|
|
|
last edited 5 years ago by test1 |
Edit detail for SandBoxJohn2 revision 1 of 3
| 1 2 3 | ||
|
Editor:
Time: 2007/11/18 18:05:13 GMT-8 |
||
| Note: fix formatting | ||
changed: - This is a new SandBox test page. Since the page name begins with SandBox, no email notice should be generated if this page is changed. Solving Equations What method is used to solve equation in Axiom? \begin{reduce} off tex; solve( {st^2 * ( (x2-xa)^2 + (y2-ya)^2 ) = sa^2 * ( (x2-xt)^2 + (y2-yt)^2 ), y2 = 0}, {x2, y2} ); solve( {st^2 * ( (x2-xa)^2 + (y2-ya)^2 ) = sa^2 * ( (x2-xt)^2 + (y2-yt)^2 ), y2 = 0}, {x2, y2} ); solve( {st^2 * ( (x2-xa)^2 + (y2-ya)^2 ) = sa^2 * ( (x2-xt)^2 + (y2-yt)^2 ), y2 = m*x2 + b}, {x2, y2} ); \end{reduce} \begin{axiom} )set output tex off )set output algebra on solve( y = 3 * x + 7, x ) solve( [st * ( (x2-xa)^2 + (y2-ya)^2 ) = 0, x2 = 1], [x2, y2] ) solve( [st^2 * ( (x2-xa)^2 + (y2-ya)^2 ) = sa^2 * ( (x2-xt)^2 + (y2-yt)^2 ), y2 = m*x2 + b], [x2, y2] ) \end{axiom} \begin{axiom} solve( [st^2 * ( (x2-xa)^2 + (y2-ya)^2 ) = sa^2 * ( (x2-xt)^2 + (y2-yt)^2 ), x2 = y2], [x2, y2] ) solve( st * ( (x2-xa)^2 + (y2-ya)^2 )^(1/2) = 0,st) solve([a=4,sin(x)=a/5],[a,x]) \end{axiom}
This is a new SandBox? test page. Since the page name begins with SandBox?, no email notice should be generated if this page is changed.
Solving Equations
What method is used to solve equation in Axiom?
off tex; | reduce |
axiom
)set output tex off
axiom
)set output algebra on
solve( y = 3 * x + 7, x )
y - 7 (1) [x= -----] 3
Type: List(Equation(Fraction(Polynomial(Integer))))
axiom
solve( [st * ( (x2-xa)^2 + (y2-ya)^2 ) = 0, x2 = 1], [x2, y2] )
2 2 2 (2) [[x2= 1,ya - 2y2 ya + y2 + xa - 2xa + 1= 0]]
Type: List(List(Equation(Fraction(Polynomial(Integer)))))
axiom
solve( [st^2 * ( (x2-xa)^2 + (y2-ya)^2 ) = sa^2 * ( (x2-xt)^2 + (y2-yt)^2 ), y2 = m*x2 + b], [x2, y2] )
(3) [ y2 - b [x2= ------, m
2 2 2 2 2 2 2 2 2 2 - m sa yt + 2m sa y2 yt + m st ya - 2m st y2 ya + 2 2 2 2 2 ((m + 1)st + (- m - 1)sa )y2 + 2 2 2 2 2 2 2 2 (2m sa xt - 2m st xa - 2b st + 2b sa )y2 - m sa xt - 2b m sa xt + 2 2 2 2 2 2 2 2 m st xa + 2b m st xa + b st - b sa = 0 ] ]
Type: List(List(Equation(Fraction(Polynomial(Integer)))))
axiom
solve( [st^2 * ( (x2-xa)^2 + (y2-ya)^2 ) = sa^2 * ( (x2-xt)^2 + (y2-yt)^2 ), x2 = y2], [x2, y2] )
(4) [ [x2= y2,
2 2 2 2 2 2 2 2 2 - sa yt + 2sa y2 yt + st ya - 2st y2 ya + (2st - 2sa )y2 + 2 2 2 2 2 2 (2sa xt - 2st xa)y2 - sa xt + st xa = 0 ] ]
Type: List(List(Equation(Fraction(Polynomial(Integer)))))
axiom
solve( st * ( (x2-xa)^2 + (y2-ya)^2 )^(1/2) = 0,st)
(5) [st= 0]
Type: List(Equation(Expression(Integer)))
axiom
solve([a=4,sin(x)=a/5],[a,x])
(6) [[]]
Type: List(List(Equation(Expression(Integer))))