Simplifying Large Algebraic Expressions to Neat Equations in Mathematica

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  • Thread starter confi999
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In summary, to simplify a large algebraic expression that equals zero, use either Simplify[expression] or FullSimplify[expression] in Mathematica or the symbolic package of Matlab. It is recommended to simplify the entire equation rather than just the expression on the left, and to include any necessary assumptions for accurate simplification.
  • #1
confi999
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0
If I want to simplify an extremely large algebraic expression which equals zero to a simple neat equation -- how do I do that in Mathematica (or symbolic package of Matlab). Giving you an example of the equation below:

(c1 (-1 + E^(I dx kx)) (-1 + v4))
--------------------------------------------------------
(-1 - 6 c1 c2 v1 + 6 c1 c2 v1 Cos[dx kx])

(c1 (-1 + E^(I dx kx)) (-1 + v4))
+ -------------------------------------------------------
(1 + 6 c1 c2 v1 - 6 c1 c2 v1 Cos[dx kx])

(4 c1 c2 (-1 + v4) (-1 + Cos[dx kx]))
- ----------------------------------------------------------- = 0
(-1 - 6 c1 c2 v1 + 6 c1 c2 v1 Cos[dx kx])


In fact my equation is much more larger than this. Thank you
 
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  • #2
If you wish to reduce and expression (in this case, just the left side of the equation) to a simpler form, use either

Simplify[expression]

or

FullSimplify[expression]


These use algorithms to try to reduce the given expression to the simplest terms. You can there after set it equal to zero.
 
  • #3
I would recommend to simplify the equation as a whole rather than just the expression on the left. If you simplify the expression then c1 will remain, but if you simplify the equation as a whole c1 will drop out. Also, be sure to provide any assumptions (such as c1>0, etc.) to Simplify or FullSimplify.
 
  • #4
DaleSpam said:
I would recommend to simplify the equation as a whole rather than just the expression on the left. If you simplify the expression then c1 will remain, but if you simplify the equation as a whole c1 will drop out. Also, be sure to provide any assumptions (such as c1>0, etc.) to Simplify or FullSimplify.

In mathematica FullSimplify[expression] is valid but is FullSimplify[expression=0] a valid expression or will it work as we expect (like what you explained). I tried but it didnot give any improvement... it simply showed the expression on left and zero on the right of the equal. Is there any special clue that I am missing.
 
  • #5
Use the logical equals instead of the set equal. I.e. FullSimplify[expression==0] Also, as I suggested earlier be sure to include any assumptions.
 

1. How do I perform basic arithmetic operations in Mathematica?

To perform basic arithmetic operations in Mathematica, you can use the following symbols: + for addition, - for subtraction, * for multiplication, / for division, and ^ for exponentiation. For example, to add two numbers, you can type 3 + 5 and press Enter. You can also use parentheses to specify the order of operations, such as (3 + 5) * 2 for multiplying the sum of 3 and 5 by 2.

2. How do I define and use variables in Mathematica?

To define a variable in Mathematica, you can use the = symbol. For example, to define x as 5, you can type x = 5 and press Enter. You can then use this variable in subsequent calculations. To view the value of a variable, you can simply type its name and press Enter. To clear a variable, you can use the Clear function, such as Clear[x].

3. How do I plot a function in Mathematica?

To plot a function in Mathematica, you can use the Plot function. For example, to plot the function y = x^2, you can type Plot[x^2, {x, 0, 5}] and press Enter. This will create a plot from x = 0 to x = 5. You can also customize the plot by adding labels, changing the color and style of the plot, and more.

4. How do I import and export data in Mathematica?

To import data into Mathematica, you can use the Import function. This function allows you to import data from various file formats such as CSV, Excel, and text files. To export data from Mathematica, you can use the Export function. This function allows you to save your data in various file formats as well. You can also use the ListPlot function to plot imported data.

5. How do I find and use built-in functions in Mathematica?

To find built-in functions in Mathematica, you can use the Documentation function. This will open the Wolfram Documentation Center, where you can search for specific functions and find information on how to use them. You can also use the ?function command to get a brief description of a specific function. To use a built-in function, you can simply type its name and input the required parameters.

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