Here is a function that will do the plotting for you, all you have to do is pass the expression that you want plotted and the range, just like you do for plot. Copy and paste this code into your worksheet and you will be able to use the function anywere in your worksheet. Click here to download the worksheet to try it on your computer

When viewing the Worksheet below, the Pi symbols appear as "p". When you download the worksheet it will look better

> trigPlot := proc( thePlot, range )
local start, finish, offset, spacing, truestart, ticks,tick, tickName, pos;
spacing := Pi/2;
start := op(1, op(2,range) );
finish := op(2, op(2,range ) );

ticks := [];
pos := start;
while( evalf(pos) <= evalf(finish) ) do

tickName := convert( pos, string );
tickName := StringTools[Substitute]( tickName, "Pi", "p" );
ticks := [op(ticks), evalf(pos)=tickName];
pos := pos + spacing;
end do:

plot( thePlot, range, axesfont= [SYMBOL],tickmarks = [ticks,default] );
end proc:

Here are some examples of its usage

> trigPlot(cos(x), x=-Pi..Pi);

> trigPlot(sin(x),x=-2*Pi..Pi/2);

> trigPlot(sin(x)^2, x=0..2*Pi);

>

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Here is your code again:

> restart;

>

> numsol:=proc(eta,tau,lambda,beta,gamma0,cA,cB,VVAA,VVBB)

> local lambda_H, lambda_L, yAH, yAL, yBL, yBH, psi, g, Sigma, focA, focB, focvA, focvB, sys:

> global vA,vB,lAH,lBL,lAL,lBH:

> lambda_H:=1+lambda+beta*(1-eta):

> lambda_L:=1+lambda+beta*eta:

> yAH:=1+(lambda_H-1)*tau:

> yAL:=1-tau:

> yBL:=1+(lambda_L-1)*tau:

> yBH:=1-tau:

> lBH:=(eta-vA*lAH)/vB:

> lAL:=(1-eta-vB*lBL)/vA:

> psi:=x->1-exp(-x):

> g:=x->(1+x)*exp(-x):

> Sigma:=(1-psi(lAH))*(1-psi(lAL))*yAL-(1-psi(lBL))*(1-psi(lBH))*yBH:

> focA:=(1-psi(lAH))*(yAH-yAL)+Sigma-gamma0/eta*(3*vA*lAH-eta*(1+vA/(vA+vB)))=0:

> focB:=(1-psi(lBL)*(yBL-yBH)-Sigma-gamma0/(1-eta)*(3*vB*lBL-(1-eta)*(1+vB/(vA+vB))))=0:

> focvA:=yAH-g(lAH)*(yAH-yAL)-g(lAH+lAL)*yAL+gamma0*vA*lAH^2/eta+gamma0*vA*lAL^2/(1-eta)-cA=0:

> focvB:=yBL-g(lBH)*(yBL-yBH)-g(lBL+lBH)*yBH+gamma0*vB*lBL^2/(1-eta)+gamma0*vB*lBH^2/(1-eta)-cB=0:

> sys:={focA,focB,focvA,focvB}:

> fsolve(sys,{vA,vB,lAH,lBL},{vA=0..VVAA,vB=0..VVBB,lAH=0..2,lBL=0..2});

> end proc:

> lAHstar:=(eta,tau,gamma0)->subs(numsol(eta,tau,.1,.1,gamma0,.25,.25,20,20),lAH);

> lBLstar:=(eta,tau,gamma0)->subs(numsol(eta,tau,.1,.1,gamma0,.25,.25,20,20),lBL);

> vAstar:=(eta,tau,gamma0)->subs(numsol(eta,tau,.1,.1,gamma0,.25,.25,20,20),vA);

> vBstar:=(eta,tau,gamma0)->subs(numsol(eta,tau,.1,.1,gamma0,.25,.25,20,20),vB);

>

>

>

In order to be able to plot your function, you need to be able to give it a set of numeric values and have it return a number.

> lAHstar(1,2,3);

Error, (in numsol) numeric exception: division by zero

> lBLstar(5,6,3);

Error, (in lBLstar) invalid input: subs received fsolve({4.2*exp(-lAH)-5*exp(-lAH)*exp(-(-4-vB*lBL)/vA)+5*exp(-lBL)*exp(-(5-vA*lAH)/vB)-9/5*vA*lAH+3+3*vA/(vA+vB) = 0, -5.6+9.6*exp(-lBL)+5*exp(-lAH)*exp(-(-4-vB*lBL)/vA)-5*exp(-lBL)*exp(-(5-vA*lAH)/vB)+9/4*vB*lBL+3*vB/(vA+vB) = 0, -1.05-4.2*(1+lAH)*exp(-lAH)+5*(1+lAH+(-4-vB*lBL)/vA)*exp(-lAH-(-4-vB*lBL)/vA)+3/5*vA*lAH^2-3/4*(-4-vB*lBL)^2/vA = 0, 4.35-9.6*(1+(5-vA*lAH)/vB)*exp(-(5-vA*lAH)/vB)+5*(1+lBL+(5-vA*lAH)/vB)*exp(-lBL-(5-vA*lAH)/vB)-3/4*vB*lBL^2-3/4*(5-vA*lAH)^2/vB = 0}, {vA, vB, lAH, lBL}, {lAH = 0 .. 2, lBL = 0 .. 2, vA = 0 .. 20, vB = 0 .. 20}), which is not valid for its 1st argument

> vAstar(53,4,32);

Error, (in vAstar) invalid input: subs received fsolve({-19.65+16.4*(1+lAH)*exp(-lAH)+3*(1+lAH+(-52-vB*lBL)/vA)*exp(-lAH-(-52-vB*lBL)/vA)+32/53*vA*lAH^2-8/13*(-52-vB*lBL)^2/vA = 0, -16.4*exp(-lAH)-3*exp(-lAH)*exp(-(-52-vB*lBL)/vA)+3*exp(-lBL)*exp(-(53-vA*lAH)/vB)-96/53*vA*lAH+32+32*vA/(vA+vB) = 0, 7.4+25.6*exp(-lBL)+3*exp(-lAH)*exp(-(-52-vB*lBL)/vA)-3*exp(-lBL)*exp(-(53-vA*lAH)/vB)+24/13*vB*lBL+32*vB/(vA+vB) = 0, 22.35-25.6*(1+(53-vA*lAH)/vB)*exp(-(53-vA*lAH)/vB)+3*(1+lBL+(53-vA*lAH)/vB)*exp(-lBL-(53-vA*lAH)/vB)-8/13*vB*lBL^2-8/13*(53-vA*lAH)^2/vB = 0}, {vA, vB, lAH, lBL}, {lAH = 0 .. 2, lBL = 0 .. 2, vA = 0 .. 20, vB = 0 .. 20}), which is not valid for its 1st argument

> vBstar(6,3,46);

Error, (in vBstar) invalid input: subs received fsolve({1.8*exp(-lAH)-2*exp(-lAH)*exp(-(-5-vB*lBL)/vA)+2*exp(-lBL)*exp(-(6-vA*lAH)/vB)-23*vA*lAH+46+46*vA/(vA+vB) = 0, 41.9+5.1*exp(-lBL)+2*exp(-lAH)*exp(-(-5-vB*lBL)/vA)-2*exp(-lBL)*exp(-(6-vA*lAH)/vB)+138/5*vB*lBL+46*vB/(vA+vB) = 0, -.45-1.8*(1+lAH)*exp(-lAH)+2*(1+lAH+(-5-vB*lBL)/vA)*exp(-lAH-(-5-vB*lBL)/vA)+23/3*vA*lAH^2-46/5*(-5-vB*lBL)^2/vA = 0, 2.85-5.1*(1+(6-vA*lAH)/vB)*exp(-(6-vA*lAH)/vB)+2*(1+lBL+(6-vA*lAH)/vB)*exp(-lBL-(6-vA*lAH)/vB)-46/5*vB*lBL^2-46/5*(6-vA*lAH)^2/vB = 0}, {vA, vB, lAH, lBL}, {lAH = 0 .. 2, lBL = 0 .. 2, vA = 0 .. 20, vB = 0 .. 20}), which is not valid for its 1st argument

Each of your functions currently gives an error. Maybe I don't know the range of values that are valid. Can you please post examples where the functions give a good value? Or post valid ranges for the variables.

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Here is your code again:

> restart;

>

> numsol:=proc(eta,tau,lambda,beta,gamma0,cA,cB,VVAA,VVBB)

> local lambda_H, lambda_L, yAH, yAL, yBL, yBH, psi, g, Sigma, focA, focB, focvA, focvB, sys:

> global vA,vB,lAH,lBL,lAL,lBH:

> lambda_H:=1+lambda+beta*(1-eta):

> lambda_L:=1+lambda+beta*eta:

> yAH:=1+(lambda_H-1)*tau:

> yAL:=1-tau:

> yBL:=1+(lambda_L-1)*tau:

> yBH:=1-tau:

> lBH:=(eta-vA*lAH)/vB:

> lAL:=(1-eta-vB*lBL)/vA:

> psi:=x->1-exp(-x):

> g:=x->(1+x)*exp(-x):

> Sigma:=(1-psi(lAH))*(1-psi(lAL))*yAL-(1-psi(lBL))*(1-psi(lBH))*yBH:

> focA:=(1-psi(lAH))*(yAH-yAL)+Sigma-gamma0/eta*(3*vA*lAH-eta*(1+vA/(vA+vB)))=0:

> focB:=(1-psi(lBL)*(yBL-yBH)-Sigma-gamma0/(1-eta)*(3*vB*lBL-(1-eta)*(1+vB/(vA+vB))))=0:

> focvA:=yAH-g(lAH)*(yAH-yAL)-g(lAH+lAL)*yAL+gamma0*vA*lAH^2/eta+gamma0*vA*lAL^2/(1-eta)-cA=0:

> focvB:=yBL-g(lBH)*(yBL-yBH)-g(lBL+lBH)*yBH+gamma0*vB*lBL^2/(1-eta)+gamma0*vB*lBH^2/(1-eta)-cB=0:

> sys:={focA,focB,focvA,focvB}:

> fsolve(sys,{vA,vB,lAH,lBL},{vA=0..VVAA,vB=0..VVBB,lAH=0..2,lBL=0..2});

> end proc:

> lAHstar:=(eta,tau,gamma0)->subs(numsol(eta,tau,.1,.1,gamma0,.25,.25,20,20),lAH);

> lBLstar:=(eta,tau,gamma0)->subs(numsol(eta,tau,.1,.1,gamma0,.25,.25,20,20),lBL);

> vAstar:=(eta,tau,gamma0)->subs(numsol(eta,tau,.1,.1,gamma0,.25,.25,20,20),vA);

> vBstar:=(eta,tau,gamma0)->subs(numsol(eta,tau,.1,.1,gamma0,.25,.25,20,20),vB);

>

>

>

In order to be able to plot your function, you need to be able to give it a set of numeric values and have it return a number.

> lAHstar(1,2,3);

Error, (in numsol) numeric exception: division by zero

> lBLstar(5,6,3);

Error, (in lBLstar) invalid input: subs received fsolve({4.2*exp(-lAH)-5*exp(-lAH)*exp(-(-4-vB*lBL)/vA)+5*exp(-lBL)*exp(-(5-vA*lAH)/vB)-9/5*vA*lAH+3+3*vA/(vA+vB) = 0, -5.6+9.6*exp(-lBL)+5*exp(-lAH)*exp(-(-4-vB*lBL)/vA)-5*exp(-lBL)*exp(-(5-vA*lAH)/vB)+9/4*vB*lBL+3*vB/(vA+vB) = 0, -1.05-4.2*(1+lAH)*exp(-lAH)+5*(1+lAH+(-4-vB*lBL)/vA)*exp(-lAH-(-4-vB*lBL)/vA)+3/5*vA*lAH^2-3/4*(-4-vB*lBL)^2/vA = 0, 4.35-9.6*(1+(5-vA*lAH)/vB)*exp(-(5-vA*lAH)/vB)+5*(1+lBL+(5-vA*lAH)/vB)*exp(-lBL-(5-vA*lAH)/vB)-3/4*vB*lBL^2-3/4*(5-vA*lAH)^2/vB = 0}, {vA, vB, lAH, lBL}, {lAH = 0 .. 2, lBL = 0 .. 2, vA = 0 .. 20, vB = 0 .. 20}), which is not valid for its 1st argument

> vAstar(53,4,32);

Error, (in vAstar) invalid input: subs received fsolve({-19.65+16.4*(1+lAH)*exp(-lAH)+3*(1+lAH+(-52-vB*lBL)/vA)*exp(-lAH-(-52-vB*lBL)/vA)+32/53*vA*lAH^2-8/13*(-52-vB*lBL)^2/vA = 0, -16.4*exp(-lAH)-3*exp(-lAH)*exp(-(-52-vB*lBL)/vA)+3*exp(-lBL)*exp(-(53-vA*lAH)/vB)-96/53*vA*lAH+32+32*vA/(vA+vB) = 0, 7.4+25.6*exp(-lBL)+3*exp(-lAH)*exp(-(-52-vB*lBL)/vA)-3*exp(-lBL)*exp(-(53-vA*lAH)/vB)+24/13*vB*lBL+32*vB/(vA+vB) = 0, 22.35-25.6*(1+(53-vA*lAH)/vB)*exp(-(53-vA*lAH)/vB)+3*(1+lBL+(53-vA*lAH)/vB)*exp(-lBL-(53-vA*lAH)/vB)-8/13*vB*lBL^2-8/13*(53-vA*lAH)^2/vB = 0}, {vA, vB, lAH, lBL}, {lAH = 0 .. 2, lBL = 0 .. 2, vA = 0 .. 20, vB = 0 .. 20}), which is not valid for its 1st argument

> vBstar(6,3,46);

Error, (in vBstar) invalid input: subs received fsolve({1.8*exp(-lAH)-2*exp(-lAH)*exp(-(-5-vB*lBL)/vA)+2*exp(-lBL)*exp(-(6-vA*lAH)/vB)-23*vA*lAH+46+46*vA/(vA+vB) = 0, 41.9+5.1*exp(-lBL)+2*exp(-lAH)*exp(-(-5-vB*lBL)/vA)-2*exp(-lBL)*exp(-(6-vA*lAH)/vB)+138/5*vB*lBL+46*vB/(vA+vB) = 0, -.45-1.8*(1+lAH)*exp(-lAH)+2*(1+lAH+(-5-vB*lBL)/vA)*exp(-lAH-(-5-vB*lBL)/vA)+23/3*vA*lAH^2-46/5*(-5-vB*lBL)^2/vA = 0, 2.85-5.1*(1+(6-vA*lAH)/vB)*exp(-(6-vA*lAH)/vB)+2*(1+lBL+(6-vA*lAH)/vB)*exp(-lBL-(6-vA*lAH)/vB)-46/5*vB*lBL^2-46/5*(6-vA*lAH)^2/vB = 0}, {vA, vB, lAH, lBL}, {lAH = 0 .. 2, lBL = 0 .. 2, vA = 0 .. 20, vB = 0 .. 20}), which is not valid for its 1st argument

Each of your functions currently gives an error. Maybe I don't know the range of values that are valid. Can you please post examples where the functions give a good value? Or post valid ranges for the variables.

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What is it that you are looking for? Because when I enter both of your questions into Maple, I do get a good response.

> solve(y(x)+3*int((s+t)*y(t), t = 0 .. 1) = x^2+1, x);

> solve(y(x)+3*int((s+t)*y(t), t = 0 .. 1) = x^2+1, s);

>

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Sorry about not answering your actual question. I passed your problem on to the Math group here and this is what I got back:

> restart; with(student):> f:= x->x; #anything, just so long as f is a function.> b:= leftsum( f, x=1..2, 6);

"Too many levels of recursion" is not a trappable error. However, the problem in this case is that the question is malformed. If you examine the original assignment to c, you have:

> c:= evalf(b);

c;
Error, too many levels of recursion

That "r" is an escaped local, and whatever it is assigned is not happy when evaluating:

> op(1,eval(c,1));

op(2,eval(%,1));

%;
Error, too many levels of recursion

The root cause is the passing if a function (rather than an expression) to the leftsum command. If "f" is rerplaced by f(x) (or even 'f'(x)) then the calculation works fine:

> b:= leftsum( 'f'(x), x=1..2, 6);

c:= evalf(b);

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It looks like the tickmarks option does not have an effect on the loglogplot. However, by using plots[display], you can get around this. As you can see below.

> with(plots): a:= loglogplot(exp(10^x), x = 1 .. 20):

display(a,tickmarks=[0,0]);

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