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# Edit detail for SandBoxJohn2 revision 3 of 3

 1 2 3 Editor: test1 Time: 2019/08/11 18:21:28 GMT+0 Note:

```changed:
-  What method is used to solve equation in Axiom?
What method is used to solve equation in FriCAS?
```

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## Solving Equations

What method is used to solve equation in FriCAS?

 ```off tex; solve( {st^2 * ( (x2-xa)^2 + (y2-ya)^2 ) = sa^2 * ( (x2-xt)^2 + (y2-yt)^2 ), y2 = 0}, {x2, y2} ); 4 2 2 2 2 2 2 2 2 2 {{x2=(sqrt( - sa *yt + sa *st *xa - 2*sa *st *xa*xt + sa *st *xt 2 2 2 2 2 2 4 2 2 2 2 2 + sa *st *ya + sa *st *yt - st *ya ) + sa *xt - st *xa)/(sa - st ), y2=0}, 4 2 2 2 2 2 2 2 2 2 {x2=( - sqrt( - sa *yt + sa *st *xa - 2*sa *st *xa*xt + sa *st *xt 2 2 2 2 2 2 4 2 2 2 2 + sa *st *ya + sa *st *yt - st *ya ) + sa *xt - st *xa)/(sa 2 - st ), y2=0}} solve( {st^2 * ( (x2-xa)^2 + (y2-ya)^2 ) = sa^2 * ( (x2-xt)^2 + (y2-yt)^2 ), y2 = m*x2 + b}, {x2, y2} ); 2 4 2 2 2 2 4 4 2 2 {{x2=(sqrt( - b *sa + 2*b *sa *st - b *st - 2*b*m*sa *xt + 2*b*m*sa *st *xa 2 2 4 4 2 2 + 2*b*m*sa *st *xt - 2*b*m*st *xa + 2*b*sa *yt - 2*b*sa *st *ya 2 2 4 2 4 2 2 2 2 2 - 2*b*sa *st *yt + 2*b*st *ya - m *sa *xt + m *sa *st *xa 2 2 2 2 2 2 2 2 2 2 2 + m *sa *st *xt + m *sa *st *ya - 2*m *sa *st *ya*yt 2 2 2 2 2 4 2 4 2 2 + m *sa *st *yt - m *st *xa + 2*m*sa *xt*yt - 2*m*sa *st *xa*yt 2 2 4 4 2 2 2 2 - 2*m*sa *st *xt*ya + 2*m*st *xa*ya - sa *yt + sa *st *xa 2 2 2 2 2 2 2 2 2 2 2 - 2*sa *st *xa*xt + sa *st *xt + sa *st *ya + sa *st *yt 4 2 2 2 2 2 2 - st *ya ) - b*m*sa + b*m*st + m*sa *yt - m*st *ya + sa *xt 2 2 2 2 2 2 2 - st *xa)/(m *sa - m *st + sa - st ), 2 4 2 2 2 2 4 4 2 2 y2=(sqrt( - b *sa + 2*b *sa *st - b *st - 2*b*m*sa *xt + 2*b*m*sa *st *xa 2 2 4 4 2 2 + 2*b*m*sa *st *xt - 2*b*m*st *xa + 2*b*sa *yt - 2*b*sa *st *ya 2 2 4 2 4 2 2 2 2 2 - 2*b*sa *st *yt + 2*b*st *ya - m *sa *xt + m *sa *st *xa 2 2 2 2 2 2 2 2 2 2 2 + m *sa *st *xt + m *sa *st *ya - 2*m *sa *st *ya*yt 2 2 2 2 2 4 2 4 2 2 + m *sa *st *yt - m *st *xa + 2*m*sa *xt*yt - 2*m*sa *st *xa*yt 2 2 4 4 2 2 2 2 - 2*m*sa *st *xt*ya + 2*m*st *xa*ya - sa *yt + sa *st *xa 2 2 2 2 2 2 2 2 2 2 2 - 2*sa *st *xa*xt + sa *st *xt + sa *st *ya + sa *st *yt 4 2 2 2 2 2 2 2 2 - st *ya )*m + b*sa - b*st + m *sa *yt - m *st *ya + m*sa *xt 2 2 2 2 2 2 2 - m*st *xa)/(m *sa - m *st + sa - st )}, 2 4 2 2 2 2 4 4 {x2=( - sqrt( - b *sa + 2*b *sa *st - b *st - 2*b*m*sa *xt 2 2 2 2 4 4 + 2*b*m*sa *st *xa + 2*b*m*sa *st *xt - 2*b*m*st *xa + 2*b*sa *yt 2 2 2 2 4 2 4 2 - 2*b*sa *st *ya - 2*b*sa *st *yt + 2*b*st *ya - m *sa *xt 2 2 2 2 2 2 2 2 2 2 2 2 + m *sa *st *xa + m *sa *st *xt + m *sa *st *ya 2 2 2 2 2 2 2 2 4 2 - 2*m *sa *st *ya*yt + m *sa *st *yt - m *st *xa 4 2 2 2 2 + 2*m*sa *xt*yt - 2*m*sa *st *xa*yt - 2*m*sa *st *xt*ya 4 4 2 2 2 2 2 2 + 2*m*st *xa*ya - sa *yt + sa *st *xa - 2*sa *st *xa*xt 2 2 2 2 2 2 2 2 2 4 2 2 + sa *st *xt + sa *st *ya + sa *st *yt - st *ya ) - b*m*sa 2 2 2 2 2 2 2 2 2 2 + b*m*st + m*sa *yt - m*st *ya + sa *xt - st *xa)/(m *sa - m *st + sa 2 - st ), 2 4 2 2 2 2 4 4 y2=( - sqrt( - b *sa + 2*b *sa *st - b *st - 2*b*m*sa *xt 2 2 2 2 4 4 + 2*b*m*sa *st *xa + 2*b*m*sa *st *xt - 2*b*m*st *xa + 2*b*sa *yt 2 2 2 2 4 2 4 2 - 2*b*sa *st *ya - 2*b*sa *st *yt + 2*b*st *ya - m *sa *xt 2 2 2 2 2 2 2 2 2 2 2 2 + m *sa *st *xa + m *sa *st *xt + m *sa *st *ya 2 2 2 2 2 2 2 2 4 2 - 2*m *sa *st *ya*yt + m *sa *st *yt - m *st *xa 4 2 2 2 2 + 2*m*sa *xt*yt - 2*m*sa *st *xa*yt - 2*m*sa *st *xt*ya 4 4 2 2 2 2 2 2 + 2*m*st *xa*ya - sa *yt + sa *st *xa - 2*sa *st *xa*xt 2 2 2 2 2 2 2 2 2 4 2 2 + sa *st *xt + sa *st *ya + sa *st *yt - st *ya )*m + b*sa 2 2 2 2 2 2 2 2 2 2 2 - b*st + m *sa *yt - m *st *ya + m*sa *xt - m*st *xa)/(m *sa - m *st 2 2 + sa - st )}}``` reduce

fricas
```)set output tex off
```
fricas
```)set output algebra on
solve( y = 3 * x + 7, x )
y - 7
(1)  [x = -----]
3```
Type: List(Equation(Fraction(Polynomial(Integer))))
fricas
```solve( [st * ( (x2-xa)^2 + (y2-ya)^2 ) = 0, x2 = 1], [x2, y2] )
2               2     2
(2)  [[x2 = 1, ya  - 2 y2 ya + y2  + xa  - 2 xa + 1 = 0]]```
Type: List(List(Equation(Fraction(Polynomial(Integer)))))
fricas
```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  + 2 m sa y2 yt + m st ya  - 2 m st y2 ya
+
2       2       2       2   2
((m  + 1)st  + (- m  - 1)sa )y2
+
2           2           2         2       2  2  2
(2 m sa xt - 2 m st xa - 2 b st  + 2 b sa )y2 - m sa xt
+
2      2  2  2           2      2  2    2  2
- 2 b m sa xt + m st xa  + 2 b m st xa + b st  - b sa
=
0
]
]```
Type: List(List(Equation(Fraction(Polynomial(Integer)))))

fricas
```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  + 2 sa y2 yt + st ya  - 2 st y2 ya + (2 st  - 2 sa )y2
+
2         2          2  2     2  2
(2 sa xt - 2 st xa)y2 - sa xt  + st xa
=
0
]
]```
Type: List(List(Equation(Fraction(Polynomial(Integer)))))
fricas
```solve( st * ( (x2-xa)^2 + (y2-ya)^2 )^(1/2) = 0,st)
(5)  [st = 0]```
Type: List(Equation(Expression(Integer)))
fricas
```solve([a=4,sin(x)=a/5],[a,x])
(6)  [[]]```
Type: List(List(Equation(Expression(Integer))))