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Question: Is the symbol _i somehow special by default (ie with just the default packages loaded)? Where can I find it in the documentation?

Question:Is the symbol _i somehow special by default (ie with just the default packages loaded)? Where can I find it in the documentation?

zenterix 310 Maple 2022
vector physics duplicate-question
December 30 2022
0

I've been trying to figure out what i_  means in Maple. In what follows is some experimentation and then my questions.

Just a few initial experiments without loading any packages.

i_

i_

 (1)

i_ = i_NULL

_i

_i

 (2)

_i = _iNULL

D(_i)

D(_i)

 (3)

f := proc (t) options operator, arrow; _i end proc

proc (t) options operator, arrow; _i end proc

 (4)

D(f)

0

 (5)

f := proc (t) options operator, arrow; t*_i end proc

proc (t) options operator, arrow; t*_i end proc

 (6)

D(f)

proc (t) options operator, arrow; _i end proc

 (7)

D(t*_i)

D(t)*_i+t*D(_i)

 (8)

Impression: _i is treated like an algebraic basis vector when the result of a function; but not in an expression.

NULL

with(Physics)

_i

_i

 (9)

_i = _iNULL

D(_i)

D(_i)

 (10)

f := proc (t) options operator, arrow; t*_i end proc

proc (t) options operator, arrow; Physics:-`*`(t, _i) end proc

 (11)

D(f)

proc (t) options operator, arrow; _i end proc

 (12)

Nothing really seemed to change with the Physics package being used. However, if we use the following package

with(Physics[Vectors])

_i

_i

 (13)

i_

i_

 (14)

_i = _iNULL

i_ = i_NULL

In the middle of v__0 := v__x0*_i = v__x0*_i text. Doesn't work as expected.

In the middle of v__0 = v__x0*_i = v__x0*_i = v__x0*_i text.

 

NULL

My question is: is the symbol _i somehow special by default? Where can I find it in the documentation?

Note the second-to-last line in the Maple document pasted above: "Doesn't work as expected". The difference between this line and the next one is simply the presence of a := instead of an =. The assignment makes the vector notation differ. Is this difference a bug or some feature I am unaware of?

Here is yet another behavior that seems kinda weird to me. Given the function f defined above, D(f) gives us the expected result but D(f(x)) does not. Yet, int(f) gives an error, and we have to use int(f(x)). 

EDIT: a little more research indicates there is a difference between the D operator and the function diff. 

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