Actual Mathomatic output from the linear script
Mathomatic version 15.1.4 (www.mathomatic.org)
Copyright (C) 1987-2010 George Gesslein II.
100 equation spaces available, 1920 kilobytes per equation space.
HTML color mode enabled; disable with the -c option or "set no color".
1—> ; Combine 3 simultaneous linear equations with 3 unknowns (x, y, z).
1—> ; Solve for all 3 unknowns using the eliminate, solve, and simplify commands.
1—>
1—> clear all ; restart Mathomatic
1—> ; enter all 3 equations:
1—> d1=a1*x+b1*y+c1*z
#1: d1 = (a1·x) + (b1·y) + (c1·z)
1—> d2=a2*x+b2*y+c2*z
#2: d2 = (a2·x) + (b2·y) + (c2·z)
2—> d3=a3*x+b3*y+c3*z
#3: d3 = (a3·x) + (b3·y) + (c3·z)
3—> 2 ; select equation number 2 as the current equation
#2: d2 = (a2·x) + (b2·y) + (c2·z)
2—> eliminate x ; eliminate variable x from the current equation
Solving equation #1 for (x) and substituting into the current equation...
a2·((b1·y) + (c1·z) − d1)
#2: d2 = (b2·y) − ------------------------- + (c2·z)
a1
2—> 3 ; select equation number 3
#3: d3 = (a3·x) + (b3·y) + (c3·z)
3—> eliminate x y ; eliminate variables x and then y from the current equation
Substituting the RHS of equation #1 into the current equation for variable (x)...
Solving equation #2 for (y) and substituting into the current equation...
b1·((z·((c2·a1) − (a2·c1))) + (a2·d1) − (d2·a1))
a3·(------------------------------------------------ + (c1·z) − d1)
b3·((z·((c2·a1) − (a2·c1))) + (a2·d1) − (d2·a1)) ((a2·b1) − (b2·a1))
#3: d3 = ------------------------------------------------ − ------------------------------------------------------------------- + (c3·z)
((a2·b1) − (b2·a1)) a1
3—> z ; solve and find z
((d3·((a2·b1) − (a1·b2))) + (b3·((d2·a1) − (a2·d1))) + (a3·((b2·d1) − (b1·d2))))
#3: z = --------------------------------------------------------------------------------
((b3·((c2·a1) − (a2·c1))) + (a3·((b2·c1) − (b1·c2))) + (c3·((a2·b1) − (a1·b2))))
3—> 2 ; select equation number 2
((z·((c2·a1) − (a2·c1))) + (a2·d1) − (d2·a1))
#2: y = ---------------------------------------------
((a2·b1) − (b2·a1))
2—> eliminate z using 3 ; find y by combining equation numbers 2 and 3
Substituting the RHS of equation #3 into the current equation for variable (z)...
((d3·((a2·b1) − (a1·b2))) + (b3·((d2·a1) − (a2·d1))) + (a3·((b2·d1) − (b1·d2))))·((c2·a1) − (a2·c1))
(---------------------------------------------------------------------------------------------------- + (a2·d1) − (d2·a1))
((b3·((c2·a1) − (a2·c1))) + (a3·((b2·c1) − (b1·c2))) + (c3·((a2·b1) − (a1·b2))))
#2: y = --------------------------------------------------------------------------------------------------------------------------
((a2·b1) − (b2·a1))
2—> simplify
((a1·((d3·c2) − (d2·c3))) + (d1·((a2·c3) − (c2·a3))) + (c1·((d2·a3) − (d3·a2))))
#2: y = --------------------------------------------------------------------------------
((a1·((b3·c2) − (c3·b2))) + (c1·((a3·b2) − (b3·a2))) + (b1·((c3·a2) − (a3·c2))))
2—> 1 ; select equation number 1
-((b1·y) + (c1·z) − d1)
#1: x = -----------------------
a1
1—> eliminate z using 3 y using 2; find x
Substituting the RHS of equation #3 into the current equation for variable (z)...
Substituting the RHS of equation #2 into the current equation for variable (y)...
b1·((a1·((d3·c2) − (d2·c3))) + (d1·((a2·c3) − (c2·a3))) + (c1·((d2·a3) − (d3·a2)))) c1·((d3·((a2·b1) − (a1·b2))) + (b3·((d2·a1) − (a2·d1))) + (a3·((b2·d1) − (b1·d2))))
-(----------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------- − d1)
((a1·((b3·c2) − (c3·b2))) + (c1·((a3·b2) − (b3·a2))) + (b1·((c3·a2) − (a3·c2)))) ((b3·((c2·a1) − (a2·c1))) + (a3·((b2·c1) − (b1·c2))) + (c3·((a2·b1) − (a1·b2))))
#1: x = ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
a1
1—>
1—> simplify all ; simplify and list all solutions
((c1·((b2·d3) − (b3·d2))) + (b1·((c3·d2) − (c2·d3))) + (d1·((b3·c2) − (c3·b2))))
#1: x = --------------------------------------------------------------------------------
((a1·((b3·c2) − (c3·b2))) + (c1·((a3·b2) − (b3·a2))) + (b1·((c3·a2) − (a3·c2))))
((a1·((d3·c2) − (d2·c3))) + (d1·((a2·c3) − (c2·a3))) + (c1·((d2·a3) − (d3·a2))))
#2: y = --------------------------------------------------------------------------------
((a1·((b3·c2) − (c3·b2))) + (c1·((a3·b2) − (b3·a2))) + (b1·((c3·a2) − (a3·c2))))
((b1·((d3·a2) − (a3·d2))) + (a1·((b3·d2) − (d3·b2))) + (d1·((a3·b2) − (b3·a2))))
#3: z = --------------------------------------------------------------------------------
((a1·((b3·c2) − (c3·b2))) + (c1·((a3·b2) − (b3·a2))) + (b1·((c3·a2) − (a3·c2))))
Finished reading file "linear.in".
1—>
End of input.
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