login  home  contents  what's new  discussion  bug reports help  links  subscribe  changes  refresh  edit

fricas
(1) -> )set output tex on

fricas
)set output algebra off

fricas
)set output mathml off

Indefinite intregral

arctan = atan

fricas
integrate(1/atan(x),x)
 (1)
Type: Union(Expression(Integer),...)

Definite intregral

fricas
integrate(1/(a+z^3), z=0..1,"noPole")
 (2)
Type: Union(f1: OrderedCompletion?(Expression(Integer)),...)

fricas
integrate(a/(b+z^2),z=0..1,"noPole")
 (3)
Type: Union(f2: List(OrderedCompletion?(Expression(Integer))),...)

Solutions of Transcendental Equations

fricas
solve(cos(x)-y=-sin(x),x)
 (4)
Type: List(Equation(Expression(Integer)))

fricas
solve(cos(x)-y=-sin(x),y)
 (5)
Type: List(Equation(Expression(Integer)))

fricas
solve(cos(x)-y=-sin(x),x)
 (6)
Type: List(Equation(Expression(Integer)))

fricas
solve(cos(x)=0,x)
 (7)
Type: List(Equation(Expression(Integer)))

fricas
solve(sin(e) - e = 0, e)
 (8)
Type: List(Equation(Expression(Integer)))

fricas
solve(a*cos(t1) + b*sin(t1) = c, t1)
 (9)
Type: List(Equation(Expression(Integer)))

fricas
solve(cos(x)-y=-sin(x),x)
 (10)
Type: List(Equation(Expression(Integer)))

Matrices

fricas
A:=matrix[[cos(x)-y,-sin(x)],[sin(x),cos(x)-y]]
 (11)
Type: Matrix(Expression(Integer))

There is no matrix solve:

fricas
solve(A=0,y)
There are 20 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
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(SquareMatrix(2,Expression(Integer)))
Variable(y)
Perhaps you should use "@" to indicate the required return type,
or "$" to specify which version of the function you need. fricas A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]  (12) Type: Matrix(Expression(Integer)) fricas B:=solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L)  (13) Type: List(Equation(Expression(Integer))) fricas B(1)  (14) Type: Equation(Expression(Integer)) fricas A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]  (15) Type: Matrix(Expression(Integer)) fricas B=solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L)  (16) Type: Equation(List(Equation(Expression(Integer)))) fricas B(1)  (17) Type: Equation(Expression(Integer)) fricas v:=vector[v11,v12]  (18) Type: Vector(OrderedVariableList([v11,v12])) fricas v:=matrix[[B.1],[B.2]]  (19) Type: Matrix(Equation(Expression(Integer))) fricas [a,b]:=solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L)  (20) Type: List(Equation(Expression(Integer))) fricas a  (21) Type: Equation(Expression(Integer)) fricas b  (22) Type: Equation(Expression(Integer)) fricas LA1:=[sqrt(-1)*sin(x)+cos(x),-sqrt(-1)*sin(x)+cos(x)]  (23) Type: List(Expression(Integer)) fricas LA1:=matrix[[sqrt(-1)*sin(x)+cos(x),-sqrt(-1)*sin(x)+cos(x)]]  (24) Type: Matrix(Expression(Integer)) Complex Values fricas LA1:=matrix[[sqrt(-1)*sin(x)]]  (25) Type: Matrix(Expression(Integer)) fricas A:=matrix[[cos(x)-L]]  (26) Type: Matrix(Expression(Integer)) Due to mismatched type the following produces scripted symbol! fricas A:=matrix[a,b]  (27) Type: Symbol fricas A:=matrix[[a,b]]  (28) Type: Matrix(Equation(Expression(Integer))) fricas A:=matrix[[a],[b]]  (29) Type: Matrix(Equation(Expression(Integer))) Again, due to mismatched types we get scripted symbol! fricas A:=matrix[[sqrt(-1)*sin(x)+cos(x)],[b]]  (30) Type: Symbol fricas A:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)*cos(x)]]  (31) Type: Matrix(Expression(Integer)) fricas LA1:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]  (32) Type: Matrix(Expression(Integer)) fricas LAM:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]  (33) Type: Matrix(Expression(Integer)) fricas A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]  (34) Type: Matrix(Expression(Integer)) fricas D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]  (35) Type: Matrix(Expression(Integer)) fricas A*D  (36) Type: Matrix(Expression(Integer)) fricas v:=matrix[[v11],[v12]]  (37) Type: Matrix(Polynomial(Integer)) fricas A*v  (38) Type: Matrix(Expression(Integer)) fricas D(1,1)*v  (39) Type: Matrix(Expression(Integer)) fricas solve([w = 0 for w in parts(A*v - D(1,1)*v)], [v11, v12])  (40) Type: List(List(Equation(Expression(Integer)))) Note that the following does not work: fricas solve(A*vA*v=D(1,1)*v,v) There are 20 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(Matrix(Expression(Integer))) Matrix(Polynomial(Integer)) Perhaps you should use "@" to indicate the required return type, or "$" to specify which version of the function you need.

despite possibility of creating matrix equations:

fricas
A*vA*v=D(1,1)*v
 (41)
Type: Equation(Matrix(Expression(Integer)))

Undetermined example:

fricas
A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]]
 (42)
Type: Matrix(Expression(Integer))
fricas
D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]
 (43)
Type: Matrix(Expression(Integer))
fricas
v:=matrix[[v11],[v12]]
 (44)
Type: Matrix(Polynomial(Integer))
fricas
A*v
 (45)
Type: Matrix(Expression(Integer))
fricas
D(1,1)*v
 (46)
Type: Matrix(Expression(Integer))
fricas
A*v-D(1,1)*v
 (47)
Type: Matrix(Expression(Integer))
fricas
solve([w = 0 for w in parts(A*v-D(1,1)*v)], [v11, v12])
 (48)
Type: List(List(Equation(Expression(Integer))))

fricas
A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]]
 (49)
Type: Matrix(Expression(Integer))

Differential Equations

fricas
)clear all
All user variables and function definitions have been cleared.
y := operator 'y
 (50)
Type: BasicOperator?
fricas
solve(D(y x, x)^2+y x=1,y,x)
>> Error detected within library code:
getlincoeff: not an appropriate ordinary differential equation

fricas
deq := (x^2 + 1) * D(y x, x, 2) + 3 * x * D(y x, x) + y x = 0
 (51)
Type: Equation(Expression(Integer))
fricas
solve(deq, y, x)
 (52)
Type: Union(Record(particular: Expression(Integer),basis: List(Expression(Integer))),...)

fricas
solve(D(y(x),x)-y(x)^2=1,y,x)
 (53)
Type: Union(Expression(Integer),...)

Just trying to understand the syntax

fricas
solve(a*x^2+b*x+c,x)
 (54)
Type: List(Equation(Fraction(Polynomial(Integer))))

fricas
solve(a*x^2+b*x+c=0,x)
 (55)
Type: List(Equation(Fraction(Polynomial(Integer))))

fricas
zerosOf(a*x^2+b*x+c,x)
 (56)
Type: List(Expression(Integer))

fricas
zerosOf(sqrt(h^2+a^2)-a=d,a)
There are 2 exposed and 0 unexposed library operations named zerosOf
having 2 argument(s) but none was determined to be applicable.
Use HyperDoc Browse, or issue
)display op zerosOf
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
zerosOf with argument type(s)
Equation(Expression(Integer))
Variable(a)
Perhaps you should use "@" to indicate the required return type,
or "\$" to specify which version of the function you need.

fricas
solve(x^2+x+1=98,x)
 (57)
Type: List(Equation(Fraction(Polynomial(Integer))))

fricas
solve(x^2+2*x+1=0,x)
 (58)
Type: List(Equation(Fraction(Polynomial(Integer))))

Solutions in Expression domain

fricas
solve((x^2+x+1=98)::Equation Expression Integer,x)
 (59)
Type: List(Equation(Expression(Integer)))

fricas
solve((x^3 * b + x^2*(b*d - b + 1) + x*(3*d - b*d - 1) + 2*d^2 - 2*d = 0)::Equation Expression Integer, x)
 (60)
Type: List(Equation(Expression(Integer)))

 Subject:   Be Bold !! ( 15 subscribers )