B Finding Online PEMDAS Calculators

[pairofstrings]

TL;DR Summary

Online app for arranging terms with P.E.M.D.A.S.

Hello. I have an equation that looks like following:

I want to re-write the terms of the above equation adhering to PEMDAS.
I have seen the web but I could find none.

Thanks.

 

[Mark44]

Why? What do you mean when you say you want to "rewrite the terms" of this equation?
For what purpose?
What does PEMDAS have to do with what you're trying to do?

In two other threads you asked about this same equation:
https://www.physicsforums.com/threa...ation-for-the-same-curve.1001592/post-6478050
https://www.physicsforums.com/threads/y-for-heart-curve.996738/post-6436282

In those posts you seemed to want to graph this equation, but were stumped by a much simpler equation of x + y + xy = 1.

 

[Mark44]

Back in January, you wrote this:

The graph of the equation 1 = x + y is easy to draw. It says 'x' is 1 and 'y' is 1.
Therefore, I can plot the point at x = 1 and y = 1.

If you meant the point with coordinates (1, 1) -- i.e., x = 1 and y = 1, then no, that point is not on the line x + y = 1. If x = 1, then y = 0, and if y = 1, then x = 0, so the points (1, 0) and (0, 1) are on this graph, but it was not at all clear that this might have been what you meant.

If your goal is to graph the heart equation an online PEMDAS calculator is not what you need, but the graphing capabilities of wolframalpha (wolframalpha.com) could do it.

 

[fresh_42]

https://www.physicsforums.com/threa...th-and-other-curiosities.970262/#post-6164027

contains a list of calculators and graphic programs, in case you're not satisfied with WolframAlpha.

 

[berkeman]

Summary:: Online app for arranging terms with P.E.M.D.A.S.

I have an equation that looks like following:

I want to re-write the terms of the above equation adhering to PEMDAS.

Can you show us what you want the output to look like? That would help us to understand what you are looking for. Do you mean putting parenthesis around each term and moving the non-exponential terms to the end of the multiplication in each term?

 

[pairofstrings]

What do you mean when you say you want to "rewrite the terms" of this equation?

I am sorry. It is my mistake. I wanted to say "rearrange the terms".

..but it was not at all clear that this might have been what you meant.

Sorry about that.

Can you show us what you want the output to look like?

I want the equation that has all its terms conforming to PEMDAS.

In the above equation I think that after x⁶ I should consider y⁶ then 3x⁴y² then 3x²y⁴ then 3y⁴ then x²y³ then 3x⁴ then 6x²y² then 3y⁴ then 3y².
I am considering this order of terms to manipulate x⁶ with all the other terms until I get a curve.

 

[Mark44]

It is my mistake. I wanted to say "rearrange the terms".

I want the equation that has all its terms conforming to PEMDAS.

In the above equation I think that after x⁶ I should consider y⁶ then 3x⁴y² then 3x²y⁴ then 3y⁴ then x²y³ then 3x⁴ then 6x²y² then 3y⁴ then 3y².
I am considering this order of terms to manipulate x⁶ with all the other terms until I get a curve.

Changing the order of the terms makes absolutely no sense, and is completely unrelated to what PEMDAS is about. Looking at two of the terms, $x^2 + 3x^4y^2$, what PEMDAS says are these steps, in this order:

1. the exponent operations should be performed
2. the multiplications should then be performed; i.e. $3$ times $x^4$ times $y^2$
3. the addition should be performed

What PEMDAS conveys is the order in which different types of operations should be performed. For an expression such as a + b + c, the two additions are at the same level, so it makes no difference whether you add a + b first, or b + c first.

I think you have an incorrect idea about what PEMDAS is about.

 

[fresh_42]

In the above equation I think that after x⁶ I should consider y⁶ then 3x⁴y² then 3x²y⁴ then 3y⁴ then x²y³ then 3x⁴ then 6x²y² then 3y⁴ then 3y².

This is called a lexicographic order, in that case, exponents before variable names. It is usually the other way around. The Buchberger algorithm uses lexicographic ordering on multinomials to compute Gröbner bases, and I think Mathematica has an implementation. So this is a way to achieve what you are looking for.

However, ...
... it is a cannon shooting sparrows. It is probably far easier to implement a lexicographic ordering by yourself in a language of your choice. It is simple string handling, an easy exercise in a programmer course.

 

[mfb]

PEMDAS is just telling you how to read expressions like the one you posted. It doesn't have any specific preference for the order of terms that are added/subtracted.
If you want to have some specific order then you need to define what order you want. Then just rearrange things based on your preference.

 

[pairofstrings]

If there is PEMDAS then all of the following equations are equivalent to each other?

$x^2+x-y=1$
$x+x^2-y=1$
$-y+x^2+x=1$
.
.
.

 

[Mark44]

If there is PEMDAS then all of the following equations are equivalent to each other?

$x^2+x-y=1$
$x+x^2-y=1$
$-y+x^2+x=1$.

Yes. The exponentiated term, $x^2$ has higher precedence than all of the other terms.

You could think of the first equation as being the same as $(x^2) + x + (-y) = 1$. Written this way, all of the terms on the left side could be shown in any order due to the commutative property of addition.

Taken one step further, you could write the equation as $(x^2) + x + (-y) + (-1) = 0$. Then all four terms on the left side could be written in any order, again due to commutativity of addition. Subtraction isn't commutative, which is why I've enclosed the 3rd and 4th terms with parentheses.