## Plot - which curve is which!?...

Hi is there a way to identify curves in your plot? Especially when you dont know it yourself?

For example, I have 10 polynomials all order 5 and up, whilst I can trial and error identify which one is which it is very inefficient.

I used to use Mathematica, and I could manually label the curves with color which allows to see which curve is which. I assume there is something of the sort for Maple?

## How to solve the following equation in Maple?...

I have the following mathematical expression

where a=0.2, b=0.09, c=0.57, p=0.3 and q=1-p=0.7, Now i want to find the value of n for which the value of the expression will be 1, i.e., for what value of n , A_n will be 1?

## Maximizing Planck's Intensity Function...

I am attempting to maximize Planck's intesnity function for any given temperature T with respect to lambda. The function is as follows:

My initial attempt was to simply take the derivative of this function with respect to labda, set it equal to zero, and then solve for lamda. Theoretically this should give me the value of lambda that maximizes the intesity with respect to the constants / values h, c, k, and T (where T is temperature).

However doing this in maple just leads to the result "warning, solutions may have been lost".

Does anyone know how I can go about maximizing this?

Thanks!

## how to seq and sum over a range of subscript...

we always have subscript variable in the math book, but how could this be natral done in maple

I want to get a seq aaa3

seq(a[i],i=1..3)

but how could I get a  aij

seq(a[i_j],i=1..3);

and

seq(a[ij],i=1..3);  both was not right

## How do you insert a left bracket containing multip...

Is there a way with Maple 18 to place a bracket as shown below to contain two DE's? I am not trying to solve them. Only for note-taking purposes. If there is can you please share how to do it?

## Automatic simplification and a new Assume (as...

by:

Hi
Two new things recently added to the latest version of Physics available on Maplesoft's R&D Physics webpage are worth mentioning outside the framework of Physics.

• automaticsimplification. This means that after "Physics:-Setup(automaticsimplification=true)", the output corresponding to every single input (literally) gets automatically simplified in size before being returned to the screen. This is fantastically convenient for interactive work in most situations.

• Add Physics:-Library:-Assume, to perform the same operations one typically performs with the  assume command, but without the side effect that the variables get redefined. So the variables do not get redefined, they only receive assumptions.

This new Assume implements the concept of an "extended assuming". It permits re-using expressions involving the variables being assumed, expressions that were entered before the assumptions were placed, as well as reusing all the expressions computed while the variables had assumptions, even after removing the variable's assumptions. None of this is possible when placing assumptions using the standard assume. The new routine also permits placing assumptions on global variables that have special meaning, that cannot be redefined, e.g. the cartesian, cylindrical or spherical coordinates sets, or the coordinates of a coordinate spacetime system within the Physics package, etc.

Examples:

 >

This is Physics from today:

 >
 (1.1)
 • Automatic simplification is here. At this point automaticsimplification is OFF by default.
 >
 (1.2)

Hence, for instance, if you input the following expression, the computer just echoes your input:

 >
 (1.3)

There is however some structure behind (1.3) and, in most situations, it is convenient to have these structures
apparent, in part because they frequently provide hints on how to proceed ahead, but also because a more
compact expression is, roughly speaking, simpler to understand. To see this
automaticsimplification in action,
turn it ON:

 >
 (1.4)

Recall this same expression (you could input it with the equation label (1.3) as well)

 >
 (1.5)

What happened: this output, as everything else after you set  and with no
exceptions, is now further processed with simplify/size before being returned. And enjoy computing with frankly
shorter expressions all around! And no need anymore for "simplify(%, size)" every three or four input lines.

Another  example, typical in computer algebra where expressions become uncomfortably large and difficult to
read: convert the following input to 2D math input mode first, in order to compare what is being entered with the
automatically simplified output on the screen

 >
 (1.6)

You can turn automaticsimplification OFF the same way

 >
 (1.7)
 • New  facility; welcome to the world of "extended assuming" :)

Consider a generic variable, x. Nothing is known about it

 >

Each variable has associated a number that depends on the session, and the computer (internally) uses this
number to refer to the variable.

 >
 (1.8)

When using the assume  command to place assumptions on a variable, this number, associated to it, changes,
for example:

 >
 >
 (1.9)

Indeed, the variable x got redefined and renamed, it is not anymore the variable x referenced in (1.8).

 >
 Originally x, renamed x~:   is assumed to be: RealRange(Open(0),Open(1/2*Pi))

The semantics may seem confusing but that is what happened, you enter x and the computer thinks x~, not x
anymore.This means two things:

1) all the equations/expressions, entered before placing the assumptions on x using assume, involve a variable x
that is different than the one that exists after placing the assumptions, and so these previous expressions
cannot
be reused
. They involve a different variable.

2) Also, because, after placing the assumptions using assume, x refers to a different object, programs that depend
on the
x that existed before placing the assumptions will not recognize the new x redefined by assume .

For example, if x was part of a coordinate system and the spacetime metric depends on it, the new variable x
redefined within assume, being a different symbol, will not be recognized as part of the dependency of  This
posed constant obstacles to working with curved spacetimes that depend on parameters or on coordinates that
have a restricted range. These problems are resolved entirely with this new
Library:-Assume, because it does not
redefine the variables. It only places assumptions on them, and in this sense it works like
assuming , not assume .
As another example, all the
Physics:-Vectors commands look for the cartesian, cylindrical or spherical coordinates
sets
in order to determine how to proceed, but these variables disappear if you use
assume to place assumptions on them. For that reason, only assuming  was fully compatible with Physics, not assume.

To undo assumptions placed using the assume command one reassigns the variable x to itself:

 >
 (1.10)

Check the numerical address: it is again equal to (1.8)

 >
 (1.11)

·All these issues get resolved with the new Library:-Assume, that uses all the implementation of the existing
assume command but with a different approach: the variables being assumed do not get redefined, and hence:
a) you can reuse expressions/equations entered before placing the assumptions, you can also undo the
assumptions and reuse results obtained with assumptions. This is the concept of an
extended assuming. Also,
commands that depend on these assumed variables will all continue to work normally, before, during or after
placing the assumption, because
the variables do not get redefined.

Example:

 >

So this simplification attempt accomplishes nothing

 >
 (1.12)

Let's assume now that

 >
 (1.13)

The new command echoes the internal format representing the assumption placed.

a) The address is still the same as (1.8)

 >
 (1.14)

So the variable did not get redefined. The system however knows about the assumption - all the machinery of the
assume command is being used

 >
 Originally x, renamed x:   is assumed to be: RealRange(Open(0),Open(1/2*Pi))

Note that the renaming is to the variable itself - i.e. no renaming.

Hence, expressions entered before placing assumptions can be reused. For example, for (1.12), we now have

 >
 (1.15)

To clear the assumptions on x, you can use either of Library:-Assume(x=x) or Library:-Assume(clear = {x, ...}) in
the case of many variables being cleared in one go, or in the case of a single variable being cleared:

 >
 >

The implementation includes the additionally functionality, for that purpose add the keyword
anywhere in the calling sequence. For example:

 >
 (1.16)
 >
 Originally x, renamed x:   is assumed to be: RealRange(Open(0),infinity)
 >
 (1.17)
 >

In summary, the new Library:-Assume command implements the concept of an extended assuming, that can be
turned ON and OFF at will at any moment without changing the variables involved.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

## substitution a sequnce of numbers in a function...

Hi all

Assume that we have a function, say f(t) and we want to substitute t in it where t is:

t=[0,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1]

by subs or other better command, how can we do it?

best wishes

Ph.D Candidate

Applied Mathematics Department

## differentiation...

Hi all

I want to produce following c_nm's(which are differentiation based formula) . assume that N and M are known and f(t) is arbitrary. also n=1,2,...,N and m=0,1,..,M-1

how can we do this?

regards

Ph.D Candidate

Applied Mathematics Department

## Help! Maple 18 wont write essential math symbols: ...

Just got Maple 18 on academic license. I've used Maple 15, 16 and 17 before this.

It wont write simple math symbols as + - * and :=

I have tried both document- and worksheet, reinstalling and so on...

What is the problem?

Thanks

## Right clicking does nothing...

I am using Maple 12 in Win 64. I have some difficulties in evaluating expressions in Maple. For example simply writing cos(x) then differentiating it w.r.t x. After writing cos(x) in 2D Math mode, I do right click for selecting diff but it does not work. The pointer turns in to busy mode and nothing comes to select. Also, I tried this operation in the tutorial file teaching differentiation, however problem persists.

## Is there a way to import an equation from maple to...

I have some lengthy formulas in the maple. I don't want to waste time on rewritting them in a word document.
Is there a way to import those equations in a clean and tidy form to a word document or the mathtype program or something else! :)

## Block Diagonal Matrix...

Hi Again

Assume that we have known matrix namely, Q, of order (m+1)*(m+1) and we want to construct following matrix

where 0(bar) is zero matrix of orde (m+1)*(m+1) and New matrix should be of order {N*(m+1)}*{N*(m+1)} where N is known constant.

thanks for any guide

Ph.D Candidate

Applied Mathematics Department

Maple

Take a look at this link.

## DEs and Mathematical Functions Updates

by:

This is the first presentation of updates for the DE and Mathematical Functions programs of Maple 18. It includes several improvements, all in the Mathematical Functions sector, as well as some fixes. The update and instructions for its installation are available on the Maplesoft R&D webpage for DEs and mathematical functions. Some of the items below were mentioned here in Mapleprimes - you are welcome to present suggestions or issues; if possible they will be addressed right away in the next update.

• Filling gaps in the FunctionAdvisor regarding all the 6 complex components: abs, argument, conjugate, Im, Re, signum, as well as regarding Heaviside (step function), Dirac, min and max.
• Fix the simplification and differentation rule for doublefactorial
• Make convert(..., hypergeometric) work the same way as convert(blabla, hypergeom)
• Implement integral forms for Heaviside(z) and JacobiAM(z, k) via convert(..., Int)
• Implement appropriate display for the inert %intat function as well as its conversion to the inert Int
• Make the FunctionAdvisor/DE return not just the PDE system satisfied by f(z, k) = JacobiAM(z, k)and also (new) the ODE satisfied by f(z) = JacobiAM(z, k)
• Fix conversion rule from Heaviside(z) to Sum
• Fix unexpected error interruption when differentiating min(...) and max(...) containing more than three arguments
• Fix issue in simplify/conjugate
• Improvement in expand/int: factors in disguise are put outside the integration sign
• Various improvements in the case of multiple integrals involving the Dirac function
• Make Intat fully inert (before it was evaluating its arguments)
• Make value of inert indexed objects work

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft