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converting string to latex file

asked 2023-05-05 13:58:50 +0100

moon gravatar image

updated 2023-05-05 14:03:14 +0100

Hi, I'm in trouble fixing a little problem. My context: I do generate math expressions as strings. I'm able to use them as math expressions without any issue. However when I need to get the LaTeX format (to drop in a file for a later use) I'm obliged to use the eval function that kills the structure. here is the code my very naive code (as I'm just a neewby)

oper=[">", ">=", "<", "<="]
a=randint(-20,20)
b=randint(-10,10)
c,d=0,0
while c*x+d ==0:
    c=randint(-20,20)
    d=randint(-10,10)
f=(a*x+b)/(c*x+d)
a=randint(-20,20)
b=randint(-10,10)

    c,d=0,0
    while c*x+d ==0:
        c=randint(-20,20)
        d=randint(-10,10)
    g=(a*x+b)/(c*x+d)
    mystr= str(f) + str(sample(oper,1)[0]) + str(g)
    show(latex(mystr))
    print(latex(eval(mystr)))

I didn't want to set specific values for my variables and just dropped the whole piece of code to allow you guys to check if you got some time. Obviously for all those cases that doesn't have simplifications it works fine for me. You help will be much appreciated!

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Comments

I don't understand what you aim to achieve. Could you explain your goal(s) ?

Emmanuel Charpentier gravatar imageEmmanuel Charpentier ( 2023-05-05 22:10:17 +0100 )edit

Sorry for not have been clear enough. mystr is the string that I need to use: 1- for evaluation using solve e.g solve(f>=g,x). This works fine 2- to display mystr LaTex format The only solution that worked for me is to use eval print(latex(eval(mystr))) However when in mystr there are possible simplifications, I lose the intergers because of the eval function. In other words, how to translate mystr in LaTeX without evaluating its content, or better keeping all the coefficients as integers

Hope it's better now.

moon gravatar imagemoon ( 2023-05-05 22:48:04 +0100 )edit

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answered 2023-05-06 06:57:54 +0100

dsejas gravatar image

Hello, @moon! I am not 100% sure of what you want, but perhaps the following works for you?

import operator as op  # Python's standard library of operators (+, -, <, >, <=, >=, etc.)
oper = [op.gt, op.ge, op.lt, op.le]  # store the operators themselves instead of strings
# The following is as in your code:
a = randint(-20, 20)
b=randint(-10, 10)
c, d=0, 0
while c*x+d == 0:
    c = randint(-20, 20)
    d = randint(-10, 10)
f = (a*x + b) / (c*x + d)
a = randint(-20, 20)
b = randint(-10, 10)

c, d = 0, 0
while c*x+d == 0:
    c = randint(-20, 20)
    d = randint(-10, 10)
g = (a*x + b) / (c*x + d)

# The following is what does what you want (explained below)
expr = sample(oper,1)[0](f, g)  # (1)
show(expr)  # (2)
print(solve(expr, x))  # (3)
print(latex(expr))  # (4)

Line (1) takes one random element from ´oper´. For example, ´oper[0]´ is ´op.gt´, which is equivalent to ´>´; ´oper[1]´ is ´op.ge´, ehich is equivalent to ´>=´, etc. The part ´sample(oper,1)[0]´ chooses one of them, as you already know. Now, this operators are actually functions (in the programming sense), so you should write ´op.gt(f, g)´ instead of ´f > g´. That is why we have the ´(f, g)´ part in (1). This is an expression, as far as Sage concerns, so we call it, creatively enough, ´expr´.

Line (2) is there just to show the resulting expression. Line (3) is to show that you can use ´solve´ without ´eval´ (remember, because ´expr´ is already an expression). Finally, what you wanted: line (4) shows that this expression can be readily converted to LaTeX without using ´eval´; this should preserve the structure of the expression, as far as I know.

Additionally, please allow me to make a couple of suggestions:

  1. Instead of using ´sample(oper,1)[0]´, it could be better to use Sage's ´choice´ function, which I believe should be more clearly readable and more efficient (given that it is design exactly for the purpose of making a random choice from a list). Then, line (1) should become

    expr = choice(oper)(f, g)
    
  2. The ´while´ loops could be more clearly written as

    while (c == 0 and d == 0):
    

    This is equivalent to the form you wrote, but it's more standard.

  3. Depending on how many times you want to use line (1) or in the alternative form of the previous suggestion, it could be convenient to encapsulate it in a function like

    def ineq(f, g):
        return choice(oper)(f, g)
    

This is possible, given that Sage can work with expressions. The reason why this could be convenient, is because it more clear to write, for example, ´solve(ineq(f,g), x)´ than ´solve(choice(oper)(f,g), x)´. However, there is the possibility to store in a variable, as you do, so perhaps this is not as much a suggestion as it is an alternative approach. Alas, I not 100% sure if it's worth.

I hope this helps!

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@ dsejas very much appreciated ! all works fine and the explanations really good. It helps me gaining knowledge.

moon gravatar imagemoon ( 2023-05-06 22:54:22 +0100 )edit

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Asked: 2023-05-05 13:58:50 +0100

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Last updated: May 06 '23