Alex Smith

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17 years, 17 days

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These are replies submitted by Alex Smith

In fact Maple 8 returns the impliciplot much, much faster than Maple10.

And as we have noted, Maple11 is clueless.

In the syntax

implicitplot(0=int(erf(  (T-e*t)/sqrt(2)  )*t^2*exp(-t/2),t=0..infinity),e=0..1,T=0..10);

t is a dummy variable of integration. So the equation depends only on T and e.

Maple10 treats this correctly and returns a curve. Maple11 chokes, and seems to think that the dummy variable t is a variable.

Time to downgrade to Maple10?

 

 

In Maple 10

convert(Ei(1,z),Sum); 

does work as the help says.

But as you note, the same command does not work in Maple 11.


 

Replace the next to last line by

dA:=diff(value(A),c);

Or equivalently, replace the appearances of Int in the definition of A by int.

Replace the next to last line by

dA:=diff(value(A),c);

Or equivalently, replace the appearances of Int in the definition of A by int.

Axel says that Mathematica does not evaluate the indefinite integral, but in fact it does. It is the mess below. Note it does not include the Sum. However, Mathematica's antiderivative is also discontinuous, and when used to evaluate the definite integral, yields the same incorrect answer

-8.710344354 + 19.73920881 I

f:=x->x*ln(2 + 2*cos(x)^2 + cos(x)^4) + 2*(-(x*ln((3 - 2*I) + cos(2*x)))/2 + ((2*I)*x^2 - 4*arcsin(sqrt(2 - I))* arctanh(((1 + I)*tan(x))/ sqrt(1 - 3*I)) - (2*x + 2*arcsin(sqrt(2 - I)))* ln(1 + ((3 - 2*I) - 2*sqrt(1 - 3*I))* exp((2*I)*x)) - (2*x - 2*arcsin(sqrt(2 - I)))* ln(1 + ((3 - 2*I) + 2*sqrt(1 - 3*I))* exp((2*I)*x)) + 2*x*ln((3 - 2*I) + cos(2*x)) + I*(polylog(2, -(((3 - 2*I) - 2*sqrt(1 - 3*I))* exp((2*I)*x))) + polylog(2, -(((3 - 2*I) + 2*sqrt(1 - 3*I))* exp((2*I)*x)))))/4) + 2*(-(x*ln((3 + 2*I) + cos(2*x)))/2 + ((2*I)*x^2 - (4*I)*arcsin( sqrt(2 + I))*arctan( ((1 + I)*tan(x))/ sqrt(1 + 3*I)) - (2*x + 2*arcsin(sqrt(2 + I)))* ln(1 + ((3 + 2*I) - 2*sqrt(1 + 3*I))* exp((2*I)*x)) - (2*x - 2*arcsin(sqrt(2 + I)))* ln(1 + ((3 + 2*I) + 2*sqrt(1 + 3*I))* exp((2*I)*x)) + 2*x*ln((3 + 2*I) + cos(2*x)) + I*(polylog(2, -(((3 + 2*I) - 2*sqrt(1 + 3*I))* exp((2*I)*x))) + polylog(2, -(((3 + 2*I) + 2*sqrt(1 + 3*I))* exp((2*I)*x)))))/4);

 

As many seasoned users of Maple have pointed out, it is illogical to use Document mode.

Document mode should be avoided like head lice and the plague.

 

Thanks for catching this.

transform((x,y,z)->[x,y,0])(FG); is silly because it would act like the identity in this case.

plot3d has better color and related options, so

transform((x,y,z)->[x,y])

is a nice way to bring these effects into 2D plots.

 

 

 

 

You have a nice idea. As an alternative to the orientation option, you can use plottools[transform] to convert the 3D plot structure to an honest 2D structure:

 

with(plots):with(plottools):

f:=x->x: g:=x->x^2:

F:=spacecurve([x,f(x),0],x=-0.2..1.2,color=blue, thickness=3):

G:=spacecurve([x,g(x),0],x=-0.2..1.2,color=red, thickness=3):

region:=plot3d([x,y,0],x=0..1,y=g(x)..f(x),color=grey, style=patchnogrid):

FG:=display(region,F,G,axes=normal, scaling=constrained):

transform((x,y,z)->[x,y,0])(FG);
 

When I start a new document (as opposed to a worksheet) and replicate Evan's commands, using "point and click" to create the matrix A, I also get the same error message. If I start a new worksheet (as opposed to a document) and replicate Evan's commands, using "point and click" to create the matrix A, I do not get the error message. It looks like the problem has to do with document mode vs. worksheet mode. Why, on God's green Earth (idiom), would Maplesoft even think of making document mode the default? The best advise to any new user is to over ride the default, and use worksheet mode.
When I start a new document (as opposed to a worksheet) and replicate Evan's commands, using "point and click" to create the matrix A, I also get the same error message. If I start a new worksheet (as opposed to a document) and replicate Evan's commands, using "point and click" to create the matrix A, I do not get the error message. It looks like the problem has to do with document mode vs. worksheet mode. Why, on God's green Earth (idiom), would Maplesoft even think of making document mode the default? The best advise to any new user is to over ride the default, and use worksheet mode.
One insidious thing you can do to evaluate the integral "symbolically" is to use the following form: Int(sqrt(sin(x))/(sqrt(sin(x))+sqrt(cos(x))), x = 0 .. (1/2)*Pi); identify(evalf(%)); This gives Pi/4 rather quickly.
It seems like this is what you want: sum(int((x[i]-b)*exp((x[i]-b)^2/(2*sigma^2)),b=c..d),i=1..k)+ sum(int((y[j]-b)*exp((y[j]-b)^2/(2*sigma^2)),b=c..d),j=1..n); Unless one knows more about the x[i], y[j], etc. then it seems unlikely that this can be further simplified.
It seems like this is what you want: sum(int((x[i]-b)*exp((x[i]-b)^2/(2*sigma^2)),b=c..d),i=1..k)+ sum(int((y[j]-b)*exp((y[j]-b)^2/(2*sigma^2)),b=c..d),j=1..n); Unless one knows more about the x[i], y[j], etc. then it seems unlikely that this can be further simplified.
So if the philosophy is that we should always recheck definite integrals because Maple (like other systems) has a history of incorrectly calculating definite integrals, then it makes sense that Maple should automatically cross-check by comparing with evalf(Int(f(x),x=a..b)) whenever the result is numeric (no left over parameters). But acer says people would not appreciate this because it would slow down int(f(x),x=a..b). Surely having Maple do the reality check would take less time than having the human remember to follow with evalf(Int(f(x),x=a..b)).
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