C_R

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These are questions asked by C_R

The Examples section on the help page of a command is important for learning, but cannot cover all uses. This is especially true for general purpose commands like "solve" or "simplify". Searching all help pages that contain the word "solve" results in too many irrelevant hits that do not contain examples.

Why does adding a bracket to a command not filter for help pages with examples using the command?

Inside a help page Find/Replace finds such strings.

Inverse kinematics can be done in several ways (this webinar gives a very good overview https://www.youtube.com/watch?v=X0OZ9EM6dns). A effective and simple method is to run a model in reverse direction. This can’t be done with causal modeling tools, where information flow is fixed by design (https://de.maplesoft.com/support/help/MapleSim/view.aspx?path=MapleSimUserGuide/Chapter01).

Inverse kinematics, which is possible with acausal modeling tools, is only an example for running a model in the reverse (i.e., inverted) direction.

Without success, I tried to find a reference who first came up with that elegant approach.

Anyone knows more?

 I came across this question while trying to verify the equality of expressions containing elliptic integrals.

 

That's what Maple returns for EllipticK(1)

EllipticK(1)

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

 

However

evalf(EllipticK(1.))

Float(infinity)

(1)

limit(EllipticK(k), k = 1, left)

infinity

(2)

indicate infinity.

Float(infinity) = infinity

Float(infinity) = infinity

(3)

is(Float(infinity) = infinity)

true

(4)

NULL

Download EllpticK(1).mw

I have no experience with elliptic integrals. Can I assume in this case that infinity is correct?

Evaluating this integral

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

Int(1/((1-x)^(1/2)*(-x^2+1)^(1/2)), x = 0 .. 1) = infinity*(Pi+1)

(1)

simplify(Int(1/((1-x)^(1/2)*(-x^2+1)^(1/2)), x = 0 .. 1) = infinity*(Pi+1))

Int(1/((1-x)^(1/2)*(-x^2+1)^(1/2)), x = 0 .. 1) = infinity

(2)

NULL

produces an infinite product as output. Why does Maple not automatically simplify to infinity. Can the extra information (1+pi) be of any use?


Download Infinity_times_something.mw

 

The expression

f := arctan(y, x)+arctan(-y, x)

arctan(y, x)+arctan(-y, x)

(1)

simplifies to zero in the real range if y=0 is excluded.

x < 0, y::real, y <> 0; `assuming`([simplify(f), is(f = 0)], [%])

0, true

(2)

x >= 0, y::real, y <> 0; `assuming`([simplify(f), is(f = 0)], [%])

0, true

(3)

Combining the above assumptions as attempted bellow does not simplify to zero

x::real, y::real, y <> 0; `assuming`([simplify(f), is(f = 0)], [%])

arctan(y, x)+arctan(-y, x), FAIL

(4)

`or`(x < 0, x >= 0), y::real, y <> 0; `assuming`([simplify(f), is(f = 0)], [%])

arctan(y, x)+arctan(-y, x), FAIL

(5)

Or(x < 0, x >= 0), y::real, y <> 0; `assuming`([simplify(f), is(f = 0)], [%])

arctan(y, x)+arctan(-y, x), FAIL

(6)

`and`(-infinity <= x, x <= infinity), y::real, y <> 0; `assuming`([simplify(f), is(f = 0)], [%])

arctan(y, x)+arctan(-y, x), FAIL

(7)

interface(version)

`Standard Worksheet Interface, Maple 2022.0, Windows 10, March 8 2022 Build ID 1599809`

(8)

 

 

Download assuming_and_differently_combined_inequalities.mw

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