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# Edit detail for SandBox Solve revision 7 of 7

 1 2 3 4 5 6 7 Editor: test1 Time: 2013/06/15 16:46:37 GMT+0 Note:

changed:
-       V_q*rho_q+V_l*rho_l+ V_d*rho_d+V_a*rho_a=rho_ma,i   _
V_q*rho_q+V_l*rho_l+ V_d*rho_d+V_a*rho_a=rho_ma,    _

changed:
-But really, you should use 'zerosOf':
-
-\begin{axiom}
-zerosOf(v^4+b*v^3+c*v^2+d, v)
-\end{axiom}
But really, you should use 'zeroOf':

\begin{axiom}
zeroOf(v^4+b*v^3+c*v^2+d, v)
\end{axiom}

changed:
-Furthermore, it's '%pi', not '%PI'. Finally, the underscore is the escape
-character (like \\) and is also used as the the line continuation character
-when it occurs at the end of th line. So 'K_sc' is equivalent to just Ksc,
-but 'K__sc' is actually K_sc.
Furthermore, it's '%pi', not '%PI'.

changed:
-solve(x**2+x-1,x)
-\end{axiom}
-
-\begin{axiom}
-\end{axiom}
solve(x^2+x-1,x)
\end{axiom}

\begin{axiom}
\end{axiom}

changed:
-This doesn't work on mine michen:
This doesn't work:

changed:
-But it should, observe this:
-\begin{axiom}
-solve([L.1,L.2],[P1,P2])
-solve([L.3,L.4],[Q1,Q2])
-\end{axiom}
-First two equationa do not depend on $Q_i$, the later two don't depend on $P_i$.
The reason is that above Q1 and Q2 are parameters.  In such case FriCAS seeks
solution in rational functions of Q1 and Q2 and there is no such solution.
Instead one should solve also for Q1 and Q2:
\begin{axiom}
)set output tex off
)set output algebra on
solve(L, [P1,P2,Q1,Q2])
\end{axiom}

changed:
-)set output algebra on
-)set output tex off
-)set output algebra off
-)set output tex on
-\end{axiom}
-
-From unknown Fri Jun 24 04:20:49 -0500 2005
-From: unknown
-Date: Fri, 24 Jun 2005 04:20:49 -0500
-Subject: test
-Message-ID: <20050624042049-0500@page.axiom-developer.org>
-
-\begin{axiom}
-solve(sin(x)=4/5,x)
-\end{axiom}
)set output algebra off
)set output tex on
\end{axiom}

removed:
-Use braces { } not parenthesis ( )

removed:
-From unknown Sun Mar 5 15:26:14 -0600 2006
-From: unknown
-Date: Sun, 05 Mar 2006 15:26:14 -0600
-Subject:
-Message-ID: <20060305152614-0600@wiki.axiom-developer.org>
-
-\begin{axiom}
-solve(sin(x)=4/5,x)
-\end{axiom}
-
-From unknown Tue May 23 08:40:27 -0500 2006
-From: unknown
-Date: Tue, 23 May 2006 08:40:27 -0500
-Subject:
-Message-ID: <20060523084027-0500@wiki.axiom-developer.org>
-
-\begin{axiom}
-L := [ A = 2*P1+P2, B = 2*P2+P1, C = 2*Q1+Q2, D = 2*Q2+Q1]
-solve(L, [P1,P2])
-\end{axiom}

removed:
-
-
-From tester Sat Oct 11 12:29:57 -0700 2008
-From: tester
-Date: Sat, 11 Oct 2008 12:29:57 -0700
-Subject: l
-Message-ID: <20081011122957-0700@axiom-wiki.newsynthesis.org>
-
-solve((-v^3 * cos(x) * sin(x)^2 / sqrt(v^2 * cos(x)^2 + 2*a*h) - v^2 * sin(x)^2 + v * cos(x) * sqrt(v^2 * cos(x)^2 + 2 * a * h) + v^2 * cos(x)^2) / a
-
-From tester Sat Oct 11 12:31:57 -0700 2008
-From: tester
-Date: Sat, 11 Oct 2008 12:31:57 -0700
-Subject: test
-Message-ID: <20081011123157-0700@axiom-wiki.newsynthesis.org>
-
-\begin{axiom}
-solve((-v^3 * cos(x) * sin(x)^2 / sqrt(v^2 * cos(x)^2 + 2*a*h) - v^2 * sin(x)^2 + v * cos(x) * sqrt(v^2 * cos(x)^2 + 2 * a * h) + v^2 * cos(x)^2) / a
-\end{axiom}
-

removed:
-
-From tester Sat Oct 11 12:34:03 -0700 2008
-From: tester
-Date: Sat, 11 Oct 2008 12:34:03 -0700
-Subject:
-Message-ID: <20081011123403-0700@axiom-wiki.newsynthesis.org>
-
-\begin{axiom}
-solve((-v^3 * cos(x) * sin(x)^2 / sqrt(v^2 * cos(x)^2 + 2*a*h) - v^2 * sin(x)^2 + v * cos(x) * sqrt(v^2 * cos(x)^2 + 2 * a * h) + v^2 * cos(x)^2) / a)
-\end{axiom}
-
-
-From Xenon Sun Mar 15 13:13:12 -0700 2009
-From: Xenon
-Date: Sun, 15 Mar 2009 13:13:12 -0700
-Subject: test
-Message-ID: <20090315131312-0700@axiom-wiki.newsynthesis.org>
-
-solve(x^2 + 2 = 0, x)


## Solving Equations

What method is used to solve equation in Axiom?

fricas
solve(sin(x)=4/5,x)
 (1)
Type: List(Equation(Expression(Integer)))
fricas
solve([a=4,sin(x)=a/5],[a,x])
 (2)
Type: List(List(Equation(Expression(Integer))))

In the following, a workaround is necessary because of bug #128:

fricas
)set output algebra on

fricas
)set output tex off
solve([V_q*U_q+V_l*U_l+V_d*U_d+V_a*U_a=U_ma,               _
V_q*rho_q+V_l*rho_l+ V_d*rho_d+V_a*rho_a=rho_ma,    _
V_q*t_q+V_l*t_l+V_d*t_d+V_a*t_a=t_ma,               _
V_q+V_l+V_d+V_a=1],                                 _
[V_q,V_l,V_d,V_a] )
(3)
[
[
V_q
=
((U_d - U_a)rho_l + (- U_l + U_a)rho_d + (U_l - U_d)rho_a)t_ma
+
((- U_d + U_a)rho_ma + (U_ma - U_a)rho_d + (- U_ma + U_d)rho_a)t_l
+
((U_l - U_a)rho_ma + (- U_ma + U_a)rho_l + (U_ma - U_l)rho_a)t_d
+
((- U_l + U_d)rho_ma + (U_ma - U_d)rho_l + (- U_ma + U_l)rho_d)t_a
/
((U_d - U_a)rho_l + (- U_l + U_a)rho_d + (U_l - U_d)rho_a)t_q
+
((- U_d + U_a)rho_q + (U_q - U_a)rho_d + (- U_q + U_d)rho_a)t_l
+
((U_l - U_a)rho_q + (- U_q + U_a)rho_l + (U_q - U_l)rho_a)t_d
+
((- U_l + U_d)rho_q + (U_q - U_d)rho_l + (- U_q + U_l)rho_d)t_a
,
V_l
=
((U_d - U_a)rho_ma + (- U_ma + U_a)rho_d + (U_ma - U_d)rho_a)t_q
+
((- U_d + U_a)rho_q + (U_q - U_a)rho_d + (- U_q + U_d)rho_a)t_ma
+
((U_ma - U_a)rho_q + (- U_q + U_a)rho_ma + (U_q - U_ma)rho_a)t_d
+
((- U_ma + U_d)rho_q + (U_q - U_d)rho_ma + (- U_q + U_ma)rho_d)t_a
/
((U_d - U_a)rho_l + (- U_l + U_a)rho_d + (U_l - U_d)rho_a)t_q
+
((- U_d + U_a)rho_q + (U_q - U_a)rho_d + (- U_q + U_d)rho_a)t_l
+
((U_l - U_a)rho_q + (- U_q + U_a)rho_l + (U_q - U_l)rho_a)t_d
+
((- U_l + U_d)rho_q + (U_q - U_d)rho_l + (- U_q + U_l)rho_d)t_a
,
V_d
=
((- U_l + U_a)rho_ma + (U_ma - U_a)rho_l + (- U_ma + U_l)rho_a)t_q
+
((U_l - U_a)rho_q + (- U_q + U_a)rho_l + (U_q - U_l)rho_a)t_ma
+
((- U_ma + U_a)rho_q + (U_q - U_a)rho_ma + (- U_q + U_ma)rho_a)t_l
+
((U_ma - U_l)rho_q + (- U_q + U_l)rho_ma + (U_q - U_ma)rho_l)t_a
/
((U_d - U_a)rho_l + (- U_l + U_a)rho_d + (U_l - U_d)rho_a)t_q
+
((- U_d + U_a)rho_q + (U_q - U_a)rho_d + (- U_q + U_d)rho_a)t_l
+
((U_l - U_a)rho_q + (- U_q + U_a)rho_l + (U_q - U_l)rho_a)t_d
+
((- U_l + U_d)rho_q + (U_q - U_d)rho_l + (- U_q + U_l)rho_d)t_a
,
V_a
=
((U_l - U_d)rho_ma + (- U_ma + U_d)rho_l + (U_ma - U_l)rho_d)t_q
+
((- U_l + U_d)rho_q + (U_q - U_d)rho_l + (- U_q + U_l)rho_d)t_ma
+
((U_ma - U_d)rho_q + (- U_q + U_d)rho_ma + (U_q - U_ma)rho_d)t_l
+
((- U_ma + U_l)rho_q + (U_q - U_l)rho_ma + (- U_q + U_ma)rho_l)t_d
/
((U_d - U_a)rho_l + (- U_l + U_a)rho_d + (U_l - U_d)rho_a)t_q
+
((- U_d + U_a)rho_q + (U_q - U_a)rho_d + (- U_q + U_d)rho_a)t_l
+
((U_l - U_a)rho_q + (- U_q + U_a)rho_l + (U_q - U_l)rho_a)t_d
+
((- U_l + U_d)rho_q + (U_q - U_d)rho_l + (- U_q + U_l)rho_d)t_a
]
]
Type: List(List(Equation(Fraction(Polynomial(Integer)))))
fricas
)set output algebra off

fricas
)set output tex on

fricas
solve(v^4+b*v^3+c*v^2+d=0,v)
 (3)
Type: List(Equation(Fraction(Polynomial(Integer))))

This didn't work since solve returns solutions expressible as members of the ground field only. Above, the ground field of defaults to Fraction Polynomial Integer...

Thus, the proper call is

fricas
solve((v^4+b*v^3+c*v^2+d)::EXPR INT=0,v)
 (4)
Type: List(Equation(Expression(Integer)))

But really, you should use 'zeroOf':

fricas
zeroOf(v^4+b*v^3+c*v^2+d, v)
 (5)
Type: Expression(Integer)

In the following, we have to do three things:

• convert the list of Fraction Polynomial Float to a list of Fraction Polynomial Integer, since solve can only handle the latter,
• ask for an approximate solution and
• set precision to a lower value then 68, since it would take too much time otherwise

Furthermore, it's %pi, not %PI.

Here is one way to use macros and _ to define more complex names that print nicely in LaTeX form:

fricas
K_sc  ==> K___{sc_}
Type: Void
fricas
mu_sc ==> _\mu___{sc_}
Type: Void

fricas
digits(7);
Type: PositiveInteger?
fricas
l:=  [0.01*(2.25-K_sc)*K_sc/(0.01*%pi*mu_sc*(mu_sc+3.0*K_sc)/                         _
(4.0*mu_sc+3.0*K_sc)+2.25)+0.7*(37.0-K_sc)*(4.0*mu_sc/3.0+K_sc)/                _
(4.0*mu_sc/3.0+37.0)+0.29*(2.25-K_sc)*(4.0*mu_sc/3.0+K_sc)/                     _
(4.0*mu_sc/3.0+2.25),                                                           _
-0.002*mu_sc*(2.0*(2.0*mu_sc/3.0+2.25)/                                         _
(0.01*%pi*mu_sc*(mu_sc+3.0*K_sc)/                                               _
(4.0*mu_sc+3.0*K_sc)+2.25)+800.0*mu_sc/                                         _
(%pi*(2.0*mu_sc*(mu_sc+3.0*K_sc)/                                               _
(4.0*mu_sc+3.0*K_sc)+mu_sc))+1.0)+0.7*(44.0-mu_sc)*(mu_sc*(8.0*mu_sc+9.0*K_sc)/ _
(6.0*(2.0*mu_sc+K_sc))+mu_sc)/                                                  _
(mu_sc*(8.0*mu_sc+9.0*K_sc)/                                                    _
(6.0*(2.0*mu_sc+K_sc))+44.0)-1.74*(2.0*mu_sc+K_sc)*(mu_sc*(8.0*mu_sc+9.0*K_sc)/ _
(6.0*(2.0*mu_sc+K_sc))+mu_sc)/(8.0*mu_sc+9.0*K_sc)]
 (6)
Type: List(Fraction(Polynomial(Float)))
fricas
-- solve exactly for fractions
a:=solve (l::LIST FRAC POLY FRAC INT::LIST FRAC POLY INT);
Type: List(List(Equation(Fraction(Polynomial(Integer)))))
fricas
-- Number of results:
#a
 (7)
Type: PositiveInteger?
fricas
-- But only the first one is of interest.
-- Display it as a floating point result
a.1::List Equation Fraction POLY FLOAT
 (8)
Type: List(Equation(Fraction(Polynomial(Float))))
fricas
-- Now check it
map(x+->subst(x,(a.1)::List Equation FRAC POLY FLOAT),l)
 (9)
Type: List(Expression(Float))

fricas
)clear all
All user variables and function definitions have been cleared.

fricas
solve((x=-1+x^2)::EQ EXPR INT,x)
 (10)
Type: List(Equation(Expression(Integer)))

fricas
solve(a*x^2+b*x+c=0,x)
 (11)
Type: List(Equation(Fraction(Polynomial(Integer))))

fricas
solve(a*x+b=0,x)
 (12)
Type: List(Equation(Fraction(Polynomial(Integer))))

fricas
solve(x^2+x-1,x)
 (13)
Type: List(Equation(Fraction(Polynomial(Integer))))

fricas
radicalSolve(a*x^2+b*x+c=0,x)
 (14)
Type: List(Equation(Expression(Integer)))

This doesn't work:
fricas
L := [ A = 2*P1+P2, B = 2*P2+P1, C = 2*Q1+Q2, D = 2*Q2+Q1]
 (15)
Type: List(Equation(Polynomial(Integer)))
fricas
solve(L, [P1,P2])
 (16)
Type: List(List(Equation(Fraction(Polynomial(Integer)))))

The reason is that above Q1 and Q2 are parameters. In such case FriCAS seeks solution in rational functions of Q1 and Q2 and there is no such solution. Instead one should solve also for Q1 and Q2:

fricas
)set output tex off

fricas
)set output algebra on
solve(L, [P1,P2,Q1,Q2])
- B + 2 A       2 B - A       - D + 2 C       2 D - C
(8)  [[P1 = ---------, P2 = -------, Q1 = ---------, Q2 = -------]]
3              3              3              3
Type: List(List(Equation(Fraction(Polynomial(Integer)))))

fricas
radicalSolve(a*x^3+b*x^2+c*x+d=0,x)
(9)
[
x
=
2 +---+      2
(- 9 a \|- 3  + 9 a )
*
ROOT
+----------------------------------------------+
|    2 2                    3          3    2 2
3 |27 a d  + (- 18 a b c + 4 b )d + 4 a c  - b c
54 a  |----------------------------------------------
|                         4
\|                    108 a
+
2                 3
- 27 a d + 9 a b c - 2 b
/
3
54 a
,
3
^
2
+
+---+
(- 3 a b\|- 3  - 3 a b)
*
ROOT
+----------------------------------------------+
|    2 2                    3          3    2 2
3 |27 a d  + (- 18 a b c + 4 b )d + 4 a c  - b c
54 a  |----------------------------------------------
|                         4
\|                    108 a
+
2                 3
- 27 a d + 9 a b c - 2 b
/
3
54 a
,
3
+
2
6 a c - 2 b
/
2 +---+      2
(9 a \|- 3  + 9 a )
*
ROOT
+----------------------------------------------+
|    2 2                    3          3    2 2
3 |27 a d  + (- 18 a b c + 4 b )d + 4 a c  - b c
54 a  |----------------------------------------------
|                         4
\|                    108 a
+
2                 3
- 27 a d + 9 a b c - 2 b
/
3
54 a
,
3
,
x
=
2 +---+      2
(- 9 a \|- 3  - 9 a )
*
ROOT
+----------------------------------------------+
|    2 2                    3          3    2 2
3 |27 a d  + (- 18 a b c + 4 b )d + 4 a c  - b c
54 a  |----------------------------------------------
|                         4
\|                    108 a
+
2                 3
- 27 a d + 9 a b c - 2 b
/
3
54 a
,
3
^
2
+
+---+
(- 3 a b\|- 3  + 3 a b)
*
ROOT
+----------------------------------------------+
|    2 2                    3          3    2 2
3 |27 a d  + (- 18 a b c + 4 b )d + 4 a c  - b c
54 a  |----------------------------------------------
|                         4
\|                    108 a
+
2                 3
- 27 a d + 9 a b c - 2 b
/
3
54 a
,
3
+
2
- 6 a c + 2 b
/
2 +---+      2
(9 a \|- 3  - 9 a )
*
ROOT
+----------------------------------------------+
|    2 2                    3          3    2 2
3 |27 a d  + (- 18 a b c + 4 b )d + 4 a c  - b c
54 a  |----------------------------------------------
|                         4
\|                    108 a
+
2                 3
- 27 a d + 9 a b c - 2 b
/
3
54 a
,
3
,
x
=
2
9 a
*
ROOT
+----------------------------------------------+
|    2 2                    3          3    2 2
3 |27 a d  + (- 18 a b c + 4 b )d + 4 a c  - b c
54 a  |----------------------------------------------
|                         4
\|                    108 a
+
2                 3
- 27 a d + 9 a b c - 2 b
/
3
54 a
,
3
^
2
+
-
3 a b
*
ROOT
+----------------------------------------------+
|    2 2                    3          3    2 2
3 |27 a d  + (- 18 a b c + 4 b )d + 4 a c  - b c
54 a  |----------------------------------------------
|                         4
\|                    108 a
+
2                 3
- 27 a d + 9 a b c - 2 b
/
3
54 a
,
3
+
2
- 3 a c + b
/
2
9 a
*
ROOT
+----------------------------------------------+
|    2 2                    3          3    2 2
3 |27 a d  + (- 18 a b c + 4 b )d + 4 a c  - b c
54 a  |----------------------------------------------
|                         4
\|                    108 a
+
2                 3
- 27 a d + 9 a b c - 2 b
/
3
54 a
,
3
]
Type: List(Equation(Expression(Integer)))
fricas
)set output algebra off

fricas
)set output tex on

fricas
solve(x^2=y,x)
 (17)
Type: List(Equation(Fraction(Polynomial(Integer))))

fricas
solve(x3=x0+(x1-x0)*t + (x2-x0) *u,u)
 (18)
Type: List(Equation(Fraction(Polynomial(Integer))))

fricas
solve([x+y=3,x-y=1],[x,y])
 (19)
Type: List(List(Equation(Fraction(Polynomial(Integer)))))

An error in the way MathAction folds the LaTeX output from Axiom prevents this expression from displaying properly. As a work-a-round it is necessary to disable the LaTeX output and replace it with a ASCII text equivalent.

fricas
)set output tex off

fricas
)set output algebra on
A:=i=(a*x+c*z+e)/(z+g)
c z + a x + e
(13)  i = -------------
z + g
Type: Equation(Fraction(Polynomial(Integer)))
fricas
B:=j=(b*x+d*z+f)/(z+g)
d z + b x + f
(14)  j = -------------
z + g
Type: Equation(Fraction(Polynomial(Integer)))
fricas
solve([A,B],[x,z])
(15)
(c g - e)j + (- d g + f)i - c f + d e      - a g j + b g i + a f - b e
[[x = -------------------------------------, z = ---------------------------]
a j - b i - a d + b c                 a j - b i - a d + b c
]
Type: List(List(Equation(Fraction(Polynomial(Integer)))))
fricas
)set output tex on

fricas
)set output algebra off

fricas
solve(14=x*1.1^x,x)
There are 20 exposed and 3 unexposed library operations named solve
having 2 argument(s) but none was determined to be applicable.
Use HyperDoc Browse, or issue
)display op solve
package-calling the operation or using coercions on the arguments
will allow you to apply the operation.
Cannot find a definition or applicable library operation named solve
with argument type(s)
Equation(Expression(Float))
Variable(x)
Perhaps you should use "@" to indicate the required return type,
or "\$" to specify which version of the function you need.

--I don't know --tempo, Thu, 15 Mar 2007 14:15:26 -0600 reply
fricas
)set output algebra on

fricas
)set output tex off
zerosOf((1-a)*x^4+x^3+x^2+x+1,x)
(16)
[%x6, %x7,
-
ROOT
2              2          2
(- 3 a  + 6 a - 3)%x7  + ((- 2 a  + 4 a - 2)%x6 + 2 a - 2)%x7
+
2              2
(- 3 a  + 6 a - 3)%x6  + (2 a - 2)%x6 + 4 a - 3
+
(- a + 1)%x7 + (- a + 1)%x6 + 1
/
2 a - 2
,
ROOT
2              2          2
(- 3 a  + 6 a - 3)%x7  + ((- 2 a  + 4 a - 2)%x6 + 2 a - 2)%x7
+
2              2
(- 3 a  + 6 a - 3)%x6  + (2 a - 2)%x6 + 4 a - 3
+
(- a + 1)%x7 + (- a + 1)%x6 + 1
/
2 a - 2
]
Type: List(Expression(Integer))
fricas
)set output algebra off

fricas
)set output tex on

test --faceinjarbydoor, Tue, 22 May 2007 13:53:38 -0500 reply
fricas
solve( dx_p = ( m / b ) * ( c0 - b * dv_p + c0 * log(c0) -     _
c0 * log( c0 - b * dv_p ) + v0 * log(c0) -       _
v0 * log( c0 - b * dv_p ) - ( c0 / b ) ), dv_p )
 (20)
Type: List(Equation(Expression(Integer)))

fricas
solve(((1+sqrt(5))^n-(1-sqrt(5))^n)/(sqrt(5)*2^n)=10^1001, n)
 (21)
Type: List(Equation(Expression(Integer)))

hw problem! --hintzy64, Sun, 14 Oct 2007 21:47:27 -0500 reply
fricas
)set output tex off

fricas
)set output algebra on

fricas
solve([nnH+2*niH+nnCs+2*niCs = n, (niH+niCs)*niH/nnH = SH, (niH+niCs)*niCs/nnCs = SCs, (niH+nnH)/(niCs+nnCs) = alpha],[nnH, niH, nnCs, niCs])
(19)
[
[
nnH
=
2                                        2
((- 2 SH + 2 SCs)alpha  + (- 3 SH + 3 SCs)alpha - SH + SCs)niCs
+
2
(- 2 SH alpha  + (- SH - SCs)alpha)n
+
2      2                      2
(- 4 SCs SH + 2 SCs )alpha  + (- 6 SCs SH + 4 SCs )alpha
+
2
- 2 SCs SH + 2 SCs
*
niCs
+
2                   2                     2
SCs alpha n  + ((2 SCs SH - SCs )alpha + SCs SH - SCs )n
/
2           2
(SCs alpha + SCs)n + SCs alpha + SCs
,
niH
=
2
((SH - SCs)alpha + SH - SCs)niCs
+
2                         2
(SH alpha n + (2 SCs SH - SCs )alpha + 2 SCs SH - 2 SCs )niCs
+
2
(- SCs SH + SCs )n
/
2
SCs n + SCs
,
nnCs
=
2
((- SH + SCs)alpha - SH + SCs)niCs
+
(((- SH - SCs)alpha - 2 SCs)n - 2 SCs SH alpha - 2 SCs SH)niCs
+
2
SCs n  + SCs SH n
/
2           2
(SCs alpha + SCs)n + SCs alpha + SCs
,
2                                      3
((SH - SCs)alpha  + (2 SH - 2 SCs)alpha + SH - SCs)niCs
+
2                                            2      2
(SH alpha  + (SH + SCs)alpha + SCs)n + (2 SCs SH - SCs )alpha
+
2                         2
(5 SCs SH - 3 SCs )alpha + 3 SCs SH - 2 SCs
*
2
niCs
+
2                      2          2                2
((2 SCs alpha - SCs SH + 3 SCs )n + 2 SCs SH alpha + 2 SCs SH)niCs
+
2 2      2
- SCs n  - SCs SH n
=
0
]
]
Type: List(List(Equation(Fraction(Polynomial(Integer)))))

fricas
solve((-v^3 * cos(x) * sin(x)^2 / sqrt(v^2 * cos(x)^2 + 2*a*h) - v^2 * sin(x)^2 + v * cos(x) * sqrt(v^2 * cos(x)^2 + 2 * a * h) + v^2 * cos(x)^2)) / a
>> Error detected within library code:
too many variables