# Question:power as fraction, Maple

## Question:power as fraction, Maple

Maple 2019

I defined the following function L1 and L2 to test, if  Maple is returning the same results. Mathematically they are identical. For all testpoints, L1 returns the correct results (for y := -5 the result is -15).  L2  returns identical results exept for y:=-5. For y:= -5, where you can see on the first glance that the result must be -15,  Maple is returning for L2 a complex number. I am worried about this different treatment of the functions L1 and L2, because I am calculating with functions, where you cannot prove the result as easy as it can be done here.

L1 := y -> 3*y*((y + 4)^2)^(1/3);
L1 := proc (y) options operator, arrow, function_assign;

3*y*((y+4)^2)^(1/3) end proc

L2 := y -> 3*y*(y + 4)^(2/3);
L2 := proc (y) options operator, arrow, function_assign;

3*y*(y+4)^(2/3) end proc
NULL;
for y from -5 to 0 do
print("y = ", y, "L1(y)   =  ", L1(1.0*y), "          L2(y)  =,  ", L2(1.0*y));
end do;
"y =  ", -5, "L1(y)   =  ", -15.0, "          L2(y)  =,  ",     7.500000000 - 12.99038105 I
"y =  ", -4, "L1(y)   =  ", -0., "          L2(y)  =,  ", -0.
"y =  ", -3, "L1(y)   =  ", -9.0, "          L2(y)  =,  ", -9.0
"y =  ", -2, "L1(y)   =  ", -9.524406312,              "          L2(y)  =,  ", -9.524406312
"y =  ", -1, "L1(y)   =  ", -6.240251469,              "          L2(y)  =,  ", -6.240251469
"y =  ", 0, "L1(y)   =  ", 0., "          L2(y)  =,  ", 0.

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