Solving algebraic equation programs

I have six parametric equations using 18 (not actually 26) different variables, 6 of which are unknown.

I could sit down a couple of packs of paper and find out what the equations are for each of the unknowns, but is there a simple software solution (I think in Matlab) that spits out six equations I'm looking for?

EDIT: It's a shame that it was closed, but I think I understand why. If anyone is still interested, the equations (I think) are non-linear:

r11^2 = (l_x1*s_x + m_x)^2 + (l_y1*s_y + m_y)^2
r12^2 = (l_x2*s_x + m_x)^2 + (l_y2*s_y + m_y)^2
r13^2 = (l_x3*s_x + m_x)^2 + (l_y3*s_y + m_y)^2
r21^2 = (l_x1*s_x + m_x - t_x)^2 + (l_y1*s_y + m_y - t_y)^2
r22^2 = (l_x2*s_x + m_x - t_x)^2 + (l_y2*s_y + m_y - t_y)^2
r23^2 = (l_x3*s_x + m_x - t_x)^2 + (l_y3*s_y + m_y - t_y)^2

( rS squared , good place @gnovice!)

Where do I need to find t_x t_y m_x m_y s_xands_y

Why am I calculating them? There are two points p1 (AT 0,0) AT and p2 ( t_x,t_y), for each of the three coordinates ( l_x,l_y{1,2,3}) I know the distances ( r1and r2) to the point of p1 and p2, but in a different coordinate system. Variable s_xand s_ydetermine how much I need to scale one set of coordinates to get to the other, and m_x, m_yas I need to be translated (using t_xand t_y- the method of accounting rotation differences between the two systems)

ABOUT! And I forgot to mention, I also know that point ( l_x,l_y) is lower than the highest of p1 and p2, i.e. l_y<max ( 0, t_y), as well as l_y> 0 and l_y< t_y.

It seems concrete enough that I might just have to pull out my pad and do it mathematically!

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Symbolic Toolbox, SOLVE. :

>> solve('x^2 + y^2 = z^2','z')    %# Solve for the symbolic variable z

ans =

  (x^2 + y^2)^(1/2)
 -(x^2 + y^2)^(1/2)

N N . , 2 (x y) 6 (a f):

>> S = solve('a*x + b*y = c','d*x - e*y = f','x','y')
>> S.x

ans =

(b*f + c*e)/(a*e + b*d)

>> S.y

ans =

-(a*f - c*d)/(a*e + b*d)
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? , 6x6, , ...

, .

, , , , - , , . , , , , , , , , , ( , , ), .

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( , ) - , , 6 , , :

6x + 12y = 9
7x - 8y = 14

:

|6  12| |a|   |9 |
|7  -8| |b| = |14|

( 2 ). Matlab (a, b).

Matlab, , : -)

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, , . ( , LU ( )).

, , . , Matlab () . , , - , , . , .

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Decades ago, MIT developed MACSYMA, a system of symbolic algebra for this kind of thing. MIT sold MACSYMA Symbolics, which is well-built, dried and deflated. However, due to the miracle of military funding, an early version of MACSYMA was due to be released to the government. This version was subsequently released under the GPL and continues to be supported under the name MAXIMA.

See http://maxima.sourceforge.net/ for more details .

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source

Source: https://habr.com/ru/post/1725410/


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