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on mouseup
   // See for conformation and information: https://arachnoid.com/sage/polynomial.html
   put "-1,0,1,2,3,5,7,9" into InXCoordinates
   put "-1,3,2.5,5,4,2,5,4" into InYCoordinates
   put 4 into InDegrees
    ---- More test data
   --put "0,1,2,3,4,5,6,7,8,9,10" into InXCoordinates  // 4 test
   --put "1,6,17,34,57,86,121,162,209,262,321" into InYCoordinates  // 4 test
   --put 2 into InDegrees  / 4 test
   ------
   CalcPolynomialCoefficients InDegrees,InXCoordinates,InYCoordinates,OutPolCo
   ------
   breakpoint // See OutPolCo for the coefficients
end mouseup

command CalcPolynomialCoefficients InDegrees,InXCoordinates,InYCoordinates @OutPolCo
   // See for conformation and information: https://arachnoid.com/sage/polynomial.html
   --put "-1,0,1,2,3,5,7,9" into InXCoordinates // 4 test
   --put "-1,3,2.5,5,4,2,5,4" into InYCoordinates // 4 test
   -- put 4 into InDegrees // test
   // Higest Aray number in OutPolCo gives the coefficient for the higest degree of X in a equation like y= a*X4+b*X3+c*X2+d*X+e
   // In this case with the test numbers OutPolCo[5] is the coefficient for X4
   -----------------------------------------------------------------------------------
   put the number of items of InXCoordinates into tNumberOfXItems
   put the number of items of InYCoordinates into tNumberOfYItems
   if tNumberOfXItems <> tNumberOfYItems
   then
      answer "Amount of X and Y coordinates is not equal!"
      exit CalcPolynomialCoefficients
   end if
   if InDegrees > 7
   then
      answer "Max number of degrees is 7. Larger polynomial degrees risk exceeding the resolution of the variables in use !"
      exit CalcPolynomialCoefficients
   end if
   if tNumberOfXItems < InDegrees+1
   then
      answer "Need a minimum of  " & InDegrees+1 & " sets of x,y coordinates!"
      exit CalcPolynomialCoefficients
   end if
   ---- fill X matrix -----------------------------------------
   repeat with MVC = 1  to  InDegrees+1
      Repeat with MHC = 1  to  InDegrees+1
         if MVC=1 and MHC=1
         then
            put tNumberOfXItems into tSumXiP 
         else
            put MVC+MHC-2 into tPower
            repeat for each item tXi in InXCoordinates
               --
               put "put tXi^"&tPower&" into tXiP" into tScriptLine
               do tScriptLine
               --
               add tXiP to tSumXiP
            end repeat
         end if
         put tSumXiP into tXMatrix[MVC,MHC] 
         put 0 into tSumXiP
      end Repeat
   end repeat
   -- Fill Y Matrix (MVC stands for Matrix Vertical Column)----
   repeat with MVC = 1  to  InDegrees+1
      put 0 into tCounter
      repeat for each item tYi in InYCoordinates
         add 1 to tCounter
         if MVC=1
         then
            add tYi to tSumXiPYi
         else
            put MVC-1 into tPower
            put item tCounter of InXCoordinates into tXi
            --
            put "put tXi^"&tPower&" into tXiP" into tScriptLine
            do tScriptLine
            --
            add tXiP*tYi to tSumXiPYi
         end if
      end repeat
      put tSumXiPYi into tYMatrix[MVC]
      put 0 into tSumXiPYi
   end repeat
   -- Combine matrixes by adding Y matix as last column to X matrix 
   -- creates an augmented matrix
   repeat with MVC = 1  to  InDegrees+1
      put tYMatrix[MVC] into tXMatrix[MVC,InDegrees+2]
   end repeat
   ----------------------------------------
   // Gauss-Jordan elimination 
   put InDegrees+1 into tNbrRows 
   put InDegrees+2 into tNbrColumns 
   --
   repeat with tColumnNbr = 1  to  tNbrRows 
      repeat with tRowNbr = 1  to  tNbrRows 
         if tColumnNbr <> tRowNbr
         then
            put tXMatrix[tRowNbr,tColumnNbr]/tXMatrix[tColumnNbr,tColumnNbr] into tCNumber
            repeat with k =1 to tNbrColumns
               put tXMatrix[tRowNbr,k]-tCNumber*tXMatrix[tColumnNbr,k] into tXMatrix[tRowNbr,k]
            end repeat
         end if
      end repeat
   end repeat
   --
   repeat with tRowNbr = 1  to  tNbrRows
      put tXMatrix[tRowNbr,tNbrRows+1]/tXMatrix[tRowNbr,tRowNbr]into taSolution[tRowNbr]
   end repeat
   ------------------------------------------
   put taSolution into OutPolCo
end CalcPolynomialCoefficients