# Question:problem with digits

## Question:problem with digits

Maple

hi

i have written the followin code that achieve Y from determinant of matric aa. but when i change digit my result changes. i dont know why?

> restart;
> with(LinearAlgebra);
> Digits := 100;
>
> NULL;
> upsilon := .38;
> rho := 0.122e4;
> l := 0.176e-4;
> h := 2*0.176e-4;
> L := 20*h;
> NULL;
> E := 0.144e10;
> lambda := E*upsilon/((1+upsilon)*(1-2*upsilon));
> mu := E/(2*(1+upsilon));
> aa := 3*h^2*(1/8)-3*l^2;
> bb := 3*l^2*h^2*(1/32);
> ;
> d1 := int(x^2+x^6/aa^2+36*x^10/(25*h^4*aa^2)-2*x^4/aa+12*x^6/(5*h^2*aa)-12*x^8/(5*h^2*aa^2), x = -(1/2)*h .. (1/2)*h);
> d2 := int(x^6/aa^2+36*x^10/(25*h^4*aa^2)-12*x^8/(5*h^2*aa^2), x = -(1/2)*h .. (1/2)*h);
> d3 := int(2*x^6/aa^2+72*x^10/(25*h^4*aa^2)-2*x^4/aa+12*x^6/(5*h^2*aa)-24*x^8/(5*h^2*aa^2), x = -(1/2)*h .. (1/2)*h);
> d4 := int(1+9*x^4/aa^2+36*x^8/(h^4*aa^2)-6*x^2/aa+12*x^4/(h^2*aa)-36*x^6/(h^2*aa^2), x = -(1/2)*h .. (1/2)*h);
> d5 := int(9*x^4/aa^2+36*x^8/(h^4*aa^2)-36*x^6/(h^2*aa^2), x = -(1/2)*h .. (1/2)*h);
> d6 := int(18*x^4/aa^2+72*x^8/(h^4*aa^2)-6*x^2/aa+12*x^4/(h^2*aa)-72*x^6/(h^2*aa^2), x = -(1/2)*h .. (1/2)*h);
>
> e1 := int(1+9*x^4/aa^2+36*x^8/(h^4*aa^2)+6*x^2/aa-12*x^4/(h^2*aa)-36*x^6/(h^2*aa^2), x = -(1/2)*h .. (1/2)*h);
> e2 := int(-2+18*x^4/aa^2+72*x^8/(h^4*aa^2)-72*x^6/(h^2*aa^2), x = -(1/2)*h .. (1/2)*h);
> e3 := int(9*x^4/aa^2+36*x^8/(h^4*aa^2)-36*x^6/(h^2*aa^2), x = -(1/2)*h .. (1/2)*h);
> e4 := int(18*x^4/aa^2+72*x^8/(h^4*aa^2)-6*x^2/aa+12*x^4/(h^2*aa)-72*x^6/(h^2*aa^2), x = -(1/2)*h .. (1/2)*h);
> e5 := int(18*x^4/aa^2+72*x^8/(h^4*aa^2)+6*x^2/aa-12*x^4/(h^2*aa)-72*x^6/(h^2*aa^2), x = -(1/2)*h .. (1/2)*h);
> e6 := int(36*x^2/aa^2+576*x^6/(h^4*aa^2)-288*x^4/(h^2*aa^2), x = -(1/2)*h .. (1/2)*h);
> NULL;
> a2 := d1*(lambda+2*mu)+(1/4)*d4*mu*l^2;
> a3 := d4*mu+(1/4)*e6*mu*l^2;
> a4 := d2*(lambda+2*mu)+(1/4)*e1*mu*l^2;
> a5 := (1/16)*l^4*(d5*mu+(1/4)*e6*mu*l^2);
> a6 := (1/16)*l^4*(d2*(lambda+2*mu)+(1/4)*e3*mu*l^2);
> b1 := bb^2*(d5*mu+(1/4)*e6*mu*l^2);
> b2 := bb^2*(d2*(lambda+2*mu)+(1/4)*e3*mu*l^2);
> b3 := (1/2)*l^2*(d2*(lambda+2*mu)+(1/2)*e5*((1/4)*mu*l^2));
> b4 := 2*bb*(d2*(lambda+2*mu)+(1/2)*e5*((1/4)*mu*l^2));
> b5 := (1/2)*bb*l^2*(d2*(lambda+2*mu)+(1/4)*e3*mu*l^2);
> b6 := d3*(lambda+2*mu)+(1/4)*e2*mu*l^2;
> cc1 := (1/4)*l^2*(d3*(lambda+2*mu)+(1/4)*e4*mu*l^2);
> cc2 := bb*(d3*(lambda+2*mu)+(1/4)*e4*mu*l^2);
> cc3 := (1/2)*bb*l^2*(d5*mu+(1/4)*e6*mu*l^2);
> cc4 := (1/4)*l^2*(d6*mu+2*e6*((1/4)*mu*l^2));
> cc5 := bb*(d6*mu+2*e6*((1/4)*mu*l^2));
> NULL;
> A1 := (a5+b3)*L^2/a6;
> A2 := (a4+cc4)*L^4/a6;
> A3 := a3*L^6/a6;
> A4 := rho*h*L^8/a6;
> A5 := (2*a5+b3-cc1)*L^2/(2*a6);
> A6 := b6*L^4/(2*a6);
> A7 := b5/(2*L^2*a6);
> A8 := (b4+cc3)/(2*a6);
> A9 := cc5*L^2/(2*a6);
> A10 := (a5-cc1)*L^2/a6;
> B1 := (a2-cc4)*L^4/a6;
> B2 := rho*d1*L^6/a6;
> B3 := (cc2-cc3)/(2*a6);
> B4 := (b4+cc3)*L^2/b5;
> B5 := cc5*L^4/b5;
> B6 := (cc2-cc3)*L^2/b5;
> B7 := 2*b2/(b5*L^2);
> B8 := 2*b1/b5;
> B9 := (b6-cc4)*L^4/(2*a6);
> B10 := (2*a2-cc4)*L^4/(2*a6);
> D1 := (2*a4+cc4)*L^4/(2*a6);
> D2 := (b6+cc4)*L^4/(2*a6);
> D3 := (2*a5+b3)*L^2/(2*a6);
> D4 := cc4*L^4/(2*a6);
> D5 := (2*a5-cc1)*L^2/(2*a6);
> D6 := cc3/(2*a6);
> D7 := b3*L^2/(2*a6);
> D8 := cc1*L^2/(2*a6);
> D9 := b4*L^2/b5;
> D10 := cc2*L^2/b5;
> Omega := 8*10^5;
800000
> NULL;
>
> aa := Matrix(3, 3, [-Y^8+A1*Y^6-A2*Y^4+A3*Y^2+A4*Omega^2, Y^7-A5*Y^5-A6*Y^3+A3*Y, A7*Y^7-A8*Y^5+A9*Y^3, -Y^7+A5*Y^5+A6*Y^3-A3*Y, Y^6-A10*Y^4+B1*Y^2-A3+B2*Omega^2, A7*Y^6+B3*Y^4-A9*Y^2, -Y^7+B4*Y^5-B5*Y^3, Y^6+B6*Y^4-B5*Y^2, B7*Y^6-B8*Y^4]);
Matrix(%id = 535916424)
> AAA := Determinant(aa);
>
> coeff(AAA, Y^16);
-94
-3.26 10
> coeff(EE, Y^16);
0
> POL := coeff(AAA, Y^16)*Y^16+coeff(AAA, Y^14)*Y^14+coeff(AAA, Y^12)*Y^12+coeff(AAA, Y^10)*Y^10+coeff(AAA, Y^8)*Y^8+coeff(AAA, Y^6)*Y^6+coeff(AAA, Y^4)*Y^4;
-94  16         -90  14
-3.26 10    Y   + 2.2 10    Y   - 1.6932692886132379487382978558\

70594616908554207527470578374395699605255069930282353558740356\

12  12
529328811 10   Y   + 4.314235873871823273480238991580142208462\

16
760518108462892746208739463636177485717597324318965331145772 10

10
Y   - 2.160844052287723775234204263822719663047736167220237795\

20  8
233640576642884667743982721687540621624555583 10   Y  - 1.6328\

55104621727615705245302913870969773552283154063559592380481230\

20  6
905362290417814498764768888100 10   Y  + 9.4178216619352065916\

74567353162017149925606007039473071375367726289821485907466958\

22  4
858153808156883347 10   Y

> X1 := solve(POL, Y);

in above code x1 achieve 16 root. when i change digits from 10 to 100 , my real roots doesnt change but my complex root change.

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