidated into one. ('inequal' command was not precise while taking too long).  2D_implicitplot_with_three_functions.mw

Procedure: Maple cannot determine if the...

RezaZanjirani 40 Maple 2021
procedure programming evaluation
December 16 2023
1 0

Dear Maple experts, I have written a not-very-complicated Maple procedure, including eval, if, etc. However,

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restartNULL
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with(plots)
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c := 1; cr := 0.3e-1*c; u := 1; sExp := 0.6e-1*c; s := .65*c; v := 3*c
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NULL
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NULLNULL
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FirmModelH := proc (alpha, beta, delta, h) local q, p, pr, FirmpfSiS, F1, G1, G2, G3, RecpfSiS, sol, UnsoldSiS, EnvironSiS, p0, UsedSoldPrimary, xi, ps, qs, prs, prof1F, prof1P, prof2F, prof2P, kappa; option remember; kappa := (beta*(ps-delta*v)*(1-h)+sExp*(1-beta))/(beta^2*((ps-delta*v)*(1-h)-sExp)/(u*(1-alpha))+2*cr); prof1F := (ps-c)*qs+((1/2)*beta^2*qs^2*xi^2/(u*(1-alpha))-(1/2)*(1+beta*xi)^2*qs^2/u)*(ps-s)+h*(ps-delta*v)*(beta*xi*qs-(1/2)*beta^2*qs^2*xi^2/(u*(1-alpha))); prof1P := (ps-c)*qs+((1/2)*beta^2*kappa^2/(u*(1-alpha))-(1/2)*(qs+beta*kappa)^2/u)*(ps-s)+h*(ps-delta*v)*(beta*kappa-(1/2)*beta^2*kappa^2/(u*(1-alpha))); prof2F := (ps-c)*qs-(1/2)*(ps-s)*qs^2/(alpha*u)+h*(ps-delta*v)*(beta*xi*qs-(1/2)*beta^2*qs^2*xi^2/(u*(1-alpha))); prof2P := (ps-c)*qs-(1/2)*(ps-s)*qs^2/(alpha*u)+h*(ps-delta*v)*(beta*kappa-(1/2)*beta^2*kappa^2/(u*(1-alpha))); xi := 1; if alpha <= 1/(1+beta) then p, q := (eval([ps, qs], solve({diff(prof1F, qs) = 0, qs = alpha*u*(v-ps)/(v-s), c < ps, sExp+delta*v < ps}, [ps, qs])[1]))[]; if eval(kappa, [ps = p, prs = p-delta*v]) < q then p, q := (eval([ps, qs], solve({diff(prof1P, qs) = 0, qs = alpha*u*(v-ps)/(v-s), c < ps, sExp+delta*v < ps}, [ps, qs])[1]))[] end if; xi := min(1, (eval(kappa, [ps = p]))/q); FirmpfSiS := eval(prof1F, [ps = p, qs = q]); RecpfSiS := ((1-h)*(p-delta*v)-sExp)*(beta*xi*q-(1/2)*beta^2*xi^2*q^2/(u*(1-alpha)))+sExp*xi*q-cr*xi^2*q^2; UnsoldSiS := (1/2)*(1+beta*xi)^2*q^2/u-(1/2)*beta^2*xi^2*q^2/(u*(1-alpha)); EnvironSiS := q+UnsoldSiS else p, q := (eval([ps, qs], solve({diff(prof2F, qs) = 0, qs = alpha*u*(v-ps)/(v-s), c < ps, sExp+delta*v < ps}, [ps, qs])[1]))[]; pr = p-delta*v; if eval(kappa, [ps = p]) < q then p, q := (eval([ps, qs], solve({diff(prof2P, qs) = 0, qs = alpha*u*(v-ps)/(v-s), c < ps, sExp+delta*v < ps}, [ps, qs])[1]))[] end if; kappa := (beta*(p-delta*v)*(1-h)+sExp*(1-beta))/(beta^2*((1-h)*(p-delta*v)-sExp)/(u*(1-alpha))+2*cr); xi := min(1, (eval(kappa, [ps = p]))/q); FirmpfSiS := eval(prof2F, [ps = p, qs = q]); RecpfSiS := ((1-h)*(p-delta*v)-sExp)*(beta*xi*q-(1/2)*beta^2*xi^2*q^2/(u*(1-alpha)))+sExp*xi*q-cr*xi^2*q^2; UnsoldSiS := (1/2)*(1+beta*xi)^2*q^2/u-(1/2)*beta^2*xi^2*q^2/(u*(1-alpha)); EnvironSiS := q+UnsoldSiS end if; return p, q, FirmpfSiS, RecpfSiS, EnvironSiS, UnsoldSiS, UsedSoldPrimary, xi end proc
NULL
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NULL
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NULLNULL
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NULL
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FirmModelH(.8, .15, .15, .10)[3]

Error, (in FirmModelH) cannot determine if this expression is true or false: (-0.4957031250e-11*(-0.3155744681e13*xi^2+(0.3966029880e25*xi^4-0.2830096342e26*xi^3+0.4078080001e26*xi^2+0.5006706391e26*xi+0.5289940424e27)^(1/2)+0.1144851064e14*xi+0.7761702136e13)/(63.*xi^2-240.*xi-800.)-0.9750e-2)/(-0.3717773438e-11*(-0.3155744681e13*xi^2+(0.3966029880e25*xi^4-0.2830096342e26*xi^3+0.4078080001e26*xi^2+0.5006706391e26*xi+0.5289940424e27)^(1/2)+0.1144851064e14*xi+0.7761702136e13)/(63.*xi^2-240.*xi-800.)+0.768750000e-2) < (24.89361704*xi^2-102.*xi-720.0000001+0.1250000000e-10*(0.3966029880e25*xi^4-0.2830096342e26*xi^3+0.4078080001e26*xi^2+0.500670...

  
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NULL
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NULLNULLNULLNULLNULL
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``
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pltH01A := plot('FirmModelH(alpha, .25, .40, 0)[1]', alpha = 0. .. 1, color = yellow, legend = [SiS(h__0)], labels = [alpha, "New Product Price"], labeldirections = ["horizontal", "vertical"], symbolsize = 10, numpoints = 50, adaptive = false, axes = boxed, thickness = 1.0)
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NULLNULLNULL
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TH1 := table([seq(h = sprintf("SiS:", h), h = .1 .. .5, .2)])
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WhyNotH1 := proc (alpha, h) if not [alpha, h]::(list(numeric)) then return ('procname')(args) end if; FirmModelH(alpha, 0.25, 0.40,h)[1] end proc:NULL
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pltH1 := plot([seq(WhyNotH1(alpha, h), h = .1 .. .5, .2)], alpha = 0. .. 1, linestyle = [dash, dashdot, longdash], color = [red, green, blue], legend = [seq(typeset(TH1[h], 'h' = h), h = .1 .. .5, .2)], legendstyle = [location = left], labels = [alpha, "New Product Price"], labeldirections = ["horizontal", "vertical"], legendstyle = [location = bottom], thickness = 1.0, adaptive = false, axes = boxed)
>   

Download SiS_Quadratic_(goal).mw

it faces an error saying that Maple cannot determine if the procedure is true. Would you please have a look and advise?

Conflict between plot and inequal...

RezaZanjirani 40 Maple 2021
implicitplot inequal plotting
October 19 2023
1 3

Dear Maple experts

I face an issue in using ‘implicit plot’ or ‘inequal’ commands in the attached file.

I use three Maple procedures to make some simple calculations and draw an output. It is Firm Profit versus ‘alpha’. This graph is correct and makes perfect sense.

Then, I use ‘inequal’ command to compare the same outputs when ‘alpha’ and ‘delta’ change. There is a conflict between these plots and the above diagram. For example, P2 plot says

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restartNULL
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with(plots); with(RealDomain)
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NULL
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c := 1; cr := 0.3e-1*c; u := 1; sExp := 0.6e-1*c; s := .65*c; v := 3*cNULL
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``
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FirmModelPP := proc (alpha, beta, delta) local p0, xi0, q0, Firmpf0, G01, Recpf0, Unsold0, Environ0; xi0 := 1; p0 := min(s+sqrt((v-s)*(c-s)), delta*v+sExp); q0 := u*(v-p0)/(v-s); f(N) := 1/u; F(N) := N/u; G01 := int(F(N), N = 0 .. q0); Firmpf0 := (p0-c)*q0-(p0-s)*G01; Recpf0 := (sExp-cr)*xi0*q0; Unsold0 := G01; Environ0 := q0+Unsold0; return p0, q0, Firmpf0, Recpf0, Environ0, Unsold0 end proc
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NULL
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NULLNULLNULL
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FirmModelFC := proc (alpha, beta, delta) local p00, xi00, q00, Firmpf00, G001, G002, Recpf00, Unsold00, Environ00, pr00; option remember; xi00 := 1; p00 := s+sqrt((v-s)*(c-s)); q00 := alpha*u*(v-p00)/(v-s); f(N) := 1/u; F(N) := N/u; G001 := int(F(N), N = 0 .. q00/alpha); G002 := int(F(N), N = 0 .. beta*xi00*q00/(1-alpha)); pr00 := p00-delta*v; Firmpf00 := (p00-c)*q00-alpha*(p00-s)*G001; Recpf00 := xi00*q00*(sExp-cr)+(pr00-sExp)*(beta*xi00*q00-(1-alpha)*G002); Unsold00 := alpha*G001; Environ00 := q00+Unsold00; return p00, q00, Firmpf00, Recpf00, Environ00, Unsold00 end proc
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NULLNULL``
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NULLNULL
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NULL
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FirmModelHmax := proc (alpha, beta, delta) local q, p, pr, FirmpfSiS, F1, G1, G2, G3, RecpfSiS, sol, UnsoldSiS, EnvironSiS, p0, OldSoldPrim, xi, h, ps, qs, prs, prof1m, prof2m; option remember; xi := 1; prs := ps-delta*v; prof1m := (ps-c)*qs+((1/2)*beta^2*xi^2*qs^2/(u*(1-alpha))-(1/2)*(1+beta*xi)^2*qs^2/u)*(ps-s)+(prs-sExp)*(beta*xi*qs-(1/2)*beta^2*xi^2*qs^2/(u*(1-alpha))); prof2m := (ps-c)*qs-(1/2)*(ps-s)*qs^2/(alpha*u)+(prs-sExp)*(beta*xi*qs-(1/2)*beta^2*xi^2*qs^2/(u*(1-alpha))); if alpha <= 1/(1+beta*xi) then p, q := (eval([ps, qs], solve({diff(prof1m, qs) = 0, qs = alpha*u*(v-ps)/(v-s), c < ps, sExp+delta*v < ps, qs < 2*u*(1-alpha)/(beta*xi)}, [ps, qs])[1]))[]; `h&Assign;`*(p-delta*v-sExp)/(p-delta*v); FirmpfSiS := eval(prof1m, [ps = p, qs = q, prs = p-delta*v]); RecpfSiS := (sExp-cr)*xi*q; UnsoldSiS := (1/2)*(1+beta*xi)^2*q^2/u-(1/2)*beta^2*xi^2*q^2/(u*(1-alpha)); EnvironSiS := q+UnsoldSiS else p, q := (eval([ps, qs], solve({diff(prof2m, qs) = 0, qs = alpha*u*(v-ps)/(v-s), c < ps, sExp+delta*v < ps, qs < 2*u*(1-alpha)/(beta*xi)}, [ps, qs])[1]))[]; h := (p-delta*v-sExp)/(p-delta*v); FirmpfSiS := eval(prof2m, [ps = p, qs = q, prs = p-delta*v]); RecpfSiS := (sExp-cr)*xi*q; UnsoldSiS := (1/2)*q^2/(alpha*u); EnvironSiS := q+UnsoldSiS end if; return p, q, FirmpfSiS, RecpfSiS, EnvironSiS, UnsoldSiS, h, OldSoldPrim, xi end proc
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``
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``

NULL

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NULL
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``
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NULLNULL
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NULLNULL
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pltPP3A := plot('FirmModelPP(alpha, .35, .40)[3]', alpha = 0. .. 1.0, color = red, legend = "", style = pointline, labels = [alpha, "Firm Profit"], labeldirections = ["horizontal", "vertical"], symbolsize = 10, axes = boxed, symbol = box, numpoints = 10, adaptive = false, thickness = 1.0, view = [0 .. 1, 0 .. .18])
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NULL
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pltPP3B := plot([[0., eval('FirmModelPP(0., .35, .40)[3]', alpha = 0.)]], color = red, legend = ["PP"], style = point, symbol = box, symbolsize = 10, axes = boxed, view = [0 .. 1, 0 .. .18])
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NULL
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pltFC3A := plot('FirmModelFC(alpha, .35, .40)[3]', alpha = 0. .. 1, linestyle = [solid], color = black, legend = "FC", labels = [alpha, "Firm Profit"], labeldirections = ["horizontal", "vertical"], axes = boxed, adaptive = false, thickness = .7, view = [0 .. 1.0, 0 .. .18])
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NULL
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NULLNULLNULLNULLNULL
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pltHmax3A := plot('FirmModelHmax(alpha, .35, .40)[3]', alpha = 0. .. 1.0, linestyle = [dashdot], color = brown, legend = [SiS(h__max)], labels = [alpha, "Firm Profit"], labeldirections = ["horizontal", "vertical"], symbolsize = 10, numpoints = 50, adaptive = false, thickness = 1.0, axes = boxed, view = [0 .. 1, 0 .. .19])
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``
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NULLNULLNULL
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display([pltPP3A, pltPP3B, pltFC3A, pltHmax3A])

 
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NULL
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``
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NULL
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NULL
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NULL
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``
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NULL
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``
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NULL

NULL

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diffr2 := proc (alpha, delta) if not [alpha, delta]::(list(numeric)) then return ('procname')(args) end if; FirmModelFC(alpha, .35, delta)[3]-FirmModelHmax(alpha, .35, delta)[3] end proc
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NULL
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P2 := plots:-inequal(diffr2(alpha, delta) <= 0, alpha = 0 .. 1, delta = 0 .. 1, optionsfeasible = [[color = "Spring 1"]])

 
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``
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NULL
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diffr3 := proc (alpha, delta) if not [alpha, delta]::(list(numeric)) then return ('procname')(args) end if; FirmModelHmax(alpha, .35, delta)[3]-FirmModelPP(alpha, .35, delta)[3] end proc
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NULL
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P3 := plots:-inequal(diffr3(alpha, delta) <= 0, alpha = 0 .. 1, delta = 0 .. 1, colour = "Orange")

 
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``

Download ConflcitInequal.mw

SiS is superior to FC in small ‘alpha’s. But in the initial diagram, it is obvious that it should be the opposite!

Perhaps I am making a mistake in using commands. Would you please help me?

Parameters with values in the Maple text...

RezaZanjirani 40 Maple 2021
evaluation textplot plotting
September 21 2023
2 8

Dear Maple experts, I want to write text in a specific location within a Maple plot like p<c. To do that, I use 'plots:-textplot' as follows:

plots:-textplot([[0.1, 0.80, p < c, color = black]], font = [times, 11], rotation = 'horizontal');

The issue is that in my code, 'p' and 'c' are parameters with specific values. Therefore,  in my plot, their values appear instead of p<c. Even if I use 'p<c' or "p<c" it does not work.

Would you please guide me on how to solve the issue?

Point plot for system of nonlinear equat...

RezaZanjirani 40 Maple 2021
plot solve plotting
September 05 2023
3 4

Dear Maple experts,

I have a system of several nonlinear equaitons. My code can solve it for a given parameter. But when I want to plot it, it takes too much time with no results. So, I decided to plot it for several given points. I get the answer for the points individually, but I don't know how to apply this to 'plot' command. Would you please help?

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restartNULL
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with(plots); with(RealDomain)
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NULL
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c := 1; cr := 0.3e-1*c; u := 5; sExp := 0.6e-1*c; s := .65*c; v := 3*c
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NULL
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NULL
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FirmModelPartial1 := proc (alpha, beta, delta) local L1s, qs, ps, prs, hs, `&kappa;s`, `&lambda;__1s`, `&lambda;__2s`, `&lambda;__3s`, q, p, pr, h, kappa, `&lambda;__1`, `&lambda;__2`, `&lambda;__3`, FirmpfSiS, RecpfSiS, UnsoldSiS, EnvironSiS, p0, OldSoldPrim, xi, prof1, prof2, L1, L2, E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12; prof1 := (ps-c)*qs+((1/2)*beta^2*`&kappa;s`^2/(u*(1-alpha))-(1/2)*(qs+beta*`&kappa;s`)^2/u)*(ps-s)+hs*prs*(beta*`&kappa;s`-(1/2)*beta^2*`&kappa;s`^2/(u*(1-alpha))); L1s := prof1+`&lambda;__1s`*(1-sExp/prs-hs)+`&lambda;__2s`*(qs-`&kappa;s`)+`&lambda;__3s`*(qs-alpha*beta*`&kappa;s`/(1-alpha)); E1 := qs*(diff(L1s, qs)) = 0; E2 := hs*(diff(L1s, hs)) = 0; E3 := `&lambda;__1s`*(1-sExp/prs-hs) = 0; E4 := `&lambda;__2s`*(qs-`&kappa;s`) = 0; E5 := `&lambda;__3s`*(qs-alpha*beta*`&kappa;s`/(1-alpha)) = 0; E6 := qs = alpha*u*(v-ps)/(v-s); E7 := prs = ps-delta*v; E8 := `&kappa;s` = (beta*prs*(1-hs)+sExp*(1-beta))/(beta^2*(prs*(1-hs)-sExp)/(u*(1-alpha))+2*cr); p, q, pr, h, kappa, `&lambda;__1`, `&lambda;__2`, `&lambda;__3` := (eval([ps, qs, prs, hs, `&kappa;s`, `&lambda;__1s`, `&lambda;__2s`, `&lambda;__3s`], solve({0 <= qs-alpha*beta*`&kappa;s`/(1-alpha), 0 <= qs-`&kappa;s`, 0 <= 1-sExp/prs-hs, 0 <= `&lambda;__1s`, 0 <= `&lambda;__2s`, 0 <= `&lambda;__3s`, diff(L1s, qs) <= 0, diff(L1s, hs) <= 0, c < ps, (1/2)*beta*`&kappa;s`/(u*(1-alpha)) < 1, sExp+delta*v < ps, E1, E2, E3, E4, E5, E6, E7, E8}, [ps, qs, prs, hs, `&kappa;s`, `&lambda;__1s`, `&lambda;__2s`, `&lambda;__3s`])[1]))[]; xi := kappa/q; FirmpfSiS := max(0, eval(prof1, [ps = p, qs = q, prs = p-delta*v, hs = h, `&kappa;s` = kappa])); RecpfSiS := ((1-h)*pr-sExp)*(beta*kappa-(1/2)*beta^2*kappa^2/(u*(1-alpha)))+(sExp-cr)*kappa; UnsoldSiS := (1/2)*(q+beta*kappa)^2/u-(1/2)*beta^2*kappa^2/(u*(1-alpha)); EnvironSiS := q+UnsoldSiS; return p, q, FirmpfSiS, RecpfSiS, EnvironSiS, h, UnsoldSiS, h, xi end proc
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NULL
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NULL
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FirmModelPartial1(.1, .2, .1)[3]

Error, (in FirmModelPartial1) invalid subscript selector

  
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NULL
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FirmModelPartial1(.2, .2, .1)[3]

Error, (in FirmModelPartial1) invalid subscript selector

  
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FirmModelPartial1(.3, .2, .1)[3]

.2200894743

 (1)
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NULL
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FirmModelPartial1(.4, .2, .1)[3]

.2892440018

 (2)
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FirmModelPartial1(.5, .2, .1)[3]

.3801240291

 (3)
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FirmModelPartial1(.6, .2, .1)[3]

.4921660779

 (4)
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FirmModelPartial1(.7, .2, .1)[3]

.6227094789

 (5)
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FirmModelPartial1(.8, .2, .1)[3]

.7668402612

 (6)
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FirmModelPartial1(.9, .2, .1)[3]

.9161921261

 (7)
 
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plot('FirmModelPartial1(alpha, .2, .2)[3]', alpha = .1 .. .90, adaptive = false, sample = [.1, .2, .3, .4, .5, .6, .7, .8, .9])

 

Download Reza_Tchno_(v3).mw

Besdies, it seems for some points there is no feasible solution. So, there is no need to have plot for them.

I attach the code. Thank you so much!

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