## 17418 Reputation

14 years, 138 days

On google groups. (comp.soft-sys.math.maple and sci.math.symbolic)

On stackoverflow.

On math.stackexchange.com.

## suggestions...

1) Ensure that the supposed names in your Matrix J (or in whatever it was constructed from) are correct. As you gave it, there are these:

{I[f], I[r], Lambda[r], N[H], N[f], S[H], S[r], b[Hf], b[fH],
b[fr], b[rf], beta[fH], beta[fr], beta[H*f], beta[r*f],
lambda[H], mu[B], mu[H], mu[f], mu[rd], tau[H]}

Do you really intend b[H*f] to be distinct from b[Hf]? Do you really intend b[Hf] to be distinct from b[fH]? And so on.

2) Don't use index-subscripted letter I as if it were a name or indeterminate. Use other terms instead, for example II[f] instead of I[f]. Otherwise you may start computing nonsense.

3) Either rename the lambda[H] inside Matrix J, or use an unrelated name other than lambda when calling CharacteristicPolynomial. Otherwise you may start computing nonsense.

3) Be clear about Maple terminology. The signum of an expression is not the same as its sign. I suspect that you are trying to utilize its signum.

4) Use 1-D plaintext Maple input if using 2D Input mode is causing you to make mistakes with the names.

5) Apply the command simplify(p,size) to your polynomial p constructed from your example in Maple 12.

6) Explain properly what form you are hoping for, from a solution your your signum question. There may well be too many variables to obtain or express a simple and understandable set of conditions about the separate signum or each of the coefficients.

7) Consider explaining (well) what is the motivating task. Why are you trying to compute this? Is it part of a task to try and deduce the number of roots of p, or a task to deduce something related to stability analysis? Are you trying to figure out subdomains or the parameters in which there are certain numbers (or any) real roots? Or anything similar, but in a manner which interrelates the parameters?

## something...

I do not understand your phrase, "I applied this command but answes were tolltally change ." since it is not meaningful to me as an English sentence.

Also, the names b[2] and a[2] don't appear in your system, so I don't understand why you refer to them (as b2, a2).

These conditions satisfy the equations, and for which b[-1],b[0],b[1] can be aribtrary:
{a[-1] = 0, a[0] = 0, a[1] = 0}

I notice that you didn't respond at all to my answer to your previous (and very similar question). Is it just because you don't understand how to use the solve and eliminate commands?

If you have additional examples then post them as comments on one of these earlier Questions -- I will otherwise delete entirely new Questions by your on this narrow topic, as duplicates.

 > restart;
 > kernelopts(version);

 > sys:={a[-1]^2*b[-1]^7 = 0, 7*a[-1]^2*b[-1]^6*b[0]+2*a[-1]*a[0]*b[-1]^7 = 0, -a[0]*b[1]^8+a[1]^2*b[1]^7+a[1]*b[0]*b[1]^7 = 0, -256*a[-1]*b[1]^8+2*a[0]*a[1]*b[1]^7+247*a[0]*b[0]*b[1]^7+7*a[1]^2*b[0]*b[1]^6+256*a[1]*b[-1]*b[1]^7-247*a[1]*b[0]^2*b[1]^6 = 0, 7*a[-1]^2*b[-1]^6*b[1]+21*a[-1]^2*b[-1]^5*b[0]^2+14*a[-1]*a[0]*b[-1]^6*b[0]+2*a[-1]*a[1]*b[-1]^7+a[-1]*b[-1]^7*b[0]+a[0]^2*b[-1]^7-a[0]*b[-1]^8 = 0, 2*a[-1]*a[1]*b[1]^7+4257*a[-1]*b[0]*b[1]^7+a[0]^2*b[1]^7+14*a[0]*a[1]*b[0]*b[1]^6+6552*a[0]*b[-1]*b[1]^7-4293*a[0]*b[0]^2*b[1]^6+7*a[1]^2*b[-1]*b[1]^6+21*a[1]^2*b[0]^2*b[1]^5-10809*a[1]*b[-1]*b[0]*b[1]^6+4293*a[1]*b[0]^3*b[1]^5 = 0, 42*a[-1]^2*b[-1]^5*b[0]*b[1]+35*a[-1]^2*b[-1]^4*b[0]^3+14*a[-1]*a[0]*b[-1]^6*b[1]+42*a[-1]*a[0]*b[-1]^5*b[0]^2+14*a[-1]*a[1]*b[-1]^6*b[0]+256*a[-1]*b[-1]^7*b[1]-247*a[-1]*b[-1]^6*b[0]^2+7*a[0]^2*b[-1]^6*b[0]+2*a[0]*a[1]*b[-1]^7+247*a[0]*b[-1]^7*b[0]-256*a[1]*b[-1]^8 = 0, 2*a[-1]*a[0]*b[1]^7+14*a[-1]*a[1]*b[0]*b[1]^6+63232*a[-1]*b[-1]*b[1]^7-15703*a[-1]*b[0]^2*b[1]^6+7*a[0]^2*b[0]*b[1]^6+14*a[0]*a[1]*b[-1]*b[1]^6+42*a[0]*a[1]*b[0]^2*b[1]^5-69791*a[0]*b[-1]*b[0]*b[1]^6+15619*a[0]*b[0]^3*b[1]^5+42*a[1]^2*b[-1]*b[0]*b[1]^5+35*a[1]^2*b[0]^3*b[1]^4-63232*a[1]*b[-1]^2*b[1]^6+85494*a[1]*b[-1]*b[0]^2*b[1]^5-15619*a[1]*b[0]^4*b[1]^4 = 0, 21*a[-1]^2*b[-1]^5*b[1]^2+105*a[-1]^2*b[-1]^4*b[0]^2*b[1]+35*a[-1]^2*b[-1]^3*b[0]^4+84*a[-1]*a[0]*b[-1]^5*b[0]*b[1]+70*a[-1]*a[0]*b[-1]^4*b[0]^3+14*a[-1]*a[1]*b[-1]^6*b[1]+42*a[-1]*a[1]*b[-1]^5*b[0]^2-10809*a[-1]*b[-1]^6*b[0]*b[1]+4293*a[-1]*b[-1]^5*b[0]^3+7*a[0]^2*b[-1]^6*b[1]+21*a[0]^2*b[-1]^5*b[0]^2+14*a[0]*a[1]*b[-1]^6*b[0]+6552*a[0]*b[-1]^7*b[1]-4293*a[0]*b[-1]^6*b[0]^2+a[1]^2*b[-1]^7+4257*a[1]*b[-1]^7*b[0] = 0, a[-1]^2*b[1]^7+14*a[-1]*a[0]*b[0]*b[1]^6+14*a[-1]*a[1]*b[-1]*b[1]^6+42*a[-1]*a[1]*b[0]^2*b[1]^5-150809*a[-1]*b[-1]*b[0]*b[1]^6+15493*a[-1]*b[0]^3*b[1]^5+7*a[0]^2*b[-1]*b[1]^6+21*a[0]^2*b[0]^2*b[1]^5+84*a[0]*a[1]*b[-1]*b[0]*b[1]^5+70*a[0]*a[1]*b[0]^3*b[1]^4-331612*a[0]*b[-1]^2*b[1]^6+187554*a[0]*b[-1]*b[0]^2*b[1]^5-15619*a[0]*b[0]^4*b[1]^4+21*a[1]^2*b[-1]^2*b[1]^5+105*a[1]^2*b[-1]*b[0]^2*b[1]^4+35*a[1]^2*b[0]^4*b[1]^3+482421*a[1]*b[-1]^2*b[0]*b[1]^5-203047*a[1]*b[-1]*b[0]^3*b[1]^4+15619*a[1]*b[0]^5*b[1]^3 = 0, 105*a[-1]^2*b[-1]^4*b[0]*b[1]^2+140*a[-1]^2*b[-1]^3*b[0]^3*b[1]+21*a[-1]^2*b[-1]^2*b[0]^5+42*a[-1]*a[0]*b[-1]^5*b[1]^2+210*a[-1]*a[0]*b[-1]^4*b[0]^2*b[1]+70*a[-1]*a[0]*b[-1]^3*b[0]^4+84*a[-1]*a[1]*b[-1]^5*b[0]*b[1]+70*a[-1]*a[1]*b[-1]^4*b[0]^3-63232*a[-1]*b[-1]^6*b[1]^2+85494*a[-1]*b[-1]^5*b[0]^2*b[1]-15619*a[-1]*b[-1]^4*b[0]^4+42*a[0]^2*b[-1]^5*b[0]*b[1]+35*a[0]^2*b[-1]^4*b[0]^3+14*a[0]*a[1]*b[-1]^6*b[1]+42*a[0]*a[1]*b[-1]^5*b[0]^2-69791*a[0]*b[-1]^6*b[0]*b[1]+15619*a[0]*b[-1]^5*b[0]^3+7*a[1]^2*b[-1]^6*b[0]+63232*a[1]*b[-1]^7*b[1]-15703*a[1]*b[-1]^6*b[0]^2 = 0, 7*a[-1]^2*b[0]*b[1]^6+14*a[-1]*a[0]*b[-1]*b[1]^6+42*a[-1]*a[0]*b[0]^2*b[1]^5+84*a[-1]*a[1]*b[-1]*b[0]*b[1]^5+70*a[-1]*a[1]*b[0]^3*b[1]^4-1099008*a[-1]*b[-1]^2*b[1]^6+184950*a[-1]*b[-1]*b[0]^2*b[1]^5-4419*a[-1]*b[0]^4*b[1]^4+42*a[0]^2*b[-1]*b[0]*b[1]^5+35*a[0]^2*b[0]^3*b[1]^4+42*a[0]*a[1]*b[-1]^2*b[1]^5+210*a[0]*a[1]*b[-1]*b[0]^2*b[1]^4+70*a[0]*a[1]*b[0]^4*b[1]^3+824931*a[0]*b[-1]^2*b[0]*b[1]^5-157617*a[0]*b[-1]*b[0]^3*b[1]^4+4293*a[0]*b[0]^5*b[1]^3+105*a[1]^2*b[-1]^2*b[0]*b[1]^4+140*a[1]^2*b[-1]*b[0]^3*b[1]^3+21*a[1]^2*b[0]^5*b[1]^2+1099008*a[1]*b[-1]^3*b[1]^5-1009881*a[1]*b[-1]^2*b[0]^2*b[1]^4+162036*a[1]*b[-1]*b[0]^4*b[1]^3-4293*a[1]*b[0]^6*b[1]^2 = 0, 35*a[-1]^2*b[-1]^4*b[1]^3+210*a[-1]^2*b[-1]^3*b[0]^2*b[1]^2+105*a[-1]^2*b[-1]^2*b[0]^4*b[1]+7*a[-1]^2*b[-1]*b[0]^6+210*a[-1]*a[0]*b[-1]^4*b[0]*b[1]^2+280*a[-1]*a[0]*b[-1]^3*b[0]^3*b[1]+42*a[-1]*a[0]*b[-1]^2*b[0]^5+42*a[-1]*a[1]*b[-1]^5*b[1]^2+210*a[-1]*a[1]*b[-1]^4*b[0]^2*b[1]+70*a[-1]*a[1]*b[-1]^3*b[0]^4+482421*a[-1]*b[-1]^5*b[0]*b[1]^2-203047*a[-1]*b[-1]^4*b[0]^3*b[1]+15619*a[-1]*b[-1]^3*b[0]^5+21*a[0]^2*b[-1]^5*b[1]^2+105*a[0]^2*b[-1]^4*b[0]^2*b[1]+35*a[0]^2*b[-1]^3*b[0]^4+84*a[0]*a[1]*b[-1]^5*b[0]*b[1]+70*a[0]*a[1]*b[-1]^4*b[0]^3-331612*a[0]*b[-1]^6*b[1]^2+187554*a[0]*b[-1]^5*b[0]^2*b[1]-15619*a[0]*b[-1]^4*b[0]^4+7*a[1]^2*b[-1]^6*b[1]+21*a[1]^2*b[-1]^5*b[0]^2-150809*a[1]*b[-1]^6*b[0]*b[1]+15493*a[1]*b[-1]^5*b[0]^3 = 0, 7*a[-1]^2*b[-1]*b[1]^6+21*a[-1]^2*b[0]^2*b[1]^5+84*a[-1]*a[0]*b[-1]*b[0]*b[1]^5+70*a[-1]*a[0]*b[0]^3*b[1]^4+42*a[-1]*a[1]*b[-1]^2*b[1]^5+210*a[-1]*a[1]*b[-1]*b[0]^2*b[1]^4+70*a[-1]*a[1]*b[0]^4*b[1]^3+36885*a[-1]*b[-1]^2*b[0]*b[1]^5-8167*a[-1]*b[-1]*b[0]^3*b[1]^4+163*a[-1]*b[0]^5*b[1]^3+21*a[0]^2*b[-1]^2*b[1]^5+105*a[0]^2*b[-1]*b[0]^2*b[1]^4+35*a[0]^2*b[0]^4*b[1]^3+210*a[0]*a[1]*b[-1]^2*b[0]*b[1]^4+280*a[0]*a[1]*b[-1]*b[0]^3*b[1]^3+42*a[0]*a[1]*b[0]^5*b[1]^2+2485288*a[0]*b[-1]^3*b[1]^5-711051*a[0]*b[-1]^2*b[0]^2*b[1]^4+39956*a[0]*b[-1]*b[0]^4*b[1]^3-247*a[0]*b[0]^6*b[1]^2+35*a[1]^2*b[-1]^3*b[1]^4+210*a[1]^2*b[-1]^2*b[0]^2*b[1]^3+105*a[1]^2*b[-1]*b[0]^4*b[1]^2+7*a[1]^2*b[0]^6*b[1]-2522173*a[1]*b[-1]^3*b[0]*b[1]^4+719218*a[1]*b[-1]^2*b[0]^3*b[1]^3-40119*a[1]*b[-1]*b[0]^5*b[1]^2+247*a[1]*b[0]^7*b[1] = 0, 140*a[-1]^2*b[-1]^3*b[0]*b[1]^3+210*a[-1]^2*b[-1]^2*b[0]^3*b[1]^2+42*a[-1]^2*b[-1]*b[0]^5*b[1]+a[-1]^2*b[0]^7+70*a[-1]*a[0]*b[-1]^4*b[1]^3+420*a[-1]*a[0]*b[-1]^3*b[0]^2*b[1]^2+210*a[-1]*a[0]*b[-1]^2*b[0]^4*b[1]+14*a[-1]*a[0]*b[-1]*b[0]^6+210*a[-1]*a[1]*b[-1]^4*b[0]*b[1]^2+280*a[-1]*a[1]*b[-1]^3*b[0]^3*b[1]+42*a[-1]*a[1]*b[-1]^2*b[0]^5+1099008*a[-1]*b[-1]^5*b[1]^3-1009881*a[-1]*b[-1]^4*b[0]^2*b[1]^2+162036*a[-1]*b[-1]^3*b[0]^4*b[1]-4293*a[-1]*b[-1]^2*b[0]^6+105*a[0]^2*b[-1]^4*b[0]*b[1]^2+140*a[0]^2*b[-1]^3*b[0]^3*b[1]+21*a[0]^2*b[-1]^2*b[0]^5+42*a[0]*a[1]*b[-1]^5*b[1]^2+210*a[0]*a[1]*b[-1]^4*b[0]^2*b[1]+70*a[0]*a[1]*b[-1]^3*b[0]^4+824931*a[0]*b[-1]^5*b[0]*b[1]^2-157617*a[0]*b[-1]^4*b[0]^3*b[1]+4293*a[0]*b[-1]^3*b[0]^5+42*a[1]^2*b[-1]^5*b[0]*b[1]+35*a[1]^2*b[-1]^4*b[0]^3-1099008*a[1]*b[-1]^6*b[1]^2+184950*a[1]*b[-1]^5*b[0]^2*b[1]-4419*a[1]*b[-1]^4*b[0]^4 = 0, 42*a[-1]^2*b[-1]*b[0]*b[1]^5+35*a[-1]^2*b[0]^3*b[1]^4+42*a[-1]*a[0]*b[-1]^2*b[1]^5+210*a[-1]*a[0]*b[-1]*b[0]^2*b[1]^4+70*a[-1]*a[0]*b[0]^4*b[1]^3+210*a[-1]*a[1]*b[-1]^2*b[0]*b[1]^4+280*a[-1]*a[1]*b[-1]*b[0]^3*b[1]^3+42*a[-1]*a[1]*b[0]^5*b[1]^2+3998464*a[-1]*b[-1]^3*b[1]^5-764601*a[-1]*b[-1]^2*b[0]^2*b[1]^4+23156*a[-1]*b[-1]*b[0]^4*b[1]^3-37*a[-1]*b[0]^6*b[1]^2+105*a[0]^2*b[-1]^2*b[0]*b[1]^4+140*a[0]^2*b[-1]*b[0]^3*b[1]^3+21*a[0]^2*b[0]^5*b[1]^2+70*a[0]*a[1]*b[-1]^3*b[1]^4+420*a[0]*a[1]*b[-1]^2*b[0]^2*b[1]^3+210*a[0]*a[1]*b[-1]*b[0]^4*b[1]^2+14*a[0]*a[1]*b[0]^6*b[1]-1045243*a[0]*b[-1]^3*b[0]*b[1]^4+142558*a[0]*b[-1]^2*b[0]^3*b[1]^3-2193*a[0]*b[-1]*b[0]^5*b[1]^2+a[0]*b[0]^7*b[1]+140*a[1]^2*b[-1]^3*b[0]*b[1]^3+210*a[1]^2*b[-1]^2*b[0]^3*b[1]^2+42*a[1]^2*b[-1]*b[0]^5*b[1]+a[1]^2*b[0]^7-3998464*a[1]*b[-1]^4*b[1]^4+1809844*a[1]*b[-1]^3*b[0]^2*b[1]^3-165714*a[1]*b[-1]^2*b[0]^4*b[1]^2+2230*a[1]*b[-1]*b[0]^6*b[1]-a[1]*b[0]^8 = 0, 35*a[-1]^2*b[-1]^3*b[1]^4+210*a[-1]^2*b[-1]^2*b[0]^2*b[1]^3+105*a[-1]^2*b[-1]*b[0]^4*b[1]^2+7*a[-1]^2*b[0]^6*b[1]+280*a[-1]*a[0]*b[-1]^3*b[0]*b[1]^3+420*a[-1]*a[0]*b[-1]^2*b[0]^3*b[1]^2+84*a[-1]*a[0]*b[-1]*b[0]^5*b[1]+2*a[-1]*a[0]*b[0]^7+70*a[-1]*a[1]*b[-1]^4*b[1]^3+420*a[-1]*a[1]*b[-1]^3*b[0]^2*b[1]^2+210*a[-1]*a[1]*b[-1]^2*b[0]^4*b[1]+14*a[-1]*a[1]*b[-1]*b[0]^6-2522173*a[-1]*b[-1]^4*b[0]*b[1]^3+719218*a[-1]*b[-1]^3*b[0]^3*b[1]^2-40119*a[-1]*b[-1]^2*b[0]^5*b[1]+247*a[-1]*b[-1]*b[0]^7+35*a[0]^2*b[-1]^4*b[1]^3+210*a[0]^2*b[-1]^3*b[0]^2*b[1]^2+105*a[0]^2*b[-1]^2*b[0]^4*b[1]+7*a[0]^2*b[-1]*b[0]^6+210*a[0]*a[1]*b[-1]^4*b[0]*b[1]^2+280*a[0]*a[1]*b[-1]^3*b[0]^3*b[1]+42*a[0]*a[1]*b[-1]^2*b[0]^5+2485288*a[0]*b[-1]^5*b[1]^3-711051*a[0]*b[-1]^4*b[0]^2*b[1]^2+39956*a[0]*b[-1]^3*b[0]^4*b[1]-247*a[0]*b[-1]^2*b[0]^6+21*a[1]^2*b[-1]^5*b[1]^2+105*a[1]^2*b[-1]^4*b[0]^2*b[1]+35*a[1]^2*b[-1]^3*b[0]^4+36885*a[1]*b[-1]^5*b[0]*b[1]^2-8167*a[1]*b[-1]^4*b[0]^3*b[1]+163*a[1]*b[-1]^3*b[0]^5 = 0, -21*a[-1]^2*b[-1]^2*b[1]^5-105*a[-1]^2*b[-1]*b[0]^2*b[1]^4-35*a[-1]^2*b[0]^4*b[1]^3-210*a[-1]*a[0]*b[-1]^2*b[0]*b[1]^4-280*a[-1]*a[0]*b[-1]*b[0]^3*b[1]^3-42*a[-1]*a[0]*b[0]^5*b[1]^2-70*a[-1]*a[1]*b[-1]^3*b[1]^4-420*a[-1]*a[1]*b[-1]^2*b[0]^2*b[1]^3-210*a[-1]*a[1]*b[-1]*b[0]^4*b[1]^2-14*a[-1]*a[1]*b[0]^6*b[1]-2337507*a[-1]*b[-1]^3*b[0]*b[1]^4+387342*a[-1]*b[-1]^2*b[0]^3*b[1]^3-8937*a[-1]*b[-1]*b[0]^5*b[1]^2+9*a[-1]*b[0]^7*b[1]-35*a[0]^2*b[-1]^3*b[1]^4-210*a[0]^2*b[-1]^2*b[0]^2*b[1]^3-105*a[0]^2*b[-1]*b[0]^4*b[1]^2-7*a[0]^2*b[0]^6*b[1]-280*a[0]*a[1]*b[-1]^3*b[0]*b[1]^3-420*a[0]*a[1]*b[-1]^2*b[0]^3*b[1]^2-84*a[0]*a[1]*b[-1]*b[0]^5*b[1]-2*a[0]*a[1]*b[0]^7+4675014*a[0]*b[-1]^4*b[1]^4-774684*a[0]*b[-1]^3*b[0]^2*b[1]^3+17874*a[0]*b[-1]^2*b[0]^4*b[1]^2-18*a[0]*b[-1]*b[0]^6*b[1]-35*a[1]^2*b[-1]^4*b[1]^3-210*a[1]^2*b[-1]^3*b[0]^2*b[1]^2-105*a[1]^2*b[-1]^2*b[0]^4*b[1]-7*a[1]^2*b[-1]*b[0]^6-2337507*a[1]*b[-1]^4*b[0]*b[1]^3+387342*a[1]*b[-1]^3*b[0]^3*b[1]^2-8937*a[1]*b[-1]^2*b[0]^5*b[1]+9*a[1]*b[-1]*b[0]^7 = 0, 105*a[-1]^2*b[-1]^2*b[0]*b[1]^4+140*a[-1]^2*b[-1]*b[0]^3*b[1]^3+21*a[-1]^2*b[0]^5*b[1]^2+70*a[-1]*a[0]*b[-1]^3*b[1]^4+420*a[-1]*a[0]*b[-1]^2*b[0]^2*b[1]^3+210*a[-1]*a[0]*b[-1]*b[0]^4*b[1]^2+14*a[-1]*a[0]*b[0]^6*b[1]+280*a[-1]*a[1]*b[-1]^3*b[0]*b[1]^3+420*a[-1]*a[1]*b[-1]^2*b[0]^3*b[1]^2+84*a[-1]*a[1]*b[-1]*b[0]^5*b[1]+2*a[-1]*a[1]*b[0]^7-3998464*a[-1]*b[-1]^4*b[1]^4+1809844*a[-1]*b[-1]^3*b[0]^2*b[1]^3-165714*a[-1]*b[-1]^2*b[0]^4*b[1]^2+2230*a[-1]*b[-1]*b[0]^6*b[1]-a[-1]*b[0]^8+140*a[0]^2*b[-1]^3*b[0]*b[1]^3+210*a[0]^2*b[-1]^2*b[0]^3*b[1]^2+42*a[0]^2*b[-1]*b[0]^5*b[1]+a[0]^2*b[0]^7+70*a[0]*a[1]*b[-1]^4*b[1]^3+420*a[0]*a[1]*b[-1]^3*b[0]^2*b[1]^2+210*a[0]*a[1]*b[-1]^2*b[0]^4*b[1]+14*a[0]*a[1]*b[-1]*b[0]^6-1045243*a[0]*b[-1]^4*b[0]*b[1]^3+142558*a[0]*b[-1]^3*b[0]^3*b[1]^2-2193*a[0]*b[-1]^2*b[0]^5*b[1]+a[0]*b[-1]*b[0]^7+105*a[1]^2*b[-1]^4*b[0]*b[1]^2+140*a[1]^2*b[-1]^3*b[0]^3*b[1]+21*a[1]^2*b[-1]^2*b[0]^5+3998464*a[1]*b[-1]^5*b[1]^3-764601*a[1]*b[-1]^4*b[0]^2*b[1]^2+23156*a[1]*b[-1]^3*b[0]^4*b[1]-37*a[1]*b[-1]^2*b[0]^6 = 0}:
 > indets(sys,name);

 > solve(sys, {a[-1], a[0], a[1], b[-1], b[0], b[1]});

 > eval(sys,{a[-1] = 0, a[0] = 0, a[1] = 0});

 >

## parameters...

Are you trying to solve symbolically for some names (variables) in terms of the remaining names (parameters)? If so then you should tell us whcih are the variables and which are the parameters.

Here are some ideas:

 > restart;
 > kernelopts(version);

 > sys := {x^3*a[1]*b[0]+x*a[1]^3*b[0]-x^3*a[0]-x*a[0]*a[1]^2+omega*a[1]*b[0]-omega*a[0] = 0, -x^3*a[-1]*b[-1]^2*b[0]+x^3*a[0]*b[-1]^3-omega*a[-1]*b[-1]^2*b[0]+omega*a[0]*b[-1]^3-x*a[-1]^3*b[0]+x*a[-1]^2*a[0]*b[-1] = 0, -4*x^3*a[1]*b[0]^2+4*x^3*a[0]*b[0]+8*x^3*a[1]*b[-1]+2*x*a[0]*a[1]^2*b[0]+2*x*a[1]^3*b[-1]+2*omega*a[1]*b[0]^2-8*x^3*a[-1]-2*x*a[-1]*a[1]^2-2*x*a[0]^2*a[1]-2*omega*a[0]*b[0]+2*omega*a[1]*b[-1]-2*omega*a[-1] = 0, 4*x^3*a[1]*b[-1]*b[0]^2-4*x^3*a[-1]*b[0]^2-32*x^3*a[1]*b[-1]^2+4*omega*a[1]*b[-1]*b[0]^2-32*x^3*a[-1]*b[-1]+4*x*a[-1]*a[1]^2*b[-1]+4*x*a[0]^2*a[1]*b[-1]-4*omega*a[-1]*b[0]^2+4*omega*a[1]*b[-1]^2-4*x*a[-1]^2*a[1]-4*x*a[-1]*a[0]^2-4*omega*a[-1]*b[-1] = 0, 4*x^3*a[-1]*b[-1]*b[0]^2-4*x^3*a[0]*b[-1]^2*b[0]+8*x^3*a[1]*b[-1]^3-8*x^3*a[-1]*b[-1]^2-2*omega*a[-1]*b[-1]*b[0]^2+2*omega*a[0]*b[-1]^2*b[0]+2*omega*a[1]*b[-1]^3-2*x*a[-1]^2*a[0]*b[0]+2*x*a[-1]^2*a[1]*b[-1]+2*x*a[-1]*a[0]^2*b[-1]-2*omega*a[-1]*b[-1]^2-2*x*a[-1]^3 = 0, x^3*a[1]*b[0]^3-x^3*a[0]*b[0]^2-18*x^3*a[1]*b[-1]*b[0]+omega*a[1]*b[0]^3-5*x^3*a[-1]*b[0]+23*x^3*a[0]*b[-1]+x*a[-1]*a[1]^2*b[0]+x*a[0]^2*a[1]*b[0]+5*x*a[0]*a[1]^2*b[-1]-omega*a[0]*b[0]^2+6*omega*a[1]*b[-1]*b[0]-6*x*a[-1]*a[0]*a[1]-x*a[0]^3+5*omega*a[-1]*b[0]-omega*a[0]*b[-1] = 0, -x^3*a[-1]*b[0]^3+x^3*a[0]*b[-1]*b[0]^2+5*x^3*a[1]*b[-1]^2*b[0]+18*x^3*a[-1]*b[-1]*b[0]-23*x^3*a[0]*b[-1]^2-omega*a[-1]*b[0]^3+omega*a[0]*b[-1]*b[0]^2+5*omega*a[1]*b[-1]^2*b[0]-x*a[-1]^2*a[1]*b[0]-x*a[-1]*a[0]^2*b[0]+6*x*a[-1]*a[0]*a[1]*b[-1]+x*a[0]^3*b[-1]-6*omega*a[-1]*b[-1]*b[0]+omega*a[0]*b[-1]^2-5*x*a[-1]^2*a[0] = 0}:
 > indets(sys,name);

 > EA:=eliminate(sys,x): A:=EA[1]; map(rhs-lhs,eval(sys,%)): K:={solve(%)}: KK:=map(k->remove(kk->lhs(kk)=rhs(kk),k),K): AA:=map(`union`,KK,A);

 > # check map[2](eval,sys,AA);

 > solve(sys,{x,omega});

 > solve(sys,{a[-1],a[0],a[1]});

 > solve(sys,{x,a[-1],b[-1],a[0]});

 > solve(sys,{x,a[-1],b[0],a[0]});

 > solve(sys,{x,omega,a[0]});

 > solve(sys,{omega, a[-1], a[0], a[1], b[-1], b[0]}, explicit);

 > # restrictions on A=EA[1] map(k->remove(kk->lhs(kk)=rhs(kk),k),     simplify([solve(EA[2],{omega,a[0],a[1],a[-1],b[-1]},explicit)]));

 > G:=[eliminate(sys,{x,b[0]})]:
 > G[1];

 > G[3];

 > G[4];

 > # These have restrictions on remaining parameters G[2][1]; G[5][1]; G[6][1];

 > # For example, solving restrictions on G[2][1] solve(G[2][2]);

Warning, solutions may have been lost

 > # A new system, where b[0]=a[0]/a[1] newsys:=remove(u->simplify(lhs(u)-rhs(u))=0,factor(eval(sys, b[0]=a[0]/a[1])));

 > Q:=map(`union`,[solve(newsys,{x,a[-1],a[1],a[0],b[-1]},explicit)],{b[0]=a[0]/a[1]});

 > # check simplify(map[2](eval,newsys,Q));

 >

## some ways...

I separated the construction of the data from the processing, to illustrate some performance differences in approaches to the latter.

I repeated both (and iterated each a few times).

 >
 >
 >
 >
 >
 >

memory used=0.95MiB, alloc change=0 bytes, cpu time=6.00ms, real time=7.00ms, gc time=0ns

 >

memory used=4.02MiB, alloc change=-4.00MiB, cpu time=26.60ms, real time=24.00ms, gc time=5.45ms

 >

memory used=0.57MiB, alloc change=102.56MiB, cpu time=8.40ms, real time=3.10ms, gc time=0ns

 >

memory used=16.89KiB, alloc change=0 bytes, cpu time=450.00us, real time=200.00us, gc time=0ns

 >

memory used=4.02MiB, alloc change=0 bytes, cpu time=29.85ms, real time=26.65ms, gc time=6.89ms

 >

memory used=0.56MiB, alloc change=0 bytes, cpu time=6.75ms, real time=2.10ms, gc time=0ns

 >

memory used=16.89KiB, alloc change=0 bytes, cpu time=450.00us, real time=250.00us, gc time=0ns

 >

 >

## the documentation...

The Description in the Help page for topic alias states clearly:

Because aliases are resolved at the time of parsing the original input, they substitute literally, without regard to values of variables and expressions.  For example, alias(a[1]=exp(1)) followed by evalf(a[1]) will replace a[1] with exp(1) to give the result 2.718281828, but evalf(a[i]) will not substitute a[i] for its alias even when i=1.  This is because a[i] does not literally match a[1].

You are trying to use alias for a way that directly goes against that.

It would work to parse strings made afresh, but that would be crazy. For example,

 > restart:
 > interface(version);

 > for n from 2 to 3 do   alias(a[n]=RootOf(z^n-1)): end do: alias(); n:='n':

 > dismantle(a[2]);

FUNCTION(3)
NAME(4): RootOf #[protected, _syslib]
EXPSEQ(2)
POLY(6)
EXPSEQ(2)
NAME(4): _Z #[protected, _syslib]
DEGREES(HW): 2
INTPOS(2): 1
DEGREES(HW): 0
INTNEG(2): -1

 > seq(a[n], n=2..2); map(dismantle,[%]);

TABLEREF(3)
NAME(4): a
EXPSEQ(2)
INTPOS(2): 2

 > seq(eval(parse(sprintf("%a",a[n]))), n=2..3);

 > allvalues(a[2]), allvalues(a[3]);

 > seq(allvalues(a[n]), n=2..3);

 > seq(allvalues(parse(sprintf("%a",a[n]))), n=2..3);

 >

## multiplication...

Names in Maple can be more than one letter long.

When you write xy without any space or multiplication symbol you are writing a name (of length two, using two letters). That is not the same as x*y .

So, for example, 9*xy^2*x^2 is not the same as 9*x*y^2*x^2 .

If you intend x*y and y*z then enter them that way, and do not enter xy and yz which are simply two other names unrelated to x, y, or z.

You can use Edit -> Find/Replace from the menubar to change them easily.

## xyzcoloring...

The documentation states that colorscheme with xyzcoloring is available for 3D surface shading, and thus not spacecurve, does it not?

It is possible to accomplish shading of spacecurves with custom functions of the parameter or x,y,z coordinates. One way is to do construct the whole thing, somewhat like I did here. There are other ways.

## multiplication...

You are missing a multiplication symbol between the round brackets.

Without them your input is parsed as function application, rather than multiplication.

Another choice, in 2D Input, is to use a space to denote implicit multiplication. But that approach is error-prone, since it is difficult to distinguish visually.

 >

Firsy, using an explicit multiplication symbol.

 >

 >

Next, using a space to denote the multiplication implicitly.

 >

 >

Finally, omitting both multiplication symbol and space, which makes
the input get parsed as function application.

 >

 >

 >

## coordinate system...

If you want "gridlines" which illustrate the idea of rotation then why not use a non-cartesian (and suitable) coordinate system?

For example,

 > restart;
 > with(plots):
 >
 > optwf := grid=[23,70], style=wireframe, color="Pink", thickness=3: optsurf := grid=[70,70], style=surface, transparency=0.1, color=u:
 > ee := evalc(Re(sqrt(x+I*y)));

 > ff := simplify(eval(ee,[x=v*cos(u),y=v*sin(u)])) assuming real;

 > display(seq(seq(plot3d([v*cos(u), v*sin(u), k*ff],                        u=0..2*Pi, v=0..4, opt[]),                 k=[-1,1]),opt=[[optwf],[optsurf]]),         view=[-1..1,-1..1,-1..1], orientation=[50,75,0]);

 >

I used a solid Pink above for the color of the gridlines, but you could change that to color=u so that they were colored by angle (or whatever other radial function you prefer). That covers one of your queries, it seems. For example,

 > restart;
 > with(plots):
 > optwf := grid=[23,70], style=wireframe, color=u, thickness=3: optsurf := grid=[70,70], style=surface, transparency=0.7, color=u:
 > ee := evalc(Re(sqrt(x+I*y))):
 > ff := simplify(eval(ee,[x=v*cos(u),y=v*sin(u)])) assuming real:
 > display(seq(seq(plot3d([v*cos(u), v*sin(u), k*ff],                        u=0..2*Pi, v=0..4, opt[]),                 k=[-1,1]),opt=[[optwf],[optsurf]]),         view=[-1..1,-1..1,-1..1]);

 >

I don't know why the transparency option isn't effective with fine granularity, eg. for small values.

It would be more useful if the "gridlines" could be rendered on a coarse grid but computed using the finer grid -- so that the surface and lines match.

If the grid dimensions are odd then the wireframe produced in other Answers (using cartesian coordinates especially, for this particular example) will not match the (finer grid) surface properly.

 For your approach of drawing the curves manually (in lieu of wireframe grid lines), you could generate them in another coordinate representation (eg, theta and z), coloring them by a function of theta say, and then transform to the cartesian coordinate plot. That would also give you your radial or cylindrical lines with either being shaded by angle. I don't think that your expectation makes good sense: to compute and draw the lines in cartesian coordinates while expecting a mechanism for shading radially. If you want them shaded as a function of angle then use a suitable coordinate system.

## typesetting level...

The problem with literal subscripted names (and showassumed=1 for trailing tildes) occurs with the extended typesetting level.

It apparently does not occur in my Maple 2019.2 for standard typesetting level. So that may be another workaround, see attached: assumed_literalsubscript.mw

The behavior seems to involve complicated interplay between the GUI and the Library Typesetting.

## property...

You need to specify which property of the ListBox you're trying to set. The property value denotes the selected item.

Eg,
SetProperty("ListBox0", itemlist, convert(DataSet[..,1],list));
SetProperty("ListBox0", value, DataSet[2,1]);
SetProperty("ListBox0", value, DataSet[1,1]);

Also, load the package using with as a command, without any space before the opening bracket (or else it will be parsed as implicit multiplication in 2D Input mode). Or utilize the long form, eg.
DocumentTools:-SetProperty("ListBox0", value, DataSet[1,1]);

LB.mw

## a few ways...

There are various ways to accomplish this, depending on whether you want to be able to utilize expression form versus operator form.

 > restart;
 > points :=  <<0.4000|  10.0000>, <0.7000|   10.0000>,             <1.0000|  10.0000>, <0.3000|   30.0000>,             <0.4000|  30.0000>, <0.5000|   30.0000>>:
 > Data := <0617,0767,0220,0444,0692,0789>*0.001:
 > intmethod := LinearInterpolation:
 > g := Interpolation[intmethod](points(1..-1,1),Data):
 > g(sqrt(2)/2); # observe

Error, (in ModuleApply) unable to store '(1/2)*2^(1/2)' when datatype=float[8]

 > g(evalf(sqrt(2)/2)); # observe

 > plot(g(x),x=0..1, size=[400,200]);

 > e := x/sqrt(2);

 > G := unapply('g'('evalf'(x)),x,numeric):
 > G(e);

 > g(1), G(1);

 > G(sqrt(2)/2);

 > F := 5+G(e)*x^2;

 > eval(F, x=1);

 > plot(F, x=0..0.1, size=[400,200]);

 > Optimization[Minimize](F, x=0 .. 1);

Here are some other ways...

 > f1 := unapply(5+'g'('evalf'(e))*x^2,x,numeric): f1(1); f1(x);

 > plots:-display(Array([   plot(f1, 0..0.1), plot(f1(x), x=0..0.1) ]), size=[400,200]);

 > Optimization[Minimize](f1(x),x=0 .. 1); Optimization[Minimize](f1, 0 .. 1);

 > #plots:-display(Array([ #  plot(f1, 0..1), plot(f1(x), x=0..1) ]), size=[400,200]);
 > f2 := proc(xx) if not xx::numeric then return 'procname'(args); end if;                      5+g(evalf(eval(e,x=xx)))*xx^2;             end proc: f2(1); f2(x);

 > plots:-display(Array([   plot(f2, 0..0.1), plot(f2(x), x=0..0.1) ]), size=[400,200]);

 > Optimization[Minimize](f2(x),x=0 .. 1); Optimization[Minimize](f2, 0 .. 1);

 > #plots:-display(Array([ #  plot(f2, 0..1), plot(f2(x), x=0..1) ]), size=[400,200]);
 > ee := unapply('evalf'(x/sqrt(2)),x,numeric):
 > f3 := unapply(5+'g'(ee(x))*x^2,x,numeric): f3(1); f3(x);

 > Optimization[Minimize](f3(x), x=0 .. 1, method=branchandbound); Optimization[Minimize](f3, 0 .. 1, method=branchandbound);

 >

## 2D or 1D...

Are you trying to change your setup so that input as in 1D plaintext Maple Notation in a Worksheet (which happens to default to red input)? Carl's Answer shows how to accomplish that.

Or are you trying to change the color of typeset 2D Input from default black to red (in your choice of Document or Worksheet)? If that is your situation then use the main menubar and select,
Format -> Styles...
then in the popup scroll down and select
2D Input
then in that popup push the button
Create Character Style
and in the next popup push the Color button.

If you modify some such aspect of the Style then you can also make that Style set as default moving forwards in new sheets, using Format -> Manage Style Sets...

worksheet,documenting,characterstyles

## complex powering...

Apparently it relates to whether the floating-point exponent in a call to `^` matches the type of the base.

It seems to work if the float exponents are cast to complex floats. I got the "expected" result in either of these ways:
1) instead of exponents like 1/beta I used Complex(1/beta,0.0) , and similarly for the others
or,
2) I specified the procedure's parameters alpha and beta as complex(float) rather than float.

I consider this a  bug, and will submit a report

note: I think that your code and operations could be simplified, with several steps combined, etc. I haven't done any of that.