## Solving Simultaneous Equations With Maple...

I tried to solve 4 simultaneous equations but the result is an empty matrix.

Is that because there is no solution or did I make something wrong?

SimEquations.mw

## Algebra - variables as exponents. How do I format ...

Can someone please explain the error I am making in the input syntax?

Somehow my input is causing maple to be unable to solve these equations.

*edit* i'm also getting the same result for something like:

ln(x)=-3.86

I don't understand the empty brackets, is maple telling me there's no solution, or is something wrong with my syntax? I have to be doing something wrong here, but i just don't see it yet.

## number type place holders for Solve...

_z i believe is the placeholder when Solve is intending to indicate a restriction to any integer value  only, for one of my recent projects im getting the placholder "_L" in my solutions, and would like to know where the reference table is for the full list of these global in built variable types if possible, have not been able to find it in the help interface and did sincerely look

## solve(x^3+a*x+2>0)...

In Maple 2017.2:

```solve(x^3+x*a+2 > 0, [a, x]);
[[a = -3, x < 1, -2 < x], [a = -3, 1 < x]]

solve(x^4+x*a+1 > 0, [a, x]);
Error, (in rootbound) 1st argument must be a polynomial with numeric coefficients
```

The first one clearly doesn't give the complete set of solutions. It can be made to work by adding conditions on a such as a>0.

I'm not sure if symbolic operations take index=real[i] into account or just silently ignore it:

```limit(RootOf(_Z^3+a*_Z+2, index = real[1]), a = -infinity);
0
```

In fact the root grows as sqrt at -infinity.

## solve z^(1+I)=1...

```solve(z^(1+I) = 1, z, allsolutions = true);
exp((1 + I) Pi _Z1)
getassumptions(_Z1);
{_Z1::integer}
```

Since this is a single-valued power function, there is only a finite number of solutions. evalc correctly gives exp(-2*Pi) for _Z1=-1.

evalf doesn't help here regardless of the level of precision, I think because it always generates a non-zero imaginary part for exp(-(1+I)*Pi):

```seq(print(evalf(evalf[d]((exp((-1-I)*Pi))^(1+I)))), d = 10 .. 3010, 300);
-12
0.001867442732 - 1.361179007 10    I
-312
0.001867442732 - 1.674479874 10     I
-610
1.000000000 + 2.386571217 10     I
-910
1.000000000 + 8.502509375 10     I
-1212
0.001867442732 - 1.646483173 10      I
-1514
0.001867442732 - 4.556560265 10      I
-1812
0.001867442732 - 1.287611101 10      I
-2112
0.001867442732 - 1.072784224 10      I
-2410
1.000000000 + 8.162729354 10      I
-2713
0.001867442732 - 7.375390371 10      I
-3010
1.000000000 + 1.988371005 10      I
```

Unrelated, but it would be nice to have a simple way to display lists/matrices with specified width and alignment.

## Is there a way to solve these equations x+y = 3733...

Is there a way to solve these equations x+y = 373320 and z = (x+y) / 0.44 - y -  y* (1 - 0.99) for x,y,z in Maple or excel?

Even if we set y = 37320 - x

and plug that in we get z= 37320/0.44 - (37320-x) - (37320 - x) * (1-0.99) there are still two unknown z and x

Maybe some optimization?  Thanx for any input

## how to solve this system?...

updated:
P := evalm(p2 + c*vector([cos(q1+q2+q3), sin(q1+q2+q3)]));

restart:
with(Groebner):
p1 := vector([a*cos(q1), a*sin(q1)]);
p2 := evalm(p1 + b*vector([cos(q1+q2), sin(q1+q2)]));
P := evalm(p2 + c*vector([cos(q1+q2+q3), sin(q1+q2+q3)]));
Pe := map(expand, P);
A := {cos(q1) = c1, sin(q1) =s1, cos(q2)=c2, sin(q2)=s2, cos(q3)=c3, sin(q3)=s3};
P := subs(A, op(Pe));
F1 := [x - P[1], y - P[2], s1^2+c1^2-1, s2^2+c2^2-1, s3^2+c3^2-1 ];
F2 := subs({a=1, b=1, c=1}, F1);

g2 := Basis(F2, plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[1], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[2], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[3], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[4], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[5], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[6], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[7], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[8], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[9], plex(c3, s3, c2, s2, c1, s1));

1, c1
2       2    2   2
16 y  + 16 x , s1  s2
2
8 x, c1 s2
2      2    2
2 y  + 2 x , s1  c2
2 x, c1 c2
3            2
2 x  - 2 x + 2 y  x, s2 c2
2
1, c2
2 x, s3
2, c3
originally i think
g2[1], g2[7], g2[9] have single variables c1, c2, c3 respectively
can be used to solve system

but without x and y, these equations can not be used
if choose leading term has x and y , but there is no single variable s1 or c1.

originally expect solve as follows
g2spec := subs({x=1, y=1/2}, [g2[3],g2[5],g2[6]]);
S1 := [solve([g2spec[1]])];
q1a := evalf(arccos(S1[1]));
q1b := evalf(arccos(S1[2]));
S2 := [solve(subs(s1=S1[1], g2spec[2])), solve(subs(s1=S1[2], g2spec[2])) ];
q2a := evalf(arccos(S2[1]));
q2b := evalf(arccos(S2[2]));
S3 := [solve(subs(s1=S2[1], g2spec[2])), solve(subs(s1=S2[2], g2spec[2])) ];
q2a := evalf(arccos(S3[1]));
q2b := evalf(arccos(S3[2]));

## How do you access the number that an expression ev...

I am trying to solve a system of equations (I'm using MapleTA< but I'm pretty sure that this applies to any Maple product).  I have successfully solved the system, and obtain a set of solutions, which has name Soln.  I can access the element Soln[1], which is an expression:

vn2 = 12/7

Now, I just want that 12/7, as a decimal.  I try evalf(Soln[1]), but again I end up with vn2 = 12/7.  How do I get the decimal number out, without it being an expression?

## Determining f,g such that f(x)*g(y)= H(x,y) ...

Does Maple have build-in function, which when given an expression that depends on x and y, will separate it to a product of two functions, one that depedns on x only and the other that depends on y only?

The input mathematical expression is known to be seperable.

For example, If the input is

`((3*y + y^2)*3*x)/(x + sin(x))`

Then I'd the Maple function to take the above and return list or set of two parts  {(3*y + y^2)   ,     3*x/(x + sin(x) } (if it can't separate it, it can return null).

The API can be something as

` f,g = find_product_functions(expression,[x,y])`

Something like this is used on determining for example if RHS of first order ODE is separable in order to solve it more easily.  collect() does not really work for this. So Maple allready does this internally in its ODE solver when it checks if ODE is separable or not. But is the function available for users?

## how to solve this system?...

sys1:=-.736349402144656384 = -1.332282598*10^12*(-.99999999999999966)^po1-1.332282598*10^12*(-.99999999999999966)^po2-.735533633151605248*Resid;

sys2:=.326676717828940144 = 1.331567176*10^12*(-.99999999999999966)^po1+1.331567176*10^12*(-.99999999999999966)^po2+.325144093024965720*Resid;

sys3:=.590327283775080036 = -1.072184073*10^9*(-.99999999999999966)^po1-1.072184073*10^9*(-.99999999999999966)^po2+.589610307487437146*Resid;

Minimize(sys1, {sys2,sys3},assume = nonnegative);

complex value encountered;

## Another engine dispatch i dont understand...

I found this error extremely confusing when using the solve function:

Error, (in Engine:-Dispatch) cannot determine if this expression is true or false: 1000 < 5^(1/2)

## RootOf Error needing to be dispatched to the engin...

Hi, i encountered this, error, and the link to the help page was broken.

Error, (in RootOf) expression independent of _S000100

## Can't solve arctan equation...

Trying to solve:

solve (arctan((2*x^2-1)/(2*x^2+1)) = 0, x);

The answer I get is the original function:

arctan((2*x^2-1)/(2*x^2+1))

This example is from the Maple book by Keck, and he shows the Maple V answer as

1/2 sqrt(2) -1/2 sqrt(2)

Suggestions?

## Analytical solution...

Hey friends

I want to solve this relation with respect to "M"analytically but maple answer me: "Warning, solutions may have been lost"

How I can solve this problem and get to an analytical solution. It must be noted -1<w<-1/3. we can fix "w" with any value inn this interval. It be accepted any solution for any fixed "w".

Thank you

Analytically_solution.mw

## Solution may have been lost...

Hi,

I want to solve this equation with respect to M, But Maple answer me: "solution may have been lost"

How I can solve this equation?

Thanks guyz

Solutionmayhavebeenlost.mw

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