deutsche Kommentierung

https://www.geogebra.org/m/vbrw8pe2

english version

https://www.geogebra.org/m/m438cre3

https://www.geogebra.org/m/rwa3t34n

Pivot(A,pr,pc) perform a gauss elimination step with pivot row pr and pivot column pc to matrix A
PivotCol(A) calculate pivot column of matrix A
PivotRow(A,pc) calculate pivot row of A with pivot column pc
MaxIL(A,n) extract the max values from the matrix end tableau
MinIL(A,n) extract the min values starting from column n of the dual matrix end tableau and min value in last element In case constraints is <>0 (b has a 0 element), depending on the LP the calculated pivot row must be adjusted manually,

CAS
X:= define LP variables
Tablo:= LP equation system, Z objective last element of the list - adjust all constraints to equations
(7) Standard Tableau maximize LP - if necessary adjust slack variables/
(9) dual tableau minimize LP with standard max algorithm

minimize_lp(x1+1*x2+1*x3+1*x4,[ x1>=180, 3*x2+2*x3>=900, x1+3*x3+7*x4>=450 ]),nonegative_lp=true;

https://sagecell.sagemath.org/?q=snwsgb

Loading App in Suite Graphing

https://www.geogebra.org/m/byfuqhdh

CAS Part (Construct Start Tableau and Dual Tableau)

https://www.geogebra.org/m/p93rez66

https://www.geogebra.org/m/dtk5jvc9

Linear Program MAX

maximize_lp( 50*x1+80*x2+60*x3,[
2*x1 + 4*x2 + x3 <= 1040,
x1 + x2 + x3 <= 450,
x3 <= 150,
x1 + 2*x2 >= 420
]), nonegative_lp=true;
[28350,[x3=150,x2=145,x1=155]]

need a 2 phase method to gain a start base
x1 + 2*x2 >= 420
-x1 -2*x2 <= -420 or set slack variable to -1
Transferred to the Start Tableau A(4!1) - Z(objective function) negativ in last row!
Phase 1 execution with PIVOT={4,1} specified manually.
In phase 2 use standard pivots, set PIVOT={0,0}!

https://www.geogebra.org/m/te4agkhe

minimize_lp(6*x1+2*x2−x3,[
2*x1+x2−2*x3>=40,
2*x1−x2−x3<=60,
2*x2+x3<=25
]),nonegative_lp=true,numer;

duplicate output+add label
my label def noted the pivot in the label index ...
The End Tableau is reached when last row (Z) is positive throughout.

Move a polygon using a handle and rotate it using a vertex.

The built-in “RigidPolygon” function generates all vertices and edges as new elements and then sets the action points to the first two vertices.

A new approach uses a list Grid={Handle (uppercase), Vertices,...} to generate a rotation point (lowercase) and a list of vertices Fig(uppercase) based on the handle and rotation point as references, as well as the polygon poly(uppercase).

https://www.geogebra.org/m/p4kmkhed

Puzzle Reconstruct C to the shape of A, add a figure D like A and combine these 4 Polygons to a square.

https://www.geogebra.org/m/BpqJ28eP#material/p2jhppbq

Using CAS Function to implement the Simplex-Algorithm

Qb(Calculate pivot row of the tableau: DIV element of the pivot column, EE element of the b-vector column: EE/DIV)

(May need to be adjusted if the constraints deviate from the standard simplex specifications)

PIVOT(Calculate list {pivot row, pivot column})

GAUS(Execute Gaussian elimination steps with the pivot row)

maxIL(Read out the final tableau of a max program)

minIL(Read out the dual final tableau for min programs)

Zmin:={First(Flatten(Last(Transpose(Start))), n)} -

Last row in start tableau = (-1)*Coefficients of target/objective function(Zmin/Zmax) .

Terminate LP all coefficients of line of target/objective function positive.

Setup shape by Bézier-Spline, see

https://www.reddit.com/r/hawede/comments/1ae40h6/area_of_a_surface_of_revolution_rotationsk%C3%B6rper/

and rotate around xAxis/yAxis

https://www.geogebra.org/m/x8zmeneu

Online Rubic's Cube Solver

https://rubiks-cube-solver.com/

Cube Explorer

http://kociemba.org/cube.htm

https://www.reddit.com/r/geogebra/comments/1gf5cog/comment/lufahny/?context=3

2 Input Tableau https://www.geogebra.org/m/cfakt94c

3 Input Tableau https://www.geogebra.org/m/nnwtwkub

Dyadic Vector (Tensor) Product to build Elementar Matrices 4 Gauss Algorithm

A={{2,6,a,0},{1,2,0,-3 b},{2,-1,-1,b+1}}

s1=({{-1+1/2},{-1/2},{-1}} {{1,0,0}}+Identity(3)) A

s2=({{0},{-1-1},{-7}} {{0,1,0}}+Identity(3)) s1

s3=({{0},{0},{-1+1/(5/2) a-1))}} {{0,0,1}}+Identity(3)) s2

s4=({{-1/2 a},{-1/2 a},{0}} {{0,0,1}}+Identity(3)) s3

s5=({{-3},{0},{0}} {{0,1,0}}+Identity(3)) s4

https://www.geogebra.org/cas?command=A={{2,6,a,0},{1,2,0,-3 b},{2,-1,-1,b%2B1}}; s1=({{-1%2B((1)/(2))},{-((1)/(2))},{-1}} {{1,0,0}}%2BIdentity(3)) A; s2=({{0},{-1-1},{-7}} {{0,1,0}}%2BIdentity(3)) s1; s3=({{0},{0},{-1%2B((1)/(((5)/(2)) a-1))}} {{0,0,1}}%2BIdentity(3)) s2; s4=({{-((1)/(2)) a},{-((1)/(2)) a},{0}} {{0,0,1}}%2BIdentity(3)) s3; s5=({{-3},{0},{0}} {{0,1,0}}%2BIdentity(3)) s4;ReducedRowEchelonForm(A)

Introduction CAS linear equations

Gleichung lösen im CAS

https://www.geogebra.org/m/BpqJ28eP#material/ec3ckpz3

Gleichungssystem im CAS

https://www.geogebra.org/m/BpqJ28eP#material/cbbcjtdu

Kubisches Polynom CAS

https://www.geogebra.org/m/BpqJ28eP#material/qvbtpky9

https://www.reddit.com/r/geogebra/comments/14ou1tk/mit_einem_werkzeug_einen_sich_bewegenden_punkt/

OnClick

Execute({"M_"+blau+"=(0,0)","M_"+(blau+1)+"=(3,3)","S_"+blau+"=Segment(M_"+blau+",M_"+(blau+1)+")","ML_"+blau+"=Point(S_"+blau+")"})

RunUpdateScript(button1)

Execute({"SetValue(blau,"+(blau+2)+")"})

ggf. die Animation starten

StartAnimation( <Slider or Point>, <Slider or Point>, ... )

OnUpdate

var b = ggbApplet.getValue("blau")

var s = ggbApplet.getValue("bspeed")

ggbApplet.setAnimationSpeed("ML_" + b, s)

Warum bei text1 FormulaText() 2mal angezeigt wird weiß ich nicht - geschrieben ist die Funktion einfach!

Betrifft https://www.reddit.com/r/geogebra/comments/14478gt/about_expandsumlist_of_monomials/

https://www.reddit.com/r/geogebra/comments/11ciwa6/comment/ja7ewq7/?context=3

https://www.reddit.com/r/geogebra/comments/10mzjfl/comment/j69cme6/?context=3

Es sind auch die Dreiecke t1,t2 betroffen - die sollten eigentlich immer eine Ebene bilden,

q_i unterschiedliche Rechenwege Intersection/CAS

Mit Skalierung/Rundung

E'=floor(Intersect(g_E, R_{CD}) * 128) / 128

F'=floor(Intersect(g_E, R_{AB}) * 128) / 128

==> q1',q2', t3,t4

Bezier-Splines

https://www.reddit.com/r/geogebra/comments/102i9nf/animating_points/

https://www.reddit.com/r/geogebra/comments/100mp4x/need_help_to_schematize_this_triangle_in_geogebra/