SR('I') is not consistent

[vdelecroix]

This behavior is confusing

sage: SR('I') ** 2   # complex imaginary
-1
sage: SR.var('I')
I
sage: SR('I') ** 2   # now a variable!
I^2

So far different solutions are under consideration

1. Let SR('I') always return the imaginary unit (and use SR.var(string) to create variables)
2. Add SR.I() as a method and let SR(string) always return a variable
3. Create methods SR.e(), SR.I(), SR.pi() for named constants and let SR(string) always create variables.
4. Forbid the names e, I, pi, etc as variable names.

[moritz]

I am not sure if this is really so bad. It is the same for other constants:

sage: SR('e').n()   # Euler's constant
2.71828182845905
sage: SR.var('e')   
e
sage: SR('e').n()   # now a variable
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

TypeError: cannot evaluate symbolic expression numerically

But I can imagine that it would be very useful to use e sometimes as a symbolic variable (e.g. when using a, b, c and d before..)

[jdemeyer]

I agree that this is not a bug. I is just a variable with a default value of sqrt(-1), but that value can be changed.

[vdelecroix]

My complaint is about the way SR(whatever) is interpreting its argument. When I do SR.var('my_name') I clearly want a new variable name. But the behavior of SR(whatever) depends on the variables created at a given time. It is easy to imagine

def f():
    a,b,c,d,e = SR.var('a,b,c,d,e')
    # now using the symbolic variables

m = f()
e = SR('e')  # this is not anymore exp(1)!!

[moritz]

What do you propose to do? What behavior do you want to have? Should SR.var('a,b,c,d,e') raise an error?

I think a line like a,b,c,d,e = SR.var('a,b,c,d,e') or `a,b,c,d,e = var('a,b,c,d,e')' is very natural. In fact:

sage: search_src("var\('a, b, c, d, e")
tensor/coordinate_patch.py:230:            sage: a, b, c, d, e = var('a, b, c, d, e')
tests/french_book/nonlinear_doctest.py:64:    sage: a, b, c, d, e, f, x = var('a, b, c, d, e, f, x')
matrix/special.py:3625:        sage: matrix.hankel(SR.var('a, b, c, d, e'))
matrix/special.py:3634:        sage: matrix.hankel(SR.var('a, b, c, d, e'), SR.var('f, g, h, i'))

[vdelecroix]

• option 1: keep SR.var('e') (variable creation) and make SR('e') always return exp(1) for consistency
• option 2: forbid standard variable names (e, pi, cos, etc)

[tmonteil]

One option could be to have SR.I(), SR.e(), etc working the same way as the existing SR.pi(), and let SR(string) return/inject a symbolic variable.

[slelievre]

I don't see how

sage: SR('I') ** 2   # complex imaginary
-1
sage: SR.var('I')
I
sage: SR('I') ** 2   # now a variable!
I^2

is any more confusing than

sage: exp(1)         # exponential
e
sage: exp = log
sage: exp(1)         # now logarithm!
0

[vdelecroix]

Replying to slelievre:

I don't see how

sage: SR('I') ** 2   # complex imaginary
-1
sage: SR.var('I')
I
sage: SR('I') ** 2   # now a variable!
I^2

is any more confusing than

sage: exp(1)         # exponential
e
sage: exp = log
sage: exp(1)         # now logarithm!
0

See 3.

[vdelecroix]

More precisely

def f():
    exp = log
    SR.var('e')
f()
exp(x)  # still exp(x)
SR('e') # e is a variable here

[slelievre]

I get it now. The changed behaviour would be expected after

sage: I = SR.var('I')

but not after

sage: SR.var('I')

[vdelecroix]

Replying to tmonteil:

One option could be to have SR.I(), SR.e(), etc working the same way as the existing SR.pi(), and let SR(string) return/inject a symbolic variable.

Indeed.

[vdelecroix]

update milestone 8.3 -> 8.4