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SandBox Solve

Edit detail for SandBox Solve revision 1 of 7

	1 2 3 4 5 6 7
Editor: Time: 2007/11/18 18:36:37 GMT-8
Note: problem formatting of output

changed:
-
Solving Equations

  What method is used to solve equation in Axiom?

\begin{axiom}
solve(sin(x)=4/5,x)
solve([a=4,sin(x)=a/5],[a,x])
\end{axiom}

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

\begin{axiom}
)set output algebra on
)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,i   _
       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] )
)set output algebra off
)set output tex on
\end{axiom}

\begin{axiom}
solve(v^4+b*v^3+c*v^2+d=0,v)
\end{axiom}

This didn't work since 'solve' returns solutions expressible as members of the 
ground field only. Above, the ground field of $v^4+b*v^3+c*v^2+d$ defaults to
'Fraction Polynomial Integer'...

Thus, the proper call is

\begin{axiom}
solve((v^4+b*v^3+c*v^2+d)::EXPR INT=0,v)
\end{axiom}

But really, you should use 'zerosOf':

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

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'. 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.

Here is one way to use macros and _ to define more complex names that
print nicely in LaTeX form:
\begin{axiom}
K_sc  ==> K___{sc_}
mu_sc ==> _\mu___{sc_}
\end{axiom}

\begin{axiom}
digits(7);
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)]
-- solve exactly for fractions
a:=solve (l::LIST FRAC POLY FRAC INT::LIST FRAC POLY INT);
-- Number of results:
#a
-- But only the first one is of interest.
-- Display it as a floating point result
a.1::List Equation Fraction POLY FLOAT
-- Now check it
map(x+->subst(x,(a.1)::List Equation FRAC POLY FLOAT),l)
\end{axiom}


From unknown Fri Jun 3 06:08:15 -0500 2005
From: unknown
Date: Fri, 03 Jun 2005 06:08:15 -0500
Subject: Test
Message-ID: <20050603060815-0500@page.axiom-developer.org>

\begin{axiom}
  )clear all
\end{axiom}

\begin{axiom}
  solve((x=-1+x^2)::EQ EXPR INT,x)
\end{axiom}

quadratic equation
\begin{axiom}
solve(a*x^2+b*x+c=0,x)
\end{axiom}

\begin{axiom}
solve(a*x+b=0,x)
\end{axiom}

quadratic equation

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

\begin{axiom}
radicalSolve(a*x**2+b*x+c=0,x)
\end{axiom}

From unknown Fri Jun 3 06:08:15 -0500 2005
From: unknown
Date: Fri, 03 Jun 2005 06:08:15 -0500
Subject: Test
Message-ID: <20050603060815-0500@page.axiom-developer.org>

This doesn't work on mine michen:
\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}
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 $P_i$.

From unknown Wed Jun 22 19:20:34 -0500 2005
From: unknown
Date: Wed, 22 Jun 2005 19:20:34 -0500
Subject: 
Message-ID: <20050622192034-0500@page.axiom-developer.org>

\begin{axiom}
)set output algebra on
)set output tex off
radicalSolve(a*x**3+b*x**2+c*x+d=0,x)
)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}

From unknown Fri Jun 24 04:24:51 -0500 2005
From: unknown
Date: Fri, 24 Jun 2005 04:24:51 -0500
Subject: test
Message-ID: <20050624042451-0500@page.axiom-developer.org>

\begin{axiom}
  solve(x^2=y,x)
\end{axiom}

From unknown Mon Jul 4 13:54:20 -0500 2005
From: unknown
Date: Mon, 04 Jul 2005 13:54:20 -0500
Subject: test
Message-ID: <20050704135420-0500@page.axiom-developer.org>

Use braces { } not parenthesis ( )
\begin{axiom}
solve(x3=x0+(x1-x0)*t + (x2-x0) *u,u)
\end{axiom}


From unknown Tue Nov 29 04:23:52 -0600 2005
From: unknown
Date: Tue, 29 Nov 2005 04:23:52 -0600
Subject: 
Message-ID: <20051129042352-0600@page.axiom-developer.org>

\begin{axiom}
solve([x+y=3,x-y=1],[x,y])
\end{axiom}


From unknown Mon Feb 27 17:15:50 -0600 2006
From: unknown
Date: Mon, 27 Feb 2006 17:15:50 -0600
Subject: 
Message-ID: <20060227171550-0600@wiki.axiom-developer.org>

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.

\begin{axiom}
)set output tex off
)set output algebra on
A:=i=(a*x+c*z+e)/(z+g)
B:=j=(b*x+d*z+f)/(z+g)
solve([A,B],[x,z])
)set output tex on
)set output algebra off
\end{axiom}


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}

From test Fri Oct 20 16:51:26 -0500 2006
From: test
Date: Fri, 20 Oct 2006 16:51:26 -0500
Subject: sdf
Message-ID: <20061020165126-0500@wiki.axiom-developer.org>

\begin{axiom}
solve(14=x*1.1^x,x)
\end{axiom}

From tempo Thu Mar 15 14:15:26 -0600 2007
From: tempo
Date: Thu, 15 Mar 2007 14:15:26 -0600
Subject: --I don't know
Message-ID: <20070315141526-0600@wiki.axiom-developer.org>

\begin{axiom}
)set output algebra on
)set output tex off
zerosOf((1-a)*x^4+x^3+x^2+x+1,x)
)set output algebra off
)set output tex on
\end{axiom}

From faceinjarbydoor Tue May 22 13:53:38 -0500 2007
From: faceinjarbydoor
Date: Tue, 22 May 2007 13:53:38 -0500
Subject: test
Message-ID: <20070522135338-0500@wiki.axiom-developer.org>

\begin{axiom}
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 )
\end{axiom}

From danzat Thu Sep 20 13:26:55 -0500 2007
From: danzat
Date: Thu, 20 Sep 2007 13:26:55 -0500
Subject: test
Message-ID: <20070920132655-0500@wiki.axiom-developer.org>

\begin{axiom}
solve(((1+sqrt(5))^n-(1-sqrt(5))^n)/(sqrt(5)*2^n)=10^1001, n)
\end{axiom}


From hintzy64 Sun Oct 14 21:47:27 -0500 2007
From: hintzy64
Date: Sun, 14 Oct 2007 21:47:27 -0500
Subject: hw problem!
Message-ID: <20071014214727-0500@wiki.axiom-developer.org>

\begin{axiom}
)set output tex off
)set output algebra on
\end{axiom}

\begin{axiom}
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])
\end{axiom}

Solving Equations

What method is used to solve equation in Axiom?

axiom

solve(sin(x)=4/5,x)

(1)

Type: List Equation Expression Integer

axiom

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:

axiom

)set output algebra on

axiom

)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,i   _
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] )

   There are no library operations named i
      Use HyperDoc Browse or issue
                                 )what op i
      to learn if there is any operation containing " i " in its name.

   Cannot find a definition or applicable library operation named i
      with argument type(s)
                                 Variable Vq

      Perhaps you should use "@" to indicate the required return type,
      or "$" to specify which version of the function you need.

axiom

)set output algebra off

axiom

)set output tex on

axiom

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

axiom

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 'zerosOf':

axiom

zerosOf(v^4+b*v^3+c*v^2+d, v)

(5)

Type: List 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. 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.

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

axiom

K_sc  ==> K___{sc_}

Type: Void

axiom

mu_sc ==> _\mu___{sc_}

Type: Void

axiom

digits(7);

Type: PositiveInteger?

axiom

l:=  [0.01*(2.25-K_sc)*K_sc/(0.01*%pi*mu_sc*(mu_sc+3.0&
#42;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	
5;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)*(m
u_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

axiom

-- solve exactly for fractions
a:=solve (l::LIST FRAC POLY FRAC INT::LIST FRAC POLY INT);

Type: List List Equation Fraction Polynomial Integer

axiom

-- Number of results:
#a

(7)

Type: PositiveInteger?

axiom

-- 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

axiom

-- Now check it
map(x+->subst(x,(a.1)::List Equation FRAC POLY FLOAT),l)

(9)

Type: List Expression Float

Test --unknown, Fri, 03 Jun 2005 06:08:15 -0500 reply

axiom

)clear all

   All user variables and function definitions have been cleared.

axiom

solve((x=-1+x^2)::EQ EXPR INT,x)

(10)

Type: List Equation Expression Integer

quadratic equation

axiom

solve(a*x^2+b*x+c=0,x)

(11)

Type: List Equation Fraction Polynomial Integer

axiom

solve(a*x+b=0,x)

(12)

Type: List Equation Fraction Polynomial Integer

quadratic equation

axiom

solve(x**2+x-1,x)

(13)

Type: List Equation Fraction Polynomial Integer

axiom

radicalSolve(a*x**2+b*x+c=0,x)

(14)

Type: List Equation Expression Integer

Test --unknown, Fri, 03 Jun 2005 06:08:15 -0500 reply

This doesn't work on mine michen:

axiom

L := [ A = 2*P1+P2, B = 2*P2+P1, C = 2*Q1+Q2, D = 2*Q2+Q1]

(15)

Type: List Equation Polynomial Integer

axiom

solve(L, [P1,P2])

(16)

Type: List List Equation Fraction Polynomial Integer

But it should, observe this:

axiom

solve([L.1,L.2],[P1,P2])

(17)

Type: List List Equation Fraction Polynomial Integer

axiom

solve([L.3,L.4],[Q1,Q2])

(18)

Type: List List Equation Fraction Polynomial Integer

First two equationa do not depend on , the later two don't depend on .

... --unknown, Wed, 22 Jun 2005 19:20:34 -0500 reply

axiom

)set output algebra on

axiom

)set output tex off

radicalSolve(a*x**3+b*x**2+c*x+d=0,x)

   (10)
   [
     x =
                  2 +---+     2
             (- 9a \|- 3  + 9a )
          *
               ROOT
                           +------------------------------------------+
                           |   2 2                  3         3    2 2
                         3 |27a d  + (- 18a b c + 4b )d + 4a c  - b c        2
                      54a  |------------------------------------------  - 27a d
                           |                       4
                          \|                   108a
                    +
                                 3
                      9a b c - 2b
                 /
                       3
                    54a
              ,
                  3
            **
               2
         +
                     +---+
             (- 3a b\|- 3  - 3a b)
          *
             ROOT
                         +------------------------------------------+
                         |   2 2                  3         3    2 2
                       3 |27a d  + (- 18a b c + 4b )d + 4a c  - b c        2
                    54a  |------------------------------------------  - 27a d
                         |                       4
                        \|                   108a
                  +
                               3
                    9a b c - 2b
               /
                     3
                  54a
            ,
                3
         +
                    2
           6a c - 2b
      /
              2 +---+     2
           (9a \|- 3  + 9a )
        *
           ROOT
                       +------------------------------------------+
                       |   2 2                  3         3    2 2
                     3 |27a d  + (- 18a b c + 4b )d + 4a c  - b c        2
                  54a  |------------------------------------------  - 27a d
                       |                       4
                      \|                   108a
                +
                             3
                  9a b c - 2b
             /
                   3
                54a
          ,
              3
     ,

     x =
                  2 +---+     2
             (- 9a \|- 3  - 9a )
          *
               ROOT
                           +------------------------------------------+
                           |   2 2                  3         3    2 2
                         3 |27a d  + (- 18a b c + 4b )d + 4a c  - b c        2
                      54a  |------------------------------------------  - 27a d
                           |                       4
                          \|                   108a
                    +
                                 3
                      9a b c - 2b
                 /
                       3
                    54a
              ,
                  3
            **
               2
         +
                     +---+
             (- 3a b\|- 3  + 3a b)
          *
             ROOT
                         +------------------------------------------+
                         |   2 2                  3         3    2 2
                       3 |27a d  + (- 18a b c + 4b )d + 4a c  - b c        2
                    54a  |------------------------------------------  - 27a d
                         |                       4
                        \|                   108a
                  +
                               3
                    9a b c - 2b
               /
                     3
                  54a
            ,
                3
         +
                      2
           - 6a c + 2b
      /
              2 +---+     2
           (9a \|- 3  - 9a )
        *
           ROOT
                       +------------------------------------------+
                       |   2 2                  3         3    2 2
                     3 |27a d  + (- 18a b c + 4b )d + 4a c  - b c        2
                  54a  |------------------------------------------  - 27a d
                       |                       4
                      \|                   108a
                +
                             3
                  9a b c - 2b
             /
                   3
                54a
          ,
              3
     ,

     x =
               2
             9a
          *
               ROOT
                           +------------------------------------------+
                           |   2 2                  3         3    2 2
                         3 |27a d  + (- 18a b c + 4b )d + 4a c  - b c        2
                      54a  |------------------------------------------  - 27a d
                           |                       4
                          \|                   108a
                    +
                                 3
                      9a b c - 2b
                 /
                       3
                    54a
              ,
                  3
            **
               2
         +
           -
                3a b
             *
                ROOT
                            +------------------------------------------+
                            |   2 2                  3         3    2 2
                          3 |27a d  + (- 18a b c + 4b )d + 4a c  - b c        2
                       54a  |------------------------------------------  - 27a d
                            |                       4
                           \|                   108a
                     +
                                  3
                       9a b c - 2b
                  /
                        3
                     54a
               ,
                   3
         +
                     2
           - 3a c + b
      /
             2
           9a
        *
           ROOT
                       +------------------------------------------+
                       |   2 2                  3         3    2 2
                     3 |27a d  + (- 18a b c + 4b )d + 4a c  - b c        2
                  54a  |------------------------------------------  - 27a d
                       |                       4
                      \|                   108a
                +
                             3
                  9a b c - 2b
             /
                   3
                54a
          ,
              3
     ]

Type: List Equation Expression Integer

axiom

)set output algebra off

axiom

)set output tex on

test --unknown, Fri, 24 Jun 2005 04:20:49 -0500 reply

axiom

solve(sin(x)=4/5,x)

(19)

Type: List Equation Expression Integer

test --unknown, Fri, 24 Jun 2005 04:24:51 -0500 reply

axiom

solve(x^2=y,x)

(20)

Type: List Equation Fraction Polynomial Integer

test --unknown, Mon, 04 Jul 2005 13:54:20 -0500 reply

Use braces { } not parenthesis ( )

axiom

solve(x3=x0+(x1-x0)*t + (x2-x0) *u,u)

(21)

Type: List Equation Fraction Polynomial Integer

... --unknown, Tue, 29 Nov 2005 04:23:52 -0600 reply

axiom

solve([x+y=3,x-y=1],[x,y])

(22)

Type: List List Equation Fraction Polynomial Integer

... --unknown, Mon, 27 Feb 2006 17:15:50 -0600 reply

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.

axiom

)set output tex off

axiom

)set output algebra on

A:=i=(a*x+c*z+e)/(z+g)

            c z + a x + e
   (15)  i= -------------
                z + g

Type: Equation Fraction Polynomial Integer

axiom

B:=j=(b*x+d*z+f)/(z+g)

            d z + b x + f
   (16)  j= -------------
                z + g

Type: Equation Fraction Polynomial Integer

axiom

solve([A,B],[x,z])

   (17)
        (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

axiom

)set output tex on

axiom

)set output algebra off

... --unknown, Sun, 05 Mar 2006 15:26:14 -0600 reply

axiom

solve(sin(x)=4/5,x)

(23)

Type: List Equation Expression Integer

... --unknown, Tue, 23 May 2006 08:40:27 -0500 reply

axiom

L := [ A = 2*P1+P2, B = 2*P2+P1, C = 2*Q1+Q2, D = 2*Q2+Q1]

   There are 3 exposed and 0 unexposed library operations named
      equation having 2 argument(s) but none was determined to be
      applicable. Use HyperDoc Browse, or issue
                            )display op equation
      to learn more about the available operations. Perhaps
      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
      equation with argument type(s)
                    Equation Fraction Polynomial Integer
                             Polynomial Integer

      Perhaps you should use "@" to indicate the required return type,
      or "$" to specify which version of the function you need.
solve(L, [P1,P2])

(24)

Type: List List Equation Fraction Polynomial Integer

sdf --test, Fri, 20 Oct 2006 16:51:26 -0500 reply

axiom

solve(14=x*1.1^x,x)

   There are 18 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
      to learn more about the available operations. Perhaps
      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

axiom

)set output algebra on

axiom

)set output tex off

zerosOf((1-a)*x^4+x^3+x^2+x+1,x)

   (20)
   [%x10, %x11,

         -
            ROOT
                      2              2         2
                 (- 3a  + 6a - 3)%x11  + ((- 2a  + 4a - 2)%x10 + 2a - 2)%x11
               +
                      2              2
                 (- 3a  + 6a - 3)%x10  + (2a - 2)%x10 + 4a - 3
       +
         (- a + 1)%x11 + (- a + 1)%x10 + 1
    /
       2a - 2
     ,

         ROOT
                   2              2         2
              (- 3a  + 6a - 3)%x11  + ((- 2a  + 4a - 2)%x10 + 2a - 2)%x11
            +
                   2              2
              (- 3a  + 6a - 3)%x10  + (2a - 2)%x10 + 4a - 3
       +
         (- a + 1)%x11 + (- a + 1)%x10 + 1
    /
       2a - 2
     ]

Type: List Expression Integer

axiom

)set output algebra off

axiom

)set output tex on

test --faceinjarbydoor, Tue, 22 May 2007 13:53:38 -0500 reply

axiom

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 )

(25)

Type: List Equation Expression Integer

test --danzat, Thu, 20 Sep 2007 13:26:55 -0500 reply

axiom

solve(((1+sqrt(5))^n-(1-sqrt(5))^n)/(sqrt(5)*2^n)=10^1001, n)

(26)

Type: List Equation Expression Integer

hw problem! --hintzy64, Sun, 14 Oct 2007 21:47:27 -0500 reply

axiom

)set output tex off

axiom

)set output algebra on

axiom

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])

   (23)
   [
     [
       nnH =
                                 2                                      2
             ((- 2SH + 2SCs)alpha  + (- 3SH + 3SCs)alpha - SH + SCs)niCs
           +
                             2                                          2      2
                 (- 2SH alpha  + (- SH - SCs)alpha)n + (- 4SCs SH + 2SCs )alpha
               +
                                  2                       2
                 (- 6SCs SH + 4SCs )alpha - 2SCs SH + 2SCs
            *
               niCs
           +
                        2                  2                     2
             SCs alpha n  + ((2SCs 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 + (2SCs SH - SCs )alpha + 2SCs SH - 2SCs )niCs
           +
                            2
             (- SCs SH + SCs )n
        /
                      2
           SCs n + SCs
       ,

       nnCs =
                                               2
             ((- SH + SCs)alpha - SH + SCs)niCs
           +
             (((- SH - SCs)alpha - 2SCs)n - 2SCs SH alpha - 2SCs SH)niCs
           +
                  2
             SCs n  + SCs SH n
        /
                                   2           2
           (SCs alpha + SCs)n + SCs alpha + SCs
       ,

                         2                                    3
         ((SH - SCs)alpha  + (2SH - 2SCs)alpha + SH - SCs)niCs
       +
                      2                                           2      2
             (SH alpha  + (SH + SCs)alpha + SCs)n + (2SCs SH - SCs )alpha
           +
                            2                       2
             (5SCs SH - 3SCs )alpha + 3SCs SH - 2SCs
        *
               2
           niCs
       +
               2                     2         2               2             2 2
         ((2SCs alpha - SCs SH + 3SCs )n + 2SCs SH alpha + 2SCs SH)niCs - SCs n
       +
              2
         - SCs SH n
         =
         0
       ]
     ]

Type: List List Equation Fraction Polynomial Integer