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You have clickable calc. Today I saw in your email that you have clickable physic but in french. Do you have it in english too>?

Thank you

manolo

Hi everyone,

 

At some point in my calculations, I want to do some simple manipulations wiht the use of the «clickable» features in M17.  For the moment, I can see directy how to do it by hand and I do it by copy-paste and use the mous to change it a little bit.  But I just cannot find a simple way to do it by simple click.

 

You will find in this attach question, the maipulations I want to do.  It is starting from equaiton (7).  Am I at the edge where it is simple by hand than with the features?

 Space_manipulation.mw

 

Thank you in advance.

--------------------------------------
Mario Lemelin
Maple 17.02 Ubuntu 13.10 - 64 bits
Maple 17 Win 7 - 64 bits messagerie : mario.lemelin@cgocable.ca téléphone :  (819) 376-0987
New user. How do I launch the clickable math interface as in the demo video in maple 17 student? I also need help with entering/ solving simultaneous equations step by step.

Ten more Clickable Calculus solutions have been added to the Teaching Concepts with Maple section of the Maplesoft web site. Solutions to problems include examples in algebra, differential and integral calculus, lines-and-planes in multivariate calculus, linear algebra, and vector calculus.

The algebra additions include an example illustrating how a

Apart from the online description of this new Maple 16 feature here, there is also the help-page for subexpressionmenu.

I don't know of a complete listing of its current functionality, but the key thing is that it acts in context. By that I mean that the choice of displayed actions depends on the kind of subexpression that one has selected with the mouse cursor.

Apart from arithmetic operations, rearrangements and some normalizations of equations, and plot previews, one of the more interesting pieces of functionality is the various trigonometric substitutions. Some of the formulaic trig substitutions provide functionality that has otherwise been previously (I think) needed in Maple.

In Maple 16 it is now much easier to do some trigonometric identity solving, step by step.

Here is an example executed in a worksheet. (This was produced by merely selecting subexpressions of the output at each step, and waiting briefly for the new Smart Popup menus to appear automatically. I did not right-click and use the traditional context-sensitive menus. I did not have to type in any of the red input lines below: the GUI inserts them as a convenience, for reproduction. This is not a screen-grab movie, however, and doesn't visbily show my mouse cursor selections. See the 2D Math version further below for an alternate look and feel.)

expr:=sin(3*a)=3*sin(a)-4*sin(a)^3:

expr;

sin(3*a) = 3*sin(a)-4*sin(a)^3

# full angle reduction identity: sin(3*a)=-sin(a)^3+3*cos(a)^2*sin(a)
-sin(a)^3+3*cos(a)^2*sin(a) = 3*sin(a)-4*sin(a)^3;

-sin(a)^3+3*cos(a)^2*sin(a) = 3*sin(a)-4*sin(a)^3

# subtract -sin(a)^3 from both sides
(-sin(a)^3+3*cos(a)^2*sin(a) = 3*sin(a)-4*sin(a)^3) -~ (-sin(a)^3);

3*cos(a)^2*sin(a) = 3*sin(a)-3*sin(a)^3

# divide both sides by 3
(3*cos(a)^2*sin(a) = 3*sin(a)-3*sin(a)^3) /~ (3);

cos(a)^2*sin(a) = sin(a)-sin(a)^3

# divide both sides by sin(a)
(cos(a)^2*sin(a) = sin(a)-sin(a)^3) /~ (sin(a));

cos(a)^2 = (sin(a)-sin(a)^3)/sin(a)

# normal 1/sin(a)*(sin(a)-sin(a)^3)
cos(a)^2 = normal(1/sin(a)*(sin(a)-sin(a)^3));

cos(a)^2 = 1-sin(a)^2

# Pythagoras identity: cos(a)^2=1-sin(a)^2
1-sin(a)^2 = 1-sin(a)^2;

1-sin(a)^2 = 1-sin(a)^2

 

The very first step above could also be done as a pair of simpler sin(x+y) reductions involving sin(2*a+a) and sin(a+a), depending on what one allows onself to use. There's room for improvement to this whole approach, but it looks like progress.

Download trigident1.mw

In a Document, rather than using 1D Maple notation in a Worksheet as above, the actions get documented in the more usual way, similar to context-menus, with annotated arrows between lines.

expr := sin(3*a) = 3*sin(a)-4*sin(a)^3:

expr

sin(3*a) = 3*sin(a)-4*sin(a)^3

(->)

2*cos(a)*sin(2*a)-sin(a) = 3*sin(a)-4*sin(a)^3

(->)

4*cos(a)^2*sin(a)-sin(a) = 3*sin(a)-4*sin(a)^3

(->)

4*cos(a)^2*sin(a) = 4*sin(a)-4*sin(a)^3

(->)

cos(a)^2*sin(a) = sin(a)-sin(a)^3

(->)

cos(a)^2 = (sin(a)-sin(a)^3)/sin(a)

(->)

cos(a)^2 = 1-sin(a)^2

(->)

1-sin(a)^2 = 1-sin(a)^2

(->)

1 = 1

``

Download trigident2.mw

 

I am not quite sure what is the best way to try and get some of the trig handling in a more programmatic way, ie. by using the "names" of the various transformational formulas. But some experts here may discover such by examination of the code. Ie,

eval(SubexpressionMenu);

showstat(SubexpressionMenu::TrigHandler);

The above can leads to noticing the following (undocumented) difference, for example,

> trigsubs(sin(2*a));
              
                                 1       2 tan(a)
[-sin(-2 a), 2 sin(a) cos(a), --------, -----------,
                              csc(2 a)            2
                                        1 + tan(a)

    -1/2 I (exp(2 I a) - exp(-2 I a)), 2 sin(a) cos(a), 2 sin(a) cos(a)]

> trigsubs(sin(2*a),annotate=true);

["odd function" = -sin(-2 a), "double angle" = 2 sin(a) cos(a),

                               1                       2 tan(a)
    "reciprocal function" = --------, "Weierstrass" = -----------,
                            csc(2 a)                            2
                                                      1 + tan(a)

    "Euler" = -1/2 I (exp(2 I a) - exp(-2 I a)),

    "angle reduction" = 2 sin(a) cos(a),

    "full angle reduction" = 2 sin(a) cos(a)]

And that could lead one to try constructions such as,

> map(rhs,indets(trigsubs(sin(a),annotate=true),
>                identical("double angle")=anything));

                             {2 sin(a/2) cos(a/2)}

Since the `annotate=true` option for `trigsubs` is not documented in Maple 16 there is more potential here for useful functionality.

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