Question

在mathematica中如何实现简单的公式推导？急求，谢谢！

matlab中如下公式推导程序在mathematica中如何编程实现？
matlab中的程序如下：
1. gradationEi
function[Ei]=gradationEi(d,c1)
syms s
EM=24.83855;
nM=54.14688;
EV=2.44846;
nV=442.4779;
E0=(EM*nM*(EV+nV*s)*s)/(EM*EV+(nM*EV+EM*(nM+nV))*s+nM*nV*s.^2);
v0=0.4;
K0=E0/(3*(1-2*v0/s));
u0=E0/(2*(1+v0/s));
E1=40000;
v1=0.2;
K1=E1/(3*(1-2*v1)*s);
u1=E1/(2*(1+v1)*s);
p0m=K0/(3*K0+4*u0);
q0=3*(K0+2*u0)/(5*(3*K0+4*u0));
a=0.001;
q0m=q0+12*a*u0*q0*(1-2*q0)/(5*d);
K=K0+(c1*K0*(K1-K0))/(K0+3*p0m*(1-c1)*(K1-K0));
u=u0+(c1*u0*(5*d*(u1-u0)-12*a*u0*u1))/(5*d*u0+10*d*q0m*(1-c1)*(u1-u0)+12*c1*a*u0*u1);
E=9*K*u/(3*K+u);
Ei=simplify(E)

2. gradationE
dg=0.001*[16 13.2 9.5 4.75 2.36];
c1g=[0 0.020467 0.224982 0.28574 0.065297];
for j=1:5
Eg(j)=gradationEi(dg(j),c1g(j));
end
syms s
P1=1;
P2=0.975;
P3=0.70;
P4=0.35;
P5=0.275;
Egg = 0.5*((Eg(1)+Eg(2))*(P1-P2)+(Eg(2)+Eg(3))*(P2-P3)+(Eg(3)+Eg(4))*(P3-P4)+(Eg(4)+Eg(5))*(P4-P5))
急求，十分感谢！

• 你的回答被采纳后将获得：
• 系统奖励15（财富值+成长值）+难题奖励10（财富值+成长值）+提问者悬赏10（财富值+成长值）

Answer 1

(*公式推导程序在mathematica中的程序如下：1. *) gradationEi[d_, c1_] := Module[{EM = 24.83855, nM = 54.14688, EV = 2.44846,
nV = 442.4779, s, E0, v0 = 0.4, K0, u0, E1 = 40000, v1 = 0.2, K1,
u1, p0m, q0, a = 0.001, q0m, K, u(*,E2*)},
E0 = (EM*nM*(EV + nV*s)*s)/(EM*EV + (nM*EV + EM*(nM + nV))*s + nM*nV*s^2);
K0 = E0/(3*(1 - 2*v0/s));
u0 = E0/(2*(1 + v0/s));
K1 = E1/(3*(1 - 2*v1)*s);
u1 = E1/(2*(1 + v1)*s);
p0m = K0/(3*K0 + 4*u0);
q0 = 3*(K0 + 2*u0)/(5*(3*K0 + 4*u0));
q0m = q0 + 12*a*u0*q0*(1 - 2*q0)/(5*d);
K = K0 + (c1*K0*(K1 - K0))/(K0 + 3*p0m*(1 - c1)*(K1 - K0));
u = u0 + (c1*u0*(5*d*(u1 - u0) - 12*a*u0*u1))/(5*d*u0 +
10*d*q0m*(1 - c1)*(u1 - u0) + 12*c1*a*u0*u1);
Simplify[9*K*u/(3*K + u)]]

dg = 0.001*{16, 13.2, 9.5, 4.75, 2.36};
c1g = {0, 0.020467, 0.224982, 0.28574, 0.065297};
Eg = ConstantArray[0, 5];
For[ j = 1, j <= 5, j++, Eg[[j]] = gradationEi[dg[[j]], c1g[[j]] ]]
P1 = 1; P2 = 0.975; P3 = 0.70; P4 = 0.35; P5 = 0.275;
Egg = 0.5*((Eg (1) + Eg (2))*(P1 - P2) + (Eg (2) + Eg (3))*(P2 -
P3) + (Eg (3) + Eg (4))*(P3 - P4) + (Eg (4) + Eg (5))*(P4 -P5))