|
|
|
last edited 10 years ago by test1 |
Edit detail for SandBox Solve revision 2 of 7
| 1 2 3 4 5 6 7 | ||
|
Editor: tester
Time: 2008/10/11 12:29:57 GMT-7 |
||
| Note: l | ||
added:
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
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 Floatto a list ofFraction Polynomial Integer, sincesolvecan 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
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 
.
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)
 | (19) |
Type: List Equation Expression Integer
axiom
solve(x^2=y,x)
 | (20) |
Type: List Equation Fraction Polynomial Integer
Use braces { } not parenthesis ( )
axiom
solve(x3=x0+(x1-x0)*t + (x2-x0) *u,u)
 | (21) |
Type: List Equation Fraction Polynomial Integer
axiom
solve([x+y=3,x-y=1],[x,y])
 | (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)
 | (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 "$" to specify which version of the function you need. solve(L, [P1,P2])
 | (24) |
Type: List List Equation Fraction Polynomial Integer
axiom
solve(14=x*1.1^x,x)
There are 18 exposed and 3 unexposed library operations named solve having 2 argument(s) but none was determined to be applicable. Use HyperDoc Browse, or issue )display op solve to learn more about the available operations. Perhaps package-calling the operation or using coercions on the arguments will allow you to apply the operation.
Cannot find a definition or applicable library operation named solve with argument type(s) Equation Expression Float Variable x
Perhaps you should use "@" to indicate the required return type, or "$" to specify which version of the function you need.
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
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
axiom
solve(((1+sqrt(5))^n-(1-sqrt(5))^n)/(sqrt(5)*2^n)=10^1001, n)
 | (26) |
Type: List Equation Expression Integer
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