Evaluating symbolic expression, when some variables are finally fixed

1

asked 8 years ago

wjur
11 ●1 ●1 ●4

updated 7 years ago

tmonteil
27483 ●32 ●205 ●519 http://wiki.sagemath.o...

Hello

I'm looking for solution when bigger number of variables is in the picture.

Simple example: There is relationship I = V/R then we know that R = 3, with that knowledge let's plot I(V)
in sage it should look something like:

V = var('V')
R = var('R')
I = V/R
R = 3
plot(I)

but above is not working, because in plot(I) I is still V/R not V/3 (knowledge of R=3 is not used), so I'm looking for some operation that turns V/R into V/3, something like

I = evaluate(I)

but such evaluate() apparently does not exist

there are however two different ways
(1) repeat I=V/R after R=3 and in such situation I becomes V/3 as needed
(2) I = I(R=R) and with earlier R=3, I also becomes V/3
both however seems for me be solution(s) for simple expression with just few variables, and not good (not as straightforward as hypothetical I = evaluate(I) for more complex expression with several variables.

Is such evaluate() or so, available already, and I failed to find it?
Is there a (easy) way to implement that proposed evaluate() ?

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1

answered 8 years ago

tmonteil
27483 ●32 ●205 ●519 http://wiki.sagemath.o...

updated 8 years ago

When you write R = SR.var('R'), the left-hand R is a Python name pointing to the right-hand SR.var('R'), which is a symbolic expression. Then when you write R = 3, the Python name R points to the integer 3, so there is no relationship anymore between R and SR.var('R'):

sage: R = SR.var('R')
sage: type(R)
<type 'sage.symbolic.expression.Expression'>
sage: R = 3
sage: type(R)
<type 'sage.rings.integer.Integer'>

If you want to substitute R with 3 in I, you should do:

sage: I.substitute({R:3})
1/3*V

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Needs a minor edit of V to R...

paulmasson ( 8 years ago )

Edited, thanks.

tmonteil ( 8 years ago )

Either that or you can (partially) evaluate expressions using call syntax:

sage: var(R,V)
(R,V)
sage: I=V/R
sage: I
V/R
sage: I(R=3)
1/3*V

It has the slight advantage that the binding of R is irrelevant

sage: R="not a valid value"
sage: I(R=3)
1/3*V

The "R=" is a python construct and, for calling symbolic expressions, gets interpreted in terms of the symbolic ring

nbruin ( 8 years ago )

BTW, more on substituting multiple values is on
Substituting multiple values question&answer

wjur ( 8 years ago )

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0

answered 8 years ago

This post is a wiki. Anyone with karma >750 is welcome to improve it.

Thanks to other answers, which concentrated on particular example, I wanted to explain better what I'm after (i.e. the general solution), and in that process I've got the answer:

I = eval(preparse(str(I)))

where

str(I) converts the 'I' expression to string
preparse(...) preparses the code of expression in the sage style ('^' as power, and so on)
eval(...) finally evaluates expression (in particular example: taking into account that R is already set to 3)

The code thus would be:

V = var('V')
R = var('R')
I = V/R
R = 3  # this is one line representation of possible several lines of code
       # to compute value in general case. Let's also note that the value can 
       # even be provided externally (read from file, or so) 
I = eval(preparse(str(I)))
plot(I)

and having in mind even more general solution with evaluate() definition:

def evaluate(expression):
    return eval(preparse(str(expression)))

V = var('V')
R = var('R')
I = V/R
R = 3  # this is one line representation of possible several lines of code
       # to compute value in general case. Let's also note that the value can 
       # even be provided externally (read from file, or so) 
I = evaluate(I)
plot(I)

Few days later:
There is a small improvement possible - by adding simplify(), and so making the whole thing
I = simplify(eval(preparse(str(I))))

Please let know if the code could be more elegant (pythonic or sageonic) and if there are some disadvantages or threads in such solution

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if it makes sense also in the more complicated case, you may simply define $I=V/R$ after the numerical value of $R$ has been computed. if it's not what you're after, you may create a function which computes the numerical values returning a dictionary, say numerical_values, and evaluate the current as in I = I.subs(numerical_values).

mforets ( 8 years ago )

BTW, Solution I found thanks to other sage question&answer
problems with sage_eval and eval

wjur ( 8 years ago )

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answered 8 years ago

mforets
1413 ●9 ●27 ●44 http://marcelo-forets.fr/

updated 8 years ago

Moreover, notice that the "intuitive evaluation" is also ok, since both:

var('V R')
I = V/R 
plot(I(R=3), (V, 0, 2))

and

var('V R')
I(R) = V/R 
plot(I(3), (V, 0, 2))

work.

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Although the first one has the advantage that it is clear which variable is evaluated ( $R$ ).

mforets ( 8 years ago )

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