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How to enter and solve a series of equations?

How to enter and solve a series of equations?

Postby dbaechtel » Wed Nov 10, 2010 4:35 pm
How to enter and solve a series of equations?
How do I eneter more than one line?
How do I enter conditions?
dbaechtel
 
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Re: How to enter and solve a series of equations?

Postby briangilbert » Sat Nov 13, 2010 7:53 am
I assume you mean a series of dependent equations with numeric intermediate solutions.
1. The basic way is to put each immediately solvable equation in brackets:-
(4*2)
(5+9)
these will be solved first by W|A.
You link the solutions in your higher level equation so it becomes
(4+2)/(=5+9)
You can go up to higher levels in the same way.
You may find that W|A limits the length of the whole thing.

I will call this a 'complex' equation.
If you make a mistake inentering a very complex equation then it is hard to debug.
To get round this you can solve the lower level equations individually and build up till you meet the bug.
You can also save the intermediate results in numeric variables which W|A will show in the output. Do this as follows:-
x_1=4+2,x_2=5+9,x_1/x_2
(x_1 displays as xsubscript1)

2. The end of an input line has no significance as far as I know so you just input everything in a single string. I do not know the limit but W|A does sometimes just refuse to accept any more characters.
In a widget the end of the line wraps round automatically but it is still interpreted as a single string.

3. I don't think there is a way of entering conditions in the programming sense. I think you are expected to use an API (Application Programming Interface) for this, though I have not done so. You can use words to impose some conditions as in
'Population USA' as opposed to just 'Population' which gives you the World. In the output you will often see a red link saying 'assuming'. For instance it might say 'assuming inches' which allows you to alter the output to assume say 'centimetres'. You may asls be able with careful wording to say 'assuming centimeters' in your query. If you alter the initial assumptions while creating a widget they will be remembered when the widget is run.

Non-numeric steps are trickier. I have not been able to create a nonpnumeric variable yet.
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Re: How to enter and solve a series of equations?

Postby cajon » Wed Nov 17, 2010 11:29 pm
You can solve 2 equations with 2 unknowns by entering:
2x+y=4, x+y=3
This produces:
Solution:
x = 1, y = 2
along with a graph of the 2 lines showing the solution.

You may add a condition by adding ,x>0,y>0

Naturally, if you add a condition like x<0 for the above set of equations you will get the result "no solutions exist".

You can extend this to more equations with more unknowns using the same format.
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