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Edit detail for SandBox Solve revision 3 of 7

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Editor: tester
Time: 2008/10/11 12:31:57 GMT-7
Note: test

added:

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}


Solving Equations

What method is used to solve equation in Axiom?

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

But really, you should use 'zerosOf':

axiom
zerosOf(v^4+b*v^3+c*v^2+d, v)
LatexWiki Image(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)]
LatexWiki Image(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
LatexWiki Image(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
LatexWiki Image(8)
Type: List Equation Fraction Polynomial Float
axiom
-- Now check it
map(x+->subst(x,(a.1)::List Equation FRAC POLY FLOAT),l)
LatexWiki Image(9)
Type: List Expression Float

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

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

quadratic equation

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

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

quadratic equation

axiom
solve(x**2+x-1,x)
LatexWiki Image(13)
Type: List Equation Fraction Polynomial Integer

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

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]
LatexWiki Image(15)
Type: List Equation Polynomial Integer
axiom
solve(L, [P1,P2])
LatexWiki Image(16)
Type: List List Equation Fraction Polynomial Integer

But it should, observe this:

axiom
solve([L.1,L.2],[P1,P2])
LatexWiki Image(17)
Type: List List Equation Fraction Polynomial Integer
axiom
solve([L.3,L.4],[Q1,Q2])
LatexWiki Image(18)
Type: List List Equation Fraction Polynomial Integer

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

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

axiom
solve(sin(x)=4/5,x)
LatexWiki Image(19)
Type: List Equation Expression Integer

axiom
solve(x^2=y,x)
LatexWiki Image(20)
Type: List Equation Fraction Polynomial Integer

Use braces { } not parenthesis ( )
axiom
solve(x3=x0+(x1-x0)*t + (x2-x0) *u,u)
LatexWiki Image(21)
Type: List Equation Fraction Polynomial Integer

axiom
solve([x+y=3,x-y=1],[x,y])
LatexWiki Image(22)
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.

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

axiom
solve(sin(x)=4/5,x)
LatexWiki Image(23)
Type: List Equation Expression Integer

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])
LatexWiki Image(24)
Type: List List Equation Fraction Polynomial Integer

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 )
LatexWiki Image(25)
Type: List Equation Expression Integer

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

solve((-v^3 cos(x) sin(x)^2 / sqrt(v^2 cos(x)^2 + 2ah) - v^2 sin(x)^2 + v cos(x) sqrt(v^2 cos(x)^2 + 2 a h) + v^2 cos(x)^2) / a

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
Line 1: 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 .....A.............................................................................. ................................................................B Error A: Missing mate. Error B: syntax error at top level Error B: Possibly missing a ) 3 error(s) parsing