Hi.

I am new to SMath.

Is there a new a easy way to solve 2 equations with 2 unknowns?
Like 3*a-4*b=24 and 5*a+2*b=-3 ?

I did this in MathCAD just to show what I think is an easy and fast way.


// Wuxen

Why not use linear algebra?

That is a good way! But I know that many high-school student don't really know linear algebra and that is why i asked
But thanks for the fast answer!

// Wuxen

Present it otherwise as you wish.

In the attached, in "So much from so little"
experiment 7.2 and 7.201 vs result !!!



Solve [x,y,z] Compactum.sm (62 KiB) downloaded 87 time(s).

I understand what you are saying, but the thing I am looking for is:

In Matlab I can also solve 2 eqs. with 2 unknowns without using linear alg.
in Matlab I can solve it with solve(3*a-4*b=24 AND 5*a+2*b=-3,[a b])

I hope you understand what I'm looking for - It is to solve it without using linear alg.

// Wuxen

You can use the built-in function roots()



Settings about roots' range are in Tools > Options > Calculation > Roots (range); you can also give an initial guess as third argument.

Wrote

I understand what you are saying, but the thing I am looking for is:

In Matlab I can also solve 2 eqs. with 2 unknowns without using linear alg.
in Matlab I can solve it with solve(3*a-4*b=24 AND 5*a 2*b=-3,[a b])

I hope you understand what I'm looking for - It is to solve it without using linear alg.

There are many ways to solve, about ½ dozen more. Where do you see "linear alg"
in my reply ? My typical answer is over 3 centuries old, coded universal in any
system handling maths. Mathcad, Matlab ... they just code the solving like Smath
coding 2*3 =6. If you would have a system 1000 variables/unknowns, you would use
"linsolve", doing the same but more efficiently for speed of computation.

Gauss elimination, Cramer are not efficient. Above a certain size, Cramer will
never end between all big blues of the world together, and you will be dead
sucking roots for centuries.

... consider productive solving:

Wrote

Hi Davide,
unfortunately, your sanity check isn't good, because the result f(a,b )=[0;0] says the opposite: it's the result of logical expressions "is 3*a-4*b equal to 24? No (0)!" and "is 5*a+2*b equal to -3? No (0)!"

The error is small though, less that 4*10^-14.

Hi. To handle this needs a complete set of instructions, and a new system variable:

$MaxExtraPrecision is used implicitly in various exact numerical computations, including equality tests, comparisons, and functions such as Round and Sign.


See Possible issues under https://reference.wolfram.com/language/ref/Equal.html

Best regards.

Alvaro.

Wrote

Wrote

Hi Davide,
unfortunately, your sanity check isn't good, because the result f(a,b )=[0;0] says the opposite: it's the result of logical expressions "is 3*a-4*b equal to 24? No (0)!" and "is 5*a+2*b equal to -3? No (0)!"

The error is small though, less that 4*10^-14.

Busted! Thank you Mike

(screenshot fixed)

NO Davide: not so much "busted". Even -3.00000000000004 is caused by
the machine ULP in the sanity reverse computation. Nothng to worry about.

Jean



Solve SANITY.sm (11 KiB) downloaded 58 time(s).

... naturally: Mathcad sanity check itself exactly,
not so exactly in Smath [molecular inexactitude !!!]