# Question:calling proc gives a different answer the second time.

## Question:calling proc gives a different answer the second time.

Maple 2023

Would Any one be able to give some explanation as to why calling a proc, which does not change anything globally but only acts on the input given, returns different answer the second time it is called with the same exact input? I am not able to understand this result at all.

Maple 2023.2 on windows 10.

 > restart;

 > W:=Matrix(3, 3, [[x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*cos(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x)),-x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*sin(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x)),x^(-1/6*(44+12*69^(1/2))^(1/3)+10/3/(44+12*69^(1/2))^(1/3)+2/3)],[x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)/x*cos(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))-1/2*x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))/x*sin(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x)),-x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)/x*sin(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))-1/2*x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))/x*cos(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x)),x^(-1/6*(44+12*69^(1/2))^(1/3)+10/3/(44+12*69^(1/2))^(1/3)+2/3)*(-1/6*(44+12*69^(1/2))^(1/3)+10/3/(44+12*69^(1/2))^(1/3)+2/3)/x],[x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)^2/x^2*cos(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))-x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)/x^2*cos(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))-x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)/x^2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*sin(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))+1/2*x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))/x^2*sin(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))-3/4*x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))^2/x^2*cos(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x)),-x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)^2/x^2*sin(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))+x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)/x^2*sin(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))-x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)/x^2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*cos(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))+1/2*x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))/x^2*cos(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x))+3/4*x^(1/12*(44+12*69^(1/2))^(1/3)-5/3/(44+12*69^(1/2))^(1/3)+2/3)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))^2/x^2*sin(1/2*3^(1/2)*(-1/6*(44+12*69^(1/2))^(1/3)-10/3/(44+12*69^(1/2))^(1/3))*ln(x)),x^(-1/6*(44+12*69^(1/2))^(1/3)+10/3/(44+12*69^(1/2))^(1/3)+2/3)*(-1/6*(44+12*69^(1/2))^(1/3)+10/3/(44+12*69^(1/2))^(1/3)+2/3)^2/x^2-x^(-1/6*(44+12*69^(1/2))^(1/3)+10/3/(44+12*69^(1/2))^(1/3)+2/3)*(-1/6*(44+12*69^(1/2))^(1/3)+10/3/(44+12*69^(1/2))^(1/3)+2/3)/x^2]]):
 > foo:=proc(W::Matrix,x::symbol)    local W1:=W,W_det,W1_det;    local F:=2*x^3-ln(x):    W_det := LinearAlgebra:-Determinant(W);    #change the first column    W1[1..3,1] := Vector['column']([0,0,F/x^3]):    W1_det := simplify(LinearAlgebra:-Determinant(W1)):    simplify(W1_det/W_det); end proc:
 > foo(W,x);

 > foo(W,x)

 >