Consider the following code:

van_der_Waals := (p + a / V[m]^2) * (V[m] - b) = R * T:
expand(van_der_Waals);

The objective of the exercise is express the equation in a cubic form. Obvious solution is to take the output of the code above and multiplie both sides by V[m]^2. However, I would like to know if there exists a different aproach to get the same result.

How can I write a decimal number with period in maple? For example, in the following code;

restart;
number := 3.123123123123:
convert(number, rational);

I got 1040 / 333. However if number := 3.123123 then output is 76123 / 24374, so, in order to solve the exercise assign to the variable number a value of 3.123123123123123123123123123... How can I do it in abreviate form?

simplify is a procedure in Maple that have as parameter an assumption ¿Have the assumption a default value? For example, if we consider the following code:

restart;
f:= (x^3 - 27) / (x^2 - 3 * x):
print(f = simplify(f));

The output of that code assume that denominator is not zero, so I think the procedure have a default value for assume parameter.

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In this question I have to do what I said in the title. Really I don't understand the question very well, or at least I don't understand the objetive, because if I use solve I get an error and if I use isolate I only can get sin in terms of cos and even wen I could get all answer, I needed a starting point, it's say an identity to solve the exercise. Therefore, my question is, Maple have some comand to express trigonometric functions in terms of another without introducing identities?

I drew a methane molecula and display three times because I wanted to get two-fold and three-fold symmetry axis. ,I would is that I would like to get a more exact output and doing it without clicking, it's say, using code. Can someone help me?tareaclase6.mw
 

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