C_R

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5 years, 209 days

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These are questions asked by C_R

Converting index expressions to atomic worked.
I then tried to uncheck atomic in the context menu which did not work.

I opened a new worksheet to try it again but now conversion to atomic disappeared from the menu

no_conv_to_atomic.mw

 

A restart of Maple did not bring convert to atomic back. Any idea why this happened and how to restore Maple?

My world of trigonometric functions has a very simple structure: sin, cos and tan are what I need.

That's why I very much welcomed the simplification of sin/cos to tan recently introduced with Maple 2023.

What I neither need nor want is the simplification of 1/sin and 1/cos to sec and csc. I'm not used to that (and probably won't get used to it).

Can this simplification to sec and ccs be turned off (and preferably the simplification to tan be kept)?

In the following example, the information in which range fsolve should search for a solution and the range in which a function is defined is somehow redundant. (This example has been adopted from here where fsolve without assumptions does not throw an error but evaluates forever.)

Why can’t fsolve not always assume that the range equals the domain of interest? This would make life easier and provide more solutions to inexperienced users who have not yet learned the need for assumptions.

If there are good reasons (and there probably are) that such an implicit assumption (i.e. range equals domain) would be too restrictive: can’t fsolve give a hint or provide an new option to use ranges as assumptions?

Example with incomplete elliptic integral of the first kind

f := proc (x__0) options operator, arrow; int(1/(sqrt(x__0-x)*sqrt(-x^2+1)), x = 0 .. x__0) end proc

proc (x__0) options operator, arrow; int(1/(sqrt(x__0-x)*sqrt(-x^2+1)), x = 0 .. x__0) end proc

(1)

Range := 0 .. 1; plot(f(x__0), x__0 = Range, labels = [x__0, 'f(x__0)'])

 

f(.5) = 1.524886838NULL

Defining the inverse of f

g := proc (y) options operator, arrow; fsolve(`assuming`([f(x__0) = y, x__0 = Range], [lhs(Range) <= x__0 and x__0 <= rhs(Range)])) end proc

proc (y) options operator, arrow; fsolve(`assuming`([f(x__0) = y, x__0 = Range], [lhs(Range) <= x__0 and x__0 <= rhs(Range)])) end proc

(2)

x__0 = g(f(.5)) → x__0 = .5000000000NULL

Now without assumptions

h := proc (y) options operator, arrow; fsolve(f(x__0) = y, x__0 = Range) end proc

proc (y) options operator, arrow; fsolve(f(x__0) = y, x__0 = Range) end proc

(3)

h(f(.5))

Error, (in fsolve) cannot determine if this expression is true or false: abs(Re(x))+abs(Im(x)) <= 0.

 

``

Download ranges_as_assumptions.mw

 

ODE for electrical circuit (right click on Documentblock, unselect show command does not work. Command still visble)u(t) = T*(diff(`&varphi;`(t), t))+L*(diff(i(t), t))+i(t)*R

u(t) = T*(diff(varphi(t), t))+L*(diff(i(t), t))+i(t)*R

(1)

 

ODE for motor (toggle Documentblock, unselect show command is only effective on equations  3 and 4)i(t)*T = J*(diff(`&varphi;`(t), t, t))

i(t)*T = J*(diff(diff(varphi(t), t), t))

(2)

Isolate i(t) and taking the derivative

i(t) = J*(diff(diff(varphi(t), t), t))/T

(3)

``

diff(i(t), t) = J*(diff(diff(diff(varphi(t), t), t), t))/T

(4)

``

Download Document_Block_hide_command.mw

Q1: In the above, why can I only convert radians to radians. Or: Why does the menu "Chose unit" not offer arcdeg?

Q2: In the above, why is nothing happening when I enter arcdeg in the field "Enter Unit"?

Q3: How to change the displayed symbol for arcdeg to ° (in the attachment are failed attempts)?

arcdeg.mw

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