how to override plus + operator so that apply on matrix operation such as linearalgebra package

for example if + =  a^2+b^2

1 + 2 result in 5

and also apply on matrix multiplcation for each element

sign is different runnning the same script in maple 12 and maple 15 in different machine, just using matrixmultiply and matrix(xxx, shape=hermitian)

assume my window 7 infected by virus, can maple prevent virus change

its accuracy?

or

is there any change between maple 12 and maple 15? 

i feel that i will have to make large effort in order to find reason such as reinstall maple 12.

window 7 maple 15

[[a = 3.720799777 10 , b = -3.720817167 10 ]], 0.3469023622
[(-0.737729376724384 + 0. I) ((-0.737729376724384100 + 0. I) a

+ (-0.738311510115612690 + 0. I) b) + (-0.590656319609631

- 0. I) ((-0.590656319609630831 + 0. I) a

+ (-0.589459378339369122 + 0. I) b) + (0.326925800179577

- 0. I) ((0.326925800179577230 + 0. I) a

+ (0.327770888454982090 + 0. I) b) = -0.736196608749071 + 0. I,

(-0.590656319609631 + 0. I) ((-0.591008582207233624 + 0. I) a

+ (-0.589459378339369010 + 0. I) b) + (0.331003458223746

+ 0. I) ((0.331003458223746439 + 0. I) a

+ (0.327770888454981812 + 0. I) b) + (-0.735625969091165

- 0. I) ((-0.735625969091165288 + 0. I) a

+ (-0.738311510115613134 + 0. I) b) = 0.327869065042947 + 0. I

]

window 8 maple 12

[[a = 0.2249293777, b = 1.221244758]], 0.9888653482, "************"
[(0.737729376724384100 + 0. I) ((0.737729376724384100 + 0. I) a

+ (-0.738311510115612690 + 0. I) b) + (0.590656319609631053 - 0. I)

((0.590656319609631053 + 0. I) a + (-0.589459378339369122 + 0. I) b) +

(0.326925800179576676 - 0. I) ((0.326925800179576676 + 0. I) a

+ (0.327770888454982090 + 0. I) b) = -0.736196608749071002 + 0. I,

(0.590656319609631053 + 0. I) ((0.591008582207233624 + 0. I) a

+ (-0.589459378339369010 + 0. I) b) + (-0.331003458223746605 + 0. I) ((
-0.331003458223746605 + 0. I) a + (0.327770888454981812 + 0. I) b) + (
-0.735625969091165178 - 0. I) ((-0.735625969091165178 + 0. I) a

+ (-0.738311510115613134 + 0. I) b) = 0.327869065042946218 + 0. I]
7

1. how to do optimization with partial differential equation as constraints in maple

2. how to do optimization with  partial differential equation as objective function in order to make output obey this model

 support type error when plot, and moreover how to animate this plot

restart;
with(ExcelTools):
with(ListTools):
with(DynamicSystems):
filename := "0257.HK";
open3 := Import(cat(cat("C://Temp//HK//Bank//",filename),".xls"), filename, "B2:B100");
high3 := Import(cat(cat("C://Temp//HK//Bank//",filename),".xls"), filename, "C2:C100");
low3 := Import(cat(cat("C://Temp//HK//Bank//",filename),".xls"), filename, "D2:D100");
close3 := Import(cat(cat("C://Temp//HK//Bank//",filename),".xls"), filename, "E2:E100");
with(CurveFitting):
n := 31;
f := Vector(n);
f2 := Vector(n);
open2 := Vector(n);high2 := Vector(n);gain2 := Vector(n);algebra2 := Vector(n);creative2 := Vector(n);creative3 := Vector(n);
upper2 := Vector(n);lower2 := Vector(n);upperloweratio := Vector(n);
deltaopen2 := Vector(n); deltahigh2 := Vector(n); deltalow2 := Vector(n); deltaclose2 := Vector(n);
logn := Vector(n);
for i from 0 to n-4 do
open2[i+1] := PolynomialInterpolation([[0,open3[n-i][1]],[1,open3[n-(i+1)][1]],[2,open3[n-(i+2)][1]],[4,open3[n-(i+3)][1]]],t):
high2[i+1] := PolynomialInterpolation([[0,high3[n-i][1]],[1,high3[n-(i+1)][1]],[2,high3[n-(i+2)][1]],[4,high3[n-(i+3)][1]]],t):
low2[i+1] := PolynomialInterpolation([[0,low3[n-i][1]],[1,low3[n-(i+1)][1]],[2,low3[n-(i+2)][1]],[4,low3[n-(i+3)][1]]],t):
if (close3[i+1][1]/close3[i+2][1]-1) < 0 then
gain2[i+1] := -1*round(100*abs(close3[i+1][1]/close3[i+2][1]-1)):
else
gain2[i+1] := round(abs(100*(close3[i+1][1]/close3[i+2][1]-1))):
end if;
od;
n := 31;
newclose := Vector(n);
for j from 0 to n-4 do
for i from 0 to n-4 do
x1 := close3[i+1];
y1 := close3[i+1];
newclose[i+1] := subs(y=y1, subs(x=x1, (1/2)*(-y+sqrt(-3*y^2-4*y*x))/y))
od;
close3 := newclose;
plot(close3(x), x=1..31);
od;

which theory can explain the interaction of composition of group for combination of composition of group

if succeed to search a list of groups, what is the next step research them?