# Question:Error, (in solve) a constant is invalid as a variable

## Question:Error, (in solve) a constant is invalid as a variable

Maple 2018

Hi,

I would like to ask you a question on the following program. Where does the error come from?

som:=0:

for b1 from 10 to 20 by 1 do
for b2 from 1 to 10 by 0.1 do
for alpha from 0.5 to 0.9 by 0.1 do
for beta from 0.1 to 0.4 by 0.1 do
for c from 1 to 1 by 1 do
for f from 1 to 10 by 1 do
for g from 8 to 470 by 1 do
for lambdai from 0.2 to 0.2 by 0.1 do
for lambdaj from 0.2 to 0.2 by 0.1 do
for gammai from 0.4 to 0.4 by 0.1 do
for gammaj from 0.4 to 0.4 by 0.1 do

aiSQ:=(alpha*b1)/(alpha*b2+beta*b2+c);
ajSQ:=(beta*b1)/(alpha*b2+beta*b2+c);
UiSQ:=(1/2)*alpha*b1^2*(alpha^2*b2+2*alpha*beta*b2+c*alpha+beta^2*b2+2*beta*c)/(alpha*b2+beta*b2+c)^2;
UjSQ:=(1/2)*beta*b1^2*(alpha^2*b2+2*alpha*beta*b2+2*c*alpha+beta^2*b2+beta*c)/(alpha*b2+beta*b2+c)^2;
USQ:=(1/2)*b1^2*(alpha+beta)*(alpha*b2+beta*b2+2*c)/(alpha*b2+beta*b2+c)^2;

ai:=(c*b1*alpha+c*p*f+p*f*beta*b2-alpha*b2*p*f)/(c*(alpha*b2+beta*b2+c));
aj:=(-p*f*beta*b2+alpha*b2*p*f+c*beta*b1+c*p*f)/(c*(alpha*b2+beta*b2+c));
aineg:=(-p*f*lambdai*b2*beta+c*b1-c*b1*lambdai+b2*p*f*lambdaj+b2*alpha*p*f*lambdaj-p*f*lambdai*b2+c*b1*alpha-c*p*f*lambdai)/(c*(b2*alpha-b2*lambdai+b2*beta-b2*lambdaj+c+2*b2));
ajneg:=-(b2*alpha*p*f*lambdaj-p*f*lambdai*b2-p*f*lambdai*b2*beta+b2*p*f*lambdaj+c*p*f*lambdaj-c*b1-c*beta*b1+c*lambdaj*b1)/(c*(b2*alpha-b2*lambdai+b2*beta-b2*lambdaj+c+2*b2));
ui:=alpha*(b1*(aineg+ajneg)-(b2/2)*(aineg+ajneg)^2)-(c/2)*aineg^2-p*f*(aineg-ai);
uj:=beta*(b1*(aineg+ajneg)-(b2/2)*(aineg+ajneg)^2)-(c/2)*ajneg^2-p*f*(ajneg-aj);
u:=(b1*(aineg+ajneg)-(b2/2)*(aineg+ajneg)^2)+p*f*(aineg-ai)+p*f*(ajneg-aj);
eqti:=gammai*(u-tj-USQ)-((1-gammai)/(1-lambdai))*(ui-UiSQ);
eqtj:=gammaj*(u-ti-USQ)-((1-gammaj)/(1-lambdaj))*(uj-UjSQ);
solt:=solve({eqti, eqtj}, {ti, tj});
ti:=subs(solt,ti);
tj:=subs(solt,tj);
dai:=diff(ai,p);
daj:=diff(aj,p);
daineg:=diff(aineg,p);
dajneg:=diff(ajneg,p);
dti:=diff(ti,p);
dtj:=diff(tj,p);
eqp:=(b1-b2*(ai+aj))*(dai+daj)-dti-dtj+f*(aineg-ai)+p*f(daineg-dai)+f*(ajneg-aj)+p*f(dajneg-daj)-g*p=0;
p:=solve(eqp,p);

Uip:=alpha*(b1*(ai+aj)-(b2/2)*(ai+aj)^2)-(c/2)*ai^2-p*f*(aineg-ai)+(1-lambdai)*ti;
Ujp:=beta*(b1*(ai+aj)-(b2/2)*(ai+aj)^2)-(c/2)*aj^2-p*f*(ajneg-aj)+(1-lambdaj)*tj;
Up:=(b1*(ai+aj)-(b2/2)*(ai+aj)^2)+p*f*(aineg-ai)+p*f*(ajneg-aj)-((g^2)/2)*p-ti-tj;

CSQ:=b1-b2*(aiSQ+ajSQ);
Cabat:=b1-b2*(ai+aj);
Cneg:=b1-b2*(aineg+ajneg);

if (CSQ>0 and Cabat>0  and Cneg>0 and beta<alpha and p>0 and p<1)
then
print(b1,b2,alpha,beta,c,f,g,lambdai,lambdaj,`aiSQ=`,aiSQ,`ajSQ=`,ajSQ,`UiSQ=`,UiSQ,`UjSQ=`,UjSQ,`USQ=`,USQ,`ai=`,ai,`aj=`,aj,`aineg=`,aineg,`ajneg=`,ajneg,`ti=`,ti,`tj=`,tj,`p=`,p,`Uip=`,Uip,`Ujp=`,Ujp,`Up=`,Up);
som:=som+1;
fi;
od;od;od;od;od;od;od;od;od;od;od;
som;

10, 1, 0.5, 0.1, 1, 1, 8, 0.2, 0.2, aiSQ=, 3.12500000000000, ajSQ=,

0.625000000000000, UiSQ=, 10.3515625000000, UjSQ=, 2.85156250000000, USQ=,

30.4687500000000, ai=, 3.14314584993738, aj=, 0.667340316520551, aineg=,

4.06068541500626, ajneg=, 2.80826596834794, ti=, 19.2559726892491, tj=,

7.44890809994178, p=, 0.0483889331663441, Uip=, 25.8431760998162, Ujp=,

8.71735374786572, Up=, 2.73962847065372
Error, (in solve) a constant is invalid as a variable, 7.44890809994178, 19.2559726892491
1

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