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Algebraic Solution - Mathematica vs Algebrator

Posted 11 years ago
Way back when I purchased Mathematica in the hopes that it would help me decipher Algebra.

It didn't work.

It boiled down to not understanding the explanation or not knowing enough to adequately enter or
interpret the answer.

Now, I have a raspberry Pi for which Wolfram has been kind enough to make available - Mathematica.

So, mathematical incompetent that I am, all these years later, I figure I'll give the same goal a go.

As an example, I figured, reducing polynomials (or factoring, or solving) - see, all these years later,
I still can't tell you what a polynomial is, or, if it IS defined somewhere, that definition makes little sense to
me.  I can look at this example:

and understand how it works, why it works

but, of the examples I've seen in Mathematica, I'm not sure how to arrive at the same point / place
in mathematica.


a^4b^6-x^8 / a^2b^3+x^4

the same thing as presented at the link above?

If so, to arrive at a comparable solution as in the link above, would that be:

NSolve, Solve, Factor, Reduce (or something else)?

I've tried NSolve, Solve, and Reduce and if any of those is "correct", they don't
look or behave (at least to my eye) anything like the process in the link.

Am I just ignorant (a given here) and not adequately understanding the answer,
or, am I doing something wrong and should be using a different method or process
to arrive at the same answer OR is it just not possible because of what Mathematica
is designed to do and how it does it?

by comparison,

I tried:

Solve[2x+y = 13,x]

and that answer made perfect sense to me.

To say that mathematics is not my strong suit is a gross understatement here.

Please factor that into your answer.

POSTED BY: Mike Moore
5 Replies
Thanx guys.

I used the "Calculator" section to enter the data.

Funny, if I just enter:

a^4 b^6 - x^8 (over) - I used the box line to get the standard format
a^2 b^3 + x^4

Shift Enter gives me:

a^4 b^6 - x^8 (over)
a^2 b^3 + x^4

If I factor it down to the next level as shown at the link:

(a^2b^3+x^4)(a^2b^3-x^4) (over)

it factors down properly, eliminating


leaving me with:


So why doesn't it reach the same solution with the previous entry?

Also, I tried rearranging the variables to see what would happen:

(y^3z^2-a^5)(y^3z^2+z^5) - (over)

I was expecting:


and got instead:


Equally correct, but, rearranged.

So, it would seem, either there's something I don't understand about
math or something I need to understand about Mathematica either in how
it treats variables or how it treats variables by default.

I'm not sure there's a difference (other than order), I wouldn't think in outcome  between:




but, as I said, mathematics isn't my strong suit.

I tried both methods suggested.

I also found this tutorial to be of GREAT help in this regard:
POSTED BY: Mike Moore
I tried:
Solve[2x+y = 13,x]
and that answer made perfect sense to me.

Did you copy that from Mathematica as is?  Using Mathematica 9.01 on windows 7, I get the error
Set::write: Tag Plus in 2 x+y is Protected. >>
Solve::naqs: 13 is not a quantified system of equations and inequalities. >>
or may be it is this editor that did this? It should be "==" and not "=" in there.  "==" is for equations, "=" is for assignment.
POSTED BY: Nasser M. Abbasi
I used Mathematica 10 on the Raspberry Pi.

I based it on this tutorial:


Click on the [+] - (left hand side)

Freeform Input


Solve[2x+y =13,x]

That gave me the answer:

x = 13-y / 2

POSTED BY: Mike Moore
If you're switching between algebra books and Mathematica a lot, it might also be useful to know about TraditionalForm:
a^4 b^6 - x^8/a^2 b^3 + x^4 // TraditionalForm

and you can see that your algebraic input has been interpreted according to the rules of (BODMAS? BEDMAS? PEMDAS? BEDMAS?  BIDMAS?)  - the things Bill's talking about in his reply - rather than according to the ideas which you had in your head. emoticon
POSTED BY: C ormullion
Posted 11 years ago
You wrote: "Is: a^4b^6-x^8 / a^2b^3+x^4 the same thing as presented at the link above?"

Nope, not unless you have clicked on Palettes on the menu bar at the top and then clicked on Basic Math Assistant and then looked down towards the bottom of that huge popup window with a hundred different buttons.

One of those buttons has a tiny black square above a little horizontal line above a little empty square. If you have an empty notebook page open while you click on that little button then that will give you a fraction where you can click on either the top or bottom box and enter things to try to make them look like the Algebrator page. You can use some of those buttons to get exponents placed up above numbers or variables,

You can try experimenting with that and see if it makes enough sense.

If you don't use that then you fall back on the torment of beginning algebra students where () come before exponents come before multiplication and division come before addition and subtraction.

I hope this might have given you a little bit of help
POSTED BY: Bill Simpson
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